Optimal power flow with stability constraints

Youssof Kheder

The optimal power flow (OPF) problem aims to control the generation and consumption of generators and loads. The main objectives are to minimise the generation cost, power losses while maintaining stability of the generators in the network. The network used for analysis and testing of OPF with stability constraints is the ‘WSCC 9 bus 3 machine’ [1] network (refer to chapter 5). MATLAB is used to develop algorithms for three alternative simulations that all encompass the same fault and clearing time in order to compare the outcomes. The first simulation includes load flow analysis followed by the stability analysis, leading to an unstable outcome to the network. This is used as the reference point. The second simulation is of the OPF analysis, followed by a stability analysis and optimisation using the Nelder-Mead algorithm [2]. The stability constraints were not yet introduced, so the outcome is also unstable. However, when compared to the load flow (LF) simulation it demonstrates improved cost effectiveness - real power losses are reduced, power demand is met and the simulation is efficient. Finally, the optimal power flow with stability constraint (OPFSC) is analysed and compared with the OPF simulation without stability constraints. This proves to be a stable network but is more time consuming. The OPFSC simulation is the final simulation with the stability constraints included and illustrates the result of a stable network for the three generators. The main determinants for analysis in the simulation are the power demand, the power losses, network costing and time efficiency. The simulation time is reduced using various techniques that allow the algorithm to continue solving the problem without compromising the final result. Time to completion was initially 9.53 seconds. Following implementation of alternative techniques, this was introduced to 2.96 seconds. This improvement in time efficiency translates to a reduction in CPU processing requirements and stability maintenance.

Optimal power flow with stability constraints

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