In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are addressed.First,an iterative sums of squares(SOS)programming approach ...In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are addressed.First,an iterative sums of squares(SOS)programming approach is developed for reachable set estimation.It characterizes the over-approximations of the forward reachable sets by sub-level sets of time-varying Lyapunovlike functions that satisfy an invariance condition,and formulates the problem of searching for the Lyapunov-like functions as a bilinear SOS program,which can be solved via an iterative algorithm.To make the over-approximation tight,the proposed approach seeks to minimize the volume of the overapproximation set with a desired shape.Then,the reachable set estimation approach is extended for safety verification,via explicitly encoding the safety constraint such that the Lyapunov-like functions guarantee both reaching and avoidance.The efficiency of the presented method is illustrated by some numerical examples.展开更多
In DC power systems dominated by power electronic devices,constant power loads(CPLs)and saturation components significantly impact large-signal stability.During the large-signal stability analysis process,the presence...In DC power systems dominated by power electronic devices,constant power loads(CPLs)and saturation components significantly impact large-signal stability.During the large-signal stability analysis process,the presence of multiple state variables and high-order system poses substantial challenges.To address this,considering the complete control dynamics,this paper proposes an equivalent single-machine(ESM)model of the droop-based DC power systems to reduce the complexity of the large-signal analysis.Building on the proposed ESM model,considering the dynamics of CPL and saturation constraints,a region of attraction(ROA)estimation algorithm based on sum of squares(SOS)programming is proposed,which significantly reduces the conservativeness compared with other existing methods.Furthermore,a control parameter optimization algorithm based on SOS programming is proposed with the aim of expanding the ROA.Furthermgre,with the aim of expanding the ROA,controller sythesis is conducted with proposed control parameter optimization algorithm based on SOS programming.Ultimately,simulation experiments validate the accuracy of the proposed ESM model and the proposed ROA estimation algorithm,as well as the effectiveness of the control parameter optimization algorithm.展开更多
This paper presents an Expanding Annular Domain(EAD)algorithm combined with Sum of Squares(SOS)programming to estimate and maximize the domain of attraction(DA)of power systems.The proposed algorithm can systematicall...This paper presents an Expanding Annular Domain(EAD)algorithm combined with Sum of Squares(SOS)programming to estimate and maximize the domain of attraction(DA)of power systems.The proposed algorithm can systematically construct polynomial Lyapunov functions for power systems with transfer conductance and reliably determine a less conservative approximated DA,which are quite difficult to achieve with traditional methods.With linear SOS programming,we begin from an initial estimated DA,then enlarge it by iteratively determining a series of so-called annular domains of attraction,each of which is characterized by level sets of two successively obtained Lyapunov functions.Moreover,the EAD algorithm is theoretically analyzed in detail and its validity and convergence are shown under certain conditions.In the end,our method is tested on two classical power system cases and is demonstrated to be superior to existing methods in terms of computational speed and conservativeness of results.展开更多
Transient voltage stability analysis(TVSA)of power systems is one of the most computationally challenging tasks in dynamic security assessment.To reduce the complexity of TVSA,this paper proposes an improved expanding...Transient voltage stability analysis(TVSA)of power systems is one of the most computationally challenging tasks in dynamic security assessment.To reduce the complexity of TVSA,this paper proposes an improved expanding annular domain(improved EAD)algorithm to estimate the domain of attraction(DA)of power systems containing multiple induction motors(IMs),whose improvements are concerned with relaxing the restriction on critical value and simplifying iteration steps.The proposed algorithm can systematically construct Lyapunov function for lossy power systems with IMs and their slip constraints.First,the extended Lyapunov stability theory and sum of squares(SOS)programming are presented,which are powerful tools to construct Lyapunov function.Second,the internal node model of IM is developed by an analogy with that of a synchronous generator,and a multi-machine power system model by eliminating algebraic variables is derived.Then,an improved EAD algorithm with SOS programming is proposed to estimate the DA for a power system considering the slip constraint of IM.Finally,the superiority of our method is demonstrated on two modified IEEE test cases.Simulation results show that the proposed algorithm can provide a better estimated DA and critical clearing slip for power systems with multiple IMs.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos.12171159 and 61772203in part by the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY20F020020。
文摘In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are addressed.First,an iterative sums of squares(SOS)programming approach is developed for reachable set estimation.It characterizes the over-approximations of the forward reachable sets by sub-level sets of time-varying Lyapunovlike functions that satisfy an invariance condition,and formulates the problem of searching for the Lyapunov-like functions as a bilinear SOS program,which can be solved via an iterative algorithm.To make the over-approximation tight,the proposed approach seeks to minimize the volume of the overapproximation set with a desired shape.Then,the reachable set estimation approach is extended for safety verification,via explicitly encoding the safety constraint such that the Lyapunov-like functions guarantee both reaching and avoidance.The efficiency of the presented method is illustrated by some numerical examples.
