Voltage Stability in the German Power System
Univ.-Prof. Dr.-Ing. Albert Moser
Bremen, 23th June 2016
Summer School “Stability of Electricity Grids“
Agenda
Agenda
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
1
Agenda
Agenda
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
2
3
System Stability Basics
Classification of System Stability
System
Stability
Rotor-Angle
Stability
SmallSignal
Frequency
Stability
Voltage
Stability
LargeSignal
ShortTerm
ShortTerm
LongTerm
Affected System Variable
SmallSignal
LargeSignal
Size of Disturbance
ShortTerm
LongTerm
Time Frame of Dynamics
(Definition and Classification of Power System Stability,
IEEE/CIGRE Joint Task Force on Stability Terms and Definitions)
4
System Stability Basics
Rotor Angle Stability
rotor angle response to disturbance
first swing
unstable
remain in synchronism after being subject to a
disturbance
 Depends on ability to maintain/restore equilibrium
between electromagnetic and mechanical torque of
synchronous machines
 Loss of equilibrium leads to (de)acceleration of rotor
 Large disturbance (e.g. short circuit)
 Monotonic rotor acceleration due to missing voltage
 System response may involve large excursions of rotor
angle
 Small-signal disturbances (e.g. load oscillations)
 Inter-area-oscillations initiated even by small
disturbances
 Use of Power System Stabilizers (PSS) to provide
damping (via excitation control) to prevent power
system oscillations
unstable
rotor angle 𝛿
 Ability of synchronous machines in power systems to
stable
time
power-angle curve
5
System Stability Basics
Frequency Stability
50 Hz





of a power system to maintain a steady
frequency after a severe disturbance.
Disturbances mainly related to power
imbalance of generation and consumption
(e.g. due to power plant outages).
As frequency is a system-wide reference
variable, frequency instabilities have an
wide-area impact.
Spinning reserve of synchronously
connected generating units with rotating
masses limit steepness of frequency drops.
Load-frequency control activates reserves
to countermeasure frequency drops.
Due to a decrease of synchronously
connected power plants, frequency stability
may be endangered in the future.
51 Hz
49 Hz
 Frequency stability is defined as the ability
𝑓
spinning reserve
Δ𝑓𝑠𝑡𝑒𝑎𝑑𝑦−𝑠𝑡𝑎𝑡𝑒
Δ𝑓𝑑𝑦𝑛
primary control
𝑡
6
System Stability Basics
Voltage Stability
 Voltage stability is defined as the ability
 Short-term voltage stability
 Transient phenomena within few seconds
 Caused by sudden changes of the
operating point, e.g. short curcuits
 Often locally limited phenomenon
Voltage stable/unstable system
Vstable
voltage
of a power system to remain within
operational voltage limits after being
subject of disturbance.
disturbance
voltage tolerance band
Vunstable
time
 Long-term voltage stability
 Steady state phenomena within a time range up to a few hours
 Involves slowly reacting grid components such as transformer tap changer, behaviour of
loads, voltage control of synchronous generators and converters
 Instability by exceeding transmission capacity of the system
 German “Energiewende” influences long-term voltage stability due to increased
power transfer needs and distances as well as decreasing reactive power resources.
System Stability Basics
Time Domain of Transients
7
8
System Stability Basics
Focus of this Lecture
System
Stability
Rotor-Angle
Stability
SmallSignal
Frequency
Stability
Voltage
Stability
LargeSignal
ShortTerm
ShortTerm
LongTerm
Affected System Variable
SmallSignal
LargeSignal
Size of Disturbance
ShortTerm
LongTerm
Time Frame of Dynamics
(Definition and Classification of Power System Stability,
IEEE/CIGRE Joint Task Force on Stability Terms and Definitions)
9
System Stability Basics
Voltage Stability and Transmission Line Loading
 Load increase (i.e. resistance decrease) is causing voltage drop at end of line.
 Voltage control in the distribution grid, such as transformers with on-load tap
changers, constant power loads or converters lead to instability below voltage 𝑉𝑐𝑟𝑖𝑡 .
 Thermal limit high-temperature conductors (HTC) may be beyond maximum power.
