Optimal PMU placement

In the current scenario; most of the appliances are mainly depending upon electric power for their operation, so the demand for electric power increasing day by day. Now there is a big challenge in supplying power with proper continuation and reliability to the appliances. To accept the challenge of observability of the grid in a proper way Phasor Measurement Units (PMUs) are used for real-time data collection. In recent years, there has been growing interest in synchro phasor measurements like PMUs Power systems are now being gradually populated by PMUs since they provide significant phasor information for the protection and control of power systems during normal and abnormal situations. There are several applications of PMUs, out of which state estimation is widely used. To improve the robustness of state estimation, different approaches for the placement of PMUs have been studied. This dissertation introduces two works related to PMU in them one is the strategicPMU installation approach and the second is a PMU application based fault detection, allocation and fault classification approach. Due to the high installation and operating cost of PMUs, it is required to reduce the number of PMUs.In this reference, many researchers proposed various OPP techniques which help to reduce the number of PMUs with maximum observability. After observing the OPP location with complete power system observability, it is to be seen the requirement of strategic PMU installation. In this view, many researchers strategically installed PMUs by proposing different methodologies. This dissertation tries to extend the strategic PMU installation work in a new way at already-found OPP locations. In the extension of the strategic PMU installation, this dissertation proposed a strategic approach for PMU installation in the power system. This approach has particular selection criteria for the OPP location to install PMU. The selection criteria for the selection of an OPP location to install PMU depends on two conditional parameters namely Degree of Connectivity and shortest path. Finally, the proposed approach generates a best-suited path for PMU installation that has the shortest travelled distance and particular priority of OPP locations. The proposed approach is verified with IEEE-14 and IEEE-30 bus systems and it assures complete power system observability. As we know that with the growth in the world population, the supply points are also increasing and due to which grid size also increasing. In a large size grid, there is more possibility of occurring faults or abnormalities and sometimes these faults become a cause of major power failures like a blackout. To rectify this problem it is necessary to detect the fault in the power system and also find the fault location. In early times the fault location finds in the traditional way or in other words checks the whole line and after then the fault location is obtained. This way to find the fault location is very time-consuming and sometimes becomes inaccurate. With accepting the challenges of fault detection and allocation many researchers developed various types of methodologies and also this work is pursued in present time. As we know that there is a new welcoming technology Phasor measurement unit. It can measure the magnitude and phase angle of an electrical phasor quantity like voltage or current and also provide the frequency measurement. This dissertation proposes a PMU application-based approach for fault analysis which is based on the frequency characteristic analysis of voltage and current phasor quantity. Although, ideally frequency of voltage and current are the same in the abnormal condition they may differ from each other. This difference in frequency is separately measured by PMU block at MATLAB Simulink Platform. The PMU (PLL-Based, Positive-Sequence) block is inspired by the IEEE Std. C37.118.1-2011. In this fault analysis work, we detect, allocate and identify the nature of short circuit faults in the system. The frequency characteristics analysis is done from the simulation performed on the two models. These models are created and simulated in the MATLAB Simulink environment. The proposed approach is tested on two MATLAB Simulink models and observed a satisfactory. The proposed fault analysis approach is capable to analyze short circuit faults only at source side and load side bus.

Metering systems planning in transmission networks can be modeled as an optimization problem in which the metering system cost is minimized, subjected to redundancy constraints that enable the state estimation function to observe system state and debug bad measurement data. However, the budget for investments in the metering system is commonly insufficient to achieve such a goal for the entire power system. On the other hand, there are areas of the power network considered more important for system operation than others. Consequently, a more qualified supervision of such areas is necessary to ensure adequate decision making regarding network operation and control. This work proposes a methodology flexible and easily adaptable to cope with limited investment budgets. An ant colony optimization algorithm (ACO-PCH) is employed to solve the optimal meter placement problem. A fast and cost-effective algorithm based on a decomposition strategy (ACO-PCH-DS) that takes into account the local nature of the state estimation problem is also proposed in order to improve computational efficiency of planning metering systems for large power networks. Tests with the IEEE bus systems and part of a real Brazilian system are carried out to validate the proposed methodology. If the stop criteria are the time limit (200 s), the ACO-PCH-DS reduces in 15% the cost of the measurement plan in IEEE 118-bus system, when compared to the ACO-PCH. For 300 min as a time limit, the ACO-PCH-DS do not provide a better cost only for reliability in the IEEE-300 bus system.

This research examines an admissible search algorithm-dependent A-star strategy and takes into account redundancy and cost/benefit analysis under normal operating conditions. The goal is to allocate a phasor measurement unit (PMU) for maximal observability of the interconnected power network. To determine the fewest number of PMU required to make the connected power network totally observable using redundancy analysis, the A-star approach is utilized. The redundancy analysis of the power network is carried out in order to determine the appropriate PMU placement, which results in the acquisition of total power network observability and reliability. To put the suggested technique through its paces, it has been tested on IEEEstandard test systems such as IEEE-14 bus, IEEE-30 bus, New England-39 bus, IEEE-57 bus, and IEEE-118 bus. The results obtained using the suggested methodology are compared to those obtained through standard literature research. The experimental findings of the suggested method revealed the resilience and accuracy of the A-star algorithm as well as its effectiveness in achieving maximum observability of the connected power network.

