stability fundamentals

Fundamentals on Power System Stability 1

Power System Stability

On Island Networks

DIgSILENT GmbH

Prepared for IRENA Workshop, 8 - 12 April 2013, Palau


• Definition of power system stability

• Rotor angle stability

• Frequency Stability

• Voltage stability

• Renewable energy integration and stability

Overview


What is Power System Stability?


Definition of stability:

Power system stability is the ability of an electric power

system, for a given initial operating condition, to regain a

state of operating equilibrium after being subjected to a

physical disturbance, with most system variables bounded

so that practically the entire system remains intact.

Source: IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, “Definition and Classification of Power System Stability”, IEEE Transactions on Power Systems, 2004

Power System Stability


• Rotor angle stability (transient stability, small-signal stability)

• Frequency stability

• Voltage stability (short-term, long-term, small disturbance, large disturbance)

Types of Stability


Rotor Angle Stability


What is Rotor Angle?

Reference Machine Synchronous Machine 2

Rotor angle


Large signal rotor angle stability (Transient stability)

Ability of a power system to maintain synchronism during severe

disturbances, e.g.

– Short circuit fault

– Loss of generation

– Large step loading (or loss of load)

Large signal stability depends on system properties and the type

of disturbance (not only a system property)

– Analysis using time domain simulations

– Critical fault clearing time

Transient Stability


Transient Stability

Left: Active power (red) and reactive power (green) Right: Generator speed

Case 1: Stable

10.008.006.004.002.000.00 [s]

1500.00

1000.00

500.00

0.00

-500.00

-1000.00

G1: Positive-Sequence, Active Power in MW

G1: Positive-Sequence, Reactive Power in Mvar

10.008.006.004.002.000.00 [s]

1.013

1.008

1.003

0.998

0.993

0.988

G1: Speed in p.u.

10.008.006.004.002.000.00 [s]

2000.00

1500.00

1000.00

500.00

0.00

-500.00

G1: Positive-Sequence, Active Power in MW

G1: Positive-Sequence, Reactive Power in Mvar


Transient Stability


Case 2: Critically Stable

10.008.006.004.002.000.00 [s]

1.0325

1.0200

1.0075

0.9950

0.9825

0.9700

G1: Speed in p.u.


Transient Stability


Case 3: Unstable

10.008.006.004.002.000.00 [s]

1.90

1.70

1.50

1.30

1.10

0.90

G1: Speed in p.u.


• Significance of transient stability depends on several factors,

e.g.

– Distribution of synchronous generation: highly centralised

vs highly dispersed

– Types of machines and controllers: same type of prime

mover, AVR and governor vs completely different types

• Highly centralised power systems with generators of the same

make / model are typically more robust against transient instability

Transient Stability in Island Networks


Small signal rotor angle stability (Oscillatory stability)

Ability of a power system to maintain synchronism under small disturbances

The following oscillatory phenomena are of particular concern:

– Local modes

– Inter-area modes

– Control modes

– Torsional modes

Analysis using modal / eigenvalue analysis

Small Signal Stability


Small Signal Stability

• Td = damping torque

• Ts = synchronising torque


• Most studies suggest that small-signal stability is not a

significant issue

– In the EirGrid study [1], increased wind penetration actually

improved damping in the oscillatory modes

– A study by Potamianakis and Vournas [2], which reflects small

systems in the Greek isles, also shows that small-signal stability

is not a major issue

Small-Signal Stability in Island Networks


Frequency Stability


Frequency stability

Ability of a power system to compensate for a power deficit

Frequency Stability

Source: EirGrid [1]


Frequency Stability


How a typical power system compensates for a power deficit:

1. Inertial reserve (network time constant)

– Lost power is compensated by the energy stored in rotating masses of all generators -> Frequency decreasing

2. Primary control (1s to 15s):

– Lost power is compensated by an increase in production of primary controlled units. -> Frequency drop partly compensated

3. Secondary control (15s to 3min):

– Lost power is compensated by secondary controlled units. Frequency and area exchange flows reestablished

4. Re-Dispatch of Generation

Frequency Stability


• Frequency disturbance following an unbalance in active power

Frequency Deviation according to UCTE design criterion

-0,9

-0,8

-0,7

-0,6

-0,5

-0,4

-0,3

-0,2

-0,1

0

0,1

-10 0 10 20 30 40 50 60 70 80 90

dF in Hz

t in s

Rotor Inertia Dynamic Governor Action Steady State Deviation

Frequency Stability


• Effects of off-nominal frequencies:

– Resonances in rotating machines causing mechanical vibration

damage

– Overheating of transformer and generator core laminations if

Volts/Hz ratio is too high

– Change in induction machine operating speed

– Flicker in lighting equipment

– Time error in AC powered clocks

Frequency Stability


Frequency Disturbance Example – Ireland 2005

Source: Lalor [3]


• Frequency stability is a significant issue in small island grids

due to low system inertias

– Low system inertia => high sensitivity to frequency deviations

– Large frequency deviations after a disturbance are more likely

– Frequency deviations may cause activation of load-shedding,

over/under-frequency or ROCOF relays

Frequency Stability in Island Networks


• Considerations:

– Spinning reserve to cover contingencies and limit frequency

deviations

• More spinning reserve = higher level of contingency that can

be suffered by the system without collapse

• More spinning reserve = more inertia = smaller freq deviations

• More spinning reserve = higher generator running costs

– Minimum loading of thermal generators (e.g. typically 40 – 60%

for diesel generators to avoid cylinder bore glazing)

Frequency Stability in Island Networks


Voltage Stability


Voltage stability refers to the ability of a power system to

maintain steady voltages at all buses in the system after being

subjected to a disturbance.

