ECE 692 Advanced Topics on Power System Stability 5 - Voltage Stabilityweb.eecs.utk.edu/~kaisun/ECE692/ECE692_VoltageSta… ·  · 2016-03-29Advanced Topics on Power System Stability

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Spring 2016

Instructor: Kai Sun

ECE 692 Advanced Topics on

Power System Stability

5 - Voltage Stability

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Content

•Basic concepts

– Voltage collapse and Saddle-node bifurcation

– P-V curve and V-Q curve

•Causes and prevention of voltage instability

•Voltage Stability Analysis (VSA)

– Modal analysis

– Continuation powerflow

•Measurement-based VSA

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References

• Chapter 14 of Kundur’s book

• “Survey of the voltage collapse phenomenon”, NERC Interconnection Dynamics Task Force Report, Aug. 1991

• EPRI Tutorial’s Chapter 6

• Carson W. Taylor, “Power System Voltage Stability” McGraw Hil, 1994

• “Voltage Stability Assessment: Concepts, Practices and Tools”, IEEE-PES Power Systems Stability Subcommittee Special Publication, Aug. 2002

• V. Ajjarapu, C. Christy, “The continuation power flow: a tool for steady state voltage stability analysis”, IEEE Trans Power Syst., vol. 7, no. 1, Feb, 1992

• K. Vu, M.M. Begovic, D. Novosel, M.M. Saha, “Use of local measurements to estimate voltage-stability margin”, IEEE Trans Power Syst., vol. 14, no. 3, Aug, 1999

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Voltage Stability

•Voltage stability is concerned with the ability of a power system to maintain acceptable voltages at all buses in the system under normal conditions and after being subjected to a disturbance.

•A system enters a state of voltage instability (or voltage collapse) when a disturbance, e.g. increase in load demand, or change in system condition causes a progressive and uncontrollable decline in voltage

•The main factor causing instability is the inability of the power system to meet the demand for reactive power

•Voltage stability problems normally occur in heavily stressed systems.

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Factors Influencing Q Transfer

• Q is transmitted from the high voltage side to the low voltage side.

• But Q cannot be transmitted over long distances because

– It would require a large voltage gradient to do so.

– An increase in Q transfer causes an increase in Qloss as well as Ploss

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Voltage Stability vs. Rotor Angle stability

• Rotor angle stability is basically stability of generators while voltage stability is basically stability of loads

– Rotor angle stability is often concerned with remote power plants connected to a large system over long transmission lines.

– Voltage stability is concerned with load areas and load characteristics. In a large interconnected system, voltage collapse of a load area is possible without loss of synchronism of any generators.

• However, transient voltage stability is usually closely associated with transient rotor angle stability. If voltage collapse at a point in a transmission system remote from loads, it is, in nature, an angle instability problem.

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A simple radial system

where

ZLD decreases (assume constant ZLN)

S

LN LD

EI

Z Z

2 2( cos cos ) ( sin sin )

S

LN LD LN LD

EI

Z Z Z Z

1 S

LN

EI

ZF

2

1 2 cos( )LD LD

LN LN

Z ZF

Z Z

• How does VR change as PR increases?

R LDV Z I cosR RP V I

1 LDR LD S

LN

ZV Z I E

ZF

2

cos cosSLDR R

LN

EZP V I

F Z

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Load increases (ZLD decreases)

How does voltage instability happen?

• Voltage stability depends on the load

characteristics (dynamics and control)

• Under normal conditions, ZLD>> ZLN

and an increase in power PR is

equivalent to a decrease in ZLD

• However, when ZLD<ZLN (heavy load

conditions), a decrease in ZLD reduces

PR, so a control on power by varying

ZLD may become unstable

• For instance, consider a load supplied

by a transformer with automatic

ULTC. The tap-changer tries to raise

the load voltage (absorbing more

Mvar from the primary side), which

has the effect of reducing the effective

ZLD and in turn lowers VR further (as

seen from the primary side) and may

lead to a progressive reduction of

voltage if the primary side is weak.

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Using an ULTC to control voltage• Normally, when the turns ratio is adjusted, the Mvar flow across the

transformer is also adjusted

• However, since a transformer absorbs Mvar to build its internal magnetic field, when its secondary voltage is raised via a tap change, its Mvar usage increases and its primary voltage often drops. The greater the tap change and the weaker the primary side, the greater the primary voltage drop.

