Real‐time calculation of power system bus voltage using a hybrid approach combining the Newton–Raphson method and dynamic programming

Abstract

The calculation of the magnitudes and phase angles of the bus voltage is a challenging task in real-time applications for power systems. Voltage profile, which denotes the present conditions of a power system, is determined by executing the traditional AC power flow program or by searching the supervisory control and data acquisition system. The AC power flow program is not suitable for several real-time applications, such as contingency analysis and security control calculations, because of its complexity and convergence problems. Fast computation is the major concern in such applications. In this paper, a new method based on sensitivity factors, referred to as Jacobian-based distribution factors (JBDFs), is proposed for calculating the magnitudes and phase angles of bus voltages. This method requires setting up JBDFs and deriving optimal solution paths of bus voltage for non-swing buses through dynamic programming under base-case loading conditions. Under real-time conditions, the proposed method initially calculates real and reactive power line flows via JBDFs, and then computes the voltage magnitudes and phase angles of non-swing buses through the derived optimal solution paths. The excellence of the proposed hybrid calculation method is verified by IEEE test systems. Simulation results demonstrate that the proposed method exhibits fast computation and high accuracy. Thus, the method is suitable for real-time applications.flow, security control [14], and line flow computation after a fault occurs.In [15], a Jacobian-based distribution factor (JBDF) is proposed for overcoming the shortcomings of GSDF, GGDF, and ZBD. The correlative partial differential terms of JBDF are derived according to base-case power flow solutions and the inverse Jacobian matrix. Then, the active and reactive power JBDF terms are established [15]. This approach reflects changes in the complex injection power. Changes in load conditions from base-case loads, with either conforming or nonconforming changes in complex power in each bus, can be used to compute active and reactive power flows without iterations, rapidly. The use of JBDF for solving line flow after a change in load demand is fine except for solving the magnitude and phase angle of bus voltage. In this paper, both line flow and the bus voltage can be solved by the proposed hybrid approach based on sensitivity factors. Consequently, the Newton-Raphson method is employed as the base-case solution framework. The essential difference is that the proposed approach computes solutions of the bus voltage equations via JBDF bus voltage formulas instead of iterative nonlinear equations. Figure 1 shows the schematic diagram of the proposed approach and its real-time applications for modern power systems. This approach can simplify the solution procedure. With this simplification, a reduction in the overall execution time is expected. Thus, the proposed approach, which combines the Newton-Raphson method and dynamic programming, is a fast and effective soft calculation method for real-time...