Medium-Voltage AC (MVAC)
Power Generating System
Author: Yucheng Zhang
Advisor: Roger A. Dougal
Date: 09/23/2009
1. Introduction
MVAC power generating system produces AC electric power to the loads (AC, DC). It is
composed of turbine-generator (gas turbine, synchronous generator with excitation system),
circuit breakers, AC cables and lumped loads. The generators are synchronized together by the
automatic synchronizer. All of the models are based on dynamic models to present the dynamic
performance during transient status.
This MVAC power generating system could be used to analyse: protection, machine
characteristics’ analysis, grounding, stability, etc.
2. MVAC Power Generating System
The MVAC power generating system has four units of turbine-generators (two 36MW, two
4MW), consisting of a ring bus. The loads are connected to the bus ties and the power can be
shared among the turbine-generators, as shown in Fig. 1. With the structure of the ring bus, the
reliability of power delivery is enhanced within the microgrid, regardless of which power source
is producing at any time.
Bus1
TG_36MW
DC_Load
DC_Load
AC / DC
AC / DC
Bus2
TG_4MW
Cable_1_2
Cable_1_3
TG_4MW
Bus3
DC_Load
DC_Load
AC / DC
AC / DC
Cable2_4
AC_Load
AC_Load
Bus4
TG_36MW
Cable_3_4
AC_Load
AC_Load
CB
Fig. 1 Schematic of the ring bus power system
The model of one turbine-generator unit and some details of its associated controls are shown
in Fig. 2. The three phases of the turbine generator are connected to the load through bus-ties.
A synchronization controller measures terminal voltages, active and reactive powers, and
monitors the control signal from the supervisory controller. When activated, it sends bias values
to control the frequency (turbine speed) and terminal voltage (rotor current) set-points of the
turbine-generator and then closes the bus ties at the moment when the line up of all generator
variables is within tolerances.
Fig. 2 One unit of automatic synchronizing subsystem
For a “dark start”, the supervisory controller detects the zero-voltage condition and commands
the first power-generating unit to be the master. The supervisory controller is modeled for
deciding the sequence of power-generating units in networks. The first power generating unit
then starts up and the frequency and terminal voltages are built up while the unit is still
disconnected from the distribution grid. Once the turbine-generator achieves a stable operating
point, the synchronization controller issues commands to close the three-phase bus-ties so that
any connected load receives power from the first turbine-generator. Before the second
generator is started, the supervisory controller detects that the network is already “alive” and
commands the second power-generating unit to be a slave. The synchronization controller then
monitors the differences between the phases, voltages, and frequencies and slightly adjusts the
set points for frequency and terminal voltage to bring the two generators into synchronism.
When the second generator achieves stable operation and the differences in voltage, phase, and
frequency are within tolerances, the three-phase breaker is closed to connect the second
generator to the grid.
2.1. Gas Turbine Model
The turbine model is based on the heavy-duty turbine model [1]. It is suitable for the analysis of
dynamic power system studies. The structure of the gas turbine and its speed-governor is shown
in Fig. 3. With proper parameters in governor, the gas turbine can easily works in either droop
mode or isochronous mode. A droop governor is a straight proportional speed controller in
which the output is a proportional to the speed error [1]. An isochronous governor is a
proportional-plus-reset speed controller in which the rate of change of the output is
proportional to the speed error [1]. The coefficients for these two modes are listed in Table. 1.
KD = 1 / Droop; K = 25 typically for 4 percent droop setting. Droop setting is adjustable from 2 to
10 percent.
0.23
+
Set
Point
-
W ( Xs  1)
Ys  Z
Governor
Low
Value
Select
X
+
1
a
bs  c
Fs 1
Valve Positioner Fuel System
+
0.77
Saturation
-
1
Is
Acceleration Limiter
1
Is
Inertia
s
+
0.1
Rotor
Speed p.u.
Wf
-
f
Turbine
Electromagnetic
Torque
Fig.3 Structure of Gas Turbine with Speed-governor
Table.1 Speed governor transfer function coefficients
Type
w
Droop
KD 0
Isochronous 30
x
y
z
0.05 1
2.5 0.10 0
N
1
 CD s  1
In the schematic the turbine block implements the following Eq. (1):


