Optimal Coordination Of PSS And POD By Sequential Quadratic Programming With Adaptive Gradient Sampling

The increasing penetration of renewable energies deteriorates the smallsignal stability of power systems,causing the severe challenge of low-frequency oscillations.In this circumstance,how to improve the system damping is an immediate problem.Optimizing and coordinating the parameters of the damping controller is an essential means to enhance the small-signal stability of systems.However,the coordination problem involving eigenvalue optimization is a nonsmooth optimization problem.Solving a non-smooth optimization problem was a difficult problem in mathematics.Though many researchers have been trying to solve the non-smooth problem with heuristic algorithms or mathematical programming methods,these algorithms fail to guarantee the optimality and convergence at the same time.To tackle the problem,we propose a Sequential Quadratic Programming(SQP)with the Adaptive Gradient Sampling(AGS)method to solve the parameters coordination problem of power system stabilizer(PSS)and power oscillation damper(POD)equipping in a doubly-fed induction generator or a static synchronous compensator.The main contributions of this paper are listed below.1.We propose an optimization model for coordinating the parameters of PSS and POD.The model ensures the system small-signal stability and the robustness of the parameters by minimizing the spectral abscissa and considering multiple operating conditions.Even in the worst condition,the optimized parameters can still ensure system stability.Compared with the traditional tuning method,the proposed coordination method with the proposed model has a prominent ability to enhance system damping,and the optimized parameters of the model are more robust.2.We propose a Sequential Quadratic Programming with Adaptive Gradient Sampling method to tackle the non-smooth problem of spectral abscissa function.The method breaks through the bottleneck that existing heuristic algorithms and mathematical programming methods can not guarantee the optimality and convergence when dealing with non-smooth problems,solving the proposed coordinating optimization model successfully without suffering any convergence problem.3.We improve gradient sampling by employing the adaptive gradient sampling procedure.As a result,the SQP-AGS method can utilize historical sampling data efficiently during gradient sampling.The computational time of the method is much saved,and computational efficiency is highly improved.4.Since the key part of the proposed method is the gradient evaluation of non-smooth function,we employ closed-form sensitivity as the gradient further to improve computational efficiency.The closed-form eigenvalue sensitivity derived from the matrix calculus has strict mathematical significance and high computational efficiency,reducing the computational time of the proposed method efficiently when solving the optimal coordination problem.