Figure 1. Optimal PMU placement for a 14-bus test system The PMU at bus 2 can not only measure the voltage phasor of bus 2, but also the current phasors of branches 2-1, 2-3, 2-4 and 2-5. Using Ohm’s law, the voltage phasors at buses 1, 3, 4 and 5 can be obtained from the branch currents and the voltage at bus 2. Having determined voltage phasors at buses 1, 2, 3, 4, and 5, the current phasors of branches 1-5, 3-4 and 4-5 can be calculated. Following the same logic, PMU at bus 6 can measure the voltage phasor at bus 6 and the current phasors of branches 6-5, 6-11, 6-12 and 6-13, thus allowing the calculation of the voltage phasors at buses 5, 11, 12, 13 and the current phasor of branch 12-13. PMU at bus 9 can measure the voltage phasor at bus 9 and the current phasors of branches 9-4, 9-7, 9-10, 9-14 and allow the calculation of the voltage phasors at buses 4, 7, 10, 14, and the current phasors of branches 4-7. As voltage phasors of buses 10, 11, 13, 14 are known, current phasors of branches 10-11 and 13-14 can now also be calculated. Using the known current phasors of branches 4-7 and 9-7, and the zero injection at bus 7, the current phasor of branch 7-8 can be derived using the Kirchhoff’s Current Law. The only remaining unknown voltage phasor at bus 8 can now be calculated by using the voltage phasor at bus 7 and the current phasor of branch 7-8. Thus the entire system becomes observable by placing only three PMUs at buses 2, 6, 9 and by considering the zero injection at bus 7.
ABSTRACT—The Phasor Measurement Unit (PMU) is an important tool for monitoring and control of the power system. It gives real time, synchronized measurements of voltages at the buses and also current phase values which are incident to those buses where these PMUs are located. This paper presents a topological approach to determine the optimal PMU placement in order to make the system completely observable using binary integer linear programming. The proposed formulation istested on various IEEE test systems and results so obtained for complete observability of system at normal condition and with loss of single PMU are also presented in this paper. The proposed PMU placement has been implemented on IEEE -14, 30, 57 and 118 bus systems, practical 75-bus system of Utter-Pradesh State Electricity Board (UPSEB) and New England 39-bus system.
ABSTRACT: In wide-area measurement systems, PMUs are the main component measuring real time- synchronized data from different buses. Installation of PMUs at all buses is a primary way to provide full observability of the power network. However, it is not practical in real networks due to the relatively expensive cost of PMUs and other technical limitations. Optimal PMU Placement (OPP) is an optimization problem providing full observability of the power network with a minimum number of PMUs. However, additional goals are often considered in OPP problem. In this paper, OPP problem is solved from voltage stability viewpoints. The presence of VSC-HVDC based resources and decomposition of the power network into intentional islanded parts are selected as two main approaches to improve the voltage stability margin in the power network. Hence, OPP solution is obtained considering both integrated and islanded operation modes of the network with the presence of HVDC links and their voltage stability considerations. Since the location of HVDC could simultaneously affect the network voltage stability and OPP results, the proposed algorithm is designed as a multi stage method to obtain optimal locations for both HVDC link and PMUs. Due to the linear and binary structure of the problem, Binary Integer Linear Programming (BILP) is used to solve the problem. The performance of the proposed OPP problem is investigated on IEEE 14-, 30- and 118-bus test systems considering normal operation and different contingencies consist of Single PMU Failure (SPF) and Single Line Outage (SLO).
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74 Moreover the proposed algorithm was based on the unrealistic assumption of an infinite channel capacity of available PMUs. But in practice the PMU has a limited channel capacity, in fact some of the studies have shown that it is neither economical nor necessary to use PMUs with a channel limit of more than 3 or 4 [11, 12]. Here it may be noted that in the present work a PMU channel implies how many branch currents the PMU can measure in addition to the bus voltage at which it is installed. The actual number of PMU channels may be more as it has to measure three phase current and voltage. The primary objective of the present work is to show that the channel capacity of PMU should be an integral consideration while devising an intentional islanding methodology. To make the study general, it is assumed that the PMUs available can monitor current through only one branch in addition to the voltage of the bus at which the PMU is installed. These PMUs are termed as branch PMUs as the PMU belongs to a branch and may be installed on any of the two buses at the ends of that branch, unlike a particular bus in case of multiple channels PMU. Some of the large utilities in the world have deployed a special type of PMU having only a single channel. The branch PMU offers significant benefits like uniform distribution in the network, adaptable to deployment in multiple stages, higher reliability and these units may be daisy-chained if more branches are to be monitored at a bus .
