Optimized voltage and reactive power adjustment in power grids using the least-squares-method: Optimization of highly utilized power grids with stochastic renewable energy-sources

By adjusting the nodal voltage the reactive power is affected likewise and vice versa. In power system planning and power system management, power-flow-calculation is used to estimate the state of a power system. In the majority of cases only active power generation and consumption is known. To estimate the state of a power system, the voltage at the so called PV-nodes (nodes with variable reactive power injection but determined voltage) is determined with the nominal voltage. This approach is widely used but suboptimal: In highly utilized areas of the grid the determined voltage is too low, because the limitations of voltage become underruned at nodes with high consumption. In low utilized areas of the grid the determined voltage is too high, because limitations of voltage become overruned due to Ferrantis effect. This paper describes and evaluates an approach with the Gauss-Newton algorithm (least-squares-method) to minimize the deviation Δu = u_K - u_nN/√3 of every node and to minimize the deviation Δcos(φ) = cos(φ) -1 of every node with active power generation. The approach is physically based and uses the Jacobian matrices of the power-flow-calculation. Mainly in highly utilized states of the grid a minimized Δu is necessary to assure the voltage stability. The simulation results reveal a great benefit and a high potential for both optimal voltage adjustment and reactive power adjustment to minimize Δcos(φ). To integrate stochastic renewable energy sources into power grids, intelligent power system planning and power system management tools are needed to assure reliable states of operation.