Ttpu  f Mpu ,WF  1.3(WF  0.23)  0.5(1  Mpu )
(1)
Where WF is the unit fuel flow in per unit (p.u.) calculated from the preceding block and ωMpu
is the mechanical speed in p.u.
The created model captures the following dynamics of the prime mover:
•
Turbine rotational inertia
•
Delay associated with the fuel valve
•
Delay associated with the combustion chamber
•
Speed governor
2.2. Synchronous Generator Model with AVR
Synchronous generators form the principal source of electric energy in power systems. As the
main type of generators widely used in utility grid, distributed generation and isolated power
system, the mathematical model of synchronous machine is modeled in detail to review its
steady-state and transient performance characteristic.
The synchronous generator model is formulated in d-q-0 frame with two q-axis amortisseur
circuits as described in [2]. The positive q-axis is defined as leading the positive d-axis by π/2.
The transformation equations from the abc reference frame to the dq0 reference frame are
given by:

 cos
id 

i   2   sin 
 q
3
i0 
 1

 2
2
2 
) cos( 
)
3
3  ia 
2
2   
 sin(   )  sin(  
) ib
3
3  
 ic 
1
1

2
2

cos( 
And the inverse transformation is given by:
(2)

 sin 
 cos

ia 
i   2 cos(  2 )  sin(   2 )
 b
3
3
3

ic 
cos(  2 )  sin(   2 )
3
3

1

2  i 
d
1  
iq
2  
1  i0 
2 
(3)
For voltage and flux, the transformation is in the same format.
The complete set of electrical equations is expressed as below. And the definitions of
parameters are listed in Table.2. In the following equations, two q-axis amortisseur circuits and
one d-axis amortisseur circuit are considered.
Stator voltage equations:
ed  p d  qr  Ra id

eq  p q  d r  Ra iq
e  p  R i
0
a 0
 0
(4)
Rotor voltage equations:
e fd  p fd  R fd i fd
0  p  R i

1d
1d 1d

0  p 1q  R1qi1q
0  p 2 q  R2 qi2 q
(5)
Stator flux linkage equations:
 d  ( Lad  Ll )id  Lad i fd  Lad i1d

 q  ( Laq  Ll )iq  Laqi1q  Laqi2 q
   L i
0 0
 0
Rotor flux linkage equation:
(6)
 fd  L ffdi fd  L f 1d i1d  Lad id
  L i  L i  L i
 1d
f 1d fd
11d 1d
ad d

 1q  L11qi1q  Laqi2 q  Laqiq
 2 q  Laqi1q  L22qi2 q  Laqiq
(7)
Table.2 Definitions of parameters in the model of synchronous generator
Name
Description
ed , eq , e0
Instantaneous stator phase to neutral voltage in
dq0 axes
id , iq , i0
Instantaneous stator currents in dq0 axes
e fd
Field voltage
d , q , 0
Stator flux linkage in dq0 axes
 fd ,  1d ,  1q ,  2 q
Filed and rotor flux linkage in dq0 axes
Ra
Armature resistance per phase
R fd , R1d , R1q , R2 q
Field and rotor resistances in dq0 axes
Lad , Laq , L0
Mutual inductances between stator and rotor
circuits in dq0 axes
L ffd , L11d , L11q , L22q
Self-inductances of rotor circuits
L f 1d
Mutual inductances in d-axis
i fd , i1d , i1q , i2 q
Instantaneous rotor currents of field in d-axis,
amortisseur-1 in d-axis, amortisseur-1 in q-axis,
amortisseur-2 in q-axis
The equivalent circuits, shown in Fig. 4, present the complete electrical characteristics of the
machine. Damping circuits, mutual interactions between the armature windings and the
excitation circuit are included, and the rotor is assumed cylindrical without saturation. The
electromechanical torque is expressed in Eq. (8).
Te   d iq   qid