• If the primary side is weak, the tap change may not necessarily increase the secondary voltage. Therefore, spare Mvar must be available for a tap change to be successful.

(5/16x10%= +3.125% ~ 142.3kV)

(+10% ~ 151.8kV)

An example:

10% / 33-position ULTC

(Neutral point: 0% ~ 138kV)

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Constant P

PR=P

Constant Z

PR=aVR2

• The critical point (also called the “nose” or “knee” point) is referred to as “saddle-point

bifurcation”

• Does voltage collapse necessarily happen when the system passes the critical point?

ZLD decreases (assume constant ZLN)

P-V Curve

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Saddle-node bifurcation

• A saddle-node bifurcation is the disappearance of a system

equilibrium as parameters change slowly.

• This is an inherently nonlinear phenomenon and cannot

occur in a linear model.

Bifurcation at the

limit p*

Equilibrium

disappears

Two equilibriums

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ES=1.0pu, ZLN=j0.5pu, cos=0.97.

• Sketch the PR-VR curve at bus R and find values

of PR and VR at the critical point

• If the real power load is represented by a ZIP

load mode PR=P0(VR2+0.9VR+4.0) , where P0

varies depending on the load level. Estimate the

minimum |VR| before voltage collapse.

2

1 2 cos( )

2 2cos( ) 2.486

LD LD

LN LN

Z ZF

Z Z

10.634 puLD

R S

LN

ZV E

ZF

2

cos 0.780 puSLDR

LN

EZP

F Z

Example: P-V Curve with ZIP Load

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Normalized P-V curves ( varies)

• Normally, only the operating points above the critical points represent

satisfactory operating conditions

A sudden reduction in

(increase in QR)

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V-Q Curve

• If QI is injected by a var source at the

load bus:

ZLN jXLN*

*( ) S RR R I R R

LN

E VP j Q Q V I V

jX

=VR0o

=ES QI

2cosS R RR I

LN

E V VQ Q

X

PR=ESVRsin/XLN

2( )cos R I LN R

S R

Q Q X V

E V

sin R LN

S R

P X

E V

2 222

2

S RRI R R

LN LN

E VVQ Q P

X X

Eliminate by

cos2+sin2=1

SE

22

2

22

tan S

LN

RRRI R

LN

PE VV

QX X

P

QI

VR

V-Q curve for specific PR and

(one loading condition)

PR increases

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Normalized V-Q curves (PR varies)

Voltage stability limit is reached

when dQI/dVR=0

QI /PRMAX

• A V-Q curve shows sensitivity and

variation of a bus voltage with respect to Q

injected at the bus. It indicates the QI

required in order to maintain the bus

voltage at desired value VR

• A V-Q curve is generated by applying a

fictitious var source, e.g. synchronous

condenser, at the test bus, i.e. converting

the bus to a PV bus with open var limits, so

it can be used to examine needs for var

compensation

• Voltage instability happens when

dQI/dVR<0 since

– All var control devices are designed to

operate when an increase in Q is

accompanied by an increase in V

– Protective devices may be activated

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39-bus test system

PAera 1 - V530

Uniformly scale up the area load

with constant

A

B

C

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• Probable remedial actions before the limit is reached

– Inject Q at Bus 530 to increase V

– Reduce load near Bus 530

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Causes of voltage instability• A typical scenario on the principal driving force for voltage instability:

– In response to a disturbance, power consumed by loads tends to be restored by motor slip adjustment, distribution voltage regulators and thermostats

– Restored loads increase stress on the high-voltage network causing further voltage reduction

– Voltage instability occurs when load dynamics attempt to restore power consumption beyond the capability of the transmission network

• Principal causes

– The load on transmission lines is too high

– The voltage sources are too far from load centers

– The source voltages are too low

– There is insufficient load reactive compensation

• Contributing factors

– Generator reactive power and voltage control limitations

– Load Characteristics

– Distribution system voltage regulators and transformer tap-changer actions

– Reactive power compensating device characteristics

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Influence of Generation Characteristics

• Actions of generator AVRs provide the primary sources of voltage support

• Under normal conditions, generator terminal voltages are maintained constant

• During conditions of low/high voltages, the var output of a generator may reach its limit. Consequently, the terminal voltage is not longer maintained constant

• Then, with constant field current, the point of constant voltage is now Eq behind the synchronous reactance XSXd. That increases the network reactance significantly to further aggravate the voltage collapse condition

