voltage stability in the german power system - june...

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



Methodology

Exemplary Results


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


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


Voltage stable/unstable system

time

Vunstable

Vstable

disturbance voltage tolerance band

volt

age

Time Domain of Transients


Focus of this Lecture


(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


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


𝑽

𝝀

predictor

corrector

𝜆crit



Methodology

Exemplary Results


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





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





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





-100

0

100

200

-100 100 300P

Q

Comparison with snapshots

Source snapshots : Amprion GmbH

snapshots

modelMvar

MW



Methodology

Exemplary Results


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



Methodology

Exemplary Results


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



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



35

40

45

50

55

60

75 80 85 90

GW

GW



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


market based

voltage stability critical

voltage stability optimized

Power plant Dispatch

Evaluation of system relevance of conventional power plants

Exemplary Results



Methodology

Exemplary Results


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


29Summary and Conclusion

voltage stability in the german power system - june...

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