Nikolaos Theodorakatos

Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary p...

Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary polynomial models to encounter the optimal number of PMUs with suitable PMU positioning sites. All optimization models are implemented with powerful optimization solvers in MATLAB to obtain the global solution point.

The Phasor Measurement Unit (PMU) is a monitoring device capable with high-precision time synchronization that measures magnitudes and phase angle of voltage and current from a specific power network bus. Aiming at achieving the optimal PMU positioning problem (OPP) solving, this study proposes a multi-objective optimization function minimized under a set of 0-1 Boolean observability inequality constraints whereas a binary restriction is satisfied. Genetic algorithms (GAs) in conjunction with a Binary Particle Swarm Optimization (BPSO) are used to solve the multi-objective constraint linear integer program (m-CILP) towards optimality. This GA-PSO probabilistic approach aims simultaneously at minimizing the number of PMUs needed and maximizing the measurement redundancy (MR) index. The success of this heuristic approach is proved by comparing its results with those achieved by a Branch-and-Bound (B&B) algorithm which solves the 0-1 m-CILP towards optimality. The minimization models are tested on standard IEEE power networks to show their applicability regarding this multi-objective optimization making problem. The numerical results derived by the GA-PSO models in MATLAB language show that the optimal solutions with regard to the maximum MR are achieved with efficiency and at once minimizing the whole cost in the optimization process.

Fault location observability is an essential procedure among smart monitoring and outage management system issues used to realize self-healing networks, one of the most important characteristics of modern power systems. Further, the determination of the location of a faulty transmission line in a power grid is a vital topic to facilitate the self-healing network and to maintain the continuity of power supply. The self-healing procedure is to constantly keep the energy supplies to the customers in case of a power system configuration change such as a fault event happening on an electrical power transmission network. Self-healing is an operational aspect of electrical power networks for real-time identification and localization of faulty transmission lines for the whole power network. The implementation of PMUs as an accurate measurement device is a promising key entry for fault location and clearing utilizations. This paper proposes algorithmic models that determine the optimal number of PMUs and their placement sites to achieve a fault observable system whereas the state-estimation issue is examined. The optimization models discussed herein find a configuration of PMU locations with a least number of devices that locates any fault occurring in a transmission power network. An optimization process is presented within a nonlinear programming model coupling a synchronized phasor as well as conventional measurements. As a comparative optimization tool, a zero-one integer constraint linear program is implemented that satisfies global optimality with sufficient precision. Evolutionary algorithms such as a binary-particle swarm optimization and genetic algorithms have been adopted to characterize a fault observable power system. The algorithmic models are illustrated with an IEEE-14 bus system. Simulation results are tested on different size power systems to verify the efficacy of the proposed algorithmic approach without taking into account the fault classification, pre-fault loading conditions or considering the fault resistance. We present that this wide-area measuring implementation and its numerical results is an outstanding approach that improves the state-of-the-art in measurement driven methods regarding the finding of an optimal PMU set solution to pinpoint a fault event occurring anywhere in the power transmission grid. As proved via the numerical optimization, the mathematical and evolutionary algorithms are efficient and robust in finding some new benchmark optimal results for faulty conditions occurring in a modern power grid for any IEEE power system and case study.

This paper studies mathematical algorithms for delivery maximum power network observability using synchronized measurements. This problem is an intrinsic extension of the minimization of phasor measurement units (PMUs) by considering the least cost number of these devices around the power network and maximizing the reliability for better performance of power electrical networks. Optimization properties are investigated and used to lie a Βranch-and-Βound algorithm (BBA) jointly with Successive Quadratic Programming (SQP) and Interior Point Methods (IPMs) to find optimality. Τo evaluate optimal solutions with maximum measurement redundancy, solution algorithms such as BBA, SQP, IPM are used. The nonlinear algorithms mainly rely on local search procedure as the convergence indicator to optimality, whereas BBA is implemented to build a binary-tree to find an optimal solution. Thus, it is reasonable and necessary to compare nonlinear algorithms with BBA to show their difference and their efficiency convergence properties towards global optimality whereas the maximum observability is preserved. Moreover, the polyhedron being constructed for the implementation of the BBA scheme is transformed into a polytope solved by a Semi-Define-Programming approach to find appropriate optimal solutions for further optimization study. Numerical studies show significant improvement about the maximum observability over existing optimization schemes already published in the recent bibliography.

