Abstract: A computer system provides online state estimation (SE) and topology identification (TI) using advanced metering infrastructure (AMI) measurements in a distribution network. The computer system obtains input data including the AMI measurements, a network configuration, and line parameters; solves an SE and TI problem formulated from the input data and power equations of the distribution network; and periodically updates states and topology of the distribution network during power system operation. To solve the SE and TI problem, the computer system constructs a mixed-integer convex approximation programming (MICP) model to obtain an initial topology; generates neighboring spanning trees according to the MICP model and the initial topology; evaluates performance of each neighboring spanning tree with a matching index that is an indication of power flow performance; and chooses a tree topology of a neighboring spanning tree having a minimum matching index as a final network topology of the distribution network.

Abstract: A computer system provides online state estimation (SE) and topology identification (TI) using advanced metering infrastructure (AMI) measurements in a distribution network. The computer system obtains input data including the AMI measurements, a network configuration, and line parameters; solves an SE and TI problem formulated from the input data and power equations of the distribution network; and periodically updates states and topology of the distribution network during power system operation. To solve the SE and TI problem, the computer system constructs a mixed-integer convex approximation programming (MICP) model to obtain an initial topology; generates neighboring spanning trees according to the MICP model and the initial topology; evaluates performance of each neighboring spanning tree with a matching index that is an indication of power flow performance; and chooses a tree topology of a neighboring spanning tree having a minimum matching index as a final network topology of the distribution network.

Abstract: An online static security assessment (SSA) method based on a quasi steady-state (QSS) model is applied to a power system. An input to the method includes a post-contingency state of the power system for each of a set of contingencies. The following operations are performed for each contingency. Using the QSS model of the post contingency state of the power system, a steady-state voltage magnitude is calculated for each bus in the power system by solving a system of equations. The system of equations is formulated according to a time-domain stability model of the power system and includes nonlinear differential algebraic equations (DAE) with continuous and discreet variables. The derivative terms of short-term state variables in the DAE are set to zero. The method compares the calculated voltage magnitude with a limit, classifies each contingency as secure, critical or insecure, and determines a control action in response to the classification.

Abstract: A method for state estimation of a distribution network comprises: (a) obtaining measurements from phasor measurement units (PMUs) placed at buses in the distribution network; (b) constructing a quotient gradient system (QGS) based on a constraint set H that relates the measurements to state variables of the distribution network; (c) integrating the QGS to reach a steady state; (d) identifying one or more of the state variables whose measurement residuals violate a measurement residual constraint in the constraint set H; (e) integrating a reconstructed QGS, which is reconstructed based on the constraint set H by setting the identified one or more state variables to values of corresponding PMU measurements; (f) iterating steps of (d) and (e) until no measurement residuals violate the measurement residual constraint, to thereby obtain the state estimation; and (g) reporting the state estimation to a control system during real-time monitoring of the distribution network.

Abstract: A method for state estimation of a distribution network comprises: (a) obtaining measurements from phasor measurement units (PMUs) placed at buses in the distribution network; (b) constructing a quotient gradient system (QGS) based on a constraint set H that relates the measurements to state variables of the distribution network; (c) integrating the QGS to reach a steady state; (d) identifying one or more of the state variables whose measurement residuals violate a measurement residual constraint in the constraint set H; (e) integrating a reconstructed QGS, which is reconstructed based on the constraint set H by setting the identified one or more state variables to values of corresponding PMU measurements; (f) iterating steps of (d) and (e) until no measurement residuals violate the measurement residual constraint, to thereby obtain the state estimation; and (g) reporting the state estimation to a control system during real-time monitoring of the distribution network.

Abstract: A computer system provides real-time control of power dispatch for a power system. The power system includes power generators, renewable power generators, load, and storage devices interconnected by a power grid. The computer system obtains input data, and solves an online multi-period power dispatch problem formulated from the input data and incorporates AC power flow in the power grid. The computer system generates control signals according to a solution of the online multi-period power dispatch problem, and sends the control signals to controllers of the power generators and the storage devices. In every time period during operation of the power system, the computer system updates the solution, generates updated control signals according to the updated solution, and sends the updated control signals to the controllers to continuously operate the power system with minimized operational cost while fully utilizing renewable power output.