M.Tech Student, Department of Electrical Engineering, Government college of Engineering, Amaravati, India 1 Associate Professor, Department of Electrical Engineering, Government college of Engineering, Amaravati, India 2 ABSTRACT: Optimalphasor measurement units (PMUs) placement involves the process of minimizing the number of PMUs needed while ensuring the entire power system completely observable. A power system is identified observable when the voltages of all buses in the power system are known. Cases with and without the zero injection measurements are considered. The optimal PMU placement problem can be achieved using linear constraints. This implies that optimal PMU placement problem with zero injection busses can be solved by standard Binary Integer Programming (BIP) solvers. Subsequently, a simple and an effective methodology has been presented to handle single PMU outage as well as single line outage in the system.
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In this paper, a MILP method is introduced in order to find the least number of required PMUs for system observability and their most suitable locations to maximize total measurement redundancy of the power system. Measurement redundancy means the number of times that a bus is observed by different PMUs more than once . An inventive method is proposed to incorporate conventional measurements of branch flow measurements and zero injection buses into the redundant optimal PMU placement. Furthermore, the effect of single branch outage and single PMU failure is incorporated in the proposed method. When a branch with a flow measurement goes out, the network loses one observability path (the branch) and one conventional measurement (the flow measurement). Or, when a branch connected to a zero injection bus goes out, the other terminal bus loses its chance to be seen by zero injection bus property. The permutation matrix proposed here is able to model both cases mentioned above; this is not done in previous works, where merely the outage of branches is considered without any change to the set of flow measurements.
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replaced by the weaker constraint 0 ≤ x ≤ 1. The algorithm searches for a binary integer feasible solution and updates the best binary integer feasible point found so far as the search tree grows. It verifies that no better integer feasible solution is possible by solving a series of linear programming problems. Only the branch-bus model of the network is needed for reducing the number of PMUs and their optimal locations. In this paper, a simple method is presented to implement suitable constraints in power systems having zero injections and conventional measurements. The proposed OPP method while considering channel limits is based on nodal connectivity and branch selectivity matrices. This paper has been organized into five sections. Section I presented a brief about Optimal PMU placement problem along with the literature survey as the topic. Section II detailed in brief about the power system observability analysis .Optimal PMU Placement Problem and modeling has been elaborated in detail in Section III. The results of simulated studies on different test systems have been reported in Section IV. The observations from all the results obtained has been concluded in Section V. Simulations are conducted on standard IEEE 14-bus, IEEE 39-bus, IEEE 57-bus and IEEE 118-bus systems and results were found to be efficient in comparison with the recent literature published. [5 , -  ,  , .
This paper proposes a generalized integer linear programming formulation for optimal PMU placement under different cases of redundant PMU placement, full observability and incomplete observability. This generalized formulation, considering the situations with and without zero injection measurements, shows that the problem of optimal PMU placement can be modeled linearly and can be solved by integer linear programming. The generalized formulation paves an efficient way for future research in PMU placement and related topics. From the simulation results we can see that the proposed algorithm is computationally efficient and can be used in practice.
We consider the reconstruction of shared secrets in communication networks, which are modelled by graphs whose components are subject to possible failure. The recon- struction probability can be approximated using minimal cuts, if the failure proba- bilities of vertices and edges are close to zero. As the main contribution of this paper, node separators are used to design a heuristic for the near-optimal placement of se- crets sets on the vertices of the graph.
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systems. Though TCSCs can be placed at any feasible location in the power system, their locations and ratings are to be fixed optimally as they turn out to be costlier than the conventional compensating devices. Here the problem of device placement is guided through the WIPSO algorithm which gives the solution for the comprehensive objective function consisting of cost of the device, load voltage deviations and line loadings. The proposed method yields an efficient solution when compared to PSO and considerably reduces load voltage deviations and relieve the lines off their over loads under various load conditions.
In this paper, application of Bat algorithm to the optimal placement and sizing of capacitors in radial distribution systems has been discussed in two approaches. The practical application and efficiency of these approaches are evaluated using two test systems (34 and 85 bus). From the comparative analysis it is concluded that, BAT algorithm gives better results than other existing methods, in terms of solution quality. According to convergence BAT converged very quickly due to simple evolution process.. In fact, for any optimization algorithm parameter tuning plays an important role in the performance of the algorithm. From the results; BAT are proved to be promising tools to solve such type of constrained objective optimization problems. So, it may be concluded that the solution given by BAT to the specific problem is best so far. Thus the results obtained pave the way for new and promising research area, utilizing BAT algorithms with proper modifications, may give better results with high convergence speed.
In ,a particle swarm algorithm by considering the harmonic distortion for the capacitor placement is presented in radial distribution network. The objective function is combination of the capacitor costs and active losses costs. In , the PSO algorithm to solve this problem, with the aim of minimizing the losses in radial distribution network has been used.