The impact of the generalized pattern search algorithm (GPSA) on power system complete observability utilizing synchrophasors is proposed in this work. This algorithmic technique is an inherent extension of phasor measurement unit (PMU) minimization in a derivative-free framework by evaluating a linear objective function under a set of equality constraints that is smaller than the decision variables in number. A comprehensive study about the utility of such a system of equality constraints under a quadratic objective has been given in our previous paper. The one issue studied in this paper is the impact of a linear cost function to detect optimality in a shorter number of iterations, whereas the cost is minimized. The GPSA evaluates a linear cost function through the iterations needed to satisfy feasibility and optimality criteria. The other issue is how to improve the performance of convergence towards optimality using a gradient-free mathematical algorithm. The GPSA detects an opt...

This paper introduces an underdetermined nonlinear programming model where the equality constraints are fewer than the design variables defined on a compact set for the solution of the optimal Phasor Measurement Unit (PMU) placement. The minimization model is efficiently solved by a recursive quadratic programming (RQP) method. The focus of this work is on applying an RQP to attempt to find guaranteed global minima. The proposed minimization model is conducted on IEEE systems. For all simulation runs, the RQP converges superlinearly towards optimality in a finite number of iterations without to be rejected the full step-length. The simulation results indicate that the RQP finds out the minimal number and the optimal locations of PMUs to make the power system wholly observable.

The impact of the generalized pattern search algorithm (GPSA) on power system complete observability utilizing synchrophasors is proposed in this work. This algorithmic technique is an inherent extension of phasor measurement unit (PMU) minimization in a derivative-free framework by evaluating a linear objective function under a set of equality constraints that is smaller than the decision variables in number. A comprehensive study about the utility of such a system of equality constraints under a quadratic objective has been given in our previous paper. The one issue studied in this paper is the impact of a linear cost function to detect optimality in a shorter number of iterations, whereas the cost is minimized. The GPSA evaluates a linear cost function through the iterations needed to satisfy feasibility and optimality criteria. The other issue is how to improve the performance of convergence towards optimality using a gradient-free mathematical algorithm. The GPSA detects an optimal solution in a fewer number of iterations than those spent by a recursive quadratic programming (RQP) algorithm. Numerical studies on standard benchmark power networks show significant improvement in the maximum observability over the existing measurement redundancy generated by the RQP optimization scheme already published in our former paper.

This paper proposes Interior-Point (IP) methods for the solution of the optimal placement of phasor measurement units (PMUs) ensuring complete observability. The optimization problem consists of a quadratic function under a well-determined system of constraints that is, nonlinear equations equal to the number of the design variables defined over the whole search space . A hybrid-optimization technique coupling a branch-and-bound and a local search-procedure based on the (IP) methods is used in solving the model. The (IP) methods detect solution points that yield a minimum objective value as the one obtained by branch-and-bound algorithm. The (IP) methods optimizes the required PMU numbers whereas practical constraints as well as contingency issues as single PMU failure, costs of communication infrastructure (CI) from Phasor Data Concentrator to PMUs and prohibitive installations are satisfied. A large-scale system is also analysed to exhibit the applicability of (IP) methods to practical power system cases.

This paper introduces an underdetermined nonlinear programming model where the equality constraints are fewer than the design variables defined on a compact set for the solution of the optimal Phasor Measurement Unit (PMU) placement. The minimization model is efficiently solved by a recursive quadratic programming (RQP) method. The focus of this work is on applying an RQP to attempt to find guaranteed global minima. The proposed minimization model is conducted on IEEE systems. For all simulation runs, the RQP converges superlinearly towards optimality in a finite number of iterations without to be rejected the full step-length. The simulation results indicate that the RQP finds out the minimal number and the optimal locations of PMUs to make the power system wholly observable.

