Phasor Measurement Units Loss Research Articles

A Graph-Theoretic Approach for Optimal Phasor Measurement Units Placement Using Binary Firefly Algorithm

The pursuit of achieving total power network observability in smart grids using Phasor Measurement Units (PMUs) carries a significant promise of real-time Wide-Area Monitoring, Protection, and Control (WAMPAC). PMU applications eliminate periodical measurements, thereby increasing accuracy through a high sampling rate of the measured power systems quantities. The high costs of installation of PMUs for total power system observability presents a challenge in the implementation of PMUs. This is due to the expensive costs of PMU devices. This has led to a prominent optimal PMU placement (OPP) problem that researchers tirelessly aim to solve by ensuring a complete power network observability while using the least installed PMU devices possible. In this paper, a novel Binary Firefly Algorithm (BFA) based on the node degree centrality scores of each bus is proposed to minimize PMU installations. The BFA solves the OPP problem in consideration of the effect of Zero Injection Buses (ZIBs) under normal operation and single PMU outage (SPO). The robustness and efficiency of the proposed algorithm is tested on IEEE-approved test systems and visualized with a force-directed technique on an undirected power network graph. The proposed BFA yields the same but better optimal PMU numbers, obtained by existing meta-heuristic optimization techniques found in the literature for each of the IEEE test cases, as well as highlighting the cost–benefit of having a robust system against single PMU loss while considering the ZIB effect for an improved system measurement availability.

A Multiobjective Intelligent Decision-Making Method for Multistage Placement of PMU in Power Grid Enterprises

The wide area measurement system (WAMS) based on synchronous phasor measurement technology plays an increasingly important role in dynamic monitoring and wide area protection of modern power systems. If the phasor measurement unit (PMU) is placed on all buses of the power system, the voltage and branch current of all buses can be directly observed. However, due to the high placement cost of PMU and its ability to measure the voltage phasor of the installed bus and the current of the associated branch, it is unrealistic and unnecessary to install PMU on all buses of the system. This paper discusses the incomplete observability under single PMU loss (N-1) contingencies and its effect on PMUs placement. An improved two-archive algorithm is proposed to solve the five-objective placement optimization model. In addition, a fuzzy decision-making method combining subjective and objective is proposed to help power grid enterprises select the most appropriate solution. The proposed method is tested on several IEEE bus systems and Polish 2383-bus system, and the test results verify its effectiveness.

Optimal Placement of Phasor Measurement Unit in Smart Grids Considering Multiple Constraints

The distribution of measurement noise is usually assumed to be Gaussian in the optimal phasor measurement unit (PMU) placement (OPP) problem. However, this is not always accurate in practice. This paper proposes a new OPP method for smart grids in which the effects of conventional measurements, limited channels of PMUs, zero-injection buses (ZIBs), single PMU loss contingency, state estimation error (SEE), and the maximum SEE variance (MSEEV) are considered. The SEE and MSEEV are both obtained using a robust <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> -distribution maximum likelihood estimator (MLE) because <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> -distribution is more flexible for modeling both Gaussian and non-Gaussian noises. The A- and G-optimal experimental criteria are utilized to form the SEE and MSEEV constraints. This allows the optimization problem to be converted into a linear objective function subject to linear matrix inequality observability constraints. The performance of the proposed OPP method is verified by the simulations of the IEEE 14-bus, 30-bus, and 118-bus systems as well as the 188-bus practical distribution system in China.

Evaluating Performance of a Linear Hybrid State Estimator Utilizing Measurements From RTUs and Optimally Placed PMUs

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.

WITHDRAWN: Critical bus ranking constrained optimal allocation of PMUs for network observability

The paper presents critical bus ranking to allocate Phasor Measurement Units (PMUs) in network considering Integer Linear Programming (ILP). A Reactive Load Sensitive Index (RLSI) is proposed which depends upon reactive power change at load to find critical buses. Contingency cases like PMU loss or N-1 outages are chosen for PMU placement (OPP). Zero Injection (ZI) model is formulated to further minimize allocations in network for OPP. ZI modeling for normal and outage conditions is formulated and compared. Performance of observability of network is checked with Complete Network Observability Index (CNOI) approach. IEEE 14, 30 and 57-bus test cases are programmed for proposed method in MATLAB and are compared with existing techniques to present its efficacy.

