Hot Topic: Power Systems Equivalents

Hot Topic: Power Systems Equivalents

Part 1: The Nature of the Problem!

Simulation of power systems using electromagnetic transients (EMT) programs provides the user with a very powerful tool to study the behavior of the system over a wide range of operating conditions and frequencies.  An EMT simulator capable of continuous real-time operation has the added benefit of allowing interconnection of physical control and protection equipment to the simulation and thereby provide the opportunity to observe the operation of the physical equipment and interaction with the system.

When faced with the task of preparing a model of the power system that will be used to test a particular device or to investigate some system behavior, the studies engineer must decide how much of the system needs to be represented in detail, how much can be represented by an equivalent and what can be ignored.  The required fidelity of the model, the nature of the study, the size of the model that can practically be represented on the available computer hardware and the availability of reliable data all contribute to the development of the model.

It is often the case that an ideal source behind an impedance (see Figure 1) is placed a few buses away from the area of interest to represent the portion of the system that is not represented in detail.  The source impedance is chosen so that it represents the short circuit impedance at that bus and the source magnitude and angle are set to match a given load flow condition.  Such an equivalent does not contemplate component dynamics, frequency dependence, zero sequence impedance or that system may not be completely radial.



Figure 1: Source Behind Impedance

Although there may be circumstances where such an equivalent is adequate, there are situations where it is not suitable and may well lead to unrealistic results.  Take, for example, the system shown in Figure 2.


Figure 2: Test System


Here two simulation cases are run, one with a detailed generator model at G4 and one where generator G4 is replaced with the simple equivalent of Figure 1.  The impedance of the equivalent is calculated by considering the series combination of the stator resistance, d-axis transient reactance and generator transformer reactance. The source voltage magnitude and angle were calculated from a solved loadflow.  As can be seen from the plots of Figure 3, initial steady-state power flows for the two cases are the same.  However, when an event causes a transmission line to be removed both the dynamics and the resultant new steady-state conditions are quite different for the two cases.  In the case with the detailed model, generator controls act to ensure that the generator power and voltage set-points are met and a new load flow is established.  With the system equivalent the source voltage and angle remain constant and the new load flow that is established results in the system equivalent at G4 absorbing real power.  Since the connection at G4 has only generation the case with the system equivalent has come to a non-realistic operating condition.

The example here is contrived and it would be unusual to replace a single generator with an equivalent.  Such non-realistic operating conditions, however, have been observed in more realistic cases where the system equivalent represents a more complex portion of the system.

A disturbance in the system of Figure 2 would result in a swing of the generator rotors relative to the system.  Typically, the generator swings damp out and new rotor angles are established.  Under severe conditions a generator swing could be such that the generator loses synchronism with the rest of the system.  An equivalent that includes an ideal source does not exhibit such power swings and thus could provide unrealistic and optimistic results.  Since the impact of the disturbance diminishes with distance and generators with large inertia more closely approximate ideal sources there are circumstances where simple system equivalents are suitable.  Determining when and where such equivalents can be used requires engineering judgement.


Figure 3a: Power Flow with Generator model at G4    Figure 3b: Power Flow with System Equivalent at G4

Stay tuned for future posts which will highlight different techniques that are available for the creation of system equivalents, where such techniques are suitable and their advantages and disadvantages. Should you have any questions, please do not hesitate to contact us at

Author: Arunprasanth Sakthivel
July, 2017