Regarding the high cost of PMU units, optimal placement and minimizing of their numbers are of great importance. Also, this paper proposes a new procedure for determining the optimal placement and less numbers of PMUs in distribution network based on the best state estimation criterion. For Distribution State Estimation solution, combinations of Nelder-Mead (NM) simplex search and Ant Colony Optimization (ACO) algorithm have been used. The hybrid method can estimate voltage phasor at each node by minimizing difference between measured and calculated values of state variables and also, it can guarantee observability of distribution system under normal operation conditions. To demonstrate the effectiveness of new procedure, simulation studies are applied on 30bus radial test feeder. Finally, achievement results for convergence characterestic of DSE solution and estimation error of state variables with regard to the optimal placement and numbers of PMUs in distribution test feeder have been presented.

In this paper, an improved model for complete observability of electrical power networks in optimal PMU placement is presented. Here a goal function is introduced based on the Integer Linear Programming (ILP) to find the optimal number and position for PMUs. Hitherto, modeling of zero injection busses constraints had been a challenge due to the intrinsic nonlinearity associated with it. We show that zero injection constraints can also be modeled as linear constraints. Also in this paper, a novel and topology based method is suggested when zero injection busses are considered in power grid. The ILP approach is implemented to solve the models. The models is tested in IEEE 14, 30, 57 and 118 busses systems. The simulation results are confirmed with the schemes concluded from authoritative publications. © 2014 Elixir All rights reserved ARTICLE INF O Articl e h istory: Received: 10 February 2014; Received in revised form: 6 June 2014; Accepted: 12 June 2014;

This paper presents an optimization model to calculation of the minimum number of phasor measurement units (PMUs) for complete observability of electrical power networks. Minimum PMU placement problem has multiple solutions. We propose a flow chart and indicators in order to find all solution and rank these multiple solutions, respectively. The proposed model is capable of obtaining the full set of optimal solutions instead of only one or partial solutions. The integer linear programming (ILP) approach is implemented to solve this model. We propose a procedure for multistaging of PMU placement in a given time horizon due to financial and physical constraints using an ILP framework. In addition, network expansion scenarios associated with intermediate stages are taken into account. Numerical studies are conducted on a nine-bus system and the IEEE 57-bus system and the results are analyzed. © 2013 Elixir All rights reserved ARTICLE INF O Articl e h istory: Received: 22 October 2013; R...

This paper compares 12 methods of optimization techniques for the optimal placement of phasor measurement units (PMUs) in power systems. These techniques are further explained for minimizing the no. of pmu’s in the real time power system. The planned methodology result in a reduction in the number of PMUs even though the system topological observability is complete. First, the number of PMUs is minimized in such a way that the system topological observability is complete. The optimal placement is also done to maximize the measurements redundancy which allows a bus to be observed more than one time. All these methods are categorized under Mathematical Programming Methods, Heuristic Methods and Meta-Heuristic Methods have been discussed.

Theoretical background: Directional overcurrent relays are applied for power system protection to ensure safe, reliable, and efficient operation. The coordination of directional overcurrent relays is non-linear and highly constrained optimization problem. The main goal of the optimization is to minimize the summation of operating times of primary relays, by setting optimal values for decision variables as time multiplier setting (TMS) and plug setting (PS).
Aims: The main objective of this research is to develop a hybrid optimization algorithm which consists of modified firefly algorithm and genetic algorithm to find better solutions.
Methodology: First, this study modified the original firefly to obtain a global solution by updating the firefly's brightness and to avoid the distance between individual fireflies from being too far. Additionally, the randomized movements were controlled to produce a high convergence rate. Second, the optimization problem is solved using standard genetic algorithm. Finally, the solution obtained from the modified firefly algorithm is used as the initial population for the standard genetic algorithm. The modified firefly algorithm, genetic algorithm and hybrid firefly-genetic algorithm have been tested on IEEE 3-bus, 8-bus, 9-bus and 15-bus networks.
Main Results: The results indicate the effectiveness and superiority of the proposed algorithms in minimizing the overall operating time of primary relays compared to other algorithms mentioned in the literature for directional overcurrent relays coordination.
Conclusion: Compared to modified firefly algorithm and standard genetic algorithm, the proposed hybrid algorithm has minimized coordination interval time between primary and backup relay pairs.

Sensing and measurement systems are quintessential to the safe and reliable operation of electric power grids. Their strategic placement is of ultimate importance because it is not economically viable to install measurement systems on every node and branch of a power grid, though they need to be monitored. An overwhelming number of strategies have been developed to meet oftentimes multiple conflicting objectives. The prime challenge in formulating the problem lies in developing a heuristic or an optimization model that, though mathematically tractable and constrained in cost, leads to trustworthy technical solutions. Further, large-scale, long-term deployments pose additional challenges because the boundary conditions change as technologies evolve. For instance, the advent of new technologies in sensing and measurement, as well as in communications and networking, might impact the cost and performance of available solutions and shift initially set conditions. Also, the placement strategies developed for transmission grids might not be suitable for distribution grids, and vice versa, because of unique characteristics; therefore, the strategies need to be flexible, to a certain extent, because no two power grids are alike. Despite the extensive literature on the present topic, the focus of published works tends to be on a specific subject, such as the optimal placement of measurements to ensure observability in transmission grids. There is a dearth of work providing a comprehensive picture for developing optimal placement strategies. Because of the ongoing efforts on the modernization of electric power grids, there is a need to consolidate the status quo while exposing its limitations to inform policymakers, industry stakeholders, and researchers on the research-anddevelopment needs to push the boundaries for innovation. Accordingly, this paper first reviews the state of the art considering both transmission and distribution grids. Then, it consolidates the key factors to be considered in the problem formulation. Finally, it provides a set of perspectives on the measurement placement problem, and it concludes with future research directions. pp. 1-23 Determinant of a matrix • Im(•) Imaginary part of the complex-valued variable • Re(•) Real part of the complex-valued variable • * https:// gmlc.doe.gov/ * * https:// globalpst.org/ 15-69 kV Distribution 7.2-15 kV Customer site 100-240 V Smart meter Power quality monitor Digital fault recorder Digital protective relay PMU Micro-PMU Merging unit [14, 15] observable solely by phasor measurement units (PMUs). The details of this problem, including the definition of observability, will be given in the next section. For now, it is sufficient to know that at least 300 PMUs are needed [16].

