Power system analysis software: Load flow

One of the earliest programs to be developed for power system analysis was the load flow (power flow) program. It was originally developed in the late 1950s. All complete packages in use today have load flow programs as an integral part, as this is one of the cornerstones of any electrical network analysis.

Although an electrical network is linear, load flow analysis is iterative due to the interactive influences of voltages, currents, frequency and reactance on one another. The generators are scheduled to deliver a specific active power to the system and usually the voltage magnitude of the generator terminals is fixed by automatic voltage regulation. Usually, one generator busbar only has its voltage magnitude specified, as losses in the system cannot be determined before the load flow solution. This bus also has its voltage angle defined to some arbitrary value, usually zero, which is only a reference point for the rest of the network. This busbar is known as the slack bus, or utility bus in some programs. The slack bus is a mathematical requirement for the program and has no exact equivalent in reality.

The total load plus the losses are not known in operating practice, and they fluctuate continuously. When a system is not in power balance, i.e., when the input power does not equal the load power plus losses, the imbalance modifies the rotational energy stored in the system. The system frequency thus rises if the input power is too large and falls if the input power is too little. Usually a generating station with one machine is given the task of keeping the frequency constant by varying the input power. The algorithms originally developed had the advantages of simple programming and minimum storage but were slow to converge requiring many iterations. The introduction of ordered elimination of the network matrix, and programming techniques that reduce storage requirements, allowed much better algorithms to be used. The Newton-Raphson method gave convergence to the solution in only a few iterations. Using Newtonian methods of specifying the problem, a Jacobian matrix containing the partial derivatives of the system at each node can be constructed. The solution by this method has quadratic convergence. This method was followed quite quickly by the fast decoupled Newton-Raphson method. This exploited the fact that under normal operating conditions, and providing that the network is predominately reactive, the voltage angles are not affected by reactive power flow and voltage magnitudes are not effected by real power flow. The fast decoupled method requires more iterations to converge but each iteration uses less computational effort than the Newton-Raphson method. The results of a load flow study can be seen as a snapshot of the system once steady-state conditions have been reached with all loads staying at constant values. The study calculates the voltage on each bus, the voltage drop on each feeder, the current, power flow and losses in all branches, as well as total system losses. Branch loads can include load diversity considerations.