Experimental Validation of High-Performance HIL-Based Real-Time PMU Model for WAMS

This article presents a novel real-time hardware-in-loop-based model for synchronized phasor measurement unit (PMU) which incorporates an adaptive observer to estimate the phasor quantities of the actual hardware-based PMU model. The proposed model is feasible for a wide-area monitoring system (WAMS) in modern power grids. The performance of the proposed model is compared to the conventional algorithms of the performance (P)-class and measurement (M)-class PMU models in terms of total vector error and rate of change of frequency under different scenarios (frequency ramp, unbalance with interharmonics, and out-of-bound offnominal frequency). The main advantages of the proposed model compared to existing models are as follows: (1) combining the advantages of both P and M classes in terms of achieving required standard steady-state performance (IEEE C37.118-2005) while capturing the dynamic system performance, (2) improving the redundancy due to PMU loss, (3) allowing faster implementations and advanced visualization tools, and (4) enhancing WAMS accuracy performance. Despite the advantageous introduced utilizing the proposed model, there is still a tradeoff gap between the investment cost of the installed hardware-based PMUs and system redundancy. Moreover, a laboratory-scale six-bus setup is built and tested to demonstrate the practical validity of the proposed model.

Convolutional neural network-based power system transient stability assessment and instability mode prediction

Online transient stability assessment (TSA) is vital for power system control as it provides the basis for operators to decide emergency control actions. But none of previous TSA research has taken into consideration the difference between two instability modes (aperiodic instability and oscillatory instability), which may threaten secure operation of power system. To address this problem, a TSA and instability mode prediction method based on convolutional neural network is proposed. The method takes the bus voltage phasor sampled by phasor measurement units (PMUs) during a short observation window after disturbance as input, and outputs the prediction result promptly: stable, aperiodic unstable or oscillatory unstable. The end-to-end model automatically extracts needed features from the raw measurement data, thus freeing itself from reliance on expertise. At the offline training stage, stochastic gradient descent with warm restart (SGDR) optimization algorithm is employed so that the model tends to converge to 'flat' and 'wide' minima with better generalization ability. Case studies conducted on New England 39-bus system and Western Electricity Coordinating Council (WECC) 179-bus system demonstrate superior accuracy, adaptability and scalability of the proposed method compared with conventional machine learning methods. Furthermore, the proposed model is empirically proven to be robust to PMU noise and loss.

Optimal PMU Placement using Binary Particle Swarm and Artificial Bee Colony with Channel Limitations and Redundancy.

Phasor Measurement Unit (PMU) being expensive and to be placed optimally, a meta-heuristic approach of Binary particle swarm optimization (BPSO) and Binary artificial bee colony optimization (BABC) is made for the optimal allocation of PMU in a power system. The PMU locations resulted are served by basic system conditions like network configuration, critical generators, and loads. The pattern of locations on including Zero-Injection Buess (ZIB) is also discussed. The redundancy in case of PMU loss is coined so as to obtain a complete observability of the power system. the channel limitations of device is also taken into consideration for better results in real-time systems. Optimal PMU locations for IEEE 30-bus and 14-bus systems with channel limits are compared with all above considerations. The number of PMU locations is reduced as channel limits increases. The simulated PMU locations are decreased with improved observability by Binary Artificial Bee Colony Optimization as compared to Binary Particle Swarm Optimization.

A Missing-Data Tolerant Method for Data-Driven Short-Term Voltage Stability Assessment of Power Systems

With the widespread deployment of phasor measurement units (PMUs), synchronized measurements of the power system has opened opportunities for data-driven short-term voltage stability (STVS) assessment. The existing intelligent system-based methods for data-driven stability assessment assume full and complete data input is always available. However, in practice, after a fault occurs in the system, some PMU data may not be fully available due to PMU loss and/or fault-induced topology change, which deteriorates the stability assessment performance. To address this issue, this paper proposes a missing-data tolerant method for post-fault STVS assessment. The buses in the system are strategically grouped to maintain a high level of grid observability for the stability assessment model under any PMU loss and/or topology change scenario, and a structure-adaptive ensemble learning model is designed to adapt its structure to only use available feature inputs for real-time STVS assessment. By marked contrast to existing methods, the proposed method demonstrates much stronger missing-data tolerance and can maintain a high STVS assessment accuracy even when a large portion of measurements are missing.

Optimal Allocation of Phasor Measurement Units Considering Various Contingencies and Measurement Redundancy

This article presents an efficient and comprehensive method to find out the minimum number of and the corresponding locations of phasor measurement units (PMUs) guaranteeing full numerical observability of a power system as well as maximize the measurement redundancy in conjunction with preexisting conventional measurements. Furthermore, the effect of 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 of 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 the successful execution of state estimation (SE). The problem is formulated as a binary semidefinite programming (BSDP) model with binary decision variables, minimizing a linear objective function subject to linear matrix inequality (LMI) observability constraints. The BSDP 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.