𝑉𝐿 𝑅𝐿 → ∞
𝑃𝑒
𝐸𝐺
~
𝑋𝑁
𝑉𝐿
𝑅𝐿
𝑉𝑐𝑟𝑖𝑡
stable
𝑃𝑒
𝑅𝐿 → 0
𝑃𝑡ℎ𝑒𝑟𝑚
 Wide range of nonlinearities existent in electrical power systems
 Limiters of exciter systems (synchronous generators)
 Min./max. cos 𝜑 of converters (distributed energy sources)
 Power plant dispatch
 Continuation Power Flow is able to reflect such nonlinearities.
𝑃𝑚𝑎𝑥 𝑃𝑡ℎ𝑒𝑟𝑚,𝐻𝑇𝐶
10
System Stability Basics
Continuation Power Flow
 Continuation Power Flow (CPF) commonly used approach to determine voltage
stability limit
 Definition of a parameter variation variable 𝜆 for the load in power flow equations
 Increase until 𝜆 = 𝜆𝑐𝑟𝑖𝑡 results in voltage stability limit 𝑓 𝑧crit , 𝜆𝑐rit = 0
 Two-staged iterative approach
1) Predictor: Estimation of P-V-characteristic of
predictor
𝑽
a variation in 𝜆 using linearized continuation
corrector
2) Corrector: Newton-Raphson algorithm to determine
exact solution of underdetermined power flow
equation 𝑓 𝑧, 𝜆
𝜆crit
 No parameter variation for distributed generation feed-in
 No determination of equipment outages relevant for voltage stability
 No consideration of uncertainty of the power plant dispatch
 Recent research project: Development of models and methods
to evaluate the voltage stability in the German power system
𝝀
Agenda
Agenda
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
11
12
Parameters influencing Voltage Stability
Grid Equipment and Equipment Outages
Grid Equipment
grid / outages
 Traditional equipment like cables, overhead
lines and transformers
cap.
reactive power
compensation /
voltage control
ind.
Q
V
overhead
line
𝑃𝑛𝑎𝑡
𝑃𝑛𝑎𝑡
𝒍
P
cable
P
Thermal limit
Thermal limit
 Innovative equipment
power plant
dispatch
loads / renewable
energy sources
• High temperature
conductors allow
higher currents at
similar reactances.
• HVDC with
independent
active/reactive
power control
Equipment Outage
 As most common trigger for voltage
collapses a consideration beyond
the (n-1)-criterion is necessary.
13
Parameters influencing Voltage Stability
Reactive Power Compensation Devices
 Synchronous generator: controllable
grid / outages
reactive power
compensation /
voltage control
reactive power source connected to
transmission grid
 Installation of mechanical switched
capacitors (MSC) planned in German grid
 Supply of reactive power from shunt
capacitance is proportional to square of
voltage 𝑄𝑀𝑆𝐶 ~𝑉 2 .
 Steeper voltage gradients and increased
critical voltage
V
power plant
dispatch
Stepwise connection
of capacitors
stable
unstable
loads / renewable
energy sources
s
Trajectory of critical voltage using
capacitive shunt compensation
P
 Increased maximal power transfer
 But also endangerment of voltage collapse
at normal operating voltages
14
Parameters influencing Voltage Stability
Uncertainty of Power Plant Dispatch
 Electricity transport through grid is not only
grid / outages
reactive power
compensation /
voltage control
determined by loads and renewable energy
sources but also by central generating units.
 Power plant dispatch is a result of
European electricity trading.
 Adjustments because of grid restrictions,
forecast errors and outages by TSOs
 Power plant dispatch is uncertain when
evaluating voltage stability
 Only grid-connected power plants can
power plant
dispatch
loads / renewable
energy sources
supply reactive power.
 Implicit evaluation of conventional power
plants by means of voltage stability specific
power plant dispatches
 Voltage-stability-critical power plant
dispatch
 Market-based power plant dispatch
 Voltage-stability-optimized power plant
dispatch
15
Parameters influencing Voltage Stability
Loads and Distributed Energy Resources
 Active and reactive power balance of
grid / outages
distribution grid is changing.
