# Load Flows

## Introduction

A load flow (sometimes known as a power flow) is power system jargon for the steady-state solution of an electrical power network. It does not essentially differ from the solution of any other type of network except that certain constraints are peculiar to power systems and, in particular, the formulation is non-linear leading to the need for an iterative solution.

In previous chapters the manner in which the various components of a power system may be represented by equivalent circuits has been demonstrated. It should be stressed that the simplest representation of items of plant should always be used, consistent with the accuracy of the information available. There is no merit in using very complicated machine and line models when the load and other data are known only to a limited accuracy, for example, the long-line representation should only be used where absolutely necessary. Similarly, synchronous- machine models of more sophistication than those given in this text are needed only for very specialized purposes, for example in some stability studies. Usually, the size and complexity of the network itself provides more than sufficient intellectual stimulus without undue refinement of the components. Often, in high voltage networks, resistance may be neglected with little loss of accuracy and an immense saving in computation.

Load flow studies are performed to investigate the following features of a power system network:

- 1. Flow of MW and MVAr in the branches of the network.
- 2. Busbar (node) voltages.
- 3. Effect of rearranging circuits and incorporating new circuits on system loading.
- 4. Effect of temporary loss of generation and transmission circuits on system loading (mainly for security studies).
- 5. Effect of injecting in-phase and quadrature boost voltages on system loading.

*Electric Power Systems,* Fifth Edition. B.M. Weedy, B.J. Cory, N. Jenkins, J.B. Ekanayake and G. Strbac. © 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.

- 6. Optimum system running conditions and load distribution.
- 7. Minimizing system losses.
- 8. Optimum rating and tap-range of transformers.
- 9. Improvements from change of conductor size and system voltage.

Planning studies will normally be performed for minimum-load conditions (examining the possibility of high voltages) and maximum-load conditions (investigating the possibility of low voltages and instability). Having ascertained that a network behaves reasonably under these conditions, further load flows will be performed to optimize voltages, reactive power flows and real power losses.

The design and operation of a power network to obtain optimum economy is of paramount importance and the furtherance of this ideal is achieved by the use of centralized automatic control of generating stations through system control centres. These control systems often undertake repeated load flow calculations in close to real time.

Although the same approach can be used to solve all load flow problems, for example the nodal voltage method, the object should be to use the quickest and most efficient method for the particular type of problem. Radial networks will require less sophisticated methods than closed loops. In very large networks the problem of organizing the data is almost as important as the method of solution, and the calculation must be carried out on a systematic basis and here the nodal- voltage method is often the most convenient. Methods such as network reduction combined with the Thevenin or superposition theorems are at their best with smaller networks. In the nodal method, great numerical accuracy is required in the computation as the currents in the branches are derived from the voltage differences between the ends. These differences are small in well designed networks so the method is ideally suited for computation using digital computers and the per unit system.