Novel notions of zero injection property of buses in optimal PMU location with efficient observability enhancement focusing on security concepts

In this paper, a new method is proposed for security-oriented, optimal placement of phasor measurement units (PMUs) incorporating efficient observability redundancy. In this way, novel concepts in zero-injection buses (ZIBs) are introduced. The proposed concepts regard aspects of the ZIBs effect that have not yet been studied; thus, by applying this concept, maximum possible capacity of the ZIBs will be available for use. Therefore, the proposed method is capable of producing optimum possible results with tangibly higher ZIBs capacity usage and measurement redundancy levels than those reached in preceding works. In addition, the reliability of fragile areas monitoring from overvoltage viewpoint is enhanced. Considering the fact that complete synchronized network observability is undeniably significant for making control decision in critical conditions to avoid brownouts or blackouts, a novel practical framework is proposed based on backup observability concept in order to model branch outage in addition to PMU loss and channel failure. All proposed security models can be tested by practical, large-scale test systems such as Polish 2383- and 3375-bus. Also, in the case of branch outage, selective security criteria are considered so as to enhance security of network observability against cascading failures in electric power systems.

An Improved OPP Problem Formulation for Distribution Grid Observability

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 with the mixed integer linear programming (MILP)-based approach and the referenced works. The obtained results demonstrate the superiority of the proposed formulation and solution methodology compared to other methodologies.

ILP-Based Optimal PMU Placement with the Inclusion of the Effect of a Group of Zero-Injection Buses

Zero-injection buses (ZIBs) can reduce the number of phasor measurement units (PMUs) required to be installed for complete observability. It has been demonstrated that a group of neighboring ZIBs can further reduce this required number of PMUs. In contrast to a single ZIB, the effect of a group of ZIBs has not been incorporated into the model of optimal PMU placement (OPP) using mathematical approaches, except for some heuristics methods. In this paper, a novel methodology to incorporate the effect of a group of ZIBs into the OPP model is proposed, using the integer linear programming approach. Two common contingencies—line outage and PMU loss—are also considered. Moreover, two visualization techniques are used for illustrating the locations of PMUs obtained from OPP: (1) using a graph-based force-directed method and (2) on a map using the geographic information system. The proposed method is verified using several small- and large-scale test systems and compared with other related studies.

Optimal Location of Phasor Measurement Unit Using Ant Colony Optimization Under Contingency

Accurate and fast monitoring is achieved by using the real time synchronized phasor data obtained from Phasor Measurement Unit (PMU). As the cost of PMU is more expensive, it is not economical to install PMU at all the nodes of a power system. Therefore, it is very much essential to implement an optimal method for PMU location. In this research work, implementation of Ant Colony Optimization (ACO) for optimal PMU placement under normal and single PMU loss conditions is discussed. The PMUs are placed in such a manner that all voltage phasors and current phasors are measurable with a minimum number of PMUs. The proposed ACO is able to locate the PMUs optimally enabling the complete measurement of all voltage and current phasors with a minimum number of PMUs. The ACO is an efficient optimization algorithm to optimize the placement of the PMU for measuring the voltage and current phasors with minimum no of PMU. The proposed method is demonstrated in IEEE 14 bus, IEEE 30 bus, and IEEE 57 bus to find the optimal location of PMU under normal and for single PMU loss conditions.

Contingency constrained phasor measurement units placement with n − k redundancy criterion: a robust optimisation approach

This study presents a novel approach for the contingency constrained phasor measurement units (PMUs) placement. The proposed approach is based on n − k redundancy criterion using robust optimisation. This security criterion ensures observability of the network under any contingency state, containing the loss of up to k PMUs. In the proposed method, the effects of zero injection and power flow measurements as well as possible contingency states (such as branch outage and single or multiple PMU loss) are considered. The non-linear modelling of observability function for measurements is reformulated by linearisation process. The resulting bi-level programming model is solved by its evolution to an equivalent single-level mixed-integer programming problem. The objective function of the optimal PMU placement is aimed at minimising the number of PMUs in a way that guarantees economic goals and the observability of all network buses. The advantage of this model is to significantly reduce the computational burden compared with other methods. The proposed method is tested on modified 7-bus test network, 118- and 2383-bus IEEE test networks. The results of the case studies clearly demonstrate the simplicity and efficiency of the proposed robust optimisation method in different cases.