Ra 
r q
Ll

L f 1d  Lad
 id
ed
d d
dt


(8)
i1d
Lad

d 1d
dt

i fd
L1d
L fd

R fd d
fd

e fd dt


R1d
d-axis equivalent circuit
r d

Ra 
Ll

iq

eq
d q
dt


i1q
Laq

d 1q
i2 q
L1q
R1q
L2 q

R2 q d
2q
dt


dt
q-axis equivalent circuit
Fig.4 Complete d-axis and q-axis equivalent circuits
The automatic voltage regulator (AVR) is modeled as Westinghouse AVR in [3]. It includes the
regulator, exciter and stabilizer to maintain the generator terminal voltage at the reference
value. Fig. 5 shows the structure of the voltage regulator/exciter.
The feedback block in the schematic implements the function:
f out  ( K E  AEX e BEX EX out ) EX out
Where AEX, BEX and KE are constants.
(9)
Voltage Feedback
-
+
Reference
Voltage
-
KA
 A1 s  1
1
 A2 s  1
+
Saturation
-
1
 Es 1
Exciter
EXout
f out
KF s
 F s 1
Stabilizer
Fig.5 Automatic voltage regulator / exciter
2.3. Droop Setting and Automatic Synchronization
The synchronization process is based on the droop scheme. Droop is a straight-line function,
with a certain speed reference for every fuel position [4]. Its fuel position is related to the load.
The frequency-droop control and voltage-droop control are separately used to control active
power and reactive power. As the frequency (voltage) decreases the active power (reactive
power) increases. Therefore, the frequency (voltage) droop controls the power sharing between
generators, as shown in Fig. 6.
V (volt,p.u.)
f (Hz,p.u.)
1.04
1.04
1.00
0
P (W)
PNominal
(a) Frequency droop
1.00
0
Q (VA)
QNominal
(b) Voltage droop
Fig.6 Frequency droop and voltage droop (Droop setting = 4%)
The automatic synchronizer gets signals from power meter, voltage sensors and control signals
“On / Off” and “First”, which are from supervisory controller. Automatic synchronizer sends out
speed (voltage) reference bias to turbo-generators and switch signals to the bus-ties or breakers.
The Fig. 7 shows the scenario of automatic synchronizer.
Fig. 7 Scenario of automatic synchronizer
After the trigger signal from supervisory controller becomes true, the turbo-generator gradually
reaches the reference speed and reference voltage. During this starting time, the speed (voltage)
reference bias is zero. After the turbo-generator reaches the steady state (voltage and
frequency closes to the reference values), the process of synchronization starts. The automatic
synchronizer sends out the speed (voltage) reference bias to make: (1) the frequency of the
turbo-generator faster than the frequency of the synchronized ring bus; (2) the terminal
voltages between the switches have the same magnitude.
For frequency control, the offset value is set via automatic synchronizer, as Fig. 8 (a). For the
terminal voltage control, the control figure is shown as Fig. 8 (b). The switch block presents the
switches’ status, opening or closing. If the switches are opening, the switch block jumps to PI
controller; if the switches are closing, the switch block jumps to the droop controller.
Offset_Fre.
Fre._Bus
Fre._Gen
+
+
+
PI_Fre.
Fre._Bias
Droop_Fre.
(a) Frequency controller
Vol._Bus
Vol._Gen
+
PI_Vol.
Vol._Bias
Droop_Vol.
(b) Voltage controller
Fig.8 Frequency controller and voltage controller
When (1) the frequency difference reaches the offset and maintains stable, (2) the voltage
difference is zero and (3) the phase difference is zero, the automatic synchronizer sends out the
