Acknowledgement
Foremost, I would like to express support during my thesis.
i
Declaration of Authorship
I, Muhammad Sajjad, declare that this research work title “Achieving dynamic grid connection requirements of pump storage power plant with SM and DFIG using optimization
methods” and everything presented and explained in this report is my own work. I declare
that:
ˆ This work has been completed as the compulsory Master thesis for the degree program
“MSc. Electrical Engineering” at University of Rostock.
ˆ The parts of work which has been taken into wording and meaning of other works are
indicated in each case with naming of the original reference.
ˆ I have acknowledged all the main sources of help.
ˆ There have been no other means used than indicated.
Date: November 20, 2020
Muhammad Sajjad
ii
Abstract
In software has been used.
Keywords— Transmission system operator, Doubly Fed Induction Generator, Full rated converter, Power generating unit, Power generating system, Dynamic grid support, Short circuit current
contribution, Point of common coupling, Grid Operator, Global optimization, Dynamic simulation
iii
Nomenclature
List of Symbols
iv
Institute for Electrical Power Engineering
Ns
f
p
va
Rs
ia
Ls
eaf
Eaf
ωe
Laf
If
Xs
NC
φ
K
ωsync
∆ω
H
∆Pm
∆Pe
Vs
Vr
Rr
Is
Ir
ψs
ψr
ωs
ωr
∗
Ls
Lr
Lm
Vsd
Vsq
Vrd
Vrq
Isd
Isq
Ird
Irq
φsd
φsq
φrd
φrq
Vrd
Vrq
P
Q
Synchronous speed of SM
Frequency
Number of poles
Stator voltage for phase A
Stator resistance for phase A
Stator current for phase A
Stator inductance
Induced voltage in the stator winding
RMS voltage of internal generator induced voltage
rotational frequency
Mutual inductance in stator winding because of field winding
DC excitation field current
Stator reactance
Number of turns in the rotor coil for each phase
Rotational magnetic flux
Flux constant
Synchronous rotational speed
Speed deviation of rotor
Inertia of machine
Change in mechanical power
Change in electrical power
Stator voltage
Rotor voltage
Rotor resistance
Stator current
Rotor current
Stator flux
Rotor winding flux
Stator electrical frequency
Rotor electrical rotational frequency
demanded (reference) value
Stator inductance
Rotor inductance
Mutual inductance of rotor and stator
Stator voltage in d-axis
Stator voltage in q-axis
Rotor voltage in d-axis
Rotor voltage in q-axis
Stator current d-axis
Stator current in q-axis
Rotor current d-axis
Rotor current in q-axis
Stator flux d-axis
Stator flux q-axis
Rotor flux d-axis
Rotor flux q-axis
Rotor voltage in d-axis
Rotor voltage in q-axis
Active power
Reactive power
v
Institute for Electrical Power Engineering
List of Acronyms
NERs
TSO
LVRT
HVRT
PSHP
RPT
DFIM
SM
PSS/E
AC
DC
PGUs
AVR
PSS
VPSS
Vref
V
∆V
E1
SCL
Hz
VHz
OEL
UEL
HV
OELf
MFCL
VSI
RSC
MSC
GSC
PI
MSE
NLINEX
SLSQP
AAS
GS
GU
NER
AEMO
PGU
SLD
GUI
API
TV
GOPs
U1,U3,U5
U2,U4,U6
POC
Shgo
SMIB
National electricity rules
Transmission system operator
Low voltage ride through
High voltage ride through
Pumped storage hydro power
Reversible pump turbine
Doubly fed induction machine
Synchronous machine
Power System simulator for engineering
Alternating current
Direct current
Power generating units
Automatic voltage regulator
Power system stabilizer
Power system stabilizer output signal voltage
Generator terminal reference voltage
Generator terminal voltage
Voltage error between reference voltage and measured voltage
Exciter output DC voltage
Stator current limiter output
Hertz
Voltage per hertz limiter output
Over excitation limiter output
Under excitation limiter output
High value
Fast over excitation limiter output
Minimum field current limiter output
Voltage source inverter
Rotor side converter
Main side converter
Grid side converter
Proportional Integral
Mean square error
Non linear exponential
Sequential least square programming
Automatic access standard
Generating system
Generating unit
National electricity rules
Australian energy market operator
Power generating unit
Single line diagram
graphic user interface
Application program interface
Terminal voltage of the generator
Grid operating points
Generating unit number 1,3,5
Generating unit number 2,4,6
Point of connection voltage
Simplicial homology global optimization
Single machine infinite bus
vi
Contents
1 Introduction
1.1 Background . . . . . . . . . . . . . . . . . . .
1.2 Snowy 2.0 pumped storage hydropower plant
1.3 Thesis Objective and Goals . . . . . . . . . .
1.4 Thesis Outline . . . . . . . . . . . . . . . . .
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2
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23
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25
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27
27
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31
31
32
4 Results and discussion
4.1 Optimization for Clause S5.2.5.5 (Contingency fault analysis) . . . . . . . . . . . . . .
4.1.1 Doubly fed induction machine . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
33
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2 Fundamental theory
2.1 Synchronous machine (fixed speed power generating unit)
2.2 Excitation system . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Automatic voltage regulator . . . . . . . . . . . . .
2.2.2 Power system stabilizer . . . . . . . . . . . . . . .
2.3 Doubly fed induction machine (variable speed unit) . . . .
2.3.1 Rotor side converter control . . . . . . . . . . . .
2.3.2 Grid side converter control . . . . . . . . . . . . .
2.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Design vector . . . . . . . . . . . . . . . . . . . . .
2.4.2 Objective function . . . . . . . . . . . . . . . . . .
2.4.3 Mean square error loss function . . . . . . . . . . .
2.4.4 Non-Linear Exponential (NLINEX) Loss Function
2.4.5 Optimization algorithm method . . . . . . . . . . .
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3 Methodology
3.1 Australian grid code requirements . . . . . . . . . . . . . . . . . . . .
3.1.1 Clause S5.2.5.5 (Contingency fault analysis) . . . . . . . . . . .
3.1.2 Clause S5.2.5.13 (Step response of the voltage control system) .
3.2 Snowy 2.0 Model description . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Dynamic model of fixed speed unit . . . . . . . . . . . . . . . .
3.2.2 Dynamic model of variable speed unit . . . . . . . . . . . . . .
3.3 Simulation setup model . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Grid operating points . . . . . . . . . . . . . . . . . . . . . . .
3.4 PSSE dynamic simulation . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Post processing of dynamic simulation . . . . . . . . . . . . . .
3.5 Optimization applied to Snowy hydro 2.0 . . . . . . . . . . . . . . . .
3.5.1 Initial guess . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Design vector . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.3 Objective function . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.4 Simplicial homology global optimization (Shgo) algorithm . . .
vii
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.
Institute for Electrical Power Engineering
5 Appendix
5.1 List of figures and tables for the dynamic simulation of NER Clause S5.2.5.5 (Contingency fault analysis) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Doubly fed induction machine . . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
38
38
38
List of Figures
1.1
1.2
2.1
2.2
Basic structure of Pump storage hydropower plant with separate pump and turbine (a)
and with reversible pump turbine (b) [1] . . . . . . . . . . . . . . . . . . . . . . . . .
Snowy 2.0 Pumped storage Hydropower concept [2] . . . . . . . . . . . . . . . . . . . .
2
3
2.11
2.12
2.13
Synchronous machine with cylindrical pole rotor (a) and with salient rotor (b) [3] . . .
Synchronous machine equivalent circuit diagram with motor reference (a) and generator
reference (b) [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Synchronous machine magnetizing curve [5] . . . . . . . . . . . . . . . . . . . . . . . .
Cross section view of synchronous machine [6] . . . . . . . . . . . . . . . . . . . . . . .
Excitation control system for SM [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . .
simplified AVR model with standard PSS input . . . . . . . . . . . . . . . . . . . . . .
Block diagram of power system stabilizer PSS2B [8] . . . . . . . . . . . . . . . . . . .
Doubly fed induction machine with 2-level VSI [9] . . . . . . . . . . . . . . . . . . . .
DFIM equivalent circuit diagram in rotating reference frame [10] . . . . . . . . . . . .
Rotor side converter control block diagram for active power control (a) and reactive
power control/voltage control (b) of DFIM . . . . . . . . . . . . . . . . . . . . . . . .
MSE loss function output response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Output response of NLINEX loss function with different scaling factors . . . . . . . .
A Non-Convex Combination of Gaussian Distributions [11] . . . . . . . . . . . . . . .
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Single line diagram of Snowy 2.0 Pumped storage Hydropower plant
Block diagram for GENSAL model [12] . . . . . . . . . . . . . . . .
Single line representation of the simulation model for snowy 2.0 . . .
Flow chart for PSSE dynamic simulation function in python . . . .
Flow chart for post processing function in python . . . . . . . . . .
Optimization process flow chart for Snowy hydro 2.0 . . . . . . . . .
Flow chart for the objective function of optimization process . . . .
4.1
4.3
Output response of loss error function for technical requirements (reactive current settling time, rise time and active power return time) . . . . . . . . . . . . . . . . . . . .
Output response of loss error function for technical requirements (Damping ratio of
reactive current and reactive current requirement) . . . . . . . . . . . . . . . . . . . .
Optimization results to achieve grid code requirements of clause S5.2.5.5 for DFIM . .
35
36
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
39
40
41
42
43
44
45
46
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
4.2
GEN
GEN
GEN
GEN
GEN
GEN
GEN
GEN
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
1ph T1 100 .
1ph T2 100 .
2ph T1 100 .
2ph T2 100 .
2phg T1 100 .
2phg T2 100 .
3phSC T1 100
3phSC T2 100
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5
6
7
7
8
9
10
12
13
14
16
17
18
21
22
24
28
29
30
31
35
Institute for Electrical Power Engineering
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.30
5.31
5.32
5.33
5.34
5.35
5.36
5.37
5.38
5.39
5.40
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
DFIG
PUMP minSCR 1ph P1 100 . . . .
PUMP minSCR 1ph P2 100 . . . .
PUMP minSCR 2ph P1 100 . . . .
PUMP minSCR 2ph P2 100 . . . .
PUMP minSCR 2phg P1 100 . . . .
PUMP minSCR 2phg P2 100 . . . .
PUMP minSCR 3phSC P1 100 . . .
PUMP minSCR 3phSC P2 100 . . .
SYNCON minSCR 1ph SC1 100 . .
SYNCON minSCR 1ph SC2 100 . .
SYNCON minSCR 2ph SC1 100 . .
SYNCON minSCR 2ph SC2 100 . .
SYNCON minSCR 2phg SC1 100 .
SYNCON minSCR 2phg SC2 100 .
SYNCON minSCR 3phSC SC1 100
SYNCON minSCR 3phSC SC2 100
GEN maxSCR 1ph T1 100 . . . . .
GEN maxSCR 1ph T2 100 . . . . .
GEN maxSCR 2ph T1 100 . . . . .
GEN maxSCR 2ph T2 100 . . . . .
GEN maxSCR 2phg T1 100 . . . . .
GEN maxSCR 2phg T2 100 . . . . .
GEN maxSCR 3phSC T1 100 . . . .
GEN maxSCR 3phSC T2 100 . . . .
SYNCON maxSCR 1ph SC1 100 . .
SYNCON maxSCR 1ph SC2 100 . .
SYNCON maxSCR 2ph SC1 100 . .
SYNCON maxSCR 2ph SC2 100 . .
SYNCON maxSCR 2phg SC1 100 .
SYNCON maxSCR 2phg SC2 100 .
SYNCON maxSCR 3phSC SC1 100
SYNCON maxSCR 3phSC SC2 100
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47
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75
76
77
78
List of Tables
3.1
3.2
3.3
3.4
All generating system . . . . . . . . . . . . . . . . . . . .
Base values for SMIB model normalization . . . . . . . . .
Grid model parameters . . . . . . . . . . . . . . . . . . . .
Operating points for the dynamic simulation of Snowy 2.0
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19
23
24
26
4.1
4.2
DFIM decision variables for the design vector of optimization algorithm method . . .
NLINEX loss function scaling parameter values for DFIM optimization . . . . . . . . .
34
34
5.1
Grid code requirement values with initial design vector for DFIM operating in pump
mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Grid code requirement values with initial design vector for DFIM operating in synchronous condenser mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Grid code requirement values with initial design vector for DFIM operating in generator
mode (3phSC and 1ph fault) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Grid code requirement values with initial design vector for DFIM operating in generator
mode (2ph and 2phg fault) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Grid code requirement values with optimal design vector for DFIM operating in pump
mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Grid code requirement values with optimal design vector for DFIM operating in synchronous condenser mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 Grid code requirement values with optimal design vector for DFIM operating in generator mode (3phSC and 1ph fault) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8 Grid code requirement values with optimal design vector for DFIM operating in generator mode (2ph and 2phg fault) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Grid code requirement values with optimal design vector for DFIM operating in pump
mode (2ph and 2phg fault) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.10 Grid code requirement values with optimal design vector for DFIM operating in synchronous condenser mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.11 Grid code requirement values with optimal design vector for DFIM operating in generator mode (3phSC and 1ph fault) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.12 Grid code requirement values with optimal design vector for DFIM operating in generator mode (2ph and 2phg fault) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
79
80
81
82
83
84
85
86
87
88
89
90
Chapter 1
Introduction
1.1
Background
In recent years, fast climate change and global warming have forced the world to transfer the electricity
generation infrastructure from fossil fuels energy sources to renewable energy sources. To control this
climate change, the target is to increase the share of renewable energy at least 30% in the production
of electricity by 2030 [13]. The installation of wind and solar power plants have increased rapidly over
the past few decades as compared to other renewable energy sources. The electricity production from
these renewable energy sources is highly dependent on weather conditions, which are uncontrollable.