First and foremost, I would like to express my deepest appreciation to my advisor and committee chair, Dr. Virgilio Centeno, who has continually and convincingly kept a spirit in regard to the research and teaching. Dr. Centeno has taught me so much throughout many aspects of my study and life. Without his patient guidance and support I cannot finish my research and have today's achievement. I would like to thank Dr. Arun Phadke and Dr. James Thorp for their great help and guidance in my researches. From them, I learned an attitude and spirit of research and working. My appreciation also goes to Dr. Jaime De Ree and Dr. Sandeep Shukla. They are knowledgeable and always enthusiastic to offer help.

An islanded power system indicates a geographical and logical detach between a portion of a power system and the major grid, and often accompanies with the loss of system observability. A power system islanding contingency could be one of the most severe consequences of wide-area system failures. It might result in enormous losses to both the power utilities and the consumers. Even those relatively small and stable islanding events may largely disturb the consumers’ normal operation in the island. On the other hand, the power consumption in the U.S. has been largely increasing since 1970s with the respect to the bloom of global economy and mass manufacturing, and the daily increased requirements from the modern customers. Along with the extreme weather and natural disaster factors, the century old U.S. power grid is under severely tests for potential islanding disturbances. After 1980s, the invention of synchronized phasor measurement units (PMU) has broadened the horizon for system...

A new approach to solve Chance constrained Portfolio Optimization Problems (CPOPs) without using the Monte Carlo simulation is proposed. Specifically, according to Chebyshev inequality, the prediction interval of a stochastic function value included in CPOP is estimated from a set of samples. By using the prediction interval, CPOP is transformed into Lower-bound Portfolio Optimization Problem (LPOP). It is proved that the feasible solution of LPOP is also feasible for CPOP. Furthermore, in order to solve LPOP, Differential Evolution (DE) is used. Finally, through a numerical experiment, the usefulness of the proposed approach is demonstrated.

This paper describes a sensor placement algorithm for real-time parallel power flow computations for transmission networks. In particular, Phasor Measurement Units (PMUs) can be such sensors. Graph partitioning is used to decompose the system into several subsystems and to locate sensors in an efficient way. Power flow calculations are then run in parallel for each area. Test results on the IEEE 118and 300-bus systems show that the proposed approach is suitable for real-time applications. Keywords–Parallel computing; power system; power flow calculation; PMU placement.

In the study of large interconnected power systems, it is essential to aggregate, the power system into several parts, such that each part represents a number of generators. In the words, the coherent generators lie in one part. In this paper, the coherent generators are determined using a pattern recognition technique called hierarchical clustering method. In this method, firstly, rotor angles of the generators are obtained based on transient stability technique which are calculated by solving state space model of system during three phase short circuit fault Then, the coherency measure which is the similarity matrix is formed using the rotor angles. After that the coherent generators are determined using hierarchical clustering method. The proposed method is then applied to the 39-Bus New England test system. Results of the simulation show that this method is capable in finding the coherent generators in the power system.

This paper presents a new multiobjective model, including two objective functions of generation cost and voltage stability margin, for optimal power flow (OPF) problem. Moreover, the proposed OPF formulation contains a detailed generator model including active/reactive power generation limits, valve loading effects, multiple fuel options and prohibited operating zones of units. Furthermore, security constraints, including bus voltage limits and branch flow limits in both steady state and post-contingency state of credible contingencies, are also taken into account in the proposed formulation. To solve this OPF problem a novel robust differential evolution algorithm (RDEA) owning a new recombination operator is presented. The proposed RDEA has a minimum number of adjustable parameters. Besides, a new constraint handling method is also presented, which enhances the efficiency of the RDEA to search the solution space. To show the efficiency and advantages of the proposed solution method, it is applied to several test systems having complex solution spaces and compared with several of the most recently published approaches.

We consider drying process of bricks made of soil and cellulose mixture. The particle sizes of the soil are about 0.005 μm, which are considered to be clay. We apply a diffusion type equation to model the drying process. The model is based on macro modeling, where the particle and pore sizes are considered much smaller compared to the size of nails to measured the moisture content of the area inside the bricks. The model is a nonlinear diffusion equation where the diffusion rate depends on the moisture content. The solution is computed analytically applying a finite difference method for one and two dimensional cases. The simulation shows that the drying process of two dimensional case is slightly faster than of the one dimensional case. The cause is the diffusion to the side wall of two dimensional case where this wall is does not exist in one dimensional case

Phasor measurement units (PMUs) are becoming popular and populating the power system grids rapidly due to their wide range of benefits and applications. This research paper proposes a comprehensive, effective, and revised formulation of the optimal PMU placement (OPP) problem with a view to minimizing the required number of PMU and ensuring the maximum number of measurement redundancy subjected to the full observability of the distribution grids. The proposed formulation also incorporates the presence of passive measurements/zero injection buses (ZIB) and the channel availability of the installed PMU. Additionally, the formulation is extended to various contingency cases i.e., the single line outage and single PMU loss cases. This paper solves the proposed OPP formulation employing a heuristic technique called backtracking search algorithm (BSA) and tests its effectiveness through different IEEE standard distribution feeders. Additionally, this study compares the obtained results wi...

