As a follow on from the basic load flow analysis, where significant unbalanced load or unbalanced transmis sion 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. Trans former 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 can be evaluated using a transient stability program but in many cases this level of analysis 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 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 nstraints of the load flow equations, inequality constraints on the control parameters, and inequality con straints of dependent variables and dependent functions. The programs to do this analysis are usually referred to as optimal power flow(OPF)programs Often optimal operation conflicts with the security requirements of the system. Load flow studies are used 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 requirement enormous Extensions to Transient Stability analysis Transient stability programs have been extended to include many other system components, including FACTS (flexible ac transmission systems)and dc converters. FACTS may be either shunt or branch 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 or a combination of both direct and quadrature voltage to help maintain voltage levels and improve stability margins Dc converters for HVdc 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 ste state for every time solution of the ac system. While this may be so some time after a fault has been remot 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 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 maxi- mum 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 is then only necessary to run the computationally inexpensive QSS model within the multi machine transient stability program c 2000 by CRC Press LLC© 2000 by CRC Press LLC As a follow on from the basic load flow analysis, where significant unbalanced load or unbalanced transmis￾sion 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. Trans￾former 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 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 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 con￾straints of dependent variables and dependent functions. The programs to do this analysis are usually referred to as optimal power flow (OPF) programs. 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 FACTS (flexible ac transmission systems) and dc converters. FACTS may be either shunt or branch 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 or a combination of both direct and quadrature voltage to help maintain voltage levels and improve stability margins. Dc converters for HVdc 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 maxi￾mum 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 is then only necessary to run the computationally inexpensive QSS model within the multi machine transient stability program