Therefore, the power output from solar and wind can cause power surplus issue when power demand
is low in the grid or power deficient issue when high load power is required in the electric grid, which
causes imbalance between power demand and supply [14]. To solve these issues, the energy from these
sources can be stored in large battery banks. However, it has technical and economical limitations.
Pumped storage hydropower plants are an efficient and dynamic way to store and generate a large
quantity of electricity. These plants have the ability to store a large amount of potential energy in the
form of water in large reservoirs. Moreover, these plants exhibit high efficiency of about 90%, which
is much higher than other renewable energy sources [15]. The capacity to generate electric power
with hydropower plants is much higher than solar and wind power plants. About 10% of total energy
capacity in the United States is produced from hydroelectric power [15]. The large water dams or
reservoirs behind hydroelectric power plants are used for multipurpose like for generating electricity,
supplying water to both industry and domestic users, irrigation for agriculture, fish farming, flood
protection. They can store potential energy in the form of water for many years and can be used to
generate electricity anytime when it is required to compensate peak hour energy consumption [1].
To integrate the generating power in the national electricity grid of a country, it is essential for a
generating plant to compliance with the grid codes of that country for the stability and security of
the whole electrical network [16]. Grid codes contain the technical requirements and regulations for
the connection and smooth operation of a power plant with the national electric grid. These rules
and regulations are defined by the transmission system operators (TSOs) and are updated regularly
to ensure the stability of electric grid [17]. All the generating units in a power plant must comply
with the grid code requirements in case of any situation like low voltage ride through (LVRT), high
voltage ride through (HVRT), over and under frequency and for voltage, reactive and active power
control, etc. To analyze the compliance of a power plant with the grid codes, dynamic simulations
of all generating units are performed to see the dynamic behavior of generating units in the presence
and absence of a fault or disturbance. During dynamic simulations, some grid code requirements can
be easily achieved but some grid code requirements are achieved by optimizing the design parameters
of the machine’s control system or even by changing the machine design [18].
Designing an optimal control system is a critical part of power system operation. The control system
can be optimized by selecting the best control parameters at which the generating unit can comply
with most of the grid code requirements. Engineering design process has two major parts: the anal-
1
Institute for Electrical Power Engineering
ysis and the optimization of control system. After compiling a design model, the output results are
analyzed through the analysis process using mathematical equations and scientific rules in simulation
software. After analyzing the outputs of the model, the optimization process is used to find the optimal control parameters at which the control system gives the best output for the design model to
fulfill the grid code requirements.
1.2
Snowy 2.0 pumped storage hydropower plant
Hydroelectric power is a renewable energy that can be generated and delivered in a controlled and
an efficient way to fulfill the energy demands. Pump storage hydropower (PSHP) plants control the
flow of water to produce electricity in peak demand hours and to consume electricity in case of a
power surplus in the electric grid. When there is a need of electric power in the grid, then the natural
flow of water from a higher level to a lower level is used to run the turbine, which produces electrical
power. On the other hand, when there is a low power demand in the grid, then water is pumped from
lower level to higher level through pumps to consume power from the grid. PSHP plants can use two
separate machines for pump and turbine to control the water flow between a higher and a lower level,
as shown in Figure 1.1 (a). These plants can also use one machine at a time, which may operate in
either pump mode or in turbine mode. Such type of machines are called reversible pump turbines
(RPTs), as shown in Figure 1.1 (b) [1].
The PSHP plants that contain RPTs are called reversible pump storage hydropower plants. Both
Figure 1.1: Basic structure of Pump storage hydropower plant with separate pump and turbine
(a) and with reversible pump turbine (b) [1]
synchronous machines (SM) and doubly fed induction machines (DFIM) can be used as reversible
pump turbines in PSHP plants. SM are used because of their high efficiency. The only concern in
using SM is that they can pump the water at only one constant speed. The input power cannot be
changed during pumping mode because it is not possible to consume power from the grid dynamically.
This issue is not a concern while using variable speed DFIMs. In DFIMs, any amount of power can
be taken from the grid rapidly and efficiently [19].
Snowy 2.0 is an under construction expansion of the Snowy Hydro project, which is located in New
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Institute for Electrical Power Engineering
South Wales city of Australia and has the capacity to generate 2000 MW of hydroelectric renewable
energy. Snowy Hydro 2.0 links Tantangara and Talbingo dams with tunnels, in which Tantangra is a
higher level reservoir and Talbingo is a lower level reservoir. An underground pumped storage hydro
power station has six reversible pump/turbine and motor/generator units in which 3 generating units
are SM and 3 are DFIM. When it is required to generate electrical power, the water falling through the
tunnels from higher dam to lower dam will spin the turbines to generate power. During low electrical
power demand in the grid station, water is pumped from lower dam to higher dam by operating the
generating units in pump mode, as shown in Figure 1.2. [2]
Figure 1.2: Snowy 2.0 Pumped storage Hydropower concept [2]
1.3
Thesis Objective and Goals
For the integration of electrical power from the Snowy 2.0 pumped storage hydropower plant into
the Maragle 330 kV grid station, extensive PSS/E load flow studies and simulations of the dynamic
behavior of the large SM and DFIM are required to prove compliance with the actual australian NER
grid code (chapter 5.2 [20]) and investigating the interaction with the electrical transmission grid. The
aim is to assure the stability and performance of the electrical system during all plant operations.
The following tasks will be performed in this master thesis.
ˆ Understanding and analysis of planning criteria, guidelines, standards and NER Grid Codes of
Australia.
ˆ Simulations of reversible large hydro DFIM and SM in the operating mode as generator/motor
and synchronous condenser in PSS/E to prove compliance with the australian NER grid code
and interaction with the electrical transmission grid regarding:
1. reaction to electric fault and contingency events
2. step responses of the voltage control system
ˆ Development of python automation scripts for the dynamic simulations & post processing of
the dynamic simulation results.
ˆ By means of optimization method, determine the optimal settings and plant parameters to fulfill
NER requirements.
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Institute for Electrical Power Engineering
All the dynamic simulations will be performed in the Siemen’s software, Power System Simulator for
Engineering (PSS/E). Python language will be used to create automation files, which will run the
dynamic simulations in PSS/E. After dynamic simulations, the post-processing of simulation output
file will be performed and the desired numerical values will be calculated. The optimization method
will also be implemented in Python to get the optimal settings and the parameter values. The main
task would be to write a python automation file which will run the optimization method to achieve
the optimal parameter values of the dynamic model at which SM or DFIM will fulfill all the grid code
requirements.
1.4
Thesis Outline
In Chapter 2, literature review of SM, DFIM and optimization process is explained.
Chapter 3, has explained the Australian grid code technical requirements, Snowy 2.0 model description, simulation setup model of Snowy 2.0 in PSSE and optimization algorithm method used for the
optimization of Snowy 2.0 .
Chapter 4, has explained the optimization and dynamic simulation results for the grid code requirements.
In chapter 5,
4
Chapter 2
Fundamental theory
2.1
Synchronous machine (fixed speed power generating
unit)
The SM is an AC type machine in which the rotor’s speed of rotation in steady state condition is
synchronized with the electrical frequency of AC currents in the stator winding [3]. For the steady
state operation of the SM, both the magnetic field of the armature winding of the stator and the
magnetic field created by the DC current in the rotor winding should rotate at the same speed. The
synchronous speed is given by the following equation.
Ns =
120f
p
(2.1)
Where Ns is the synchronous speed of the SM in rev/min, p is the number of poles and f is the grid
frequency in Hz. The required number of poles of rotor are calculated according to the synchronous
speed of the SM and the required electrical frequency with equation 2.1. SM can be physically classified
into two different types: SM with cylindrical rotor and SM with salient pole rotor, as shown in figure
2.1. SM with salient pole rotor is used with slower speed; therefore, it has a large number of poles.
Figure 2.1: Synchronous machine with cylindrical pole rotor (a) and with salient rotor (b) [3]
These type of machines are well suited for hydraulic turbines because hydraulic turbines operate at
5
Institute for Electrical Power Engineering
lower speed. SM with cylindrical rotor are used in steam or gas turbines because of their fast-paced
operations [21]. SM can operate in any operating mode depending upon the angle setueen the rotor
and the stator magnetic flux. When the rotor leads the stator flux, then it will behave as a generator
and will deliver power through the stator terminals. If the magnetic flux created by the currents in
the armature winding of the stator lead the field winding rotational flux, then the electromechanical
torque acts in the direction of the machine’s rotation, which operates SM in motor mode and delivers
mechanical power to the prime mover through the shaft. To run the SM in condenser mode for the
reactive power compensation, the shaft of the SM runs freely in the absence of any load [3][4].
The equivalent circuit diagram for phase-a of a synchronous machine with motor reference has shown
in Figure 2.2 (a) and with generator reference has shown in 2.2 (b) . The terminal voltage va of SM
is the sum of voltage drop in armature winding, stator resistance and the induced voltage eaf in the
stator winding. The induced emf eaf or internal generated voltage is proportional to the rotational
magnetic flux of the rotor, which is created by the DC excitation currents in the filed winding of
rotor [4]. By considering the current direction with motor reference the terminal voltage of SM can
be expressed as
dia
va = Ra ia + Ls
+ eaf
(2.2)
dt
When the direction of current is considered according to the generator reference the terminal voltage
equation can be written as follow
va = −Ra ia − Ls
dia
+ eaf
dt
(2.3)
With DC excitation current If , mutual inductance between armature winding and field winding Laf
and rotational frequency ωe (equal to the electrical frequency of generator terminal voltage), the rms
amplitude of internal generated voltage can be expressed by the following equation [4].
Eaf =
ωe Laf If
ωe
√
=√ φ
2
2
(2.4)
Figure 2.2: Synchronous machine equivalent circuit diagram with motor reference (a) and
generator reference (b) [4]
The internal generated voltage is refereed as a terminal voltage of the generator when there is no
armature current in the stator. It can be seen from equation 2.4 that the terminal voltage of the
generator is directly proportional to magnetic flux, which is proportional to the excitation field current. Therefore by controlling the field current , the terminal voltage and the reactive power of the
generator can be controlled. Field current is supplied to the field winding of the rotor through an
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Institute for Electrical Power Engineering
external DC voltage source[22]. The relationship between field current, terminal voltage and magnetic
flux has shown in Figure 2.3. It can be seen that by increasing the field current the magnetic flux also
increases until it goes into the magnetizing saturation region. After saturation region further increase
in the field current will not increase the magnetic flux or the voltage because of the saturation effect
[5].
Figure 2.3: Synchronous machine magnetizing curve [5]
The external DC source is connected to the field winding of the rotor through slip rings on the rotor
and carbon brushes, as shown in the cross section view of SM in Figure 2.4.
Figure 2.4: Cross section view of synchronous machine [6]
The DC voltage supply is controlled through an external excitation control system, which will be
explained in the following section
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Institute for Electrical Power Engineering
2.2
Excitation system
For the stability of electrical power system, PGUs should supply electrical power to the electric grid
by keeping power, voltage and frequency of the power supply within some standard specification limits. SMs have the excitation control system, which regulates the terminal voltage of the generator by
controlling the excitation field current in the field winding of SM. The frequency and power of the
SM is controlled by controlling the mechanical power of the turbine with the governor control system.
The main parts of the excitation control system are power system stabilizer (PSS), automatic voltage
regulator (AVR) and exciter as shown in Figure 2.5.[23] [7]. The AVR takes the input from PSS,
reference voltage and feedback voltage of the main generator and gives the controlling signal to the
exciter. Exciter rectifies the AC excitation power source voltage into DC voltage and supply it to the
field winding of SM through slip rings. The control loop signal from PSS is added in the AVR to
compensate the power oscillations in the active power of SM in case of any fault in the power system
[24].
The excitation system can be categorized into three main categories according to the excitation power
source used for the exciter, AC excitation system , DC excitation system and static excitation system.
AC and DC excitation systems use AC excitation power source and DC excitation power sources
receptively with controlled or uncontrolled bridge rectifiers. The excitation power for the exciter of
static excitation system comes from the main generator through a step down transformer. Controlled
or uncontrolled bridge rectifiers of the static excitation system supply DC voltage to the filed winding
[21]. The working of static excitation system with controlled rectifier will be explained in the following
section
Figure 2.5: Excitation control system for SM [7]
2.2.1
Automatic voltage regulator
Automatic voltage regulation of the generator terminal voltage in case of any load disturbance is
achieved by AVRs. The main function of the AVR is to keep the output voltage of the generator at
a reference value by controlling the DC output voltage of the exciter. The amount of the excitation
field current is determined by taking the difference between the reference voltage and the measured
generator terminal voltage [25]. The simplified block diagram of AVR developed by Voith Hydro which
has a close resemblance with static excitation model ST6B in IEEE Std 421.5, is shown in Figure 2.6.
The proportional gain control error is calculated by subtracting generator voltage Ug from generator
set point voltage Ugsp . As shown in Figure 2.6 several inputs are provided from the external models
of voltage per hertz (V/Hz) limiter , minimum generator reference voltage (Ugspmin ), stator current
limiter (SCL), over excitation limiter (OEL), fast over excitation limiter output (OELf), minimum field
current limiter output (MFCL), power system stabilizer (PSS) and under excitation limiter (UEL).
8
Institute for Electrical Power Engineering
Figure 2.6: simplified AVR model with standard PSS input
The AC power source Ug for the rectifier is provided from the generator terminal.