The original optimizations mathematical model of the electric arc furnace’s charge preheating process mainly takes into consider 2 thermo-technological aspects: the heat transfer between fluids and particles and the heat transfer between the fizz layer and an exchange surface. According the energetically balance at the gaseous environment level, the conductive transfer model is also analyzed through the finished elements method. The results of the mathematical model are presented as the analysis and quantification of the thermo gradients obtained during the charge preheating process. These thermo gradients are determined for various temporal moments and for different capacities of the electric arc furnace. The results of the mathematical model are presented as the analysis and quantification of the thermo gradients obtained during the charge preheating process. These thermo gradients are determined for various temporal moments and for different capacities of the electric arc furnace.

Phasor measurement units (PMUs) are becoming popular and populating the power system grids rapidly due to their wide range of benefits and applications. This research paper proposes a comprehensive, effective, and revised formulation of the optimal PMU placement (OPP) problem with a view to minimizing the required number of PMU and ensuring the maximum number of measurement redundancy subjected to the full observability of the distribution grids. The proposed formulation also incorporates the presence of passive measurements/zero injection buses (ZIB) and the channel availability of the installed PMU. Additionally, the formulation is extended to various contingency cases i.e., the single line outage and single PMU loss cases. This paper solves the proposed OPP formulation employing a heuristic technique called backtracking search algorithm (BSA) and tests its effectiveness through different IEEE standard distribution feeders. Additionally, this study compares the obtained results wi...

In this paper, a solution for optimal PMU placement in the Southern Cameroon Interconnected grid (SIG) is proposed in response to a problem of dynamic stability in the network. In this power system, the monitoring of the parameters is ensured so far by the SCADA, a technology that gives unsynchronized measurements and whose state estimation of the grid is inconsistent. Furthermore, a scan rate of data makes the SCADA system inefficient for measuring the dynamic and transient behaviour occurring in the power grid. Present study uses the method of integer linear programming (ILP) considering the effect of a group of zero-injection buses (ZIBs). Then, a comparative analysis of our results is made with those of the algorithms of other existing optimization methods in order to evaluate the performance of the applied method from the viewpoint of the number of PMUs, the number of buses observable from one or more nodes, and the system observability redundancy index (SORI). The different results obtained through MATLAB 2020a clearly show that considering the effect of a group of ZIBs, the ILP method presents the most optimal solution with a number of 10 PMUs installed on the buses 5, 8, 10, 11, 13, 16, 25, 28, 33 and 39, with a complete observation of the SIG. This result is validated insofar as 50% of the buses obtained (5, 8, 11, 33 and 39) are found with all the other comparative methods. In addition, buses 5, 8, 10, 11, 13, 16, 39 represent the dominant interconnection substations of the SIG, bus 33 also being a dominant bus in the Area 3 of the SIG.

This paper proposes a novel adaptive binary differential evolution optimization algorithm based on optimal placement of phasor measurement units (PMUs) and an intelligent strategy for fault location in power systems. The novelties of the proposed adaptive binary differential evolution optimization algorithm are that the proposed approach presents two new factors, namely, "weight factor" and "reduction factor", in order to improve convergence speed and enhance the capability of the novel modified binary differential evolution optimization algorithm for detecting optimal placement of PMUs in large-scale problems. To investigate the capability of the proposed approach, it is applied to several IEEE test systems (IEEE 14 bus, IEEE 24 bus, IEEE 30 bus, IEEE 39 bus, and IEEE 57 bus test systems). In addition, a comparison with conventional optimization algorithms has been carried out. Then, according to the PMUs data, an intelligent fault location strategy will be proposed. The main advantages of the proposed intelligent fault location strategy are higher accuracy and speed than conventional fault location approaches.

This paper proposes a novel adaptive binary differential evolution optimization algorithm based on optimal placement of phasor measurement units (PMUs) and an intelligent strategy for fault location in power systems. The novelties of the proposed adaptive binary differential evolution optimization algorithm are that the proposed approach presents two new factors, namely, "weight factor" and "reduction factor", in order to improve convergence speed and enhance the capability of the novel modified binary differential evolution optimization algorithm for detecting optimal placement of PMUs in large-scale problems. To investigate the capability of the proposed approach, it is applied to several IEEE test systems (IEEE 14 bus, IEEE 24 bus, IEEE 30 bus, IEEE 39 bus, and IEEE 57 bus test systems). In addition, a comparison with conventional optimization algorithms has been carried out. Then, according to the PMUs data, an intelligent fault location strategy will be proposed. The main advantages of the proposed intelligent fault location strategy are higher accuracy and speed than conventional fault location approaches.

