Power system analysis software: Other uses for load flow analysis; Extensions to transient stability analysis; Voltage collapse

Other uses for load flow analysis

It has already been demonstrated that load flow analysis is necessary in determining the economic operation of the power system and it can also be used in the production of capability charts. Many other types of analyses require load flow to be embedded in the program, e.g.:

• Unbalanced three-phase analysis: As a follow-on from the basic load flow analysis, where significant unbalanced load or unbalanced transmission causes problems, a three-phase load flow may be required to study their effects. These programs require each phase to be represented separately and mutual coupling between phases to be taken into account. Transformer winding connections must be correctly represented and the mutual coupling between transmission lines on the same tower or on the same right-of-way must also be included.

• Motor starting studies: Motor starting can be evaluated using a transient stability program but in many cases this level of analysis is unnecessary. The voltage dip associated with motor start-up can be determined very precisely by a conventional load flow program with a motor starting module.

• Optimal power flow: Optimal power system operation requires the best use of resources subject to a number of constraints over any specified time period.

The problem consists of minimizing a scalar objective function (normally a cost criterion) through the optimal control of a vector of control parameters.

This is subject to the equality constraints of the load flow equations, inequality constraints on the control parameters, and inequality constraints of dependent variables and dependent functions. The programs to do this analysis are usually referred to as optimal power flow (OPF) programs.

• Security assessment: Often optimal operation conflicts with the security requirements of the system. Load flow studies are used to assess security (security assessment). This can be viewed as two separate functions. First, there is a need to detect any operating limit violations through continuous monitoring of the branch flows and nodal voltages. Second, there is a need to determine the effects of branch outages (contingency analysis). To reduce this to a manageable level, the list of contingencies is reduced by judicial elimination of most of the cases that are not expected to cause violations. From this the possible overloading of equipment can be forecast. The program should be designed to accommodate the condition where generation cannot meet the load because of network islanding.

The conflicting requirements of system optimization and security require that they be considered together. The more recent versions of OPF interface with contingency analysis and the computational requirements are enormous.

Extensions to transient stability analysis

Transient stability programs have been extended to include many other system components, including flexible AC transmission systems (FACTS) and DC converters.

Flexible AC transmission systems may be either shunt or series devices. Shunt devices usually attempt to control busbar voltage by varying their shunt susceptance. The device is therefore relatively simple to implement in a time domain program. Series devices may be associated with transformers. Stability improvement is achieved by injecting a quadrature component of voltage derived from the other two phases rather than by a tap changer, which injects a direct component of voltage. Fast acting power electronics can inject either direct voltage or a combination of both direct and quadrature voltage to help maintain voltage levels and improve stability margins.

DC converters for HV DC links and rectifier loads have received much attention. The converter controls are very fast acting and therefore a quasi steady-state (QSS) model can be considered accurate. That is, the model of the converter terminals contains no dynamic equations and in effect the link behaves as if it was in steady state for every time solution of the AC system. While this may be so some time after a fault has been removed, during and just after a fault the converters may well suffer from commutation failure or fire through. These events cannot be predicted or modeled with a QSS model. In this case, an appropriate method of analysis is to combine a state variable model of the converter, which can model the firing of the individual valves, with a conventional multi-machine transient stability program containing a QSS model. During the period of maximum disturbance, the two models can operate together. Information about the overall system response is passed to the state variable model at regular intervals. Similarly, the results from the detailed converter model are passed to the multi-machine model overriding its own QSS model. As the disturbance reduces, the results from the two different converter models converge and it’s then only necessary to run the computationally inexpensive QSS model within the multi-machine transient stability program.

Voltage collapse

Steady-state analyses of the problem of voltage instability and voltage collapse are often based on load flow analysis programs. However, time solutions can provide further insight into the problem.

A transient stability program can be extended to include induction machines, which are associated with many of the voltage collapse problems. In these studies, it’s the stability of the motors that are examined rather than the stability of the synchronous machines.

The asynchronous nature of the induction machine means that rotor angle is not a concern, but instead the capability of the machines to recover after a fault has depressed the voltage and allowed the machines to slow down. The re-accelerating machines draw more reactive current, which can hold the terminal voltage down below that necessary to allow recovery. Similarly starting a machine will depress the voltage, which affects other induction machines, which further lowers the voltage.

However, voltage collapse can also be due to longer-term problems. Transient stability programs then need to take into account controls that are usually ignored. These include automatic transformer tap adjustment and generator excitation limiters, which control the long-term reactive power output to keep the field currents within their rated values.