The V/Hz limiter prevents excessive magnetic flux in the generator or step up transformer, which is
produced because of low frequency and over voltage and is proportional to the V/Hz value. V/Hz
limiter calculates the ratio of per unit voltage to per unit frequency and gives it to the AVR to keep
the generator voltage under the limit, where the V/Hz value does not increase form preset value for
the specific time duration. The field winding of the generator can sustain a specific maximum value of
the field excitation current. Above this value more field current can cause overheating of the generator
and can damage the generator winding. The OEL is used to keep the excitation field current in 100%
to 110% of the rated value and prevent it to go above the maximum field current more than a specific
time duration [21]. SCL keeps the stator currents of the SM under excitation limit and prevents it
from increasing from a preset value. The SCL increases or decreases the excitation current in case of
under excited or overexcited mode of operation respectively [26].
After ensuring that the generator set point voltage is within the limits, the generator voltage is
subtracted from the set point voltage and the error signal is given to the proportional controller.
The output of proportional controller is given to the high value (HV) gate and compared with the
UEL. The UEL keeps the generator voltage above a minimum reference value by preventing the drop
of excitation field current below a minimum field current value. When the UEL value is reached ,
the HV gate gives the total control to the UEL until the voltage does not come back to its rated
value. Then output signal of HV gate is added with the output of the PSS to compensate the voltage
oscillations because of small fluctuations in the rotor speed [21].
The use of AVR for voltage regulation is very effective during steady state operation but in the
presence of any fault in the grid, when the generator operates in transient state, small active power
oscillations cause voltage fluctuations in the terminal voltage of the generator. The AVR changes the
field current to control these voltage fluctuations, which can have a negative impact on the damping of
active power oscillations by opposing the rotor damping currents. Therefore a signal from the output
of PSS is added into the AVR to compensate the voltage oscillations and to add a damping component
in phase with the rotor speed deviation as shown in Figure 2.6[7]. After adding the PSS signal, the
resulting output control signal is given to the integral controller which gives an control signal to the
bridge rectifier. The bridge rectifier converts the AC voltage Ug from the generator terminal into a
DC excitation field voltage by using the control signal from the AVR. The controlled field excitation
voltage is given to the field winding of the SM, which increases or decreases the field current and hence
control the output voltage of the generator as shown in Figure 2.5.
2.2.2
Power system stabilizer
In large electrical power systems, small signal unsuitability is a big issue, which occurred due to the
oscillations in the electrical power, load angle or in the speed of generator during fault or any other
disturbance. There are many types of small signal oscillations in which local mode power oscillations,
9
Institute for Electrical Power Engineering
inter area mode oscillations, inter unit and torsional oscillations are of big concern, which are explained
in IEEE Std 421.2-2014. These oscillations are the cause of small signal unsuitability in the power
system, which can cause continues increase in the rotor angle or it can increase the amplitude of rotor
oscillations due to insufficient synchronizing torque and damping torque respectively. Therefore it is
necessary to damp these osculations by adding a damping torque component and synchronizing torque
component in phase with speed deviation by controlling the excitation system output [21]. The PSS
is used for small signal stability, which has a main function to add a damping torque component in
phase with the speed deviation of the rotor. The damping torque acts in the opposite direction of rotor
speed fluctuations and hence damped the oscillations. Different types of PSS models are described
in IEEE Std 421.5-2016 depending upon the type of inputs used for the generation of the damping
torque component [27]. The PSS2B model has been used in this project and will be discussed here.
The PSS2B also know as integral of accelerating power (∆P ω) stabilizer, is a dual input stabilizer.
PSS2B takes generator terminal frequency and electrical power of the generator as inputs for generating
stabilizing signal as shown in Figure 2.7. There are four main parts of PSS2B, washout filters, ramp
tracking filter (M:N filter), stabilizer gain Ks1 and phase lead-lag blocks as shown in Figure 2.7 and
are explained below.
Washout filter: Washout filter are high pass filters, which filter out the unwanted oscillation
input signals. Washout filter passes the rotor speed oscillation signals without any change and also
prevent the unwanted change in the terminal voltage of the generator during the speed variations in
the overall system like system islanding conditions. The typical values for washout filters can be from
1 to 20 seconds [28].
Ramp tracking filter: Ramp tracking filter with low pass filter is used to filter out the
torsional mode oscillation components from the signal of mechanical power integral. Torsional mode
oscillations occur due to the variation in mechanical power. The purpose of ramp tracking filter is to
stop input signal with high frequency , pass the low frequency mechanical power variations and keep
the output of PSS as minimum as possible in case of rapid change in the mechanical power [29].
Lead Lag phase compensation: To damp the oscillations in the rotor, the damping torque
component produced by the PSS should be in phase with the speed deviation of rotor. Phase lead-lag
compensation blocks are used for the compensation of phase lag or phase lead between the output of
PSS and the electric torque resulted by the damping torque component of PSS [28].
Figure 2.7: Block diagram of power system stabilizer PSS2B [8]
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Institute for Electrical Power Engineering
Working principle: The working principle of PSS2B is based on the direct relationship between the speed deviation of the rotor ∆ω and the accelerating power ∆Pe , which can be represented
by the equation of rotor motion as below [29].
∂
1
∆ω =
(∆Pm − ∆Pe )
∂t
2H
(2.5)
Equation 2.5 can be rewritten as
1
∆ω =
2H
Z
(∆Pm − ∆Pe )∂t
(2.6)
From equation 2.6 the integral of mechanical power can be calculated from speed deviation and integral
of electrical power as
Z
Z
∆Pm ∂t = 2H∆ω +
∆Pe ∂t
(2.7)
Two inputs, frequency and electrical power are measured from the generator terminal and are given
to the two transducers for filtering and measurement. The mechanical power integral signal is derived
by adding the signal of speed deviation ∆ω and the integral of electrical power change ∆Pe according
to equation 2.7. The purpose of deriving the mechanical power integral signal is to pass it through
ramp tracking filter to filter out the torsional mode oscillations, which are described in IEEE Std
421.2-2014. After filtration from the ramp tracking filter, the integral of the change in electrical
power ∆Pe is subtracted from the integral of the change in mechanical power ∆Pm to get the speed
deviation signal, which is directly proportional to the change in frequency and electrical power of the
generator. Ideally the calculated equivalent speed deviation signal from the difference of change in
electrical and mechanical power should be equal to zero but its not the case in real time, therefore a
proportional controller is used with the PSS gain. The value for PSS gain Ks1 should be selected as
high as it can increase damping of the oscillations but not so much high that it affects the stability
of other components in the system. After the proportional controller phase lead-lag compensation
filters are used for the phase lead-lag compensation. The derived signal of the PSS output is given
to the excitation system to produce a damping torque in phase with speed deviation [29]. The
practical implementation of PSS2B with settings of washout filter and ramp tracking filter parameters
is explained in [29].
2.3
Doubly fed induction machine (variable speed unit)
The DFIM is an variable speed wound rotor induction machine which transfers electrical power to the
grid directly from the stator circuit and indirectly from the rotor circuit through AC-DC-AC power
converters, so it is called DFIM. The ability to take or fed electrical power from or to the the grid in
a wide range makes DFIM a suitable choice for the variable speed pump turbine unit in hydroelectric
power generation. Therefore DFIM has a significant role in PSHP plants for the consumption and
generation of electricity during short time intervals of low and peak demand [19]. As shown in Figure
2.8, the stator of the DFIM is connected directly to the main grid via step-up transformer while the
rotor of the DFIM is connected to the grid through AC-DC-AC 2-level VSIs. The rotor side converter
(RSC) and the main side converter (MSC)or grid side converter (GSC) are connected with a DC link.
Another advantage of DFIM is that only a 20-30% of the total system power is transferred through two
power converters, which reduces the power electronics cost and power losses [30]. Frequency regulation
of power system is achieved by controlling the active power of the DFIM and the voltage regulation
is achieved by controlling the reactive power of the DFIM. RSC control is used to control the speed,
active and reactive power of the generator by controlling the rotor currents and GSC control keeps the
DC link voltage stable and controls the reactive power reactive power of the excitation transformer
[31][32].
The equivalent circuit diagram of DFIM in rotating reference frame with angular speed ω is shown in
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Institute for Electrical Power Engineering
Figure 2.8: Doubly fed induction machine with 2-level VSI [9]
Figure 2.9. The equations for the dynamic model of DFIM in rotating reference frame can be written
from Figure 2.9 [10].
dψs
Vs = Rs Is +
+ jωs ψs
(2.8)
dt
dψr
+ j(ωs − ωr )ψr
(2.9)
Vr = Rr Ir +
dt
The stator flux ψs and rotor flux ψr can be calculated as below
ψs = Ls Is + Lm Ir
(2.10)
ψr = Lr Ir + Lm Is
(2.11)
The dynamic model equations for DFIM stator and rotor in d-q reference frame can be written as
below [30]
dψsd
Vsd = Rs Isd +
− ψsq ωs
(2.12)
dt
dψsq
Vsq = Rs Isq +
+ ψsd ωs
(2.13)
dt
dψrd
Vrd = Rr Ird +
− ψrq (ωs − ωr )
(2.14)
dt
dψrq
Vrq = Rr Irq +
+ ψrd (ωs − ωr )
(2.15)
dt
Considering the voltage orientation, the d-q components of stator current can be calculated from
Equation 2.10 [31].
Lm
ird
(2.16)
isd = −
Ls
ψsq
Lm
isq =
−
irq
(2.17)
Ls
Ls
From d-q components of stator current and rotor flux Equation 2.11, the d-q components for rotor
voltage can can be rewritten as below [33]
urd = Rr ird + σLr
dird
− ωslip σLr irq
dt
12
(2.18)
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Figure 2.9: DFIM equivalent circuit diagram in rotating reference frame [10]
urq = Rr irq + σLr
dirq
Lm
+ ωslip σLr ird + ωslip
ψsq
dt
Ls
(2.19)
Where ωslip = (ωs − ωr ) is the slip angular frequency of the rotor and σ = 1 − (Lm2 /Ls Lr ) is the
leakage factor. By transferring the voltage and current of DFIM into d-q reference, the active and
reactive power can be written with d-q reference frame current and voltage of stator as below
P = 3(vsd isd + vsq isq )
(2.20)
Q = 3(vsd isq + vsq isd )
(2.21)
Supply voltage angular position θe can be calculated as
Z
vβ
θe = ωdt = tan−1
vα
(2.22)
Where vα and vβ are the α , β components of the supply voltage in stationary reference frame. By
aligning the d component of the d-q reference frame along the voltage position of α-β reference frame,
vq component of the stator voltage becomes zero and hence the the new equation of active and reactive
power can be written as
P = 3vsd isd
(2.23)
Q = 3vsd isq
(2.24)
It can be seen from equation 2.23 and 2.24 that the active power and reactive power of the DFIG can
be controlled independently by controlling isd and isq respectively [33]. The frequency of the power
system is regulated by controlling the active power of the DFIM and the voltage of the power system
is regulated by controlling the reactive power of the DFIM. The control system for RSC and GSC are
explained in the following sections
2.3.1
Rotor side converter control
The rotor side control system controls the active power, reactive power or voltage of the generator by
controlling the applied voltage to the rotor circuit of the DFIM. The control of DFIG is achieved by
decoupling the rotor currents, the d-axis current ird is used to control the torque or the active power
of the DFIM and the q-axis current irq is used to control the reactive power or voltage of the DFIM
[31]. The block diagram of the RSC control is shown in Figure 2.10.
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To control the active power of the DFIM, the feedback signal of the active power p is calculated
from the terminal of the generator and the reference active power p* is given. The output of the
PI controller of active power is isd , which is used to calculate the reference d-axis component ird *
of rotor current according to the equation 2.16. The reference decoupled rotor d-axis voltage urd * is
obtained by subtracting ωslip σLr irq from the output of rotor d-axis current ird PI controller according
to equation 2.18. The q-axis component of rotor current irq is used to control the reactive power or
voltage of the generator as shown in Figure 2.10(b). In voltage control mode, reference reactive power
q* is calculated from the PI controller of the voltage control. The PI controller of the reactive power
controller gives the q-axis component of stator current iSq , which is used to calculate the reference
q-axis component of the rotor current irq* according to the equation 2.17. The reference decoupled
q-axis of rotor voltage urq* is obtained by adding σLr ird + ωslip LLms ψsq in the output of PI controller
of rotor q-axis current irq according to the equation 2.19.
After obtaining the d-q reference components of the rotor voltage, reference Vabc voltages are calculated by applying reveres Park and reverse Clark transformation on d-q reference voltages of the rotor.
The reference voltages in abc reference frame are given to the PWM of the VSI. PWM converts the
DC-link voltage into the AC voltage by controlling the switching of the IGBTs of the VSI. Then the
controlled rotor voltage is applied to the rotor circuit [33].
Figure 2.10: Rotor side converter control block diagram for active power control (a) and reactive
power control/voltage control (b) of DFIM
2.3.2
Grid side converter control
GSC control is especially used to keep the DC link voltage constant of the VSI. The reference voltages,
∗ and quadrature axis voltage v ∗ for the PWM of grid side VSI can be calculated
direct axis voltage vd1
q1
from the following equations [33]
di∗d
+ (vd + ωe Li∗q )
dt
di∗q
= −Ri∗q − L
− ωe Li∗d )
dt
∗
vd1
= −Ri∗d − L
∗
vq1
14
(2.25)
(2.26)
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The d-axis reference current i∗d is obtained from the PI controller of DC link voltage and is used to
control the DC link voltage of the VSI. The quadrature axis reference current i∗q is calculated from the
reactive power of the grid and it is used to control the reactive power of the grid. After getting the
d-q reference currents, the reference d-q voltage components are calculated from equations 2.25 and
2.26. The reference voltages in abc reference frame for the PWM are calculated by applying reverse
∗ and v ∗ . PWM keeps the DC voltage constant by controlling
Park and Clark transformation on vd1
q1
the switching signals of IGBT switches in grid side VSI [33].