The term "smartgrid" refers to the power system that integrates new digital measurements, new digital control devices, and communication technology. The first step toward this goal is to establish a two-way communication infrastructure for the purpose of data delivery among data resources, system actuators and control centers. Phasor measurement unit (PMU) is a kind of new data resources that are widely used in power systems, recently. On the other hand, state estimation (SE) is basis application in control centers and it is known as kernel of other smartgrid applications. This study aims to plan a communication infrastructure that creates communication routes from PMUs of a SE to the control center in a power network. To do this, a new concept is introduced to power system communication called dependent communication system (DCS). A DCS has been made by independent transmission media (e.g. optical power grand wire), which is typically attached to the power systems. In thi...

We propose a method for voltage stability assessment of power systems using a support vector machine (SVM). We input the information from measurement signals to the SVM. The objectives of this paper are twofold: (1) to select the minimum number of features for training an SVM using multi-objective optimization (MOO); (2) to find the minimum misclassification rate for the SVM. To address these objectives, the training data size is decreased in two stages. First, a mutual information (MI) criterion is used to remove the less significant measurements from the data set. Second, the most relevant features are selected using multi-objective biogeographybased optimization (MOBBO). The minimization objectives are the measurement data size and the misclassification rate of the SVM. The BBO-based MO methods are vector evaluated BBO (VEBBO), nondominated sorting BBO (NSBBO), niched Pareto BBO (NPBBO), and strength Pareto BBO (SPBBO). These four MOO methods are compared using Pareto front normalized hypervolume, relative coverage, and statistical analysis. The methods are applied to a 39-bus benchmark system and a 66-bus real power grid. The results verify that the reduced measurement data using MOO lead to efficient and accurate SVMs. For the real power grid, the trained SVM accurately predicts the voltage stability of the system by using only 8% of the measurement data. The misclassification rates of the SVMs are as low as 2% for the real power grid. Normalized hypervolume, relative coverage, and statistical tests indicate that NSBBO performs better than the other methods.

This paper presents a tri-objective Optimal Phasor Measurement Units (PMUs) Placement (OPP) strategy that is focused on the minimization of i) the total number of PMU channels, ii) the maximum state estimation uncertainty based only on high-rate PMU data and iii) the sensitivity of state estimation to line parameter tolerances. The proposed formulation keeps into account system observability with and without contingencies due to single-line and PMU faults. Also, it includes the effect of possible zero-injection buses and a-priori constraints on both the number of PMU channels and the type of PMU measurements performed at each bus. Due to the nonlinear combinatorial nature of the proposed OPP problem, this is solved through a custom implementation of the nondominated sorting genetic algorithm II (NSGA-II). The analysis of the proposed OPP strategy is focused on distribution systems. The placement results obtained using four test systems of different size show that increasing the number of buses instrumented with PMUs and/or the number of PMU channels beyond given thresholds just leads to larger costs with negligible further reductions in both state estimation uncertainty and sensitivity to line parameters tolerances. Moreover, if PMUs with just two three-phase channels are used, we can avoid instrumenting between 30% and 40% of buses with a minor impact on state estimation performance even in the case of contingencies. This percentage can be slightly increased if multi-channel PMUs are used. However, this choice generally is not profitable. INDEX TERMS Distribution system state estimation, multi-objective optimization, optimal PMU placement, phasor measurement unit (PMU), power systems monitoring.

This paper presents a tri-objective Optimal Phasor Measurement Units (PMUs) Placement (OPP) strategy that is focused on the minimization of i) the total number of PMU channels, ii) the maximum state estimation uncertainty based only on high-rate PMU data and iii) the sensitivity of state estimation to line parameter tolerances. The proposed formulation keeps into account system observability with and without contingencies due to single-line and PMU faults. Also, it includes the effect of possible zero-injection buses and a-priori constraints on both the number of PMU channels and the type of PMU measurements performed at each bus. Due to the nonlinear combinatorial nature of the proposed OPP problem, this is solved through a custom implementation of the nondominated sorting genetic algorithm II (NSGA-II). The analysis of the proposed OPP strategy is focused on distribution systems. The placement results obtained using four test systems of different size show that increasing the number of buses instrumented with PMUs and/or the number of PMU channels beyond given thresholds just leads to larger costs with negligible further reductions in both state estimation uncertainty and sensitivity to line parameters tolerances. Moreover, if PMUs with just two three-phase channels are used, we can avoid instrumenting between 30% and 40% of buses with a minor impact on state estimation performance even in the case of contingencies. This percentage can be slightly increased if multi-channel PMUs are used. However, this choice generally is not profitable. INDEX TERMS Distribution system state estimation, multi-objective optimization, optimal PMU placement, phasor measurement unit (PMU), power systems monitoring.

Due to the large number of applications of wide area monitoring systems (WAMSs), many power utilities are implementing phasor measurement units (PMUs)-based WAMS replacing the conventional supervisory control and data acquisition system. The biggest challenge in implementing the technology is the cost of WAMS. Many researchers are trying to minimize the cost of WAMS by making the system observable with optimal placement of PMU. Along with the cost of PMU, the cost of communication infrastructure (CI) is dominating the cost of WAMS. Hence, it is necessary to optimize the communication path link and also to find out the optimal location of phasor data concentrator (PDC). In this paper, an optimization model to find the optimal placement of PMU, optimal location of PDC, and their CI is developed. For this, both independent and simultaneous optimization carried out by using differential evolution algorithm. The multiobjective differential evolution is used for simultaneous optimization. The presence of conventional flow measurement device and its effect on overall cost of WAMS with and without considering presence of optical fiber is presented. The method is implemented with different (N − 1) contingency considerations. Also, the results with the presence of pre-existing PMUs and optical fiber paths are provided. INDEX TERMS Wide area monitoring systems (WAMS), communication infrastructure (CI), phasor measurement units (PMUs), differential evolution (DE).