In addition, some even curious about how to get the optimal placement for security cameras and minimum numbers of cameras used. This study is designed to determine an optimal placement of the field of view and the number of cameras, given a specific task constraints, and the set of possible cameras may use in the layout. The minimum numbers of cameras are placing in door spacing. The interesting part is the area to be observed by cameras may be a specific polygon additional constraint. Besides that, there may include a number of dynamic or static objects and obstacles in sensitive area such as furniture, columns, walls and holes. Therefore, C programming was used to help find the minimum cameras to cover the whole region in 2D floor. Consequently, to provide effective scientific evidence to cover industries in selecting suitable places for cameras and save costs.
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Abstract: In this research paper, PSO is joint with Newton Raphson method of power flow to optimize optimal location along with size of renewable energy source. A NR method is used to measure the losses and find the voltage at each bus. The PSO is used to locate the best location as well as sizing of renewable energy source. The main aim is to reduce the losses and keep the voltage profile acceptable. IEEE 30 bus standard system is used for the observations. There is the comparison of results of system without renewable energy source and with renewable energy source by some methods of optimization. Wind farm is considered as the renewable energy source.
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In this thesis we have shown that it is possible to design impairment-aware optical WDM networks that guarantee protection against single-link failures. We developed an ILP formulation that may be used to obtain optimal solution for small networks (with size of 11 nodes or less) and a heuritic that works for medium to large scale back- bone networks. A remarkable feature of the heuristic is that for 60 node networks, in 98.5% of the 200 cases we tested , our heuristic does give optimal solutions. For 40 node networks in 99% of the cases we tested, we obtained optimal solutions. For the isolated cases where we did not obtain solution which is known to be optimal, our heuristic needed only one additional site more that the lower limit on the number of nodes needed in an optimal solution. Current back-bone networks require less than 30 nodes. For instance, the USAnet, although spanning a wide geographical area, has only 24 nodes. Therefore, our heuristic will remain viable for the foreseeable future.
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ABSTRACT:Phasor Measurement Unit (PMU) is a relatively new technology that, when employed in power networks, offers real-time synchronised measurements of the voltages at buses and currents along the lines that connect them. This is accomplished by using a GPS based monitoring system which facilitates time synchronisation of measurements and unlike SCADA, makes the measured data available in Real-Time format. SCADA is not able to provide Real-time data due to the low speeds at which RTUs (Remote Terminal Units) provide data. Availability of time-stamped phasor measurements makes PMUs preferable for power system monitoring and control applications such as State Estimation, Instability Prediction Analysis, Real time monitoring of the system conditions, Islanding Detection, System Restoration and Bad Data Detection. Since PMUs are expensive, their procurement and installation needs to be planned both in terms of economy and utility. Usually utilities like to see that the power network becomes fully observable with minimum number of PMUs placed at strategic buses. Where full observability refers to all the buses in the network are actively monitored. Thus the problem of optimal placement of PMUs is formulated as an optimization problem where the number of PMUs is minimized subject to complete system observability. This paper solves the optimal placement of PMUs for power system observability using Integer Linear Programming (ILP) methodology. The method is tested on IEEE 14 Bus System.
PowerFactory’s optimal power flow (OPF) module optimiz- es a certain objective function in a network whilst fulfilling equality constraints (the load flow equations) and inequality constraints (that is, generator reactive power limits) . By means of simple command edit dialogues it is possible to cal- culate the optimal placement, type and size of capacitors in radial distribution networks; the optimal separation points of meshed networks and the optimal type of reinforcement cables and overhead lines. The cable-size optimization process mini- mizes the annual cost of the network. As constraints for the optimization it uses the admissible voltage band (in terms of maximum voltage drop along the feeder) and loading limits for the planned network.
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In the placement of PMU various cases are represented and zero injection buses are carried out to reduce the needed of PMU. By single failure of PMU makes the reliability of the system with improved. In order to resolve the failure instead of single PMU each bus is considered with two PMUs at least. By using WLS and LAV, the system estimation and the bus system phase angles and voltages are related the PMU with and without. After es- timation, it is clear that the LAV is well than WLS and it minimize the errors when including PMU. For the analysis of voltage stability the data are used and processed by using two indices-FVSI and LQP. The possibility study for random selection of lines with a stressful situation is carried out under various condition of operating for obtaining ideas .
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Majid Moazzami et al  discussed that by restructuring power systems, power plant companies improve power quality and the reliability of our distribution systems after using modern instruments. Also, using these distributed generation sources (DGs) and distribution static synchronized compensator (D-STATCOM) in the distribution systems are increased. The reduction of losses in the distribution systems and system energy losses costs is compared. In this article, to determine the optimal position of installation of instruments, used an objective function which consists of equipment's installation.
Garima Choudhary et al  investigated optimal placement of the Static Synchronous Compensators (STATCOMs) in order to enhance voltage stability limits and reduce the transmission losses. Continuous expansion of the power demands and the lack of supply have led to study on the Flexible Alternating Current Transmission System (FACTS) devices, as fascinated area for the research. Considering the benefits and applications of FACTS devices. 1.2 REACTIVE POWER COMPENSATION