2.4
Optimization
After designing and implementation of the control system for SM and DFIM, the next stage is the
evaluation and testing of the control system response by applying different types of disturbances. The
parameter values and settings of the control system are defined such that the machine response follows
the grid code requirements provide by the grid operator. Therefore it is required to find the optimal
control parameters for the control system of the machine. Using a traditional hit and trial method for
the tuning of these parameters is a difficult and time taking process. Therefore a optimization process
is used to get the best values for the control system parameters [34]. Optimization is the process to
find an optimal design vector of control parameters at which the objective function gives minimum
or maximum loss error value under some constraints or bounds on the design vector [35]. The main
parts of the optimization process are discussed below
2.4.1
Design vector
Control system consists of PI controllers which are used to minimize the error between the reference
value and the real time value of the controlled signal. The gain values of proportional and integral
controllers are tuned to improve the efficiency of the control system. All such parameters, which
can be changed in the control system are called design variables or decision variables and when they
are collected in a vector, it is called design vector [35]. A control system or a design model can be
described with mathematical equations which contain different variables and constants, as shown in
the following example equation
f (x) = x2 − 1
where 0 < x < 10
(2.27)
In equation 2.27, x is called the design variable, which has bound from 0 to 10 and the function f(x)
is called the objective function.
2.4.2
Objective function
The objective of a control system can be minimizing the settling time for the oscillations in the terminal
voltage, active power or reactive power during the disturbance or after the clearance of the disturbance.
For maximizing, the objective can be to increase the rise time of reactive current or the damping ratio of
the active power to damp the small oscillations in the active power. The selection of Objective function
is the most important part of optimization process because there can be several objective functions
with different design vectors but the aim of optimization process is to single out the best objective
function at which all the possible requirements are met [34][35]. The objective of the optimization
process is to minimize the difference between calculated (true values) grid code requirement values
and target values (optimal values) for grid code requirements. The difference between target values
and calculated values tells, how much the output response of the control system is near or far from
the optimal target response with the current design vector parameters. The difference of more than
one variable values is represented by a single real value by using loss function or cost function. In
optimization process, loss function or a cost function maps more than one variable or event values
on to a single real number, which represent the loss or cost of the event [36]. There are many loss
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functions like Mean absolute error, Mean square error (MSE), 0-1 loss function, Cross-Entropy Loss
function, Non-Linear Exponential (NLINEX) Loss Function etc. The loss functions which are used in
this project are NLINEX loss function and MSE loss function.
2.4.3
Mean square error loss function
MSE is very commonly used loss function to calculate the loss error. It takes the average of the
squared difference and gives a single real number representing the loss error. MSE can be represented
in the mathematical form by the following equation [37]
n
M SE =
1X
(Yi − Y )2 )
n
(2.28)
i=1
Where n is the number of variables, Yi is the value of ith variable and Y is the target value of
the ith variable. A zero MSE value represents a good estimation of the true values, it means that
the true values are approaching target values. MSE output increases as the difference between true
values and target values increases so the out of range true values are more penalized. The output
response of MSE loss function with true values (0-10)and target value of zero has shown in Figure 4.1.
Figure 2.11: MSE loss function output response
2.4.4
Non-Linear Exponential (NLINEX) Loss Function
NLINEX loss function is the combination of linear exponential of the difference and the squared
difference. NLINEX loss function can be represented by the following equation [38].
L(D) = k[exp(cD) + (cD)2 − cD − 1], k > 0, c > 0
(2.29)
Where D is the difference between the true values and target values while c, k are the scaling factors
to tune the behavior of loss function according to the requirement. The output response of NLINEX
loss function for true values (0-10) with target value zero has shown in Figure 4.2.
The output response of the loss function can be changed by tuning the scaling factors c and k according
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Institute for Electrical Power Engineering
Figure 2.12: Output response of NLINEX loss function with different scaling factors
to the range of ture values. NLINEX loss function is tuned by the scaling factors such that when the
true values are within the range, the loss error does not increase so fast and takes very small steps by
increasing the true values. When the true values increases out of the limit then, the loss error increase
very fast and takes big steps even by adding a very small increment in the trues value. Figure 4.2 is
showing the output response of NLINEX loss function for the range of 5 seconds and 7 seconds. It
can be seen that the blue curve remains almost linear until 5 seconds but after 5 seconds it increases
exponentially and the same with yellow line for 7 seconds.
2.4.5
Optimization algorithm method
An optimization algorithm is a process that solves a mathematical problem or an objective function
iteratively and gives the minimum or maximum output value for that objective function. The optimization algorithm takes an initial design vector to get the 1st solution of the objective function
and then it compares the various output solutions with different design vectors until it finds the best
solution output for the objective function [39]. The optimization algorithm can be defined in two
types on the basis of the nature of objective function output, local optimization algorithm method
and global optimization algorithm method.
Local optimization algorithm method is used when it is required to find only one local minimum or local
maximum of the objecting function. Some local optimization algorithm methods are “Trust-Region
Constrained Algorithm method” and “Sequential Least Squares Programming (SLSQP) Algorithm
method”. Global optimization method is used when the objective function has more than one local
minimums and maximums and the objective is to find the lowest local minimum or maximum of the
objective function as shown in Figure 2.13. Global optimization algorithm method like “simplicial
homology global optimization” (Shgo) global optimizer method is used for global optimization [40].
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Institute for Electrical Power Engineering
Figure 2.13: A Non-Convex Combination of Gaussian Distributions [11]
18
Chapter 3
Methodology
3.1
Australian grid code requirements
For the successful connection of Snowy 2.0 PSHP plant with the national electric grid of Australia, all
the the GUs of the power plant are required to comply with the Australian grid codes requirements.
The technical requirements for Australian grid codes are described in the chapter 5.2.5 of National
electricity rules (NERs)version 135 of Australia. These NERs are defined by the Australian energy
market operator (AEMO), which are updated regularly. The performance of the GUs of the power
plant can be accessed by the three level of access standards in which, the Automatic access standard
(AAS) is the highest level of technical performance of the GU. In this master thesis project, the
automatic access standards of the following two grid connection requirements (5.2.5.5 and 5.2.5.13)
will be achieved by means of optimization method.[20]
3.1.1
Clause S5.2.5.5 (Contingency fault analysis)
In this clause the response of the generating system is accessed in the presence of contingency fault
events like three phase short circuit faults, two phase to ground fault, single phase to ground fault
and phase to phase fault. The technical requirements are different for different generating systems as
described below.
3.1.1.1
All generating systems
All the GUs of the generating system (synchronous and asynchronous) should remain connected and
in uninterrupted operation for a specific time in case of contingency fault events as shown in Table
3.1.
Table 3.1: All generating system
Type of faults
Three phase short circuit fault
Two phase to ground fault
Single phase to ground fault
Phase to phase fault
3.1.1.2
Time for generating system to remain connected
100 ms
250 ms
250 ms
250 ms
Synchronous generating system
In case of contingency fault events listed in Table 3.1, all the GUs of a synchronous generating system
will comply with AAS if they fulfill all the following grid code requirements
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Institute for Electrical Power Engineering
ˆ During the fault the GS should supply 4% reactive current for each 1% reduction in the point
of connection voltage.
ˆ The maximum reactive current supply is limited to the 250% of maximum continues current of
the GS.
ˆ Sufficient reactive power to bring the connection point voltage in under voltage range of clause
S5.2.5.4 right after the fault clearance for continues uninterrupted operation.
ˆ Active power should return to at least 95% of its pre-fault value within 100 ms after the fault
clearance time.
3.1.1.3
Asynchronous generating system
In case of contingency fault events listed in Table 3.1, all the GUs of a asynchronous generating system
must fulfill the following requirements
ˆ During the fault the GS should supply 4% reactive current in addition to its pre-fault value for
each 1% reduction in the connection point voltage below the under voltage range (85% to 90%).
ˆ The maximum reactive current supply is limited to 100% of the maximum continues current of
the GS.
ˆ Sufficient reactive power to maintain the voltage in 90% to 110% voltage range after clearance
of the fault.
ˆ If the connection point voltage goes below 5% of the nominal voltage then the GS don’t have
to fulfill the reactive current requirements but it should supply at least maximum continues
current.
ˆ The rise time for the reactive current response must not be great than 40 ms.
ˆ The settling time of the reactive current during fault should not be greater than 70 ms.
ˆ The reactive current oscillations must be adequately damped (damping ratio > 0.1).
ˆ Active power should return to at least 95% of its pre-fault value within 100 ms after the fault
clearance time.
3.1.2
Clause S5.2.5.13 (Step response of the voltage control system)
A GS must have a voltage control system and excitation control system which has the following
capabilities
ˆ The voltage control system of GS can adequately damp the active power oscillations (damping
ratio > 1).
ˆ The excitation control system of a synchronous GS must have a settling time less than 5.0
seconds for generating voltage, active power and reactive power in case of 5% under voltage or
over voltage disturbance in the GU.
ˆ When the limited devices are activated the settling time for voltage , active power and reactive
power should be less than 7.5 seconds.
ˆ The excitation control system of an asynchronous GS must have a settling time of 2.5 seconds
for generating voltage in case of 5% voltage disturbance in the GU.
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3.2
Snowy 2.0 Model description
The Snowy 2.0 PSHP plant has six reversible pump turbines which are connected to the motor/generator.
Three power generating units (PGU) are synchronous machines (fixed speed units) and three of them
are double feed induction machines (variable speed units). Each PGU hsa a rated electrical power
of 340 MW so collectively snowy 2.0 PSHP plant can generate atleast 2000 MW of electrical power.
All PGUs are connected to the power plant switchyard via step-up transformers. The power plant
switchyard connects all PGUs to the National Electricity Market with four 330 kV overhead lines from
switchyard to the 330 kV TransGrid Maragle substation. The single line diagram (SLD) of Snowy 2.0
PSHP plant implemented in PSSE has shown in Figure 3.1.
Figure 3.1: Single line diagram of Snowy 2.0 Pumped storage Hydropower plant
3.2.1
Dynamic model of fixed speed unit
The standard PSSE dynamic models and the user-written models for Snowy 2.0 project specifically
are used for the dynamic simulation of fixed speed unit in pump, turbine and condenser modes of
operation. The dynamic models of fixed speed unit are described below
3.2.1.1
Synchronous machine
Salient pole synchronous generator model (GENSAL) has been used for the dynamic simulation of SM
in all modes of operation. GENSAL is an standard PSSE library model, which represent each SM (M2,
M4, M6) in the dyr. file of PSSE. The detailed description of GENSAL and algebraic equations are explained in [12]. The block diagram of GENSAL model has shown in Figure 3.2. The value description
of CONs and STATE variables of GENSAL can be found in the model library of PSSE documentation.
3.2.1.2
Power system stabilizer
Every synchronous generator is connected to one standard IEEE (PSS2B) PSS model, which is represented by PSS2B in dyr. file of PSSE. The block diagram of PSS2B dynamic model has shown in
Figure 2.7. The values and description of CONs, STATE variables and ICONs are explained in the
model library of PSSE documentation.
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Institute for Electrical Power Engineering
Figure 3.2: Block diagram for GENSAL model [12]
3.2.1.3
Governor system
User-written dynamic models from Voith hydro are used for governor system and governor system
including common water way model, which are represented by S2GOV0 and S2GOVW0 respectively
in the dyr. file of PSSE. S2GOV0 is used for the governor control system of both SM and DFIM
units. S2GOV0 represent the governor control system for all modes of operations (Turbine, Pump
and Synchronous condenser). S2GOVW0 has the functionality of S2GOV0 with a hydraulic water
way model which interlinks all GUs of Snowy 2.0 project. The S2GOVW0 model is attached to only
1st machine of the fixed speed unit (M2) or variable speed unit (M1) and the other machines of fixed
speed unit (M4, M6) or variable speed unit (M3, M5) are attached with S2GOV0 model.
3.2.1.4
Excitation system model
The user-written model S2AVR0 from Voith hydro is used for the Excitation system of SM. Every SM
is connected to one S2AVR0 model, which contains the following modules
ˆ Automatic voltage regulator
ˆ Under excitation limitation (UEL)
ˆ Over excitation limitation (OEL)
ˆ Static excitation with thyristor converter
ˆ Minimum field current limiter
ˆ Maximum field current limiter
ˆ Volts-Hertz limiter
ˆ Stator current limiter.
ˆ Reactive power control
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ˆ Power factor control
3.2.2
Dynamic model of variable speed unit
The variable speed GUs of Snowy 2.0 has three DFIM generators. The dynamic models of DFIM
generators of Snowy 2.0 are represented by S2DFIM0 user-written model. S2DFIM is a user-written
model from Voith hydro specifically for the DFIM generators of Snowy 2.0, which can be used for all
modes of operations (Turbine, Pump, Synchronous condenser). S2DFIM0 model contains the following
modules
ˆ Doubly-fed wound rotor induction machine
ˆ Grid-side converter
ˆ Rotor-side converter
ˆ Excitation transformer
ˆ Active power control
ˆ Reactive power control
ˆ Voltage control
ˆ Power factor control
ˆ DC Voltage control
3.3
3.3.1
Simulation setup model
Simulation model
For the analysis of Snowy 2.0 PSHP plant, single machine infinite bus (SMIB) model in PSSE has
shown in Figure 4.1. The base values for SMIB model normalization are listed in the Table 3.2. Three
DFIMs (U1, U3, U5) and three SMs (U2, U4, U6) are used as a GUs for the PSHP plant of Snowy
2.0 . The grid (POC) model is represented by a large SM, with the grid impedance values listed in
Table 3.3, which are dependent on the following short circuit ratio values (SCR).