• Small disturbance voltage stability (Steady-state voltage stability)

– Ability to maintain steady voltages when subjected to small

disturbances, e.g. increasing load, change in solar PV output

• Large signal voltage stability (Dynamic voltage stability)

– Ability to maintain steady voltages after following large disturbances,

e.g. transmission line trip

Voltage Stability


Small-Signal:

- Small disturbance

Large-Signal

- System fault

- Loss of generation

Long-Term - PV Curves (load flows)

- QV Curves

- Long-term dynamic models

including tap-changers, var-

control, excitation limiters, etc.

- PV Curves (load flows)

of the faulted state.

- Long-term dynamic models

including tap-changers, var-

control, excitation limiters, etc.

Short-Term - Typically not a problem and not

studied

- Dynamic models (short-term),

special importance on dynamic

load modeling, stall effects etc.

Voltage Stability - Analysis


Voltage Stability – QV and PV Curves

1762.641462.641162.64862.64562.64262.64

1.40

1.20

1.00

0.80

0.60

0.40

x-Achse: SC: Blindleistung in Mvar

SC: Voltage in p.u., P=1400MW




P=2000MW

P=1800MW

P=1600MW

P=1400MW

DIgS

ILEN

T

1350.001100.00850.00600.00350.00100.00

1.00

0.90

0.80

0.70

0.60

0.50

x-Achse: U_P-Curve: Total Load of selected loads in MW

Klemmleiste(1): Voltage in p.u., pf=1

Klemmleiste(1): Voltage in p.u., pf=0.95

Klemmleiste(1): Voltage in p.u., pf=0.9

pf=1

pf=0.95

pf=0.9

DIgS

ILEN

T

Volt

age

Active power

Volt

age

Reactive power

Fundamentals of Power System Stability 29

Voltage Stability: Example (PV Curves)

Outage of large generator

All generators in service


• Voltage instability is mainly caused when a power system

cannot meet its demand for reactive power.

• Problem is much the same for islands as for interconnected grids.

Factors influencing voltage stability include:

– Weaknesses in the network (subject to local voltage instability)

– High system loading

– Distances between generation and load

– Availability of reactive power support

– Dynamic effects, e.g. OLTCs, field excitation limiters, SVCs, etc

– Load characteristics, e.g. induction motors (air-conditioning)

Voltage Stability in Island Networks


Renewable Energy Integration and Stability


• Frequency stability:

– Renewable energy sources are often connected via a converter

interface and have no inertia (as seen from the grid)

– Replacing synchronous generators with sources using a

converter interface therefore reduces total system inertia and is

more sensitive to frequency deviations

– Thermal generators may run under minimum load if displaced

by renewable energy sources

• Potential mitigation measures:

– Minimum system inertia, i.e. minimum number of synchronous

generators online (spinning reserve)

– Under-frequency load shedding

– Energy storage with fast response [4]

– Demand side management (DSM), i.e. smart grid technologies

Renewable Energy Integration – Key Stability Issues



Source: Lalor [3]

No wind

FSIG

DFIG


• Transient stability:

– Effects of renewable energy integration on transient stability

must be assessed on a case-by-case basis and depends more

on distribution of synchronous generators and controller types

– Some past studies indicate that for moderate penetrations e.g.

30 – 40%, renewable energy sources do not significantly affect

transient stability [1]


– Depending on grid characteristics, it may be necessary to limit

penetration of renewable energy sources (case-by-case)



• Voltage stability:

– Renewable energy sources with limited or no reactive power

control (e.g. fixed-speed induction wind turbines, household-

scale PV inverters) will decrease voltage stability

– Integrating renewable energy sources into weak parts of the

grid can actually improve voltage stability


– Use renewable energy sources that are capable of reactive

power control

– Connect renewable energy sources at weak parts of the grid



1. EirGrid, “All Island TSO Facilitation of Renewables Studies”, 2010,

http://www.eirgrid.com/renewables/facilitationofrenewables/

2. Potamianakis, E. G., Vournas, C. D., “Modeling and Simulation of

Small Hybrid Power Systems”, IEEE PowerTech Conference, 2003

3. Lalor, G. R., “Frequency control on an island power system with

evolving plant mix”, PhD Dissertation, 2005

4. Kottick, D., Blau, M., Edelstein, D., “Battery energy storage for

frequency regulation in an island power system”, IEEE Transactions

on Energy Conversion, Vol 8 (3), 1993

References

http://www.eirgrid.com/renewables/facilitationofrenewables/

stability fundamentals

Documents

definition of stability

stability terms

electric power system

active power red

system properties

system variables

entire system

centralised power systems