POWER SYSTEM VOLTAGE STABILITY

Akash ChoudharyI.D. No. 43232B.Tech 4th yearElectrical EngineeringCollege of Technology GBPUAT

Voltage collapse is still the biggest single threat to the transmission system. It’s what keeps me awake at night

•- Phil Haris, PJM President and CEO, March 2004

Introduction•Present day power systems are being

operated closer to their stability limits due to economic constraints. Maintaining a stable and secure operation of a power system is therefore very important and challenging issue.

What is voltage stability?

Voltage stability• The definition of voltage stability as proposed

by IEEE task force is as follows: Voltage stability refer to the ability of power

system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating point. The system state enters the voltage instability region when a disturbance or an increase in load demand or alteration in system state results in an uncontrollable and continuous drop in system voltage.

Continued• A system is said to be in voltage stable state if at a

given operating condition, for every bus in the system, the bus voltage magnitude increases as the reactive power injection at the same bus is increased.

• A system is voltage unstable if for at least one bus in the system, the bus voltage magnitude decreases as the reactive power injection at the same bus is increased.

• It implies that if, V-Q sensitivity is positive for every bus the system is voltage stable and if V-Q sensitivity is negative for at least one bus, the system is voltage unstable.

Voltage Instability Time frames and mechanism• Transient Voltage stability • Longer term voltage

stability

Transient voltage stability• Time frame varies from zero to about ten seconds• Voltage collapse is caused by unfavorable fast

acting load component such as large induction motor and D.C. converters.

• During under frequency load shedding there is possibility that system voltage may collapse whenever imbalance in reactive power is more than 50%.

• HVDC circuits cause transient voltage stability problem as converters and inverters require large amount of reactive power.

Longer term voltage stability• The time frame is few minutes typically 2-3

minutes and hence operator intervention is not possible.

• Involves high loads, high power imports from remote generation and a sudden large disturbance which could be in the form of loss of large generators and loss of transmission lines.

• The disturbance causes high reactive power losses and voltage sags in load areas.

• Rapid voltage decay starts and partial or complete voltage collapse follows.

Relation of voltage stability to rotor angle stability

Comparision Rotor angle stability Voltage stability• synchronous machine

connected to infinite bus or a large system.

• Normally concerned with integrating remote power plant to a large system.

• It is basically generator stability.

• When asynchronous load connected to a large system.

• Concerned with load areas and load characteristics.

• It is basically load stability.

Continued.•If voltage collapses at a point in

transmission system remote from loads, it is an angle instability situation . However, if voltage collapses in a load area it is mainly a voltage instability situation.

Why does voltage instability occur in mature power system?

Voltage instability in mature power system•Intensive use of existing generation and

transmission.•Vast use of shunt capacitor banks for

reactive power compensation. It results into voltage collapse prone fragile network.

Series capacitor compensation• The reactive power generation due to

series capacitance compensates for the reactive power consumption due to series inductance of the line.

•Series capacitor reactive power generation increases with the current squared, thus generating reactive power when most needed.

Voltage stability of simple two bus system

Continued• Real power transfer from bus 1 to bus 2 is given by P= {E*V*sin(d)}/X -

(1)• Reactive power transfer from bus 1 to bus 2 is given

by Q=-(V^2)/X+{E*V*cos(d)}/X -(2)• Normalizing the terms in equation (1) and (2) with v=V/E p=(P*X)/E^2 q=(Q*X)/E^2• v^4+v^2(2q-1)+(p^2+q^2)=0 -

(3)

Continued• Positive real solutions of v from equation (3) are

given by v={.5 -q±(.25-p^2-q)^.5}^.5 -

(4)• Corresponding to each point (p, q) there are two

solutions for voltage, one is high voltage or stable solution which is the actual voltage at the bus, and the other one is the low voltage or unstable solution.

• The equator along which the two solutions of v are equal, represents maximum power points.

• An increase in p or q beyond maximum power point makes the voltage unstable.

Variation of bus voltage with active and reactive power loading.

Tools for voltage stability analysis•P-V curve method.•V-Q curve method and reactive power

reserve.

P-V curve method • Widely used method for voltage stability analysis.• Gives available amount of active power margin

before the point of voltage instability.• For a simple two bus system as shown in previous

fig. equation (4) gives real solution of v^2 provided (1-4*q-4*p^2) ³ 0 -

(5)• Assuming contant power factor load such as q/p=k,

the inequality can be expressed as, p £.5{(1+k^2)^.5-k}

-(6)

Continued•Equation p £.5{(1+k^2)^.5-k} determines

maximum value of p.•Thus representing the load as a constant

power factor type with a suitably chosen power factor, the active power margin can be computed from above equation.

Normalized P-V curves for 2 bus system

V-Q curve method and reactive power reserve.• Voltage security of a bus is closely related to the

available reactive power reserve, which can be easily found from the V-Q curve of the bus under consideration.

• The reactive power margin is the MVAR distance between the operating point and the nose point of the V-Q curve.

• Stiffness of the bus can be qualitatively evaluated from the slope of the right portion of the V-Q curve. The greater the slope is, the less stiff is the bus, and therefore the more vulnerable to voltage collapse it is.

Normalized V-Q curves for two bus system

Methods of improving voltage stability•Planning of generation system.•Maintenance of generation system.•Operation of generation system.•Reactive power compensation.•Capacitor bank.•Tap changing.

Continued•Planning of generation system The reliability aspect of supply can be improved

by sitting generating plants in the load areas.•Maintenance of generation system Over excitation and under excitation limiters,

alarm settings, tap changer settings need to be verified and maintained.

•Operation of generation system During peak load period, power import over the

transmission network should be reduced.

Continued• Reactive power compensation Extra high voltage transmission lines requires shunt

reactors for energization and under lightly loaded condition. These shunt reactors should be switched off during voltage emergencies.

• Capacitor bank Shunt capacitor banks act as constant reactive power

sources.• Tap changing The tap changing transformers change the

transformation ratio and thus the voltage in the secondary circuit is varied and voltage control is obtained.

Conclusion•There are many aspects of voltage

stability and also has many solutions associated to the voltage stability in terms of generation, transmission and distribution .Power system engineer job is to find low cost solution whenever possible which require special control and special power system operation.

References•S Chakrabarti, Dept. of EE, IIT Kanpur,

Notes on power system stability.•C.L. Wadhwa, Electrical power systems,

2010.•C Radhakrishna, Voltage stability

analysis-1.•Carson W. Taylor, Voltage stability for

undergraduates.

Thank you…