ˆ 9.7 SCR for a strong grid
ˆ 1.5 SCR for a weak grid
Table 3.2: Base values for SMIB model normalization
Description
Stator voltage
Grid voltage
Nominal power
Active power
Reactive power
Nominal current at 15 kV for 1 unit
Grid power
Nominal current at 330kV for 3 units
Base unit values
15 kV
330 kV
375 MVA
375 MW
375 MVar
14.434 kA
100 MVA
1.968 kA
23
Per unit values
1 pu
1 pu
1 pu
1 pu
1 pu
1 pu
1 pu
1 pu
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Figure 3.3: Single line representation of the simulation model for snowy 2.0
Table 3.3: Grid model parameters
Description
Apparent power
Resistance
Reactance
Zero sequence resistance
Zero sequence reactance
Units
MVA
pu
pu
pu
pu
Values
100000
0.291
4.89
0.756
3.817
Remarks
strong grid SCR 9.7
Apparent power
Resistance
Reactance
Zero sequence resistance
Zero sequence reactance
MVA
pu
pu
pu
pu
100000
1.56
18.57
7.595
26.198
weak grid SCR 1.5
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3.3.2
Grid operating points
For the analysis of grid code requirements, different operating points (OPs) are defined according to
the minimum capability boundary conditions of GUs at POC. The summery of OPs used in Snowy
2.0 has shown Table 3.4
ˆ T1 and T2 OPs represent the under excited and over excited conditions for the generator mode
at maximum power level.
ˆ T3 and T4 OPs represent the under excited and over excited conditions for the generator mode
at maximum continues power, which the generator can deliver.
ˆ SC1 and SC2 OPs represent the under excited and over excited conditions for the Synchronous
condenser mode
ˆ P1 and P2 OPs represent the under excited and over excited conditions for the pump mode.
ˆ V-POC is the voltage at POC in pu.
ˆ V Unit Terminal is the terminal voltage of the generator in pu.
ˆ P SM is the active power of SM, which is supplied (positive power) to the grid in generator
mode or consumed (negative power) from the grid in pump mode.
ˆ P DFIM is the active power of DFIM, which is supplied (positive power) to the grid in generator
mode or consumed (negative power) from the grid in pump mode.
3.4
PSSE dynamic simulation
PSSE software from Siemens has been used for the dynamic simulation of Snowy 2.0 project. The detailed guidelines for the functionality of PSSE can be found in the documents of PSSE documentation.
Three input files, save case data file (.sav), dynamic raw data file (.dyr) and userdll file (.dll) are used
for the dynamic simulation of snowy 2.0 PSHP plant. The operating mode of the GU is automatically
selected according to the following conditions in pu
ˆ If the active power is > 0.0 MW, the generating mode will be selected.
ˆ If the active power is < -1.5 MW, the pumping mode will be selected.
ˆ If active power is >= -1.5 MW and < 0.0 MW the SynCon operation is assumed
All the network data values of Snowy 2.0 PSHP plant are saved in .save file and the dynamic models
of all the GUs and control systems are added in the .dyr file. All the simulations for Snowy 2.0 are
performed in PSSE with automation files, written in python programming language. Spyder from
anaconda is used as a python interpreter to write the python script and to run the PSSE simulations
outside of PSSE graphic user interface (GUI). The python commands to perform different actions in
PSSE can be found in application program interface (API) document of PSSE. The PSSE python
modules, which are used to link PSSE with spyder are psspy, redirect, dyntools.
The flow chart for the basic structure and steps involved in the automation file of dynamic simulation
function has shown in Figure 3.4. The dynamic simulation function takes the .sav file and select if the
machine is DFIM or SM. If the machine is DFIM, the function turns on all DFIMs and turn off all SMs
and if the machine is SM, the function turn on all SMs and turn off all DFIMs. After the selection of
machine type and operating mode, the terminal voltage (TV)and active power of the generator and
the grid voltage is updated according to the grid operating points (GOP) listed in Table 3.4. After
adding .dyr and .dll files, the parameters for the dynamic models of machine and the control system
are updated. After the parameter selection, all the network system is solved by using Newton-Raphson
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Table 3.4: Operating points for the dynamic simulation of Snowy 2.0
Description
T1
T2
T3
T4
SC1
SC2
P1
P2
Generator mode in
over-load
under-excited
Generator mode in
over-load
over-excited
Generator mode in
normal operation
under-excited
Generator mode in
normal operation
over-excited
Synchronous condenser
mode
under-excited
Synchronous condenser
mode
over-excited
Pump
mode
under-excited
Pump
mode
over-excited
V-PoC
%
90%
100%
110%
90%
100%
110%
90%
100%
110%
90%
100%
110%
90%
100%
110%
90%
100%
110%
90%
100%
110%
90%
100%
110%
V Unit Terminal
%
86.23%
96.33%
106.43%
95.02%
104.30%
113.70%
86.07%
96.22%
106.35%
94.92%
104.20%
113.60%
85.0%
95.34%
105.70%
93.94%
103.40%
113.0%
85.40%
95.60%
105.80%
94.34%
103.64%
113.10%
26
P SM
MW
371.0
371.0
371.0
371.0
371.0
371.0
339.0
339.0
339.0
339.0
339.0
339.0
-1.5
-1.5
-1.5
-1.5
-1.5
-1.5
-337.50
-337.50
-337.50
-337.50
-337.50
-337.50
P DFIM
MW
368.0
368.0
368.0
368.0
368.0
368.0
335.4
335.40
335.40
335.40
335.40
335.40
-1.5
-1.5
-1.5
-1.5
-1.5
-1.5
-368.0
-368.0
-368.0
-368.0
-368.0
-368.0
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power flow calculation method. In the next stage, the desired output channels are selected, which can
be analyzed through .out file of PSSE dynamic simulation. Following dynamic solution parameters of
PSSE are used for the simulations of Snowy 2.0
ˆ No. iterations: 400
ˆ Acceleration: 0.2
ˆ Tolerance: 0.001
ˆ simulation time step: 0.001 seconds
After setting the dynamic simulation parameters, function runs the dynamic simulation for a specific
fault and specific simulation time. The output of dynamic simulation function are the .out PSSE files
for all grid operating point, which contains all the output signal which are selected during output
channels selection. The output signals of .out file can be seen in PSSE plot tree and they can also be
plotted in .png diagrams through post processing automation file.
3.4.1
Post processing of dynamic simulation
After dynamic simulation of Snowy 2.0 GUs, the post processing automation python script is used
to plot the required output response signals in .png diagrams from .out file of PSSE. Post processing
python function has two parts. First part of the post processing function calculates the grid code
requirement output values from the required output response signals and stores them in separate arrays for separate requirement values. The grid code requirement output values can be the settling
time, damping ratio, rise time or reactive current requirement values depending upon the grid code
requirement clauses. These values are used in the optimization process to calculate the loss error for
optimization algorithm method. The second part of the post processing file plots the required output
response signals in a .png diagram with the output signal tags, AAS requirements and unique title of
the diagram. The flow chart for the post processing automation file has shown in Figure 3.5. Post
processing function imports one or more than one PSSE .out files and compare them with the unique
names of the required output signal channels. In the next step, the required channel data is extracted
from the PSSE out files and stored in the arrays to use them in mathematical formulas. In the next
stage mathematical formulas are used to calculate the grid code requirement values, which are stored
in different arrays. After calculating grid code requirement values, the required output signals are
plotted and saved in .png diagrams. In the last step all the grid code requirement values for all GOPs
are returned in the form of arrays for the optimization process and further analysis.
3.5
Optimization applied to Snowy hydro 2.0
Optimization process has been used for Snowy hydro 2.0 project to get the optimal control parameters and settings for the control system of GS at which, the GS fulfill all the grid code requirements
explained in the clauses (S5.2.5.5 and S5.2.5.13) of NER. The flow chart for the optimization process
implemented by python has shown in Figure 3.6.
3.5.1
Initial guess
This is the 1st stage of the optimization process. In this step, initial guess parameter values are given
to the decision variables of the design vector. The decision variables are selected such that, they don’t
change the under or lower limits of the control system, which can disturb the behavior of the control
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Figure 3.4: Flow chart for PSSE dynamic simulation function in python
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Figure 3.5: Flow chart for post processing function in python
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Figure 3.6: Optimization process flow chart for Snowy hydro 2.0
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system and they should not belongs to any external hardware like rectifier bridge or crowbar circuit
etc. In this project, the initial guess values for the decision variables of the design vector are taken
from Voith Hydro calculations.
3.5.2
Design vector
Design vector is the input for the python script of objective function program. The design vector takes
1st initial guess values from the initial design vector, which are then updated in the PSSE dynamic
SMIB (single machine infinite bus) model of the Snowy 2.0 hydropower plant. The first dynamic
simulation is performed with the initial design vector. After the 1st simulation, the design vector
values are regularly updated by the optimization algorithm method until it finds the minimum loss
error value for the objective function.
3.5.3
Objective function
During the disturbance or after the disturbance, the Power generating unit (SM or DFIG) should fulfill
all the technical requirements of grid codes, which are explained in section 3.1. The steps involved in
the python script of the objective function are shown in the Flow chart 3.7. Updated values of the
design vector are given to the dynamic function, which changes the required control system parameter
values and run the dynamic simulation and save the .out files for the required output channels. The
.out files of the dynamic simulation function are given to the post processing function, which calculates
and returns the grid code requirement (true values) vales in separate arrays. After post processing,
the index by index difference is calculated between the arrays of true values and the target values.
The difference is stored in separate arrays for every grid code requirement for the calculation of loss
error.
Figure 3.7: Flow chart for the objective function of optimization process
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There are two loss functions which has been used for the calculation of loss error, MSE and NLINEX
loss functions. The most suitable and compact loss function for the optimization process is NLINEX
loss function. The output response of the NLINEX loss function can be controlled with the scaling
parameters and also it gives the clear idea for the allowed range of grid code requirement output values
as shown in Figure 4.2. At the end the objective function returns the mean of loss errors for all grid
code requirement output values to the optimization algorithm method.
3.5.4
Simplicial homology global optimization (Shgo) algorithm
Optimization algorithm acts as a decision making step in the whole optimization process. Optimization
algorithm takes the output of the objective function and then decides if the loss error is minimum
or not by comparing with other outputs of the objection function. If the loss error is minimum then
optimization algorithm returns that loss error as a global minima. If the output of objective function
is not minimum, optimization algorithm gives new decision variable values to the design vector and
then again calls the objective function to get a new loss error value. This process continues until the
optimization algorithm does not find the global minima of the objective function as shown in Figure
3.6. The design vector at which, the objective function has a global minima is called the optimal
design vector.
For Snowy 2.0 project, Shgo algorithm method has been used to find the global minima of the objective
function. To use Shgo algorithm method in python, optimize module has been imported from scipy
and shgo module has been imported from scipy.optimize. Shgo optimizer can be used in two different
ways, one way is to use the minimization methods like SLSQP and trust − constr minimization
methods as given below [41]
scipy.optimize.shgo(f unc, bounds, iters = 1, minimizer kwargs = method : SLSQP )
(3.1)
The second form of Shgo algorithm method contains sampling methods like Sobol or Simplicial instead
of minimization method as shown below [41]
scipy.optimize.shgo(f unc, bounds, n = 60, iters = 3, samplingmethod = sobol)
(3.2)
f unc is a callable objective function which is to be minimized, it should be in the form f (x), where x
is the one directional design vector array of decision variables. Bounds are the bounds on all decision
variables in the design vector in the form of sequence. There should one pair of bounds (min, max) for
each decision variable and the length of bounds pairs should be equal to the length of design vector
array. Iters is the number of iteration that will be performed for the dynamic simulation. The number
of iteration can be increased to find more local minimas in the objective function. M inimizer kwargs
contains the minimization method like SLSQP and trust − constr [41]. The optimization process has
been performed by using all the minimization methods and sampling methods, the results shows that
the shgo algorithm with sobol sampling method is faster and gives the optimal design vector which is
more acceptable. Therefore, optimization algorithm method (Shgo algorithm with ’Sobol’ sampling
method) has been used to perform the optimization for all the grid code requirements. Optimization
process for all the grid code requirements and their results are explained in the following chapter of
results and discussion.
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Chapter 4
Results and discussion
SMIB model in Figure 4.1 has been used for the analysis of Snowy 2.0 PSHP plant. All the dynamic
simulations are conducted in PSS/E 34 and the voltage control mode has been used to achieve the
grid code requirements. The grid code requirements has been accessed at all the OPs of Table 3.4
with both, strong and weak grid scenarios. To perform the optimization, first decision variables and
their bounds are identified for the design vector then the suitable scaling parameters are selected for
the loss function according to the grid code requirements and in the last step optimization algorithm
run the dynamic simulation to find the optimal design vector. The dynamic simulation results for
both clauses, S5.2.5.5 and S5.2.5.13 are discussed in the following sections.
4.1
Optimization for Clause S5.2.5.5 (Contingency fault
analysis)
In this section, all the grid code requirements explained in the section 3.1.1 were achieved by using
optimization process. All faults listed in the Table 3.1 were applied after one second on the POC at
bus 99 Maragle for both strong grid and weak grid scenarios. According to the grid code requirements
of clause S5.2.5.5, the fault clearance time of 3-phase short circuit (3phSC) fault shall be 100 ms and
it will be 250 ms for single phase to ground (1ph) fault, 2-phase to ground (2phg) fault or phase to
phase (2ph) fault. There are different grid code requirements and operating conditions for SM and
DFIM. Therefore, the control systems of both machines are optimized and simulated separately.
