Abstract: A method determines a global optimal solution of a system defined by a plurality of nonlinear equations by applying a metaheuristic method to cluster a plurality of search instances into at least one group, selecting a center point and a plurality of top points from the search instances in each group and applying a local method, starting from the center point and top points for each group, to find a local optimal solution for each group in a tier-by-tier manner. Then a TRUST-TECH methodology is applied to each local optimal solution to find a set of tier-1 local optimal solutions, and the TRUST-TECH methodology is applied to each tier-1 local optimal solution to find a set of tier-2 local optimal solutions. A best solution is identified among all the local optimal solutions as the global optimal solution. The heuristic method can be a particle swarm optimization method or a genetic algorithm method.

Abstract: A dynamical method and system generate a global optimal solution to a mixed integer nonlinear programming (MINLP) problem, where a part or all of optimization variables of the MINLP problem are restricted to have discrete values. Relaxed continuous problems of the MINLP problem are generated. For each relaxed continuous problem that has an integer solution with an objective value superior to a current bound, the method updates the current bound with the objective value, computes a set of stable equilibrium points (SEPs) around the integer solution in a nonlinear dynamical system associated with the relaxed continuous problem, identifies from the SEPs a set of starting points for the MINLP problem, and computes a set of integer solutions to the MINLP problem with progressively tightened bounds from the starting points using an MINLP solver. The global optimal solution is generated based on the integer solutions.

Abstract: An optimal power flow (OPF) problem formulates constraints and operation of an electric power system. A method and system is provided for generating a secure OPF solution that solves the OPF problem. A list of contingencies is created from system data. An OPF solution is computed for the electric power system to optimize an objective function value under the constraints of the electric power system. Voltage stability analysis is performed on the electric power system that operates in states represented by the OPF solution. Then the contingencies are ranked according to load margins of the electric power system. If there is at least an insecure contingency with a non-positive load margin in the list of contingencies, a set of preventive controls are computed and applied to control components in the electric power system. The method is performed iteratively to obtain the secure OPF solution.

Abstract: A dynamical method and system generate a global optimal solution to a mixed integer nonlinear programming (MINLP) problem, where a part or all of optimization variables of the MINLP problem are restricted to have discrete values. The method computes a first integer solution to the MINLP problem with a given starting point using an MINLP solver; computes a set of stable equilibrium points (SEPs) of a nonlinear dynamical system associated with a relaxed continuous problem of the MINLP problem, where the SEPs surround the first integer solution and form one or more tiers; identifies from the SEPs a set of new starting points for the MINLP problem; computes integer solutions to the MINLP problem with progressively tightened bounds, starting from the new starting points using the MINLP solver; and generates the global optimal solution based on the integer solutions after one or more iterations.

Abstract: A dynamical method and system generate a global optimal solution to a mixed integer nonlinear programming (MINLP) problem, where a part or all of optimization variables of the MINLP problem are restricted to have discrete values. The method computes a first integer solution to the MINLP problem with a given starting point using an MINLP solver; computes a set of stable equilibrium points (SEPs) of a nonlinear dynamical system associated with a relaxed continuous problem of the MINLP problem, where the SEPs surround the first integer solution and form one or more tiers; identifies from the SEPs a set of new starting points for the MINLP problem; computes integer solutions to the MINLP problem with progressively tightened bounds, starting from the new starting points using the MINLP solver; and generates the global optimal solution based on the integer solutions after one or more iterations.

Abstract: A method determines a global optimum of a system defined by a plurality of nonlinear equations. The method includes applying a heuristic methodology to cluster a plurality of particles into at least one group for the plurality of nonlinear equations. The method also includes selecting a center point and a plurality of top points from the particles in each group and applying a local method starting from the center point and top points for each group to find a local optimum for each group in a tier-by-tier manner. The method further includes applying a TRUST-TECH methodology to each local optimum to find a set of tier-1 optima and identifying a best solution among the local optima and the tier-1 optima as the global optimum. In some embodiments, the heuristic methodology is a particle swarm optimization methodology.

Abstract: A method predicts power flow in a distributed generation network of at least one distributed generator and at least one co-generator, where the network is defined by a plurality of network nonlinear equations. The method includes applying an iterative method to the plurality of network nonlinear equations to achieve a divergence from a power flow solution to the plurality of network nonlinear equations. The method also includes applying the iterative method to find a first solution to a plurality of simplified nonlinear equations homotopically related by parameterized power flow equations to the plurality of network nonlinear equations. The method further includes iteratively applying the iterative method to the parameterized power flow equations starting with the first solution to achieve the power flow solution to the plurality of network nonlinear equations.

Abstract: A method of placing PMUs for distribution networks having a plurality of nodes, the network comprising: a feeder line attached to a source at a source node and at least one node with a lateral branching from the node on the feeder line, the method comprising the steps of: placing a VPMU and CPMU directly after the source node; locating a next node downstream along the feeder line; and for the located next node, determining a type of node located, a type of line between the source node and the located next node and whether the located next node is an end node of the feeder line; wherein if the located next node is branching node, placing a CPMU on all laterals between the branching node and an end of the lateral; determining if any of the located next nodes are attached to a dispersed generator and placing a CPMU.

Abstract: In the present invention, in a case where a stable equilibrium point calculation is not calculable by using a Newton method, a damping factor of a mechanical system differential equation of a generator is set to be greater than an actual value of the generator of the power system. By applying pseudo-transient simulation to the nonlinear differential algebraic equation of the power system including the mechanical system differential equation of the generator, in which the damping factor is set, a norm of a mechanical system equation is found. If the found norm meets a predetermined condition, variable values of the power system at a time when the norm is found are set as initial values of the nonlinear differential algebraic equation of the power system. A stable equilibrium point is determined by applying the Newton method to the nonlinear differential algebraic equation in which the initial values are set.