 Impedances of grid and voltage control in
distribution grid are not negligible.
Distribution grid model based on public data
reactive power  Explicit modelling of distribution grids
compensation /
 Grid topology of 110 kV grids (KraftNAV)
voltage control
 Homogenized, regionally classified
consideration of medium and low-voltage grids
(StromNZV/StromNEV)
power plant
dispatch
 Regionalisation of loads and distributed power
feed-in according to public data
Grid model HV level
Comparison with snapshots
200
Mvar
100
P
0
-100
-100
100
Q
loads / renewable
energy sources
snapshots
model
MW
300
Source snapshots : Amprion GmbH
Agenda
Agenda
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
16
17
Methodology
System under consideration
Time Domain
 Quasi steady-state assessment based on the
assumption that all transient effects are decayed
Technical Domain
 Explicit consideration of the grid topology of all voltage
levels
 Assuming voltage-independent active and reactive
power consumption
 Central and decentralized power generating units
System Domain
 Focus area is the German power system
 Explicit modelling of voltage stability endangered
grid regions (critical notes)
 Implicit modelling of the rest of Germany
(uncritical nodes)
 Consideration of neighbouring countries
380/220 kV
110 kV
<110 kV
Implicit modelling
with parameter variations
Explicit modelling within
voltage stability endangered
grid regions
Surrounding area for taking into
account European power flows
18
Methodology
Overview of Methodology
Parametrization of
input data
Determination of
critical outages and
power plant dispatch
• Defining grid topology and
load/feed-in situation
• Pre-setting of marketbased power plant
dispatch
• Definition of Λ-state space
and directions 𝛼 to be
evaluated
Evaluation of voltage
stability
• model reduction
“aggregated“
For all 𝛬𝛼 , determination of
• voltage stability
endangered grid region
(critical nodes)
• critical equipment outages
• voltage stability specific
power plant dispatch (PPD)
 Pre-setting as intermediate
results
• model reduction
“implicit and explicit“
• Applying intermediate
results
For all 𝛬𝛼 , critical outages,
voltage stability specific PPD
• Determination of voltage
stability limit with multidimensional CPF
𝑓 𝑧𝑐𝑟𝑖𝑡 , 𝜆crit , 𝛬𝛼 = 0
• result evaluation 𝜆𝑐𝑟𝑖𝑡 (𝛬𝛼 )
𝜦 −state space
unstable
load/feed-in
situation
stable
𝜶
voltage stability limit
𝑓 𝑧𝑐𝑟𝑖𝑡 , 𝜆𝑐𝑟𝑖𝑡 , 𝛬𝛼 = 0
with 𝛬𝛼 = 1
𝑓 𝑧 =0
𝑓 𝑧, 𝜆 = 0
𝑓 𝑧, 𝜆, 𝛬𝛼 = 0
𝜆
𝛬𝛼
𝛼
power flow equations
equations of classic CPF
equations of multi-dimensional CPF
parameter variation variable
direction vector
direction [°]
19
Methodology
Model Reduction Methods
 Model reduction of distribution system (topology HV grid,
𝑺(𝑫𝑮𝟏 )
 Method “implicit and explicit“ for evaluation of voltage
stability
 In voltage stability endangered grid region (critical EHV nodes)
explicit representation of distribution grids
 For uncritical EHV nodes, ex-ante calculation of power balances
𝑃, 𝑄
by load flow analysis including voltage controls  implicit
𝑃, 𝑄
variation paths of power balances 𝑃𝑖 𝜆Λ𝛼 , 𝑄𝑖 𝜆Λ𝛼 for
𝑃, 𝑄
underlying distribution grid in dependence of 𝜆Λ𝛼
 Developed two-staged heuristic ensures
 required model accuracy
 solvability for real systems
EHV level
𝑺(𝑫𝑮𝟐 )
~
 Representation of underlying distribution system as cumulative
active and reactive power
EHV level
~
classes of representative MV and NV grids) to comply with
practical computation times
 Method “aggregated“ for determination of critical outages,
critical nodes, voltage stability specific power plant dispatches
𝑺(𝑫𝑮𝟐 , 𝝀𝜦𝜶 )
𝑃, 𝑄
𝑃, 𝑄
𝑃, 𝑄
20
Methodology
Determination of Critical Outages and
Power Plant Dispatches
Determination of Critical Equipment Outages
*S. Greene, I. Dobson and F. Alvarado,
“Contingency ranking for voltage
collapse via sensitivities from a single
nose curve“, IEEE Transactions on
Power Systems, Vol. 14, No. 1, 1999.