This paper presents a methodology to determine the optimal location of phasor measurement units (PMUs) in any network to make it observable. This proposed methodology is based on network connectivity information and unreachability index (URI), where URI is the difficulty to observe any node in the network and it is computed using the inverse of connectivity. In order to choose the optimal bus, it is basically considered to observe a low connectivity bus from an adjacent bus selected by weighting factors that are based on logical analysis of the observability theory combined with the URI; this process stops until the network is observable. The purpose is minimize the number of PMUs in a network with the optimal location and the aim to get a low number of critical measurements (CM) with a high total redundancy (TR), in order to obtain an optimal distribution of PMUs on the network. The proposal is considered as an easy solver for PMU's placing on the network due to important reduction in complexity and computational cost, besides comparable results are as good as those papers using recent optimization methods such as metaheuristics and stochastics, without taking into account that the proposal can handle huge networks. The algorithm is applied to the IEEE 14, 30, 57, 118 and 300-bus systems, and also to medium and large power systems of 1006, 3305, 15,000, 20,000 and 30,000 buses with success.

Synchro-phasor technology, using Phasor Measurement Unit (PMU), has improved the way power system data is collected for monitoring through state estimation. The placement of PMUs in a power system presents technical benefits, but it comes with high infrastructural costs. It is, therefore, necessary to install the minimum number of PMUs at optimal locations subject to power system observability, creating the Optimal PMU Placement Problem (OPPP). Some factors may be considered constraints in the OPPP, such as PMU outage. The main challenge with incorporating such constraints in the PMU placement problem is that the minimum number of PMUs required for system observation increases, contributing to the high infrastructural costs. This paper, therefore, proposes using a Linear Hybrid State Estimator (LHSE) that considers existing Remote Terminal Unit (RTU) measurements randomly distributed within the system and optimally placed Phasor Measurement Unit (PMU) measurements. The proposed LHSE addresses challenges associated with nonlinearity in state estimation. The LHSE is also based on the Weighted Least Absolute Value (WLAV) criterion, considered robust and able to detect and discard bad data during the estimation process. The proposed LHSE can address state estimation reliability and resiliency, specifically the PMU outage contingency, by employing existing RTU measurements and optimally placed PMU measurements based on the Artificial Bee Colony (ABC) optimization technique. The proposed approach also leverages RTU and PMU measurements to address PMU loss contingency instead of utilizing PMU measurements only as in existing studies. Three test cases (IEEE 14 Bus, IEEE 30 Bus, and IEEE 57 Bus) are considered, with the simulations performed in MATLAB using MATPOWER data. The performance of LHSE is evaluated considering PMU/RTU measurements and PMU measurements only scenarios. Both RTU/PMU measurements present a lower Normalized Cumulative Error (NCE) performance index than PMU measurements only. In case of a single PMU outage, the proposed LHSE can estimate all states based on RTU/PMU measurements instead of only PMU measurements that fail.

The conventional optimal PMU placement (OPP) methods minimize the number of PMUs along with guarantying full observability of the system. However, various OPP schemes with the same number of PMUs obtained for a power system have different performances in emergency conditions. Cascading outages as the major cause of recent large blackouts cancel out full observability of the system and decrease situational awareness. In this paper, the OPA model previously developed to simulate power system blackouts is modified in order to include observability analysis through the progress of the cascading outages. The modified process is performed in turn for a given set of OPP schemes. To rank these schemes, a criterion is proposed as a monetary value using produced data by the modified OPA model. Scalability of the proposed procedure is investigated in two test systems. Simulations show that although considering N-1 criterion in finding optimal PMU schemes decreases the consequences of transmission line cascading outages, it is not financially reasonable and does not lead to better performance of the OPP scheme. In other words, it is better to use OPP schemes in normal condition. KEYWORDS blackouts, cascading outages, observability, optimal PMU placement (OPP), self-organized criticality (SOC), wide area monitoring protection and control (WAMPAC) 1 | INTRODUCTION Power systems play an increasingly important role in our modern society. Engineering efforts have effectively improved reliability of these systems; transmission networks are being upgraded, new technologies are being developed, and operators are being trained to increase their abilities in order to successfully deal with emergency conditions. However, the frequency of blackouts has been significantly increased. Blackouts in power systems are threats with catastrophic consequences which can be described by the recently proposed complexity science especially its feature designated as SOC. 1 Power law is a fingerprint of SOC, which suggests that catastrophes are more likely than may be expected. 2 This implies that the risk of blackouts is high enough to be considered in studies of power systems. 3

This paper presents a new approach to solve line outage detection (LOD) problem utilizing current phasors obtained from phasor measurement units (PMUs). A new term that is, objective coefficient value (OCV), is introduced utilizing the rank correlation coefficient (RCC) and line outage detection is carried out based on the OCV. Moreover, the effect of bad data (BD) and measurement noises are also considered in the developed mathematical model. Furthermore, it has been proved that the suggested scheme can identify outage of parallel lines (PLs), whereas the existing voltage phasor-based algorithms fail to do so. Moreover, a new logical index that is, performance improvement w.r.t detection accuracy (PIDA) is introduced to quantify the superiority of the proposed scheme over some existing techniques. The developed algorithm is implemented on IEEE 5-bus, 14-bus, 57-bus, 118-bus systems, and large-scale Polish 2383-bus system. The comparison of test results with some existing methods proves the applicability and brevity of the developed algorithm.