Abstract: In the present invention, in a case where a stable equilibrium point calculation is not calculable by using a Newton method, a damping factor of a mechanical system differential equation of a generator is set to be greater than an actual value of the generator of the power system. By applying pseudo-transient simulation to the nonlinear differential algebraic equation of the power system including the mechanical system differential equation of the generator, in which the damping factor is set, a norm of a mechanical system equation is found. If the found norm meets a predetermined condition, variable values of the power system at a time when the norm is found are set as initial values of the nonlinear differential algebraic equation of the power system. A stable equilibrium point is determined by applying the Newton method to the nonlinear differential algebraic equation in which the initial values are set.

Abstract: This invention relates to a method of determining stability of unstable equilibrium point (UEP) computed by using BCU method, comprising selecting UEP computed by using BCU method, obtaining a test vector Xtest for the selected UEP, say XUEP using the following equation: Xtest=Xspost+0.99(XUEP?Xspost) where Xspost is the SEP, and checking boundary condition of XUEP by simulating system trajectory of post-fault original system starting from Xtest.

Abstract: This invention relates to a method of determining stability of unstable equilibrium point (UEP) computed by using BCU method, comprising selecting UEP computed by using BCU method, obtaining a test vector Xtest for the selected UEP, say XUEP using the following equation: Xtest=Xspost+0.99(XUEP?Xspost) where Xspost is the SEP, and checking boundary condition of XUEP by simulating system trajectory of post-fault original system starting from Xtest.

Abstract: This invention relates to a method of determining stability of unstable equilibrium point (UEP) computed by using BCU method, comprising selecting UEP computed by using BCU method, obtaining a test vector Xtest for the selected UEP, say XUEP using the following equation: Xtest=Xspost+0.99(XUEP?Xspost) where Xspost is the SEP, and checking boundary condition of XUEP by simulating system trajectory of post-fault original system starting from Xtest.

Abstract: A method for obtaining a global optimal solution of general nonlinear programming problems includes the steps of first finding, in a deterministic manner, all stable equilibrium points of a nonlinear dynamical system that satisfies conditions (C1) and (C2), and then finding from said points a global optimal solution. A practical numerical method for reliably computing a dynamical decomposition point for large-scale systems comprises the steps of moving along a search path ?t(xs)?{xs+ t×?, t?+} starting from xs and detecting an exit point, xex, at which the search path ?t(xs) exits a stability boundary of a stable equilibrium point xs using the exit point xex as an initial condition and integrating a nonlinear system to an equilibrium point xd, and computing said dynamical decomposition point with respect to a local optimal solution xs wherein the search path is xd.

Abstract: This invention relates to a method of determining stability of unstable equilibrium point (UEP) computed by using BCU method, comprising selecting UEP computed by using BCU method, obtaining a test vector Xtest for the selected UEP, say XUEP using the following equation: Xtest=Xspost+0.99(XUEP?Xspost) where Xspost is the SEP, and checking boundary condition of XUEP by simulating system trajectory of post-fault original system starting from Xtest.

Abstract: Dynamical methods for obtaining the global optimal solution of general optimization problems having closed form or black box objective functions, including the steps of first finding, in a deterministic manner, one local optimal solution starting from an initial point, and then finding another local optimal solution starting from the previously found one until all the local optimal solutions starting from any initial point are found, and then finding from said points the global optimal solution.

Abstract: A system for on-line dynamic screening of contingencies comprising postulated disturbances which an electric power system may experience, the system comprising a dynamic contingency screening program for evaluating a plurality of contingencies with a plurality of contingency classifiers based on the method of finding the controlling unstable equilibrium point of the power system known as the boundary of stability region based controlling unstable equilibrium point method by sequentially applying the contingencies to a network islanding problem classifier, S.E.

Abstract: Dynamical methods for obtaining the global optimal solution of general optimization problems having closed form or black box objective functions, including the steps of first finding, in a deterministic manner, one local optimal solution starting from an initial point, and then finding another local optimal solution starting from the previously found one until all the local optimal solutions starting from any initial point are found, and then finding from said points the global optimal solution.

Abstract: A system for on-line dynamic screening of contingencies comprising postulated disturbances which an electric power system may experience, the system comprising a dynamic contingency screening program for evaluating a plurality of contingencies with a plurality of contingency classifiers based on the method of finding the controlling unstable equilibrium point of the power system known as the boundary of stability region based controlling unstable equilibrium point method by sequentially applying the contingencies to a network islanding problem classifier, S.E.

Abstract: A method for obtaining a global optimal solution of general nonlinear programming problems includes the steps of first finding, in a deterministic manner, all stable equilibrium points of a nonlinear dynamical system that satisfies conditions (C1) and (C2), and then finding from said points a global optimal solution. A practical numerical method for reliably computing a dynamical decomposition point for large-scale systems comprises the steps of moving along a search path &phgr;t(xs)≡{xs+t×ŝ, t&egr;+} starting from xs and detecting an exit point, xex, at which the search path &phgr;t(xs) exits a stability boundary of a stable equilibrium point xs using the exit point Xex as an initial condition and integrating a nonlinear system to an equilibrium point Xd, and computing said dynamical decomposition point with respect to a local optimal solution xs wherein the search direction ŝ is e xd.