Integrated Mutation Strategy With Modified Binary PSO Algorithm for Optimal PMUs Placement

Optimal phasor measurement units (PMUs) placement refers to the strategic placement of PMUs to achieve the full observability of power systems with a minimum number of PMUs. A strategic placement is needed because of the economic or technical restriction that hinders the deployment of PMUs on every bus. A modified version of the binary particle swarm optimization method is proposed in this paper by integrating a mutation strategy and the V-shaped sigmoid function for placing the PMUs that maintains the full power system observability in the presence of zero-injection bus, single PMU loss, and PMU's channel limits while maximizing the measurement redundancy. The solution that has the highest measurement redundancy was selected as the best placement of PMUs. The use of mutation strategy and V-shaped sigmoid function in this paper improves the population diversity, thereby minimizing the chance of the particles being trapped in the local optima, consequently leading to a quality solution. In order to validate its effectiveness, the results obtained by the proposed method are compared with other published techniques to demonstrate the accuracy and validity of the proposed technique. The results of the IEEE 300-bus system show that the proposed method effectively managed to reduce the number of PMUs needed.

Optimal PMU placement solution: graph theory and MCDM‐based approach

In this study, a new method using graph theory and analytical hierarchy process (AHP)-based multi-criteria decision making approach has been proposed to solve optimal phasor measurement unit (PMU) placement (OPP) problem for complete network observability. The proposed approach assures maximum measurement redundancy too. A decision matrix is formed with some unique criteria from the concept of network graph theory and this helps to formulate priority vertex ranking using AHP. Candidate vertex search technique is used to enumerate the candidate PMU placement vertices from priority vertex ranking. The contribution of zero injection buses (ZIBs) in PMU placement problem has been considered. The proposed technique is further analysed for complete observability under single PMU loss or line outage cases. The proposed approach is tested on IEEE 14-bus, 24-bus, 30-bus, 57-bus, 118-bus, and New England 39-bus systems. To verify the computational efficiency and higher redundancy of solutions of the proposed method, the results are compared with some well-established methods reported in the literature. The proposed method is further applied to IEEE 300-bus, Polish 2383-bus and 3120-bus system to show the efficacy of the proposed approach in solving OPP in large scale power systems.

Multi-objective Phasor Measurement Unit Placement in Electric Power Networks: Integer Linear Programming Formulation

A multi-objective optimal phasor measurement unit placement model using integer linear programming is presented in this article. The proposed model simultaneously optimizes two objectives, i.e., minimization of phasor measurement unit numbers and maximization of measurement redundancy. To calculate the redundancy criteria, the single-line outage and the phasor measurement unit loss are considered simultaneously. A linear formulation is presented for both objective functions. Also herein, to address conflicting attributes and identify Pareto optimal solutions of the multi-objective optimal phasor measurement unit placement problem, a new multi-objective mathematical programming method is proposed. Finally, a new index, i.e., minimum distance to utopia point, is implemented to select the most preferred solution among the available Pareto front based options on the goal to achieve judicious decision makers. Two test systems, i.e., a modified 9-bus and an IEEE 118-bus test systems, are used to illustrate the effectiveness of the proposed framework.

Intelligent-search technique based strategic placement of synchronized measurements for power system observability

Synchronized phasor measurements placement problem is commonly solved by formulating it as a mathematical optimization problem, which is limited by huge computational burden especially for larger systems. This paper proposes a novel intelligent search based approach for placement of phasor measurement units (PMUs) in the power system while maintaining complete observability. The proposed approach works in two stages. Stage I utilizes best first search to identify the possible locations of PMUs in order to obtain system observability and these locations are used as inputs to stage II. Stage II determines the optimal locations of PMUs by applying pruning to the inputs received from stage I, such that the system observability is achieved with the minimum number of PMUs. The proposed approach has been further extended to incorporate the presence of conventional flow measurements. An important feature of the proposed placement method is its capability to handle both single as well as multiple flow measurements connected to a bus. The proposed method has been tested on IEEE 14-bus, IEEE 30-bus and a practical 246-bus Indian networks for system intact condition as well as during single transmission line and single PMU loss. The effectiveness of the proposed method has been demonstrated by comparing the numerical results obtained using the proposed method with the existing methods.

Probabilistic PMU Placement in Electric Power Networks: An MILP-Based Multi-objective Model

This paper presents a multiobjective probabilistic model for the placement of phasor measurement units (PMUs) in electrical power networks. The proposed model simultaneously optimizes two objectives functions: 1) minimizes the number of PMUs; and 2) maximizes the expected value of system's redundancy (or minimizes the unobservability of the system). Incorporating the impact of zero-injection buses, an efficient formulation is used to evaluate the probability of unobservability of buses resulted from line outages and PMU loss. The extracted formulation is based on the mixed integer linear programming (MILP) framework, which is efficiently solvable by high-performance commercial solvers. This multiobjective optimization problem (MOP) is solved by augmented epsilon-constraint and weighting approach. Accordingly, two new indices are introduced to compare these two multiobjective methods. Finally, the ultimate solution among the Pareto front is recognized using a fuzzy decision-making process. The IEEE 57-bus test system is used to examine the effectiveness of the proposed frameworks.