 Injection of power flow change caused by equipment outages
 Ranking of most critical outages through eigenvalue analysis of the Jacobian matrix of
power flow equations at the point of the voltage stability limit*
 Verification of most critical (n-1) and (n-2) outages as combinatorial composition
Evaluation of Uncertainty of Power Plant Dispatch (PPD)
𝚺
 Estimation of the impact of change of the power plant
Δ𝑃𝑃𝑃1
dispatch on voltage stability limit 𝚺
Δ𝑝
 Eigenvalue analysis for determination of 𝚪
as tangent of 𝚺
 Calculation of linearized change of the voltage stability
limit 𝜆𝑘,𝑛𝑒𝑤 = 𝜆𝑘 + Δ𝜆
 Subsequent application of a successive linear optimization for determination of
voltage stability specific power plant dispatches
OF
Max./Min. 𝝀𝒄𝒓𝒊𝒕
C
PF equations 𝑓 𝑧, 𝜆, 𝛬𝛼 = 0
Var
Change PPD(𝝀)
Δ𝑃𝑃𝑃2
𝚪
21
Methodology
Evaluation of Voltage Stability
Multi-dimensional Parameter Variation Method
𝚲-state space
 Reduction of the dimension of the state space by
𝜆𝑊
introducing a transformation matrix 𝑻
 Parameter variation relative to the feed-in of
generating plant and consumer load, respectively
 Variation of load 𝜆𝐿 and power supply from wind turbine
generators 𝜆𝑊
 Development of CPF for vectorial parameter variation
𝜆 𝑘 𝜦𝜶 = 𝜆 𝑘
𝜆𝐿,𝜶
𝜆𝑊,𝜶
𝜆𝐿
unstable
stable
 Predictor step: factor of power variation
 Corrector step: P-control, explicit Q-control for critical nodes or implicit Q-control for
uncritical nodes, improved Q-model for synchronous generators
 Evaluation of voltage stability by iterative
application of CPF
 for all direction vectors Ʌ𝜶
 for voltage stability specific PPD
 for critical equipment outages
Determination of voltage stability limits
𝜆𝑊
voltage stability
optimized PPD
market based PPD
voltage stability critical
PPD
equipment outage
𝜆𝐿
Agenda
Agenda
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
22
23
Exemplary Results
Considered scenario
 Approximation model of the German power system
in 2018
 Transmission grid
• According to German network development
plan (NEP) of 2013 and European TYNDP
• 14 Gvar of Q-compensation (MSC) in Germany
at locations according to the NEP
Grid
400 kV line
230 kV line
EHV/HV switch-gear
station
Load
load
 Distribution grid
• Scaling of the electricity supply task based on current
regionalization scenario of NEP 2013 B
 Load/feed-in scenario
 Peak load/Peak wind scenario (78 GW/34 GW)
 Power plant dispatch based on market simulation
 Parameter variation
 Load increase
 Wind feed-in increase
 Specified merit order
Distributed
generation
wind turbine
generators
photovoltaic
plants
bio mass
plants
24
Exemplary Results
Voltage Stability Risk in Southern Germany
 High power flow from east/north to south-east is limiting voltage stability
 Active power feed-in of wind turbines approximately 34 GW
 High active power feed-in by other distributed generation
 Market based power plant dispatch in accordance with merit order
 Voltage stability limit reached after shutdown of supporting power plants
 Increase of critical voltage by using reactive power compensation devices
Detailed evaluations 𝜦𝟖𝟗
Total result
voltage stability limit
𝜆𝑤𝑖𝑛𝑑
𝜆(Λ89 ) − 𝑉 graph
Voltage stability endangered
grid region
85
1,1
75
GW
Detailed evaluation 𝛼 = 89°
65
𝑉/𝑉𝑏
55
1
0,9
45
0,8
35
75
85
95
GW
105
𝜆𝑙𝑜𝑎𝑑
115
Endangerment of
voltage stability
00
25
15
50
30
%
45
𝜆(Λ 89 )/𝜆crit,89
100
60
25
Exemplary Results
