Voltage Stability Assessment

Voltage Stability Assessment

Power flow analysis can provide valuable insights into the voltage stability phenomenon. Based on the power flow study results, the weak areas and the weak buses of the system can be found.

The power flow solution may fail to converge close to the stability limit. Beyond the stability limit, there is no feasible solution and the power flow solver will diverge.

However, many other reasons can lead to convergence failure in the power flow solvers, before the true stability limit is reached. Such as inappropriate power flow solution parameters settings and improper power flow solution control adjustments.

As a result, it is crucial to understand the impacts of the power flow solution techniques, power flow solution parameters and power flow solution control parameters on the power flow simulations and the voltage stability analysis.

This post mainly focusses on Voltage stability analysis

Voltage stability is defined as the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition.

Voltage instability phenomena are the ones in which the receiving end voltage decreases well below its normal value and does not come back even after setting restoring mechanisms such as VAR compensators, or continues to oscillate for lack of damping against the disturbances and leads to voltage collapse.

Voltage collapse is the process by which the voltage falls to a low, unacceptable value as a result of an avalanche of events accompanying voltage instability.

Different methods exist in the literature for carrying out a steady state voltage stability analysis. The conventional methods can be broadly classified into the following types.

1. P-V curve method.

2. V-Q curve method and reactive power reserve.

3. Methods based on singularity of power flow Jacobian matrix at the point of voltage collapse.

4. Continuation power flow method.

We are going to discuss about V-Q curve method

V-Q curve method

In this method Voltage at a test bus or critical bus is plotted against reactive power at that bus. A fictitious synchronous generator with zero active power and no reactive power limit is connected to the test bus.

The power-flow test bus treated as the generator bus. Reactive power at the bus is noted from the power flow solutions and plotted against the specified voltage.

The operating point corresponding to zero reactive power represents the condition when the fictitious reactive power source is removed from the test bus.

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 either the nose point of the V-Q curve or the point where capacitor characteristics at the bus are tangent to the V-Q Curve. 

Tracing down the curve from higher to lower voltage set-points represents a decrease in the fictitious generator's MVAR output which is representative of an increase in MVAR load.

The curve is then tracing what the voltage would be as the MVAR load increases.

 At some point the MVAR value of the generator will stop decreasing and the bottom of the curve will be reached.

This point represents the maximum increase in load MVAR that can occur at this bus before voltage collapse is reached.

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.

Weak busses in the system can be determined from the slope of V-Q curve.

Simulation

Simulation has been performed for IEEE25 bus system. One bus has been taken to analyse the voltage stability with two contingency conditions. Results are plotted below

Contigency-1

Tangent is appearing near 0.68 pu at -730 MVAR

Contigency-2

Tangent is appearing near 0.62 pu at -979 MVAR

Reference

T. V. Cutsem, C. Vournas, Voltage Stability of Electric Power Systems, Kluwer Academic Publishers, 1998.