4.1.1
Doubly fed induction machine
4.1.1.1
Decision variables
The PI controller parameters in the control system of DFIG are used as a decision variables for the
design vector of optimization algorithm method. The optimization was performed by optimizing the
control parameters of various PI controllers but the decision variables and PI controllers of DFIM
control system, which were selected to achieve the grid code requirements are summarized in the
Table 4.1. The initial values and bounds of the decision variables are also listed in Table 4.1. The
design vector x for the optimization process of DFIM can be written as below
x = (T r, Kr, Ku, Kp, KIpll)
(4.1)
Trd and Trq both have the same values therefore both are represented by a single constant Tr in the
design vector, which is used to assign same values to Trd and Trq during optimization process. Krd
and Krq both have same values therefore both are represented by a single constant Kr in the design
vector, which is used to assign same values to Krd and Krq during optimization process. Kp and Kq
both have the same values, therefore only Kp is given to the design vector and Kq is calculated by
multiplying Kp with -1.
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Table 4.1: DFIM decision variables for the design vector of optimization algorithm method
Bounds
Decision variables
Description
Initial value
(min∼max)
Integral gain of Id and Iq
Trd = Trq
0.01
0.001∼0.1
PI current controller
Proportional gain of Id and Iq
Krd = Krq
0.1
0.01∼1.0
PI current controller
Proportional gain of DC link
Ku
2.0
0.2∼20.0
voltage PI controller
Proportional gain of active and
Kq = Kp*-1
0.3
0.03∼3.0
reactive power PI controller
Kipll
Integral gain of PLL controller
50.0
1.0∼100.0
Table 4.2: NLINEX loss function scaling parameter values for DFIM optimization
k factor of NLINEX c factor of NLINEX loss
Description
loss function
function
Reactive current settling time
0.00000001
300
Reactive current damping ratio
0.0000000001
0.3
Reactive current requirement
0.000000000001
0.3
Reactive current rise time
0.00004
300
Active power return time
0.00000001
200
4.1.1.2
Scaling parameters selection for the loss error function
The scaling parameter values of the NLINEX loss function, listed in the Table 4.2 were selected
according to the following objectives of the NER grid code requirements
ˆ Settling time of the reactive current should be less than 70 ms
ˆ Damping ration of the reactive current should be greater than 0.1
ˆ The average value of the reactive current during fault should be greater than zero
ˆ The rise time of the reactive current should be less that 40 ms
ˆ The return time of the active power should be less than 100 ms
The output response of the loss error functions for the above grid code requirements has shown in
Figure 4.1 and 4.2 with the scaling parameter values of Table 4.2. It can be seen in Figure 4.1 and
4.2, that as long as the output response of control system of the GU is within the range of grid code
requirements, the loss error function gives almost zero output. When the output values goes out of
the range mentioned in the grid code requirements, the loss error function gives a very big output
value even for a small out of range value.
4.1.1.3
Optimization algorithm method
To achieve the grid code requirements of clause S5.2.5.5 for DFIM, optimization algorithm method
(Shgo) with sobol sampling method was called after analyzing decision variables of the design vector, scaling parameters for the loss function and objective function of the optimization process. The
optimization function (Shgo) called the objective function with decision variables and their bounds
listed in Table 4.1 by using 80 sampling points (n) and 5 iterations (iter). Product of sampling points
and iterations define the total number of objective function evaluations to find the optimal design
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Figure 4.1: Output response of loss error function for technical requirements (reactive current
settling time, rise time and active power return time)
Figure 4.2: Output response of loss error function for technical requirements (Damping ratio
of reactive current and reactive current requirement)
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vector. Optimization algorithm keep performing the dynamic simulations until it finds the optimal
design vector for the global minima of the objective function. After finding the global minima of the
objective function and the optimal design vector, the optimization algorithm is stopped with successful
completion massage of optimization process.
For the optimization of DFIM, two GOPs (T1, T2) with 100% grid voltage were used in the optimization process. All other GOPs were analyzed with the optimal design vector obtained from the
optimization of T1 and T2. After successful termination of the optimization process, Shgo returned
the optimization results with optimal design vectors, local minimas and global minima as shown in
Figure 4.3. In Figure 4.3 , fun is the global minima of the objective function while fun1 is the array
which contains global minima and all the local minima values of the objective function. x is the
optimal design vector while xl array contains the optimal design vector and all other design vectors
for the local minimas of the objective function. nfev is the total number of objective function evaluations which the optimization algorithm performed during the optimization process. It can be seen in
Figure 4.3: Optimization results to achieve grid code requirements of clause S5.2.5.5 for DFIM
Figure 4.3 that, the optimization algorithm has performed 442 (nefev) dynamic simulations with 442
different combinations of the design vector to find the global minima of the objective function and
optimal design vector x.
4.1.1.4
Dynamic simulations with optimal design vector
To verify that all the grid code requirements are achieved with the optimal design vector, dynamic
simulations were performed for all the OPs of Table 3.4 with parameter values of the optimal design
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vector. Dynamic simulations were carried out with a simulation time t=4 seconds. All faults listed
in Table 3.1 were applied at time t=1 second for their corresponding fault clearance time. Dynamic
simulations were preformed with both strong grid and weak grid conditions. The diagrams for the
dynamic simulation of U1 or GU1 with the parameters of optimal design vector are listed in the section
5.1.1 of appendix with the following output signals.
ˆ U POC: This signal shows the pu output values of the connection point voltage over time.
ˆ U GEN DFIG1: This signal shows the pu output values of the generator terminal voltage over
time.
ˆ P GEN DFIG1: This signal shows the pu output values for the transient active power response
of the DFIG.
ˆ Q GEN DFIG1: This signal shows the pu output values for the transient reactive power response
of the DFIG.
ˆ I reac[kA]: This signal shows the total reactive current in kA, which is supplied by all (3 DFIMs)
GUs to POC.
ˆ I reac required AAS [kA]: This signal shows the threshold for the reactive current according to
grid code requirement.
ˆ I active [kA]: This signal shows the total active current in kA, which is supplied by all (3 DFIMs)
GUs to POC.
ˆ I total [kA]: This signal shows the geometric sum of total active and reactive current in kA.
ˆ Maximum continues current: This current is the nominal current at high voltage side of the
transformer for all 3 GUs. This current is not time dependent and have used only for reference.
This signal shows the total maximum continues current for all (3 DFIMs) GUs at POC.
To compare the results before and after the optimization process, the results of the dynamic simulations
for all GOPs are summarized in the tables of section 5.1.1 with the parameters of initial and optimal
design vectors. The following output values of grid code requirements are given in the tables
ˆ s time: This value represent the settling time for the reactive current response
ˆ d r: This value represent the damping ration of the reactive current
ˆ I react: This value represent the reactive current requirement, which the generator has to supply
or absorb in case of LVRTR or HVRT respectively.
ˆ r t: This value represent the rise time of the reactive current response signal
ˆ P ret t: This value represent the time take by the active power to return in the threshold of
95% of its initial vale.
In the tables of section 5.1.1, the grid code requirement output values which have not fulfilled the
technical requirements of the NER are written in bold characters. It can be seen from the tables of
section 5.1.1.3 that before optimization process, there are many grid code requirement values which
have not fulfilled the NER requirements. The following results can be concluded from the optimization
results, which are summarized in the tables of section 5.1.1.4 and 5.1.1.5 for both minSCR and maxSCR
conditions.
ˆ The settling time (s time) of the reactive current is less than 70 ms for all the GOPs in all
operating modes of the GU.
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ˆ The damping ratio (d r) of the reactive current is 1 for all the GOPs in all operating modes of
the GU, which is greater than the NER requirement of 0.1.
ˆ The average of the reactive current (I react) supply during faults is greater than zero for all the
GOPs in all operating modes of the GU.
ˆ The rise time (r t) of the reactive current is less than 40 ms for all the GOPs in all operating
modes of the GU.
ˆ The active power return time (P ret t) is less than 100 ms for all the GOPs in all operating
modes of the GU. Only two values in pump operating mode during 2ph fault are out of the
range but they are acceptable.
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Chapter 5
Appendix
5.1
List of figures and tables for the dynamic simulation
of NER Clause S5.2.5.5 (Contingency fault analysis)
5.1.1
Doubly fed induction machine
5.1.1.1
Diagrams of DFIM output response signals with minSCR=1.5
The following signals are shown in the following diagrams
ˆ U POC: This signal shows the pu output values of the connection point voltage over time.
ˆ U GEN DFIG1: This signal shows the pu output values of the generator terminal voltage over
time.
ˆ P GEN DFIG1: This signal shows the pu output values for the transient active power response
of the DFIG.
ˆ Q GEN DFIG1: This signal shows the pu output values for the transient reactive power response
of the DFIG.
ˆ I reac[kA]: This signal shows the total reactive current in kA, which is supplied by all (3 DFIMs)
GUs to POC.
ˆ I reac required AAS [kA]: This signal shows the threshold for the reactive current according to
grid code requirement.
ˆ I active [kA]: This signal shows the total active current in kA, which is supplied by all (3 DFIMs)
GUs to POC.
ˆ I total [kA]: This signal shows the geometric sum of total active and reactive current in kA.
ˆ Maximum continues current: This current is the nominal current at high voltage side of the
transformer for all 3 GUs. This current is not time dependent and have used only for reference.
This signal shows the total maximum continues current for all (3 DFIMs) GUs at POC.
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Figure 5.1: DFIG GEN minSCR 1ph T1 100
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Figure 5.2: DFIG GEN minSCR 1ph T2 100
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Figure 5.3: DFIG GEN minSCR 2ph T1 100
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Figure 5.4: DFIG GEN minSCR 2ph T2 100
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Figure 5.5: DFIG GEN minSCR 2phg T1 100
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Figure 5.6: DFIG GEN minSCR 2phg T2 100
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Figure 5.7: DFIG GEN minSCR 3phSC T1 100
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Figure 5.8: DFIG GEN minSCR 3phSC T2 100