Significant Impact of Conventional Power Plants on Voltage Stability
 Evaluating the impact of uncertainty of power plant dispatch
 Detailed analysis shows suitability of the successive linearized approach to determine
voltage stability specific power plant dispatches
 Wide range of voltage stability limits, depending on power plant dispatch
 Voltage stability limit in the worst-case power plant dispatch at maximum load
 With appropriate intervention in the power plant dispatch voltage stability is not critical
Total result voltage stability limits
𝜆𝑤𝑖𝑛𝑑
Power plant dispatches
voltage stability critical
market based
voltage stability optimized
65
always
unstable
GW
55 stable
at market
based PPD
45
always
stable
stable after
correcting
market
based
PPD
35
75
85
85
95
GW
Detailed evaluation 𝜦𝟏 - Determining critical PPD
105
Voltage stability critical PPD
Market based PPD
1
V/𝑉𝑏
0,9
0,8
0,7
Detailed evaluation
𝛼 = 1°
𝜆𝑙𝑜𝑎𝑑
0,6
0
%
50
100
25
𝜆 Λ1 /𝜆𝑐𝑟𝑖𝑡,1,𝑚𝑎𝑟𝑘𝑒𝑡−𝑏𝑎𝑠𝑒𝑑
26
Exemplary Results
Equipment Outages May Lead to Voltage Instabilities
 Most critical equipment outages in considered load/feed-in scenario
 Outage of overhead double line Redwitz – Remptendorf
 Outage of nuclear power plant Isar 2
 Equipment outages cause reduction of voltage stability in whole state space
 Voltage stability limit may be in areas of real load/feed-in scenarios
 Consideration as planning-relevant grid security criterion recommended
Voltage stability limit
at market based PPD
Voltage stability limit
at voltage stability critical PPD
60
65
Equipment outages
𝜆𝑤𝑖𝑛𝑑
55
𝜆𝑤𝑖𝑛𝑑 GW
without outage
55
GW
50
line outage
45
power plant and line
outage
45
40
35
35
75
80
GW
85
90
𝜆𝑙𝑜𝑎𝑑
75
85
GW
95
105
𝜆𝑙𝑜𝑎𝑑
27
Exemplary Results
System Relevance of Conventional Power Plants
 System relevance in accordance to ResKV quantifiable
 Comparative evaluation of voltage stability with and without power feed-in of the
conventional power plant to be evaluated
 Virtual power plant at EHV location Grafenrheinfeld assumed:
active power feed-in 𝑃 = 1,5 GW, reactive power control range 𝑄 = ±0,5 𝐺var
 Coloured surfaces quantify improvement of voltage stability by the virtual power plant
Evaluation of system relevance of conventional power plants
65
Sensitivity Calculation
𝜆𝑤𝑖𝑛𝑑
with virtual power plant
without virtual power plant
55
GW
Power plant Dispatch
voltage stability critical
market based
voltage stability optimized
45
35
75
85
GW
95
105
𝜆𝑙𝑜𝑎𝑑
Agenda
Agenda
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
28
Summary and Conclusion
Summary and Conclusion
 The induced incentives by the public and politics to install distributed generation
increase the challenges for a stable grid operation
 Increased risk of voltage instabilities
Evaluation of Voltage Stability in German Power System
 Detailed model of German distribution grid has been developed
 Multi-dimensional parameter variation method with
 Heuristic simulation of equipment outages
 Consideration of uncertainty of power plant dispatch
 Results show, among other things
 Under given assumptions load/feed-in scenarios
with insufficient voltage stability can be expected
 Critical equipment outages can significantly reduce voltage stability margin
 Strong impact of conventional power plants on voltage stability
 Voltage stability should be considered in the future as a planning-relevant network
security criterion
29