• It is important to maintain voltage control capabilities of generators

• The degree of voltage stability cannot be judged based only on how close the bus voltage is to the normal voltage level

Voltage collapse due to the Q/current limit

being reached is referred to as “limit-

induced bifurcation”

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Influence of Reactive Compensator CharacteristicsKundur’s Example 14.1

Compensation

increases

• The compensator is designed to increase compensation (Q) in order to increase voltage (V)

• At Point A (low compensation)

– The slope Q/V of the system is greater than that of the shunt capacitor

– With the compensation increase, A A’; V is increased at A’, so compensation stops increasing

– Voltage is stable

• At Point B (high compensation)

– The slope Q/V of the system is smaller than that of the shunt capacitor

– With the compensation increase, B B’; V is decreased at B’, so compensation will continue to increase (nonstop)

– Voltage is unstable

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Influence of Load Characteristics

When voltages drop

•Residential loads

– Active load will drop with voltage, which will in turn reduce line loading and hence the line reactive losses

•Industrial loads

– Active load will change little because of large components of induction motors.

– However the capacitors in the industrial area will supply less reactive power, thereby causing a net increase in the reactive load

– At voltages below 85-90% of the nominal value, some induction motors may stall to draw high reactive current, which brings the voltages down further. The voltage drop will cause many motors to drop out. The loss of motor loads will result in voltage recovery. However, after some time, the motors are restored to service, which may cause voltage to drop again if the original cause of the voltage problem still persists.

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Load modeling for accurate analysis of voltage stability

•Motors and capacitors in industrial areas

•Load regulating devices (e.g. thermostatically controlled loads)

– When the distribution voltages remain low for a few minutes, they tend to restore load to the normal full voltage value in 10-15 minutes, which makes distribution voltages drop further

•Substation transformer ULTCs and distribution voltage regulators

– Attempt to maintain voltage at points of consumption

– May have destabilizing effects during conditions of voltage collapse

– When the ULTCs reach the end of their tap range, distribution voltages drop

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Long-Term and Short-Term Voltage Stability

• The time frame by which voltage instability occurs could be in the range of a few seconds (short-term) to tens of minutes (long-term)

• Long-term voltage instability (several minutes)– Involves slower acting equipment such as transformer ULTCs, generator field

current limiters and thermostatically controlled loads– May be effectively studied using static analysis techniques with complementary use

of dynamic analysis

• Short-term voltage instability (several seconds)– Faults/short-circuits near loads could be important– Involves dynamics of fast acting load components such as induction motors,

electronically controlled loads and HVDC converters– Dynamic modeling of loads are often essential; analysis requires solution of

differential equations using time-domain simulations– Effective countermeasures include STATCOMs, particularly smaller units connected

to distribution network and fast load shedding (UVLS schemes).

• There is a trend of increasing short-term voltage instability due to– Increasing use of low inertia compressor motors for air conditioning, heat pumps

and refrigeration– Growth in the use of voltage-insensitive loads with electronic power supplies– Transmission network being pushed harder

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A Typical Scenario of Short-Term Voltage Instability

•The power system is operating in a stressed condition during hot weather with a high level of air conditioning load

•The triggering event is a multi-phase fault near a load center

– Causes voltage dips at distribution buses

– Air conditioner compressor motors decelerate, drawing high current

•Following fault clearing with transmission/distribution line tripping motors draw very high current while attempting to reaccelerate. Motors stall if the power system is weak.

•Under-voltage load rejection may not be fast enough to be effective

•Loss of much of the area load and voltage collapse

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12

3

1

2

3

1GW generation

tripped by SPS

4

4

Faulty zone 3

relay

5

5

6 8

67

7

8

Loss of key

hydro units

Tripped by

Zone 3 relay

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9

10

Tree

contact

and

relay

mis-opt.

Example of Voltage Collapse -

July 2nd, 1996 Western

Cascading Event

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•On July 3rd, 1996, i.e. the following day,

– A similar chain of events happened to cause voltages in Boise area to decline.

– Different from the previous day, Idaho Power Company system operators noted the declining voltages and immediately took the only option available: shedding of Boise area load

– Then, the system returned to normal within 1 hour

•Lessons learned:

– The July 2nd and 3rd events in Boise, Idaho area emphasize the need for effective and sufficient, rapidly responsive dynamic Mvar reserve.

– The July 3rd events illustrate the importance of system operators’ situational awareness and rapid responses.