Abstract: An online static security assessment (SSA) method based on a quasi steady-state (QSS) model is applied to a power system. An input to the method includes a post-contingency state of the power system for each of a set of contingencies. The following operations are performed for each contingency. Using the QSS model of the post contingency state of the power system, a steady-state voltage magnitude is calculated for each bus in the power system by solving a system of equations. The system of equations is formulated according to a time-domain stability model of the power system and includes nonlinear differential algebraic equations (DAE) with continuous and discreet variables. The derivative terms of short-term state variables in the DAE are set to zero. The method compares the calculated voltage magnitude with a limit, classifies each contingency as secure, critical or insecure, and determines a control action in response to the classification.

Abstract: A computer system provides real-time control of power dispatch for a power system. The power system includes power generators, renewable power generators, load, and storage devices interconnected by a power grid. The computer system obtains input data, and solves an online multi-period power dispatch problem formulated from the input data and incorporates AC power flow in the power grid. The computer system generates control signals according to a solution of the online multi-period power dispatch problem, and sends the control signals to controllers of the power generators and the storage devices. In every time period during operation of the power system, the computer system updates the solution, generates updated control signals according to the updated solution, and sends the updated control signals to the controllers to continuously operate the power system with minimized operational cost while fully utilizing renewable power output.

Abstract: A user-preference-enabling (UPE) method optimizes operations of a system based on user preferences. The operations of the system are modeled as a user-preference-based multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints. The set of constraints include system constraints and a wish list specifying a respective user-preferred range of values for one or more of the objective functions. The UPE method calculates a wish list feasible solution (WL-feasible solution) to the user-preference-based MOO problem. The UPE method can be performed iteratively to compute targeted Pareto-optimal solutions. The UPE method can be used in a hybrid method in combination with other numerical methods to reliably compute feasible solutions of both conventional MOO problems and user-preference-based MOO problems.

Abstract: The available delivery capability (ADC) of a power distribution network with respect to a power transaction is evaluated in real-time. The power transaction involves simultaneous power deliveries from power sources in a source area to loads in a sink area. First, a list of contingencies are ranked in the power distribution network with respect to static security constraints to obtain a subset of top-ranked contingencies. For each top-ranked contingency in the subset, a representation of the power transaction in a steady state of the power distribution network, in a form of parameterized three-phase power flow equations, is solved to obtain a corresponding power delivery capability (PDC) and a corresponding binding constraint among the static security constraints. The reliability of the power transaction in the power distribution network is then evaluated based on, at least in part, a first contingency PDC which is a smallest PDC among obtained corresponding PDCs.

Abstract: A user-preference-enabling (UPE) method optimizes operations of a system based on user preferences. The operations of the system are modeled as a user-preference-based multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints. The set of constraints include system constraints and a wish list specifying a respective user-preferred range of values for one or more of the objective functions. The UPE method calculates a wish list feasible solution (WL-feasible solution) to the user-preference-based MOO problem. The UPE method can be performed iteratively to compute targeted Pareto-optimal solutions. The UPE method can be used in a hybrid method in combination with other numerical methods to reliably compute feasible solutions of both conventional MOO problems and user-preference-based MOO problems.

Abstract: The available delivery capability (ADC) of a power distribution network with respect to a power transaction is evaluated in real-time. The power transaction involves simultaneous power deliveries from power sources in a source area to loads in a sink area. First, a list of contingencies are ranked in the power distribution network with respect to static security constraints to obtain a subset of top-ranked contingencies. For each top-ranked contingency in the subset, a representation of the power transaction in a steady state of the power distribution network, in a form of parameterized three-phase power flow equations, is solved to obtain a corresponding power delivery capability (PDC) and a corresponding binding constraint among the static security constraints. The reliability of the power transaction in the power distribution network is then evaluated based on, at least in part, a first contingency PDC which is a smallest PDC among obtained corresponding PDCs.

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 smart power flow solver integrates the TRUST-TECH based power flow methodology into a power flow solution. A first solver is applied to a power flow problem of a power system. If results of the first solver diverge, A Trust-Tech based solver is applied to the power flow problem by: transforming the power flow problem to an unconstrained global optimization problem; iteratively solving a dynamical system associated with the unconstrained global optimization problem; and determining whether a solution exists for the power flow problem based on whether the iteratively solving of the dynamical system converges. If a solution exists for the power flow problem, a second solver is then applied to the power flow problem. An operating state of the power system is generated based on results of the second solver to enable proper operation of the power system.

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: 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.