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Figure 5.9: DFIG PUMP minSCR 1ph P1 100
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Figure 5.10: DFIG PUMP minSCR 1ph P2 100
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Figure 5.11: DFIG PUMP minSCR 2ph P1 100
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Figure 5.12: DFIG PUMP minSCR 2ph P2 100
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Figure 5.13: DFIG PUMP minSCR 2phg P1 100
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Figure 5.14: DFIG PUMP minSCR 2phg P2 100
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Figure 5.15: DFIG PUMP minSCR 3phSC P1 100
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Figure 5.16: DFIG PUMP minSCR 3phSC P2 100
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Figure 5.17: DFIG SYNCON minSCR 1ph SC1 100
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Figure 5.18: DFIG SYNCON minSCR 1ph SC2 100
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Figure 5.19: DFIG SYNCON minSCR 2ph SC1 100
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Figure 5.20: DFIG SYNCON minSCR 2ph SC2 100
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Figure 5.21: DFIG SYNCON minSCR 2phg SC1 100
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Figure 5.22: DFIG SYNCON minSCR 2phg SC2 100
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Figure 5.23: DFIG SYNCON minSCR 3phSC SC1 100
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Figure 5.24: DFIG SYNCON minSCR 3phSC SC2 100
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5.1.1.2
Diagrams of DFIM output response signals with maxSCR=9.7
Figure 5.25: DFIG GEN maxSCR 1ph T1 100
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Figure 5.26: DFIG GEN maxSCR 1ph T2 100
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Figure 5.27: DFIG GEN maxSCR 2ph T1 100
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Figure 5.28: DFIG GEN maxSCR 2ph T2 100
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Figure 5.29: DFIG GEN maxSCR 2phg T1 100
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Figure 5.30: DFIG GEN maxSCR 2phg T2 100
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Figure 5.31: DFIG GEN maxSCR 3phSC T1 100
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Figure 5.32: DFIG GEN maxSCR 3phSC T2 100
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Figure 5.33: DFIG SYNCON maxSCR 1ph SC1 100
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Figure 5.34: DFIG SYNCON maxSCR 1ph SC2 100
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Figure 5.35: DFIG SYNCON maxSCR 2ph SC1 100
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Figure 5.36: DFIG SYNCON maxSCR 2ph SC2 100
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Figure 5.37: DFIG SYNCON maxSCR 2phg SC1 100
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Figure 5.38: DFIG SYNCON maxSCR 2phg SC2 100
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Figure 5.39: DFIG SYNCON maxSCR 3phSC SC1 100
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Figure 5.40: DFIG SYNCON maxSCR 3phSC SC2 100
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5.1.1.3
Tables for the grid code requirement output values before optimization
with minSCR=1.5
Table 5.1: Grid code requirement values with initial design vector for DFIM operating in pump
mode
Operating points
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
DFIG PUMP minSCR
3phSC P1 90.out
3phSC P1 100.out
3phSC P1 110.out
3phSC P2 90.out
3phSC P2 100.out
3phSC P2 110.out
1ph P1 90.out
1ph P1 100.out
1ph P1 110.out
1ph P2 90.out
1ph P2 100.out
1ph P2 110.out
2ph P1 90.out
2ph P1 100.out
2ph P1 110.out
2ph P2 90.out
2ph P2 100.out
2ph P2 110.out
2phg P1 90.out
2phg P1 100.out
2phg P1 110.out
2phg P2 90.out
2phg P2 100.out
2phg P2 110.out
s time
0.02799201
0.026991963
0.02799201
0.029992104
0.028992057
0.028992057
0.104995608
0.080994487
0.008991122
0.03099215
0.028992057
0.023991823
0.077994347
0.049993038
0.012991309
0.032992244
0.031992197
0.028992057
0.025991917
0.026991963
0.028992057
0.03099215
0.03099215
0.03099215
80
d r I react
1
1.648453544
1
1.770439563
1
1.889889419
1
1.769661041
1
1.880364776
1
1.999867392
1
-0.016759067
1
0.141322088
1
0.356506344
1
0.512576846
1
0.455552251
1
0.331530508
1
0.278956436
1
0.326663825
1
0.309452998
1
0.640310122
1
0.62167896
1
0.601398336
1
0.808280265
1
0.861391565
1
0.909668322
1
0.974546227
1
1.020233651
1
1.048499848
r t P ret t
0
0.150002384
0
0.156002665
0
0.179003739
0
0.13000145
0
0.124001169
0
0.164003038
0
0.161009908
0
0.15100944
0
0.143009067
0
0.105007291
0
0.154009581
0
0.133008599
0
0.158009768
0
0.169010282
0
0.171010375
0
0.108007431
0
0.121008039
0
0.171010375
0
0.1480093
0
0.165010095
0
0.183010936
0
0.119007945
0
0.118007898
0
0.161009908
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Table 5.2: Grid code requirement values with initial design vector for DFIM operating in
synchronous condenser mode
Operating points
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
DFIG SYNCON minSCR
3phSC SC1 90.out
3phSC SC1 100.out
3phSC SC1 110.out
3phSC SC2 90.out
3phSC SC2 100.out
3phSC SC2 110.out
1ph SC1 90.out
1ph SC1 100.out
1ph SC1 110.out
1ph SC2 90.out
1ph SC2 100.out
1ph SC2 110.out
2ph SC1 90.out
2ph SC1 100.out
2ph SC1 110.out
2ph SC2 90.out
2ph SC2 100.out
2ph SC2 110.out
2phg SC1 90.out
2phg SC1 100.out
2phg SC1 110.out
2phg SC2 90.out
2phg SC2 100.out
2phg SC2 110.out
s time
0.025991917
0.026991963
0.026991963
0.028992057
0.028992057
0.028992057
0.08299458
0.061993599
0.043992758
0.035992384
0.029992104
0.022991776
0.065993786
0.010991216
0.011991262
0.035992384
0.034992337
0.031992197
0.02499187
0.026991963
0.028992057
0.031992197
0.031992197
0.031992197
81
d r I react
1
1.56074498
1
1.694738238
1
1.836827333
1
1.756883909
1
1.872447959
1
1.989925559
1
0.084027178
1
0.286649548
1
0.509176797
1
0.557582384
1
0.510849533
1
0.415508909
1
0.367325457
1
0.39683842
1
0.385145282
1
0.686540399
1
0.659432912
1
0.633258577
1
0.846819451
1
0.894556323
1
0.94376843
1
1.022219987
1
1.04520205
1
1.065181322
r t P ret t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Institute for Electrical Power Engineering
Table 5.3: Grid code requirement values with initial design vector for DFIM operating in
generator mode (3phSC and 1ph fault)
Operating
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
points
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
3phSC T1 90.out
3phSC T1 100.out
3phSC T1 110.out
3phSC T2 90.out
3phSC T2 100.out
3phSC T2 110.out
3phSC T3 90.out
3phSC T3 100.out
3phSC T3 110.out
3phSC T4 90.out
3phSC T4 100.out
3phSC T4 110.out
1ph T1 90.out
1ph T1 100.out
1ph T1 110.out
1ph T2 90.out
1ph T2 100.out
1ph T2 110.out
1ph T3 90.out
1ph T3 100.out
1ph T3 110.out
1ph T4 90.out
1ph T4 100.out
1ph T4 110.out
s time
0.02799201
0.02799201
0.02799201
0.028992057
0.028992057
0.028992057
0.02799201
0.02799201
0.02799201
0.029992104
0.028992057
0.028992057
0.100995421
0.074994206
0.048992991
0.029992104
0.023991823
0.022991776
0.101995468
0.074994206
0.046992898
0.03099215
0.023991823
0.022991776
82
d r I react
1
1.667503613
1
1.784083
1
1.905062571
1
1.776548097
1
1.889993086
1
2.002708699
1
1.650990646
1
1.776164311
1
1.899732992
1
1.774932962
1
1.885121362
1
2.000776592
1
-0.002544185
1
0.152349565
1
0.369948872
1
0.519200255
1
0.478868211
1
0.355072382
1
-0.007602948
1
0.153411244
1
0.374663147
1
0.526399333
1
0.484321135
1
0.361444815
r t P ret t
0
0.140001917
0
0.160002851
0
0.152002478
0
0.126001263
0
0.087999487
0
0.174003506
0
0.137001777
0
0.128001356
0
0.164003038
0
0.127001309
0
0.121001029
0
0.090999627
0
0.094006777
0
0.08700645
0
0.123008132
0
0.029003739
0
0.083006263
0
0.019003272
0
0.113007665
0
0.102007151
0
0.132008553
0
0.086006403
0
0.037004113
0
0.081006169
Institute for Electrical Power Engineering
Table 5.4: Grid code requirement values with initial design vector for DFIM operating in
generator mode (2ph and 2phg fault)
Operating
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
DFIG GEN
points
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
minSCR
2ph T1 90.out
2ph T1 100.out
2ph T1 110.out
2ph T2 90.out
2ph T2 100.out
2ph T2 110.out
2ph T3 90.out
2ph T3 100.out
2ph T3 110.out
2ph T4 90.out
2ph T4 100.out
2ph T4 110.out
2phg T1 90.out
2phg T1 100.out
2phg T1 110.out
2phg T2 90.out
2phg T2 100.out
2phg T2 110.out
2phg T3 90.out
2phg T3 100.out
2phg T3 110.out
2phg T4 90.out
2phg T4 100.out
2phg T4 110.out
s time
0.072994113
0.045992851
0.011991262
0.032992244
0.03099215
0.02799201
0.074994206
0.043992758
0.011991262
0.032992244
0.031992197
0.02799201
0.025991917
0.026991963
0.02799201
0.029992104
0.03099215
0.03099215
0.025991917
0.026991963
0.02799201
0.03099215
0.03099215
0.03099215
83
d r I react
r t P ret t
1
0.321821711 0
0.111007571
1
0.366999088 0
0.158009768
1
0.345125823 0
0.109007478
1
0.649680057 0
0.08700645
1
0.631423018 0
0.03200388
1
0.606091865 0
0.025003552
1
0.318612435 0
0.123008132
1
0.371822587 0
0.158009768
1
0.349871935 0
0.150009394
1
0.656871114 0
0.09300673
1
0.636825657 0
0.086006403
1
0.610035846 0
0.080006123
1
0.802877945 0
0.132008553
1
0.852288838 0
0.169010282
1
0.906166303 0
0.167010188
1
0.957621857 0
0.116007805
1
1.001785578 0
0.039004207
1
1.034033978 0
0.198011637
1
0.804289495 0
0.130008459
1
0.857463832 0
0.116007805
1
0.909734936 0
0.155009627
1
0.969304082 0
0.120007992
1
1.014826318 0
0.105007291
1
1.041209042 0
0.089006543
Institute for Electrical Power Engineering
5.1.1.4
Tables for the grid code requirement output values after optimization with
minSCR=1.5
Table 5.5: Grid code requirement values with optimal design vector for DFIM
pump mode
Operating points
s time
d r I react
r t
DFIG PUMP minSCR 3phSC P1 90
0.02499187
1
1.683775519 0
DFIG PUMP minSCR 3phSC P1 100 0.026991963 1
1.810667484 0
DFIG PUMP minSCR 3phSC P1 110 0.026991963 1
1.948540259 0
DFIG PUMP minSCR 3phSC P2 90
0.02799201
1
1.81416032
0
DFIG PUMP minSCR 3phSC P2 100 0.028992057 1
1.928509305 0
DFIG PUMP minSCR 3phSC P2 110 0.028992057 1
2.050817171 0
DFIG PUMP minSCR 1ph P1 90
0.065993786 1
0.154783608 0
DFIG PUMP minSCR 1ph P1 100
0.051993132 1
0.299983496 0
DFIG PUMP minSCR 1ph P1 110
0.009991169 1
0.508652306 0
DFIG PUMP minSCR 1ph P2 90
0.02799201
1
0.515056372 0
DFIG PUMP minSCR 1ph P2 100
0.031992197 1
0.424559468 0
DFIG PUMP minSCR 1ph P2 110
0.03399229
1
0.32285352
0
DFIG PUMP minSCR 2ph P1 90
0.059993505 1
0.287263155 0
DFIG PUMP minSCR 2ph P1 100
0.037992477 1
0.358021089 0
DFIG PUMP minSCR 2ph P1 110
0.013991356 1
0.366691802 0
DFIG PUMP minSCR 2ph P2 90
0.031992197 1
0.649493999 0
DFIG PUMP minSCR 2ph P2 100
0.03099215
1
0.635968763 0
DFIG PUMP minSCR 2ph P2 110
0.03099215
1
0.620363347 0
DFIG PUMP minSCR 2phg P1 90
0.01899159
1
0.839993835 0
DFIG PUMP minSCR 2phg P1 100
0.019991636 1
0.861425701 0
DFIG PUMP minSCR 2phg P1 110
0.022991776 1
0.896827852 0
DFIG PUMP minSCR 2phg P2 90
0.029992104 1
0.997038152 0
DFIG PUMP minSCR 2phg P2 100
0.03099215
1
1.03539803
0
DFIG PUMP minSCR 2phg P2 110
0.03099215
1
1.057502115 0
84
operating in
P ret t
0.093999767
0.062998319
0.061998272
0.071998739
0.070998693
0.066998506
0.042004347
0.043004394
0.060005188
0.049004674
0.0410043
0.043004394
0.052004814
0.116007805
0.110007524
0.059005141
0.055004954
0.050004721
0.022003412
0.045004487
0.04400444
0.028003693
0.024003506
0.021003366
Institute for Electrical Power Engineering
Table 5.6: Grid code requirement values with optimal design vector for DFIM
synchronous condenser mode
Operating points
s time
d r I react
DFIG SYNCON minSCR 3phSC SC1 90
0.02499187
1
1.629641871
DFIG SYNCON minSCR 3phSC SC1 100 0.025991917 1
1.773144564
DFIG SYNCON minSCR 3phSC SC1 110 0.026991963 1
1.920260966
DFIG SYNCON minSCR 3phSC SC2 90
0.028992057 1
1.798363234
DFIG SYNCON minSCR 3phSC SC2 100 0.028992057 1
1.925503761
DFIG SYNCON minSCR 3phSC SC2 110 0.028992057 1
2.054395823
DFIG SYNCON minSCR 1ph SC1 90
0.056993365 1
0.185413366
DFIG SYNCON minSCR 1ph SC1 100
0.043992758 1
0.391875596
