This paper proposes a novel generalized linear Hopfield neural network-based power flow analysis technique using Moore–Penrose Inverse (MPI) to solve the nonlinear power flow equations (PFEs). The Hopfield neural network (HNN) with linear activation function augmented by a feed forward layer is used to compute the MPI. In this work, the inverse of Jacobian matrix in solving the PFEs is determined by including feed forward network along with feedback network. The developed power flow technique is coded in MATLAB, and its effectiveness is tested on well-conditioned IEEE bus systems (9-bus, 14-bus, 30-bus, and 118-bus), naturally ill-conditioned systems (11-bus and 13-bus), and real-time Malaysian 87-bus system. The results of voltage magnitude and phase angle obtained are compared with standard Newton–Raphson method in case of well-conditioned system. Further, the sensitivity analysis of this approach is carried out against change in initial conditions, line outage, and increase in power generation to validate its robustness. The computational cost of convergence time is compared with well-known power flow techniques of Modified HNN, fourth-order Runge–Kutta (RK4), Iwamoto, and Euler method. The convergence of solution obtained from proposed technique is ensured by Lyapunov notion of stability.

本文提出了一种新的基于广义线性Hopfield神经网络的潮流分析技术，该模型使用Moore-Penrose逆（MPI）求解非线性潮流方程（PFE）。具有前馈层增强的线性激活功能的Hopfield神经网络（HNN）用于计算MPI。在这项工作中，通过包括前馈网络和反馈网络来确定求解PFE的雅可比矩阵的逆。先进的潮流技术在MATLAB中进行了编码，并在条件良好的IEEE总线系统（9总线，14总线，30总线和118总线），自然不适的系统（11总线）上对其有效性进行了测试。和13辆巴士），以及实时的马来西亚87辆巴士系统。如果系统条件良好，则将所得电压幅度和相角的结果与标准牛顿-拉夫森法进行比较。此外，针对初始条件的变化，线路中断和发电量的增加对这种方法进行了敏感性分析，以验证其耐用性。将收敛时间的计算成本与改进的HNN，四阶Runge-Kutta（RK4），Iwamoto和Euler方法的知名潮流技术进行了比较。Lyapunov稳定性概念确保了从提出的技术获得的解决方案的收敛性。将收敛时间的计算成本与改进的HNN，四阶Runge-Kutta（RK4），Iwamoto和Euler方法的知名潮流技术进行了比较。Lyapunov稳定性概念确保了从提出的技术获得的解决方案的收敛性。将收敛时间的计算成本与改进的HNN，四阶Runge-Kutta（RK4），Iwamoto和Euler方法的知名潮流技术进行了比较。Lyapunov稳定性概念确保了从提出的技术获得的解决方案的收敛性。