PLACEMENT OF PHASOR MEASUREMENT UNITS AND CONTROL OF ROTOR ANGLE STABILITY IN POWER SYSTEMS

Abstract

For secure and reliable operation of an interconnected power system, it is required to monitor wide area system and its stability in real time. The recent development of synchro phasor technology has brought a paradigm shift in real time analysis of power system. Phasor Measurement Unit (PMU) is the backbone of this Synchronized Measurement Technology (SMT). PMU measures the instantaneous voltage, current, and frequency from dispersed locations of a wide network. These analog system parameters are sampled 20 or more times per cycle. Phasor values are computed from these sampled values, and more than 30 phasor values are reported per second. Precise time stamp is added to each phasor value. Therefore, phasor measurement provides an electrical real-time picture with high resolution. This high-resolution picture aids in all kinds of monitoring, control, and protection applications. This thesis primarily focuses on application of PMU measurements in wide area monitoring and control of rotor- angle/dynamic stability. In wide area monitoring, the very first step, is to install phasor measurement units in the system. The prime objective of PMU installation is to make given system observable, either completely or incompletely. In practical scenario, PMU deployment requires large expenditure on its installation. Proper site preparation, establishment of adequate communication and Global Positioning System (GPS) are other essential requirements, which increase these financial constraints more. As a solution, PMU placement locations are selected optimally. Rich literature is available on various placement methodologies, such as Integer programming, depth-first search, and spanning tree methods. Intelligent techniques like genetic algorithm, Tabu search, simulated annealing, particle swarm optimization techniques are also reported. Presence of conventional measurements and loss of line or PMU are also extensively studied. However, placement methodology dealing simultaneously with three objectives i.e. observability, conventional measurements and redundancy is a requirement. In present work, all three objectives are formulated using quadratic programming approach. This quadratic problem is solved using Binary Particle Swarm Optimization (BPSO) technique to obtain optimal PMU locations. Further, to confirm efficiency of the ii approach, optimal results of BPSO are compared with locations obtained through GAMS-MIP solver. Today utilities are planning to place PMUs in large amount. In near future synchro-phasor number in the grid will increase substantially. With increase in number of synchro phasors, apart from topological and numerical observability, new methodologies are required to explore more benefits from PMU placement. In few power system applications, flow connectivity plays an important role, for example in congestion management. Therefore, it is essential to have a methodology to identify those PMU locations, through which maximum amount of power flow can be monitored. Since, power flow in the network depends on the load / demand of the network. Therefore, identification of those demand nodes, which affect maximum flow connectivity in a smart grid, is still an unanswered question. To address aforesaid problem, sequential placement scheme is suggested in present work. Proposed technique is based on power flow patterns and demand of the given system. Therefore, demand and flow coverage concept is introduced to formulate PMU placement. Formulation for multiple flow patterns is also addressed, which considers variable operating scenarios of power systems. PMU placement in phases or stages is another widely used approach for Optimal PMU Placement (OPP) problem. PMU placement in stages using Integer Linear Programming (ILP) and depth first search are reported in past. Few authors have considered phased placement with additional benefits in terms of bus and tie line observability. However, PMU placement based on control scheme for rotor-angle stability is not yet reported. As stated before, PMU placement is done to make system complete observable. For rotor angle stability, real time angular information is required, which means PMUs should be placed at generator buses. With limited number of PMUs, placement scheme dealing simultaneously with these two different issues is a need of time. In this thesis, a method is developed to identify and rank those PMU locations, which are important for rotor-angle stability. First, Eigen value analysis is carried out to determine inter-area modes. For these inter-area modes, control scheme is proposed. Based on control scheme, selection criteria namely, Generator bus observability criterion, tie-line observability criterion and bus observability criterion are introduced. Critical buses are iii identified based on these criteria and ranking of PMU locations is carried out using Analytical Hierarchical Process. Stability of power system is that property of the system, which governs continuance of intact operation following a disturbance. Stability of power system is characterized by its time varying nature. Traditionally performance of the system can be judged under a particular set of conditions. According to IEEE-CIGRE joint working group, power system stability is broadly classified into Rotor angle Stability, Voltage Stability and Frequency Stability. Rotor angle stability can be further divided into small-signal rotor angle stability and large-disturbance rotor angle stability or transient stability. Small-signal rotor angle stability is the ability of power system to maintain synchronism under small