DFIG SYNCON minSCR 1ph SC1 110
0.007991076 1
0.62321734
DFIG SYNCON minSCR 1ph SC2 90
0.032992244 1
0.558303318
DFIG SYNCON minSCR 1ph SC2 100
0.03399229
1
0.500483267
DFIG SYNCON minSCR 1ph SC2 110
0.035992384 1
0.411761281
DFIG SYNCON minSCR 2ph SC1 90
0.043992758 1
0.372146101
DFIG SYNCON minSCR 2ph SC1 100
0.010991216 1
0.411084512
DFIG SYNCON minSCR 2ph SC1 110
0.013991356 1
0.431692476
DFIG SYNCON minSCR 2ph SC2 90
0.034992337 1
0.689675767
DFIG SYNCON minSCR 2ph SC2 100
0.03399229
1
0.668779543
DFIG SYNCON minSCR 2ph SC2 110
0.03399229
1
0.65250756
DFIG SYNCON minSCR 2phg SC1 90
0.017991543 1
0.869062731
DFIG SYNCON minSCR 2phg SC1 100
0.019991636 1
0.909989737
DFIG SYNCON minSCR 2phg SC1 110
0.023991823 1
0.950681521
DFIG SYNCON minSCR 2phg SC2 90
0.031992197 1
1.025698753
DFIG SYNCON minSCR 2phg SC2 100
0.031992197 1
1.051529963
DFIG SYNCON minSCR 2phg SC2 110
0.031992197 1
1.07280811
85
operating in
r t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P ret t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Institute for Electrical Power Engineering
Table 5.7: Grid code requirement values with optimal design vector for
generator mode (3phSC and 1ph fault)
Operating points
s time
d r I react
DFIG GEN minSCR 3phSC T1 90
0.025991917 1
1.689220149
DFIG GEN minSCR 3phSC T1 100 0.026991963 1
1.823914469
DFIG GEN minSCR 3phSC T1 110 0.026991963 1
1.95053198
DFIG GEN minSCR 3phSC T2 90
0.02799201
1
1.817352058
DFIG GEN minSCR 3phSC T2 100 0.028992057 1
1.939528619
DFIG GEN minSCR 3phSC T2 110 0.028992057 1
2.062609677
DFIG GEN minSCR 3phSC T3 90
0.026991963 1
1.688670181
DFIG GEN minSCR 3phSC T3 100 0.026991963 1
1.816777203
DFIG GEN minSCR 3phSC T3 110 0.026991963 1
1.949481032
DFIG GEN minSCR 3phSC T4 90
0.028992057 1
1.816771018
DFIG GEN minSCR 3phSC T4 100 0.028992057 1
1.938962825
DFIG GEN minSCR 3phSC T4 110 0.028992057 1
2.053957848
DFIG GEN minSCR 1ph T1 90
0.064993739 1
0.131681835
DFIG GEN minSCR 1ph T1 100
0.048992991 1
0.289595577
DFIG GEN minSCR 1ph T1 110
0.008991122 1
0.510541571
DFIG GEN minSCR 1ph T2 90
0.02799201
1
0.52692622
DFIG GEN minSCR 1ph T2 100
0.03099215
1
0.459650014
DFIG GEN minSCR 1ph T2 110
0.031992197 1
0.342948858
DFIG GEN minSCR 1ph T3 90
0.063993692 1
0.127292027
DFIG GEN minSCR 1ph T3 100
0.048992991 1
0.289992006
DFIG GEN minSCR 1ph T3 110
0.008991122 1
0.5137694
DFIG GEN minSCR 1ph T4 90
0.02799201
1
0.532501868
DFIG GEN minSCR 1ph T4 100
0.03099215
1
0.466446599
DFIG GEN minSCR 1ph T4 110
0.032992244 1
0.35046419
86
DFIM operating in
r t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P ret t
0.073998833
0.024996543
0.022996449
0.047997618
0.02899673
0.02599659
0.026996636
0.02599659
0.022996449
0.049997711
0.030996823
0.026996636
0.005002618
0.005002618
0.005002618
0.025003552
0.011002898
0.005002618
0.006002665
0.005002618
0.005002618
0.020003319
0.006002665
0.005002618
Institute for Electrical Power Engineering
Table 5.8: Grid code requirement values with optimal design vector for
generator mode (2ph and 2phg fault)
Operating points
s time
d r I react
DFIG GEN minSCR 2ph T1 90
0.055993319 1
0.321581424
DFIG GEN minSCR 2ph T1 100
0.03399229
1
0.379044794
DFIG GEN minSCR 2ph T1 110
0.013991356 1
0.396562272
DFIG GEN minSCR 2ph T2 90
0.03099215
1
0.656719638
DFIG GEN minSCR 2ph T2 100
0.03099215
1
0.643122096
DFIG GEN minSCR 2ph T2 110
0.029992104 1
0.626924869
DFIG GEN minSCR 2ph T3 90
0.056993365 1
0.322008578
DFIG GEN minSCR 2ph T3 100
0.032992244 1
0.38250965
DFIG GEN minSCR 2ph T3 110
0.013991356 1
0.40197747
DFIG GEN minSCR 2ph T4 90
0.03099215
1
0.662353409
DFIG GEN minSCR 2ph T4 100
0.03099215
1
0.647220465
DFIG GEN minSCR 2ph T4 110
0.03099215
1
0.63086259
DFIG GEN minSCR 2phg T1 90
0.01899159
1
0.831175125
DFIG GEN minSCR 2phg T1 100 0.019991636 1
0.869059509
DFIG GEN minSCR 2phg T1 110 0.02199173
1
0.900431586
DFIG GEN minSCR 2phg T2 90
0.028992057 1
0.973179273
DFIG GEN minSCR 2phg T2 100 0.029992104 1
1.013719851
DFIG GEN minSCR 2phg T2 110 0.029992104 1
1.04213967
DFIG GEN minSCR 2phg T3 90
0.017991543 1
0.825187856
DFIG GEN minSCR 2phg T3 100 0.019991636 1
0.865233533
DFIG GEN minSCR 2phg T3 110 0.02199173
1
0.90455556
DFIG GEN minSCR 2phg T4 90
0.029992104 1
0.982083994
DFIG GEN minSCR 2phg T4 100 0.029992104 1
1.019932025
DFIG GEN minSCR 2phg T4 110 0.03099215
1
1.046733321
87
DFIM operating in
r t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P ret t
0.014003038
0.009002805
0.006002665
0.021003366
0.016003132
0.013002992
0.014003038
0.009002805
0.007002711
0.03800416
0.016003132
0.013002992
0.023003459
0.020003319
0.018003225
0.040004253
0.025003552
0.021003366
0.024003506
0.021003366
0.019003272
0.033003926
0.026003599
0.022003412
Institute for Electrical Power Engineering
5.1.1.5
Tables for the grid code requirement output values after optimization with
maxSCR=9.7
Table 5.9: Grid code requirement values
pump mode (2ph and 2phg fault)
Operating points
DFIG PUMP maxSCR 3phSC P1 90
DFIG PUMP maxSCR 3phSC P1 100
DFIG PUMP maxSCR 3phSC P1 110
DFIG PUMP maxSCR 3phSC P2 90
DFIG PUMP maxSCR 3phSC P2 100
DFIG PUMP maxSCR 3phSC P2 110
DFIG PUMP maxSCR 1ph P1 90
DFIG PUMP maxSCR 1ph P1 100
DFIG PUMP maxSCR 1ph P1 110
DFIG PUMP maxSCR 1ph P2 90
DFIG PUMP maxSCR 1ph P2 100
DFIG PUMP maxSCR 1ph P2 110
DFIG PUMP maxSCR 2ph P1 90
DFIG PUMP maxSCR 2ph P1 100
DFIG PUMP maxSCR 2ph P1 110
DFIG PUMP maxSCR 2ph P2 90
DFIG PUMP maxSCR 2ph P2 100
DFIG PUMP maxSCR 2ph P2 110
DFIG PUMP maxSCR 2phg P1 90
DFIG PUMP maxSCR 2phg P1 100
DFIG PUMP maxSCR 2phg P1 110
DFIG PUMP maxSCR 2phg P2 90
DFIG PUMP maxSCR 2phg P2 100
DFIG PUMP maxSCR 2phg P2 110
with optimal design vector for DFIM operating in
s time
0.02499187
0.026991963
0.026991963
0.02799201
0.028992057
0.028992057
0.063993692
0.052993178
0.039992571
0.029992104
0.03099215
0.023991823
0.049993038
0.037992477
0.012991309
0.029992104
0.028992057
0.028992057
0.017991543
0.01899159
0.019991636
0.028992057
0.029992104
0.028992057
88
d r
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
I react
1.699986117
1.830337164
1.971746202
1.83357541
1.951738428
2.077357681
0.15426083
0.434917382
0.736518569
0.373608742
0.205189359
0.057178764
0.339693075
0.376157627
0.338455805
0.650281958
0.618945071
0.573948196
0.75893202
0.750285712
0.79036084
0.919782276
0.934116994
0.938789362
r t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P ret t
0.063998365
0.081999207
0.093999767
0.065998459
0.060998225
0.056998038
0.0410043
0.039004207
0.031003833
0.039004207
0.040004253
0.03200388
0.049004674
0.082006216
0.078006029
0.051004767
0.04700458
0.080006123
0.04400444
0.04400444
0.043004394
0.023003459
0.018003225
0.043004394
Institute for Electrical Power Engineering
Table 5.10: Grid code requirement values with optimal design vector for DFIM
synchronous condenser mode
Operating points
s time
d r I react
DFIG SYNCON maxSCR 3phSC SC1 90
0.02499187
1
1.647295564
DFIG SYNCON maxSCR 3phSC SC1 100 0.025991917 1
1.794188375
DFIG SYNCON maxSCR 3phSC SC1 110 0.026991963 1
1.944652623
DFIG SYNCON maxSCR 3phSC SC2 90
0.028992057 1
1.820664437
DFIG SYNCON maxSCR 3phSC SC2 100 0.028992057 1
1.950707701
DFIG SYNCON maxSCR 3phSC SC2 110 0.028992057 1
2.082567616
DFIG SYNCON maxSCR 1ph SC1 90
0.058993459 1
0.234324621
DFIG SYNCON maxSCR 1ph SC1 100
0.047992945 1
0.554092445
DFIG SYNCON maxSCR 1ph SC1 110
0.037992477 1
0.870956992
DFIG SYNCON maxSCR 1ph SC2 90
0.028992057 1
0.415002432
DFIG SYNCON maxSCR 1ph SC2 100
0.03099215
1
0.293790172
DFIG SYNCON maxSCR 1ph SC2 110
0.028992057 1
0.180344878
DFIG SYNCON maxSCR 2ph SC1 90
0.040992618 1
0.396159566
DFIG SYNCON maxSCR 2ph SC1 100
0.010991216 1
0.416196532
DFIG SYNCON maxSCR 2ph SC1 110
0.012991309 1
0.394407558
DFIG SYNCON maxSCR 2ph SC2 90
0.029992104 1
0.656917689
DFIG SYNCON maxSCR 2ph SC2 100
0.028992057 1
0.627039322
DFIG SYNCON maxSCR 2ph SC2 110
0.028992057 1
0.597373457
DFIG SYNCON maxSCR 2phg SC1 90
0.015991449 1
0.765392978
DFIG SYNCON maxSCR 2phg SC1 100
0.017991543 1
0.79450859
DFIG SYNCON maxSCR 2phg SC1 110
0.020991683 1
0.826296791
DFIG SYNCON maxSCR 2phg SC2 90
0.029992104 1
0.92236496
DFIG SYNCON maxSCR 2phg SC2 100
0.029992104 1
0.933776444
DFIG SYNCON maxSCR 2phg SC2 110
0.029992104 1
0.939906459
89
operating in
r t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P ret t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Institute for Electrical Power Engineering
Table 5.11: Grid code requirement values with optimal design vector for
generator mode (3phSC and 1ph fault)
Operating points
s time
d r I react
DFIG GEN maxSCR 3phSC T1 90
0.025991917 1
1.705750309
DFIG GEN maxSCR 3phSC T1 100 0.026991963 1
1.844251757
DFIG GEN maxSCR 3phSC T1 110 0.026991963 1
1.974475028
DFIG GEN maxSCR 3phSC T2 90
0.02799201
1
1.838191718
DFIG GEN maxSCR 3phSC T2 100 0.028992057 1
1.963867042
DFIG GEN maxSCR 3phSC T2 110 0.028992057 1
2.090246647
DFIG GEN maxSCR 3phSC T3 90
0.026991963 1
1.705437067
DFIG GEN maxSCR 3phSC T3 100 0.026991963 1
1.83730913
DFIG GEN maxSCR 3phSC T3 110 0.02799201
1
1.973560205
DFIG GEN maxSCR 3phSC T4 90
0.028992057 1
1.837915286
DFIG GEN maxSCR 3phSC T4 100 0.028992057 1
1.963489495
DFIG GEN maxSCR 3phSC T4 110 0.028992057 1
2.081771469
DFIG GEN maxSCR 1ph T1 90
0.059993505 1
0.148908083
DFIG GEN maxSCR 1ph T1 100
0.049993038 1
0.434406681
DFIG GEN maxSCR 1ph T1 110
0.038992524 1
0.744531501
DFIG GEN maxSCR 1ph T2 90
0.03099215
1
0.384285273
DFIG GEN maxSCR 1ph T2 100
0.031992197 1
0.212674496
DFIG GEN maxSCR 1ph T2 110
0.01899159
1
0.062689771
DFIG GEN maxSCR 1ph T3 90
0.059993505 1
0.147755293
DFIG GEN maxSCR 1ph T3 100
0.049993038 1
0.438584727
DFIG GEN maxSCR 1ph T3 110
0.038992524 1
0.750352875
DFIG GEN maxSCR 1ph T4 90
0.03099215
1
0.387373058
DFIG GEN maxSCR 1ph T4 100
0.031992197 1
0.22043489
DFIG GEN maxSCR 1ph T4 110
0.023991823 1
0.072911091
90
DFIM operating in
r t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P ret t
0.079999113
0.067998552
0.017996216
0.027996683
0.022996449
0.018996263
0.02599659
0.021996403
0.018996263
0.027996683
0.022996449
0.019996309
0.005002618
0.005002618
0.004002571
0.010002851
0.005002618
0.004002571
0.005002618
0.005002618
0.004002571
0.006002665
0.005002618
0.004002571
Institute for Electrical Power Engineering
Table 5.12: Grid code requirement values with optimal design vector for
generator mode (2ph and 2phg fault)
Operating points
s time
d r I react
DFIG GEN maxSCR 2ph T1 90
0.046992898 1
0.360009512
DFIG GEN maxSCR 2ph T1 100
0.036992431 1
0.387510444
DFIG GEN maxSCR 2ph T1 110
0.011991262 1
0.352975679
DFIG GEN maxSCR 2ph T2 90
0.028992057 1
0.64774272
DFIG GEN maxSCR 2ph T2 100
0.02799201
1
0.616395824
DFIG GEN maxSCR 2ph T2 110
0.026991963 1
0.581822416
DFIG GEN maxSCR 2ph T3 90
0.047992945 1
0.356448183
DFIG GEN maxSCR 2ph T3 100
0.036992431 1
0.388989835
DFIG GEN maxSCR 2ph T3 110
0.012991309 1
0.35720047
DFIG GEN maxSCR 2ph T4 90
0.028992057 1
0.649332872
DFIG GEN maxSCR 2ph T4 100
0.02799201
1
0.618483403
DFIG GEN maxSCR 2ph T4 110
0.026991963 1
0.584868114
DFIG GEN maxSCR 2phg T1 90
0.016991496 1
0.754588091
DFIG GEN maxSCR 2phg T1 100 0.016991496 1
0.752107516
DFIG GEN maxSCR 2phg T1 110 0.019991636 1
0.790691845
DFIG GEN maxSCR 2phg T2 90
0.02799201
1
0.896316112
DFIG GEN maxSCR 2phg T2 100 0.028992057 1
0.918153978
DFIG GEN maxSCR 2phg T2 110 0.028992057 1
0.924819349
DFIG GEN maxSCR 2phg T3 90
0.016991496 1
0.743596831
DFIG GEN maxSCR 2phg T3 100 0.016991496 1
0.756115724
DFIG GEN maxSCR 2phg T3 110 0.019991636 1
0.793121547
DFIG GEN maxSCR 2phg T4 90
0.02799201
1
0.900911157
DFIG GEN maxSCR 2phg T4 100 0.028992057 1
0.920650748
DFIG GEN maxSCR 2phg T4 110 0.028992057 1
0.926943125
91
DFIM operating in
r t
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P ret t
0.014003038
0.007002711
0.006002665
0.017003179
0.012002945
0.006002665
0.014003038
0.008002758
0.006002665
0.017003179
0.012002945
0.007002711
0.020003319
0.016003132
0.013002992
0.022003412
0.017003179
0.014003038
0.021003366
0.017003179
0.013002992
0.023003459
0.018003225
0.014003038
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