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. The 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.

The transition from the conventional power systems to smart grids has led to the modernisation of the measuring infrastructure used for their monitoring and control. Among the devices used to accomplish these tasks, phasor measurement units (PMUs) play a key role since they can provide extremely accurate synchronised voltage and current phasor measurements. The optimal PMU placement (OPP) problem, which focuses on minimising the number of PMUs for full system observability, has long been a popular research topic. The vast majority of the available OPP techniques have treated each transformer tap setting (voltage turns ratio and phase-shifting angle) as a fixed network parameter. Such an assumption can lead to misdirecting residuals in adjacent valid measurements when the modelled tap setting is incorrect. The aim of this study is to propose a substation-oriented OPP method based on a binary semidefinite programming algorithm, considering the observability of the transformer tap settings and the limited PMU channel capacity. The method is illustrated using an 8-bus test system. Numerical results using different size IEEE systems are presented and discussed. The proposed approach is further applied to the Polish 3120-bus system to show its efficacy in solving the OPP problem for large-scale power systems.

This paper presents an efficient and comprehensive method to find out the minimum number and corresponding locations of phasor measurement units (PMUs) guaranteeing full numerical observability of a power system as well as maximizing the measurement redundancy in conjunction with pre-existing conventional measurements. Furthermore, the effect of the number of available channels of PMUs on their optimal placement can be taken into account. The proposed optimal PMU placement (OPP) formulation is extended to consider the case of two types of contingencies, single PMU loss and single branch outage. The objective in the OPP method is the numerical observability, unlike the majority of earlier works which are based on topological observability and do not always ensure numerical observability required for successful execution of state estimation. The problem is formulated as a binary semidefinite programming model with binary decision variables, minimizing a linear objective function subject to linear matrix inequality observability constraints. The binary semidefinite programming problem is solved using an outer approximation scheme based on binary integer linear programming. The effectiveness of the proposed method is verified on different IEEE test systems.

This paper presents an efficient and fast method, using topological and numerical procedures, for observability analysis in state estimation with phasor measurement units as well as conventional (SCADA) measurements. Power and current flow measurements are used to build topologically flow islands that, in turn, are used to construct a reduced network and an associated gain matrix. To build this reduced order gain matrix, boundary power injections, and voltage phasors at flow islands are considered. Observability checking is carried out analyzing the pivots encountered during the triangular factorization of the gain matrix, and the observable islands are identified in a noniterative manner, by performing back substitutions with its triangular factors. Additional measurements that will render the system barely observable are directly provided, using the triangular factors of a reduced Gram matrix associated with existing and candidate power injections and candidate phasor measurements at boundary buses of observable islands. The dimension of the gain and Gram matrix is equal to the number of flow islands and boundary measurements, respectively, which is relatively low even for very large systems, and that makes the proposed algorithms fast and computationally efficient. The IEEE 14 and 30-bus systems are used to illustrate the steps of the proposed algorithms.

Wide area monitoring system requires the integration of an advanced technology that provides real time synchronized phase angle measurements at all their measurement points. The phasor measurement units are the most advanced devices to achieve that. The objective of this work is first, to find the optimal placement of a minimum number of PMUs in some standardized IEEE systems. Next, the same method was applied to the Algerian 63 bus system. Two cases are taken into consideration: the minimum number of PMUs without considering the ZIB, then, considering the ZIB. The simulations are carried out using MATLAB/SIMULINK.

Wide area monitoring systems require the integration of new technologies that provide real time synchronized phase angle measurements. The Phasor measurement units (PMUs) are the most advanced devices to achieve this task so far. The objective of this work is to find the minimum number and optimal placement of PMUs in some standardized IEEE systems. The relatively new drone squadron optimization (DSO) technique is used to solve this problem. Next, fault location is studied based on the measurements collected from these PMUs. The simulations are carried out using MATLAB SIMULINK. The results show that it is possible to achieve the observability of the overall system; however, more PMUs are needed to locate the faults.

This paper presents a two-stage method for the placement of Phasor Measurement Units (PMUs) to achieve a fully observable power system while considering the PMUs channel limitation. The first stage uses the Binary Integer Linear Programming (BILP) to find the initial optimum locations of PMUs which ensure full system observability under normal conditions. The second stage uses state enumeration based on probabilistic failure of different components to ensure full system observability under single and double outages. The proposed method is validated using the IEEE 14-Bus system, IEEE 30-Bus system and IEEE 57-Bus system. The simulation results show that the method is efficient in providing detailed information about the observability of the power system under different operating conditions.

The text considers the relationship between Darwinian selection, genetic algorithms, and mathematics. The initial idea introduces some examples that can be presented to upper secondary school students. In this sense, the solution proposals differ from the traditional ones found in the literature and use IT supports already known to the students.

In this paper, the unstable natures of stock market forces were analysed using new differential equation model that could impact the expected returns of investors in stock exchange market with a stochastic volatility in the equation. The new results were obtained by developing stochastic vector differential equation, exploring the properties of the fundamental matrix solution (a function of the drift) of this equation and by placing continuity condition on the stochastic part (a function of the volatility). Example is given to illustrate the effectiveness of the model and simulation results presented graphically using MATLAB.

