Diakoptic assessment of power system voltage variations and applications in weak grids introduced by wind energy : the Nigerian power system in perspective

The electrical power system is a large interconnected system made up of electrical components to generate, transport and utilize electrical power. The size and complexity of the power system have increased significantly in recent years due to the introduction of wind energy and other renewable energy sources. Hence there is an urgent need to search for new or improved analytical tools for the system performance evaluation and assessment. Load flow analysis is the most important method of assessing the steady-state behaviour of all the components of the power network. The common approach in load flow analysis is to study the network as one-piece and this can take a long time for a very large system. An alternative solution is to reduce the size of the network by tearing apart a large system into small subnetworks, thus a cluster of computers can be supplemented to speed-up the process. Then the system can be solved as separate entities after which their solutions are connected together by mathematical modelling in order to obtain the solution of the original system as if it was solved as one-piece. This method in its original conception is known as diakoptics which, though was conceived for power systems analysis, is now widely viewed as a mathematical method rather than a power systems analysis tool. The work presented in this thesis proposes two novel diakoptic tools for the power system analysis; i.e. the branch voltage multiplier technique (BVMT) and slack bus voltage updating diakoptics (SVUD). Various research works so far have shown that the key factor is in the process of obtaining the fundamental equations of diakoptics and the final equation of solution. The BVMT is a variant of the original diakoptic algorithm mainly by the process of obtaining the diakoptic equations of solution which can reduce the number of solution steps and simplify the method considerably. The resultant algorithm is easier to apply and also more effective in load flow analysis by current injection methods where the relationship is linear. The common practice in present load flow analyses is by power injection which yields nonlinear equations. The BVMT technique has been extended by applying various transformations which make it suitable for nonlinear solutions. This yields the SVUD load flow method that incorporates the classical Gauss-Seidel method. The analysis tools produced have been validated by applying to sample systems including IEEE benchmark systems. In one-piece load flow analysis, the usual practice is to choose one slack bus whose voltage remains unchanged throughout the iterative process. In diakoptic analysis, the systems to be analysed are more than one after tearing, so the subnetworks without the original slack bus will require temporary slack buses during the load flow analysis. During iteration, the voltages of these temporary slack buses would also remain unchanged; the SVUD method ensures that their voltages vary to reflect the state they would have been in one-piece solutions. This is achieved by updating the voltages during iteration using given and computed parameters which, in this case, are the complex powers. This has resulted in the improvement of the convergence characteristics of the traditional Gauss-Seidel method. For example, in the analysis of the IEEE 30-bus network, the number of iterations in one-piece Gauss-Seidel solution was 202 while with the SVUD, the numbers of iterations were 17 when cut into two subnetworks, and 13 when cut into three subnetworks. The SVUD also removes some common problems associated with temporary slack buses. This is demonstrated in the analysis of the 14-bus system using the one-piece Gauss-Seidel, SVUD and diakoptics with the temporary slack bus voltage remaining unchanged during iteration. The one-piece method converged after 106 iterations and the SVUD converged after 5 iterations. The diakoptic analysis with constant temporary slack-bus voltage converged after 146 iterations and erroneous results were obtained. The SVUD analysis of the Nigeria 330kV power transmission network without wind power electricity shows a voltage profile with some violations at a number of buses. The analysis with wind power electricity shows voltage rises, especially at buses close to the point of common coupling. This is a generally accepted effect of electricity from wind on an existing power system. In the Nigeria case, the conventional generation capacity is far below what is required and so the voltage profile is seen to improve because the wind farm constitutes an extra generating capacity. For example, at rated wind power, the voltage magnitudes show rises of 0.12% at bus 31 and 0.15% at bus 32. Increase of wind power to 4.1018 pu shows rises of 3.9% at bus 31 and 4.5% at bus 32.