trigger signals to the bus-ties. At that moment, the power-generating subsystem unit is
synchronized to the ring bus. After the synchronizing mode and the close of the switches, the
automatic synchronizer becomes working in power sharing mode.
The control process of automatic synchronization is illustrated in Fig. 9.
If ( On / Off == True)
No
Yes
If ( First == True)
No
Yes
Measurement for:
Voltage_ Magnitudes
Frequencies and
Phase_ Differences
Bias_ Speed and
Bias_ U
for Isochronous Mode
If (
If ( Steady == True
& Active == False)
Steady == True )
No
Yes
Active == True
Yes
Bias_ Speed and
Bias_ U
for
synchronization
process
If ( Steady == True
&
Synchronization
Limitation == True )
Active == True
Fig.9 The control process of automatic synchronization
No
Bias_ Speed and
Bias_ U
for
Droop Mode
2.4. AC Cable Model
The three-phase shielded PI model of cable is presented in Fig. 10. The purpose of the model is
to take the physical characteristics of a given and compute the electrical parameters of the given
cable (resistance, capacitance, and inductance) [5]. The model was designed to provide
modeling of three-phase PI model of cables in electric power systems. This version of the model
is a RLC lumped parameter model. The electrical parameters are calculated in per unit length
and then multiplied by the length of the cable to find the lumped parameter values. The one
phase PI model is shown in Fig. 11 (a). The RLC lumped parameter model of three-phase PI model
cable is shown as the red circle in Fig. 11 (b).
Fig.10 Three phase PI model of cable in EntityBuilder
(a) one phase PI model of cable
(b) connection of three-phase PI model of cables
Fig.11 PI model of cable
The parameters are shown in Table. 3 and Fig. 12.
Table.3 Parameters of PI model of cable
Name
aRadius
bRadius
Conductivity
Frequency
InitialCurrent
Length
Permeability
Permittivity
RelativePermeability
RelativePermittivity
Description
As Fig. 8
As Fig. 8
Conductivity of the conductors
Frequency of operation
Initial current in the three phases
Length of the cable
Permeability of the material
Permittivity of the dielectric
Relative Permeability of the material
Relative Permittivity of the dielectric
Default Value
0.01262
0.0519
59000000
60
0
100
1.26E-06
8.85E-12
1
2.3
Units
m
m
S·m-1
Hz
A
m
H m-1
F/m
-
Fig.12 Geometrical parameters of the unshielded cable
The distributed parameters of resistance, inductance, and capacitance are found in per
unit/length values based upon the following equations. These distributed parameter values are
then multiplied by the length of the cable to provide the lumped parameter values used for the
modeling of the cable.
𝛿=
1
√𝜋∗𝜇∗𝜎∗𝑓
𝑚
(10)
𝜌
𝑅 = 𝜋∗(𝑎𝑅𝑎𝑑𝑖𝑢𝑠2 ) Ω/𝑚
µ
(11)
𝑏𝑅𝑎𝑑𝑖𝑢𝑠2
𝐿 = 2𝜋0 ∗ 𝐿𝑛 (𝑎𝑅𝑎𝑑𝑖𝑢𝑠2 ) 𝐻/𝑚
𝐶=
µ0
𝑏𝑅𝑎𝑑𝑖𝑢𝑠2
∗𝐿𝑛(
)
2𝜋
𝑎𝑅𝑎𝑑𝑖𝑢𝑠2
2
2
1 µ0
𝑏𝑅𝑎𝑑𝑖𝑢𝑠
µ
𝑏𝑅𝑎𝑑𝑖𝑢𝑠 2
(( ∗𝐿𝑛(
)) −( 0 ∗𝐿𝑛(
)) )
𝜇𝜀 2𝜋
2𝜋
𝑎𝑅𝑎𝑑𝑖𝑢𝑠
𝑎𝑅𝑎𝑑𝑖𝑢𝑠2
(12)
𝐹/𝑚
Where:
f = frequency of operation of the cable (Hz)
µ = Permeability
𝜇0 = Relative Permeability
ε = Permittivity
𝜀0 = Relative Permittivity
σ = Conductivity of the conductor (Ω.m)
δ = Skin depth (m)
ρ = 2.08E-8 (Ω/m)
3. Demonstration of Power Generating System in VTB 2009
The MVAC power generating system is developed in VTB 2009, as shown in Fig.13.
(13)
Fig.13 Overview of simulation environment in VTB2009
The system is divided into four subsystems:
1. Subsystem - “Supervisory_Controller”: It defines the sequence of 4 turbo-generators