基金supported by National Natural Science Foundation of China(No.52077194).
文摘In DC power systems dominated by power electronic devices,constant power loads(CPLs)and saturation components significantly impact large-signal stability.During the large-signal stability analysis process,the presence of multiple state variables and high-order system poses substantial challenges.To address this,considering the complete control dynamics,this paper proposes an equivalent single-machine(ESM)model of the droop-based DC power systems to reduce the complexity of the large-signal analysis.Building on the proposed ESM model,considering the dynamics of CPL and saturation constraints,a region of attraction(ROA)estimation algorithm based on sum of squares(SOS)programming is proposed,which significantly reduces the conservativeness compared with other existing methods.Furthermore,a control parameter optimization algorithm based on SOS programming is proposed with the aim of expanding the ROA.Furthermgre,with the aim of expanding the ROA,controller sythesis is conducted with proposed control parameter optimization algorithm based on SOS programming.Ultimately,simulation experiments validate the accuracy of the proposed ESM model and the proposed ROA estimation algorithm,as well as the effectiveness of the control parameter optimization algorithm.
基金supported in part by the State Key Program of National Natural Science Foundation of China under Grant No.U1866210Young Elite Scientists Sponsorship Program by CSEE under Grant No.CSEE-YESS-2018007.
文摘This paper presents an Expanding Annular Domain(EAD)algorithm combined with Sum of Squares(SOS)programming to estimate and maximize the domain of attraction(DA)of power systems.The proposed algorithm can systematically construct polynomial Lyapunov functions for power systems with transfer conductance and reliably determine a less conservative approximated DA,which are quite difficult to achieve with traditional methods.With linear SOS programming,we begin from an initial estimated DA,then enlarge it by iteratively determining a series of so-called annular domains of attraction,each of which is characterized by level sets of two successively obtained Lyapunov functions.Moreover,the EAD algorithm is theoretically analyzed in detail and its validity and convergence are shown under certain conditions.In the end,our method is tested on two classical power system cases and is demonstrated to be superior to existing methods in terms of computational speed and conservativeness of results.
基金supported by the Department of Science,and Technology of Guangdong Province under Grant No.2023 A1515240019。
文摘Transient voltage stability analysis(TVSA)of power systems is one of the most computationally challenging tasks in dynamic security assessment.To reduce the complexity of TVSA,this paper proposes an improved expanding annular domain(improved EAD)algorithm to estimate the domain of attraction(DA)of power systems containing multiple induction motors(IMs),whose improvements are concerned with relaxing the restriction on critical value and simplifying iteration steps.The proposed algorithm can systematically construct Lyapunov function for lossy power systems with IMs and their slip constraints.First,the extended Lyapunov stability theory and sum of squares(SOS)programming are presented,which are powerful tools to construct Lyapunov function.Second,the internal node model of IM is developed by an analogy with that of a synchronous generator,and a multi-machine power system model by eliminating algebraic variables is derived.Then,an improved EAD algorithm with SOS programming is proposed to estimate the DA for a power system considering the slip constraint of IM.Finally,the superiority of our method is demonstrated on two modified IEEE test cases.Simulation results show that the proposed algorithm can provide a better estimated DA and critical clearing slip for power systems with multiple IMs.