This paper presents a mathematical linear expansion model for the probabilistic Multistage Phasor Measurement Unit (PMU) Placement (MPP) in which zero-injection buses (ZIBs), as well as communication channel limitations, are taken into consideration. From the linearization perspective, presenting a model formulizing the probabilistic concept of observability while modelling the ZIB is of great significance, and has been done in this paper for the first time. More importantly, the proposed probabilistic MPP utilizes a technique disregarding the prevalent subsidiary optimizations for each planning stage. Although this technique, in turn, increases the problem complexity with manifold variables, it guarantees the global optimal solution in a wider and thorough search space; while in the prevalent methods, some parts of the search space might be missed. Furthermore, the proposed model indicates more realistic aspects of the MPP where system operators are allowed to follow their intention about the importance of buses such as strategic ones based on monitoring the priority principles. In addition, the model is capable of considering the network topology changes due to long-term expansions over the planning horizon. Finally, in order to demonstrate the effectiveness of the proposed formulation, the model is conducted on the IEEE 57-bus standard test system and the large scale 2383-bus Polish power system.

Despite of substantial development in measurement technology of phasor measurement units (PMUs), the utilization of PMU is still barely appreciated by the power industries due to its high installation cost. It motivated the researchers to find an optimal set of locations to obtain full observability of a network with least number of PMUs. A stage-wise optimal PMU allocation (SWOPA) approach is proposed in this paper using binary crow search algorithm (BCSA) based on the measurement reliability assessment of some sensitive buses. The effectiveness of the multiple outcomes (MOCs) obtained while solving the OPA problem is analyzed and a sensitive bus observability (SBO) assessment, associated with generator, weaker, and transformerconnected buses is mathematically modeled in this regards to determine the best outcome from those MOCs. The observability criteria of such sensitive buses are also incorporated in order to provide ranking in PMU bus nomination at each stage. The proposed method is demonstrated on IEEE 57-bus test system and its performance is verified with other methods.

This paper formulates and solves the problem of placing additional sensors into a dynamic system, with focus on enhancing the tolerance to loss of a specified number of sensors anywhere in the system under certain constraints. The placement criterion is based on a previously defined concept called control reconfigurability, which imposes a requirement on the minimum Hankel singular values for all anticipated fault scenarios. This requirement causes the placement of measurement devices to benefit the analytic redundancy in the dynamic system with respect to the anticipated sensor outages. The same principle is applicable to placing additional control devices into dynamic systems. A simple power network model is used to illustrate the fault-tolerant placement concept, and the particle swarm optimization algorithm is employed to minimize the additional number of sensors placed without violating the required control reconfigurability. The results of placing phase measurement units for the IEEE 118-bus system are presented.

Phasor measurement unit (PMU) technology is a need of the power system due to its better resolution than conventional estimation devices used for wide-area monitoring. PMUs can provide synchronized phasor and magnitude of voltage and current measurements for state estimation of the power system to prevent blackouts. The drawbacks of a PMU are the high cost of the device and its installation. The main aspect of using PMUs in electrical networks is the property to observe the adjacent buses, thereby making it possible to observe the system with fewer PMUs than the number of buses through their optimal placement. In the last two decades, exhaustive research has been done on this issue. Considering the importance of this field, a comprehensive review of the progress achieved until now is carried out and the limitations of existing reviews in the literature are highlighted. This paper can be seen as a major attempt to provide an up-to-date review of the research work carried out in this ...

Phasor measurement unit (PMU) technology is a need of the power system due to its better resolution than conventional estimation devices used for wide-area monitoring. PMUs can provide synchronized phasor and magnitude of voltage and current measurements for state estimation of the power system to prevent blackouts. The drawbacks of a PMU are the high cost of the device and its installation. The main aspect of using PMUs in electrical networks is the property to observe the adjacent buses, thereby making it possible to observe the system with fewer PMUs than the number of buses through their optimal placement. In the last two decades, exhaustive research has been done on this issue. Considering the importance of this field, a comprehensive review of the progress achieved until now is carried out and the limitations of existing reviews in the literature are highlighted. This paper can be seen as a major attempt to provide an up-to-date review of the research work carried out in this ...

We propose a method for voltage stability assessment of power systems using a support vector machine (SVM). We input the information from measurement signals to the SVM. The objectives of this paper are twofold: (1) to select the minimum number of features for training an SVM using multi-objective optimization (MOO); (2) to find the minimum misclassification rate for the SVM. To address these objectives, the training data size is decreased in two stages. First, a mutual information (MI) criterion is used to remove the less significant measurements from the data set. Second, the most relevant features are selected using multi-objective biogeographybased optimization (MOBBO). The minimization objectives are the measurement data size and the misclassification rate of the SVM. The BBO-based MO methods are vector evaluated BBO (VEBBO), nondominated sorting BBO (NSBBO), niched Pareto BBO (NPBBO), and strength Pareto BBO (SPBBO). These four MOO methods are compared using Pareto front normalized hypervolume, relative coverage, and statistical analysis. The methods are applied to a 39-bus benchmark system and a 66-bus real power grid. The results verify that the reduced measurement data using MOO lead to efficient and accurate SVMs. For the real power grid, the trained SVM accurately predicts the voltage stability of the system by using only 8% of the measurement data. The misclassification rates of the SVMs are as low as 2% for the real power grid. Normalized hypervolume, relative coverage, and statistical tests indicate that NSBBO performs better than the other methods.