connected to the ring bus.
Fig.14 Connection of supervisory controller
2. Subsystem – “Two_36MW_Gens”: It composes of two units 36 MW turbo-generators with
their automatic synchronization controller to make them automatically connect to the ring bus.
Fig.15 Details of two MTGs with their automatic synchronizer
(The same structure with two ATGs)
3. Subsystem – “Two_4MW_Gens”: It composes of two units 4 MW turbo-generators with their
automatic synchronization controller to make them automatically connect to the ring bus. It has
the same topology with “Two_36MW_Gens” subsystem, but the power level.
4. Subsystem – “Ring_Bus”: It connects the four turbo-generators via 4 buses in a ring
arrangement. Each bus has a lupmed load connected.Now, the load centers are presented as
lumped loads in simulations.
Fig.16 Structure of 4 buses in ring arrangement
The default parameters of the testbench are listed in Table.4.
Table.4 Default parameters of testbench
Main Turbine Generator
Auxiliary Turbine Generator 2
Inertia Constant: HTurbine = 2.5 s
Inertia Constant: HTurbine = 3.5 s
Droop Setting: 4 %
Droop Setting: 4 %
Rated Power: P = 36 MW (pf = 0.95)
Rated Power: P = 4 MW (pf = 0.95)
Rated frequency: f = 60 Hz
Rated frequency: f = 60 Hz
Transient reactance: Xd’ = 0.3
Transient reactance: Xd’ = 0.3
Transient time constant: Td0’ = 8.0 s
Transient time constant: Td0’ = 8.0 s
Inertia Constant: HGenerator = 0.5 s
Inertia Constant: HGenerator = 0.5 s
Rated Voltage: V = 4.16 kV
Rated Voltage: V = 4.16 kV
Synchronous reactance: Xd = 1.81
Synchronous reactance: Xd = 1.81
Subtransient reactance: Xd’’ = 0.23
Subtransient reactance: Xd’’ = 0.23
Subtransient time constant: Td0’’ = 0.03 s Subtransient time constant: Td0’’ = 0.03 s
Cable*
Length = 20 m
Resistance = 4.157E-005 Ohm / m
Inductance = 5.67E-007 H / m
Capacitance = 6.03E-011 F / m
RFCL
RHigh = 100 kOhm
RLow = 0.001 Ohm
increase = 100 microseconds
decrease = 100 microseconds
* the default values of PI model of cable are used for the calculation of RLC
The sharing powers from turbine generators are presented in Fig. 17. During the synchronization
process, as shown in Fig. 17(a), the total load is 32MW (lower than the capacity of MTG1
(36MW)) which is shard by 4 turbine generators. Two MTGs are 14.62MW individually, and two
ATGs are 1.55MW individually after the synchronization process completed. After that, more
loads were added to the ring-bus at 100s and the total produced power is 67.4MW (84.25% of
the system capacity (80MW)). The two MTGs are 30.4MW individually, and the two ATGs are
3.3MW individually, as shown in Fig. 17(b).
(a) Power sharing during synchronization process
(b) Power sharing at 84.25% of system capacity
Fig.17 Power distribution among the 4 turbine generators
REFERENCE:
[1]
Rowen, W. I., 1983, "Simplified Mathematical Representations of Heavy-Duty Gas
Turbines," ASME J. Eng. Power, 105, pp. 865 – 869
[2]
Prabha Kundur; “Power System Stability and control”, EPRI, McGraw-Hill, 1993
[3]
P. M. Anderson and A. A. Fouad “Power system stability and control”, IEEE Press, 2002
[4]
Woodward, “Speed Droop and Power Generation”,application note 01302
[5]
Nadir Idir, Yannick Weens and Jean-Jacques Franchaud, Skin Effect and Dielectric Loss
Models of Power Cables, IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16,
No. 1; February 2009