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Voltage Stability in the German Power System
Univ.-Prof. Dr.-Ing. Albert Moser
Bremen, 23th June 2016
Summer School “Stability of Electricity Grids“
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
Agenda
Agenda 1
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
Agenda
Agenda 2
Classification of System Stability
System Stability Basics 3
(Definition and Classification of Power System Stability,IEEE/CIGRE Joint Task Force on Stability Terms and Definitions)
SystemStability
Large-Signal
Small-Signal
Rotor-AngleStability
Short-Term
Large-Signal
Small-Signal
VoltageStability
Long-Term
Short-Term
Long-Term
Short-Term
FrequencyStability
Affected System Variable
Size of Disturbance
Time Frame of Dynamics
Ability of synchronous machines in power systems toremain in synchronism after being subject to adisturbance
Depends on ability to maintain/restore equilibriumbetween electromagnetic and mechanical torque ofsynchronous 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
Rotor Angle Stability
4System Stability Basics
power-angle curve
rotor angle response to disturbance
roto
r an
gle 𝛿
time
first swingunstable unstable
stable
Frequency stability is defined as the ability 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.
Frequency Stability
5System Stability Basics
𝑓
𝑡
Δ𝑓𝑑𝑦𝑛
Δ𝑓𝑠𝑡𝑒𝑎𝑑𝑦−𝑠𝑡𝑎𝑡𝑒
50 Hz
49 Hz 51 Hz
spinning reserve
primary control
Voltage stability is defined as the abilityof a power system to remain withinoperational voltage limits after beingsubject of disturbance.
Short-term voltage stability
Transient phenomena within few seconds
Caused by sudden changes of theoperating point, e.g. short curcuits
Often locally limited phenomenon
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.
Voltage Stability
6System Stability Basics
Voltage stable/unstable system
time
Vunstable
Vstable
disturbance voltage tolerance band
volt
age
Time Domain of Transients
System Stability Basics 7
Focus of this Lecture
System Stability Basics 8
(Definition and Classification of Power System Stability,IEEE/CIGRE Joint Task Force on Stability Terms and Definitions)
SystemStability
Large-Signal
Small-Signal
Rotor-AngleStability
Short-Term
Large-Signal
Small-Signal
VoltageStability
Long-Term
Short-Term
Long-Term
Short-Term
FrequencyStability
Affected System Variable
Size of Disturbance
Time Frame of Dynamics
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.
Wide range of nonlinearities existent in electrical power systems
Limiters of exciter systems (synchronous generators)
Min./max. cos𝜑 of converters (distributed energy sources)
Power plant dispatch
Continuation Power Flow is able to reflect such nonlinearities.
Voltage Stability and Transmission Line Loading
9System Stability Basics
𝑉𝐿
𝑃𝑒
𝑉𝑐𝑟𝑖𝑡
𝑃𝑚𝑎𝑥𝑃𝑡ℎ𝑒𝑟𝑚
stable
𝑅𝐿
𝑃𝑒
𝑉𝐿𝑋𝑁𝐸𝐺 ~
𝑅𝐿 → ∞
𝑅𝐿 → 0𝑃𝑡ℎ𝑒𝑟𝑚,𝐻𝑇𝐶
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 ofa variation in 𝜆 using linearized continuation
2) Corrector: Newton-Raphson algorithm to determineexact solution of underdetermined power flow
equation 𝑓 𝑧, 𝜆
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 methodsto evaluate the voltage stability in the German power system
Continuation Power Flow
System Stability Basics 10
𝑽
𝝀
predictor
corrector
𝜆crit
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
Agenda
Agenda 11
grid / outages
reactive power compensation /voltage control
power plant dispatch
loads / renewable energy sources
Grid Equipment and Equipment Outages
Parameters influencing Voltage Stability 12
Grid Equipment
Traditional equipment like cables, overhead lines and transformers
Innovative equipment
Equipment Outage As most common trigger for voltage
collapses a consideration beyondthe (n-1)-criterion is necessary.
𝒍
P
V
Thermal limit
𝑃𝑛𝑎𝑡
• High temperature conductors allow higher currents at similar reactances.
• HVDC with independent active/reactive power control
Q
P𝑃𝑛𝑎𝑡
overhead line
cable
ind
.ca
p.
Thermal limit
Reactive Power Compensation Devices
13
Synchronous generator: controllable 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~𝑉2.