disturbances. These disturbances are considered significantly small, such that system can be analyzed by linearized equations. This instability is further sub divided into local and global. Local instability results due to presence of local mode, which are having frequencies from 1-10Hz. Power system stabilizers, are conventionally provided with each generator to control local mode. Global problems are caused by inter area modes having frequency between 0.1 to 1 Hz and have more widespread effects. To identify these local and inter area modes, which are responsible for oscillations usually Eigen value analysis is performed. These Eigen value based techniques are offline methods and does not work well for geographically large dynamic systems. Introduction of synchro phasor technology has encouraged utilization of direct measurements based techniques for mode identification. These measurement based techniques offers a real time solution to identify inter area modes. This thesis provides a real-time approach to analyze inter-area modes based on Continuous Wavelet Transform (CWT). Modal frequency and damping are estimated using Morlet based CWT with good accuracy. Results of CWT are verified through conventional Eigen value analysis. Presence of these inter area modes in an interconnected network has wide spread effects. These inter area modes results into inter area oscillations, which have adverse effects on transmission corridors. To enhance transmission through tie lines in near-by areas, additional damping is required. Recently, it is explored that remote machine can be used to provide this additional damping. With advent of phasor technology, it is easier to obtain remote machine iv speed signals with the help of PMUs. These remote machine signals are used to design wide area damping controllers. Literature reveals that robust and intelligent damping controllers are widely used for inter area oscillations. In a large practical system, it is important to select appropriate location of these damping controllers. Further, proper selection of feedback signals from generators is of immense importance. Since feedback, signals are communicated from remote locations, so they carry communication latencies or delays. In past, very few researchers have considered selection of controller location and feedback signals in detail. However, time delays are not reported in their work. In present work, first low frequency modes are identified. For identified modes, control scheme is proposed to select suitable controller location and input signal based on participation factors and controllability indices respectively. Wide area controllers based on Mamdani fuzzy inference system and Adaptive Neuro Fuzzy inference System (ANFIS) are designed to compensate time latencies and low frequency oscillations. Robustness of designed controllers is checked by varying various system parameters. According to IEEE 1344-1995 synchro-phasor standard, PMU data are uncertain due to errors in measurement of magnitude or angle of the phasor or due to error in time synchronization of synchro-phasors. Total vector error for PMUs should be less than 1%, which means measurements can have a maximum error of 1%. According to literature, PMU measurements are uncertain due to routing and packet delay. Further, PMUs cannot directly measure the internal states like rotor angle. These rotor angles are generally estimated through various rotor-estimating algorithms. Therefore, rotor angle measurements provided by PMUs depends on accuracy of these algorithms. Practically, accurate estimating algorithms also have few estimating errors, which make PMU measurements more uncertain and noisy. Therefore, for small signal stability problem a wide area-damping controller considering communication delay and measurement uncertainties is a requirement. As a solution, in this work, interval-type-2 fuzzy controllers are designed. To compensate measurement uncertainty, a method is introduced to model Foot of Uncertainty (FOU) of type-2 membership function from type-1 membership function. FOU is varied in gradual steps to test controller performance. Further, robustness of controller is verified by adding noise in the communicated signal. v In large power systems, sometimes superposition of local modes and inter area modes or occurrence of severe disturbances like three-phase to ground fault or loss of transmission lines, causes large excursions of generator rotor angles resulting into transient instability. Conventionally, time domain simulations are used for transient stability analysis. However, this technique is time consuming and requires accurate system information. As time- frame of interest in transient stability studies is usually 3-5 seconds following a disturbance which itself is of small duration. Therefore, fast and accurate transient predictor is needed to have secure operation of the system. A predictor having small prediction- time provides more time to utilities to take corrective and preventative actions. Since synchro-phasors are able to provide real time voltage and current information of the bus on which they are placed. Therefore, a transient predictor utilizing these précised information is essential for reliable performance of power system. Present thesis describes about transient stability predictor based on relevance vector machine. Three different features are considered in the work, for training predictor. These features are obtained from sampled values of generator bus voltage and angle profiles. To validate effectiveness of the predictor, sample values are gradually increased from 2 to 7 samples. Later, RVM predictor is compared with SVM predictor for different number of samples.