This study presents an algorithmic approach for optimal placement of phasor measurements units (PMUs) to ensure complete observability in the presence of conventional measurements and zero injection buses. The financial or technical restrictions prohibit the deployment of PMUs at every bus, which in turn motivates their strategic placement around the power system. Topology-based transformations are implemented for observability analysis. Τhe PMU problem allocation is optimized based on measurement observability criteria for achieving solvability of the power state estimation. The Branch-and-Bound algorithm (BB) and Binary-Coded Genetic algorithm (BCGA) are applied to solve the optimization problem. The BCG algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a penalty parameter approach for handling constraints. The proposed algorithms detect the minimum PMU number and their locations required to make the power system numerically observable. The proposed algorithms are applied to IEEE systems as well as a large-scale system with 1011 buses to exhibit the applicability of them to practical power systems. The solution points located using the BCGA are interpreted as nonstrict global minima since they are in complete agreement with those obtained by the BB algorithm in solving the (zero-one) constraint integer linear program.

This article studies deterministic and stochastic
algorithms for placing minimum number of phasor measurement
units (PMUs) in a power system in order to locate any fault in the
power system. The optimization problem is initially formulated in
a mixed integer linear programing framework with binary-valued
variables as well as in a binary integer linear programing model.
Then, the optimization problem is formulated as an equivalent
non-linear programing model, minimizing a quadratic objective
function subject to equality non-linear constraints defined over a
bounded and closed set. The problem is solved by using a
Sequential Quadratic Programming algorithm. The non-linear
program is illustrated with a 7-bus test system. Also, stochastic
algorithms such as binary-coded genetic algorithm and particle
swarm optimization have been implemented in solving the optimal
PMU placement under fault condition. The accuracy of suggested
algorithms is independent from the fault type and its resistance.
The optimization models are applied to the IEEE systems. The
numerical results indicate that the proposed algorithms locate
minimizers at the optimal objective function value in complete
agreement with those obtained by branch-and-bound algorithms.

Given an undirected graph representing the network, the optimization problem of finding the minimum number of phasor measurement units to place on the edges such that the graph is fully observed, is studied. The proposal addresses the issue of the optimization using a two-phase branch-and-bound algorithm based on combining both Depth-First Search and Breadth-First Search algorithms to attempt to find guaranteed global solutions for OPP. The problem in question is stated, outlining the underlying mathematical model in use formulated in terms of (pure) mixed-integer-linear-programming (MILP) and the branch-and-bound algorithm adopted to obtain efficient solutions in practice. A topology based on transformations considering pre-existing conventional and zero injection measurements in a power network is implemented. The (zero-one) (MILP) model is applied to IEEE systems. The numerical results indicate that the branch-and-bound ensures solution points at the optimal objective function value from a global-optimization point of view. The synchronized and conventional measurements are included in a (DC) linearized State Estimator (SE). The topological observability analysis is verified numerically based on observability criteria for achieving solvability of state estimation. Large-scale systems is also analyzed to exhibit the applicability of the proposed algorithm to practical power system cases.

The last decades, electric power industry is undergoing multiple changes due to the process of deregulation, providing efficient power generation, technological innovations, and eventually lower retail prices. In this environment, dynamic phenomena in power systems have made ever more urgent the development of reliable tools for their monitoring and control. An effective tool for the close monitoring of their operation conditions is the state estimator. The traditional estimators are based on real time measurements obtained through SCADA (Supervisory Control and Data Acquisition) system. These measurements are commonly provided by the remote terminal units (RTUs) installed at the high voltage substations. The phase angle of bus voltages can not be easily measured due to technical difficulties associated with the synchronization of measurements at RTUs. Global Positioning System (GPS) alleviated these difficulties and led to the development of Phasor Measurement Units (PMUs). This weakness was eliminated with the arrival of GPS, which led to the development of Phasor Measurement Units. A PMU unit, equipped with a GPS receiver, provides high accuracy voltage and current phasor measurements with respect to a common reference phase angle. In the first part of the paper, an overview of the PMU technology and a review about the optimal allocation of PMUs in power network are presented. The most important issues regarding design and operation of PMUs are discussed and an analysis of their commercial penetration in the electric energy markets is made. The second part of the paper presents a wide range of applications related with the choice of the strategic PMU placement as well as an algorithm for finding the optimal number of PMUs needed for full observability.