Steeper voltage gradients and increased critical voltage
Increased maximal power transfer
But also endangerment of voltage collapse at normal operating voltages
P
Stepwise connection of capacitors
V
sstable
unstableTrajectory of critical voltage using capacitive shunt compensation
grid / outages
reactive power compensation /voltage control
power plant dispatch
loads / renewable energy sources
Parameters influencing Voltage Stability
Uncertainty of Power Plant Dispatch
14
Electricity transport through grid is not only determined by loads and renewable energy sources but also by central generating units.
Power plant dispatch is a result ofEuropean 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 cansupply 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
grid / outages
reactive power compensation /voltage control
power plant dispatch
loads / renewable energy sources
Parameters influencing Voltage Stability
Loads and Distributed Energy Resources
15
Active and reactive power balance of distribution grid is changing.
Impedances of grid and voltage control in distribution grid are not negligible.
Distribution grid model based on public data
Explicit modelling of distribution grids
Grid topology of 110 kV grids (KraftNAV)
Homogenized, regionally classified consideration of medium and low-voltage grids (StromNZV/StromNEV)
Regionalisation of loads and distributed power feed-in according to public data
Grid model HV level
grid / outages
reactive power compensation /voltage control
power plant dispatch
loads / renewable energy sources
Parameters influencing Voltage Stability
-100
0
100
200
-100 100 300P
Q
Comparison with snapshots
Source snapshots : Amprion GmbH
snapshots
modelMvar
MW
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
Agenda
Agenda 16
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 endangeredgrid regions (critical notes)
Implicit modelling of the rest of Germany(uncritical nodes)
Consideration of neighbouring countries
System under consideration
Methodology 17
380/220 kV 110 kV <110 kV
Implicit modellingwith parameter variations
Surrounding area for taking intoaccount European power flows
Explicit modelling withinvoltage stability endangeredgrid regions
Overview of Methodology
18
unstable
stable
load/feed-in situation
𝜦 −state space
voltage stability limit 𝑓 𝑧𝑐𝑟𝑖𝑡, 𝜆𝑐𝑟𝑖𝑡, 𝛬𝛼 = 0
with 𝛬𝛼 = 1
Parametrization of input data
• Defining grid topology and load/feed-in situation
• Pre-setting of market-based power plant dispatch
• Definition of Λ-state space and directions 𝛼 to be evaluated
Determination of critical outages and power plant dispatch
• 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
Evaluation of voltage stability
• model reduction“implicit and explicit“
• Applying intermediate results
For all 𝛬𝛼, critical outages, voltage stability specific PPD
• Determination of voltage stability limit with multi-dimensional CPF 𝑓 𝑧𝑐𝑟𝑖𝑡, 𝜆crit, 𝛬𝛼 = 0
• result evaluation 𝜆𝑐𝑟𝑖𝑡( 𝛬𝛼)
𝜶
𝑓 𝑧 = 0 power flow equations
𝑓 𝑧, 𝜆 = 0 equations of classic CPF
𝑓 𝑧, 𝜆, 𝛬𝛼 = 0 equations of multi-dimensional CPF
𝜆 parameter variation variable
𝛬𝛼 direction vector
𝛼 direction [°]
Methodology
Model reduction of distribution system (topology HV grid, 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
Representation of underlying distribution system as cumulative active and reactive power
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 by load flow analysis including voltage controls implicit
variation paths of power balances 𝑃𝑖 𝜆Λ𝛼 , 𝑄𝑖 𝜆Λ𝛼 for
underlying distribution grid in dependence of 𝜆Λ𝛼
Developed two-staged heuristic ensures
required model accuracy
solvability for real systems
Model Reduction Methods
19
EHV level
~
𝑺(𝑫𝑮𝟏) 𝑺(𝑫𝑮𝟐)
EHV level~
𝑺(𝑫𝑮𝟐,𝝀𝜦𝜶)
𝑃, 𝑄
𝑃, 𝑄
𝑃, 𝑄
𝑃, 𝑄
𝑃, 𝑄
𝑃, 𝑄
Methodology
Determination of Critical Equipment Outages
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)
Estimation of the impact of change of the power plantdispatch on voltage stability limit 𝚺
Eigenvalue analysis for determination of 𝚪as tangent of 𝚺
Calculation of linearized change of the voltage stabilitylimit 𝜆𝑘,𝑛𝑒𝑤 = 𝜆𝑘 + Δ𝜆
Subsequent application of a successive linear optimization for determination ofvoltage stability specific power plant dispatches
Determination of Critical Outages andPower Plant Dispatches
20
OF Max./Min. 𝝀𝒄𝒓𝒊𝒕 C PF equations 𝑓 𝑧, 𝜆, 𝛬𝛼 = 0 Var Change PPD(𝝀)
𝚺
𝚪
Δ 𝑝
Δ𝑃𝑃𝑃1
Δ𝑃𝑃𝑃2
*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.
Methodology
Multi-dimensional Parameter Variation Method
Reduction of the dimension of the state space byintroducing a transformation matrix 𝑻
Parameter variation relative to the feed-in ofgenerating plant and consumer load, respectively
Variation of load 𝜆𝐿 and power supply from wind turbinegenerators 𝜆𝑊
Development of CPF for vectorial parameter variation
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 iterativeapplication of CPF
for all direction vectors Ʌ𝜶
for voltage stability specific PPD
for critical equipment outages
Evaluation of Voltage Stability
21
Determination of voltage stability limits
𝚲-state space𝜆𝑊
𝜆𝐿
stable unstable
𝜆𝑘𝜦𝜶 = 𝜆𝑘
𝜆𝐿,𝜶
𝜆𝑊,𝜶
𝜆𝐿
𝜆𝑊
market based PPD
voltage stability critical PPD
voltage stability optimized PPD
equipment outage
Methodology
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
Agenda
Agenda 22
Approximation model of the German power systemin 2018
Transmission grid
• According to German network developmentplan (NEP) of 2013 and European TYNDP
• 14 Gvar of Q-compensation (MSC) in Germany at locations according to the NEP
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
Considered scenario
Exemplary Results 23
wind turbinegenerators
photovoltaic plants
load
400 kV line
230 kV line
EHV/HV switch-gearstation
bio massplants
Grid
Load
Distributedgeneration
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
Voltage Stability Risk in Southern Germany
24
35
45
55
65
75
85
75 85 95 105 115
GW
GW
𝜆𝑙𝑜𝑎𝑑
𝜆𝑤𝑖𝑛𝑑
Total resultvoltage stability limit
Detailed evaluation 𝛼 = 89°
0,8
0,9
1
1,1
0 15 30 45 60
𝑉/𝑉𝑏
𝜆(Λ89) − 𝑉 graph
𝜆(Λ89)/𝜆crit,89
Voltage stability endangeredgrid region
Detailed evaluations 𝜦𝟖𝟗
10050250 %Endangerment ofvoltage stability
Exemplary Results
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
Significant Impact of Conventional Power Plants on Voltage Stability
Exemplary Results 25
0,6
0,7
0,8
0,9
1
0 50 100
V/𝑉𝑏
%
𝜆 Λ1 /𝜆𝑐𝑟𝑖𝑡,1,𝑚𝑎𝑟𝑘𝑒𝑡−𝑏𝑎𝑠𝑒𝑑
Market based PPDVoltage stability critical PPD
35
45
55
65
75 85 95 105
GW
𝜆𝑙𝑜𝑎𝑑
𝜆𝑤𝑖𝑛𝑑
alwaysstable
stable at marketbased PPD
stable aftercorrecting
marketbased
PPD
alwaysunstable
Total result voltage stability limits
market based
voltage stability critical
voltage stability optimized
Power plant dispatches
Detailed evaluation 𝜦𝟏 - Determining critical PPD
Detailed evaluation𝛼 = 1° 25
GW 10585
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
Equipment Outages May Lead to Voltage Instabilities
26
35
45
55
65
75 85 95 105
GW
GW
𝜆𝑙𝑜𝑎𝑑
𝜆𝑤𝑖𝑛𝑑
35
40
45
50
55
60
75 80 85 90
GW
GW
𝜆𝑙𝑜𝑎𝑑
𝜆𝑤𝑖𝑛𝑑
Voltage stability limitat voltage stability critical PPD
line outage
power plant and line outage
without outage
Equipment outages
Voltage stability limitat market based PPD
Exemplary Results
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
System Relevance of Conventional Power Plants
27
Sensitivity Calculation
with virtual power plant
without virtual power plant
35
45
55
65
75 85 95 105
GW
GW 𝜆𝑙𝑜𝑎𝑑
𝜆𝑤𝑖𝑛𝑑
market based
voltage stability critical
voltage stability optimized
Power plant Dispatch
Evaluation of system relevance of conventional power plants
Exemplary Results
System Stability Basics
Parameters influencing Voltage Stability
Methodology
Exemplary Results
Summary and Conclusion
Agenda
Agenda 28
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 scenarioswith 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
Summary and Conclusion
29Summary and Conclusion
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