G.K. Stefopoulos

PMU-based dynamic state estimation for electric power systems

This paper provides a methodology to extract the dynamic real time model of an electric power system using phasor measurement unit (PMU) data (GPS-synchronized) and other SCADA data that are available in substations. In addition to typical voltage and current measurements, PMU data include frequency and rate of change of frequency. Such data are available in raw form, as time-stamped instantaneous values, or, in the case of voltages and currents, as computed phasor data at the system fundamental frequency. A dynamic state estimator is conceptually presented that filters all available data to extract the transient swings of the system in real time. This means that the power system dynamic state estimator can be essentially used as a real time data processor, and its results can provide filtered input to many power system dynamic monitoring and control applications that are currently unavailable, such as monitoring transient stability.

Induction Motor Load Dynamics: Impact on Voltage Recovery Phenomena

This paper addresses the impact of load dynamics, and in particular induction motor loads, on voltage recovery after disturbances. The paper proposes a methodology that is based on load flow techniques with advanced modeling capabilities, augmented by a simplified induction motor dynamic model. The objective is to realistically capture the dynamic characteristics of voltage recovery phenomena, avoiding, however, the full scale transient simulation. The approach uses the quadratized power flow model with explicit induction motor representation. The paper describes the modeling approach and the overall methodology for evaluating the load dynamics on voltage recovery. Preliminary results of the application of the method on a simple power system with load dynamics are also included in the paper

A Comprehensive Approach for Bulk Power System Reliability Assessment

This paper proposes a comprehensive approach for bulk power system reliability assessment. Specifically, a framework of security-constrained adequacy evaluation (SCAE) based on analytical techniques is developed to assess the ability of a bulk power system to supply electric load while satisfying security constraints. This approach encompasses three main steps: (a) critical contingency selection, (b) effects analysis, and (c) reliability index computation. Based on an advanced single-phase quadratized power flow, a state linearization approach is developed to improve contingency selection accuracy, and a non-divergent optimal quadratized power flow (NDOQPF) algorithm is proposed to perform contingency effects analysis realistically and efficiently while assuring the convergence of power flow solution. The NDOQPF algorithm is also capable of solving the RTO/ISO operational model in the deregulated environment. In addition, a breaker-oriented system network model is developed, based on which the SCAE framework can include the effects of protection system hidden failures on bulk power system reliability as well. The comprehensive approach is demonstrated with IEEE reliability test systems.

Numerical experiments for three-phase state estimation performance and evaluation

Relatively poor performance of state estimators is a well documented experience. Yet, control and operation of electric power system requires reliable state estimators. The poor performance is attributed to implementation simplifications that use single phase asynchronous measurements and the positive sequence model of the system. These simplifications have generated practical problems. The experience is that the state estimation problem does not have 100% performance, i.e. there are cases and time periods that the SE algorithm will not converge. There are practical and theoretical reasons for this and they are explained in the paper. The paper also demonstrates that these problems are correctable by using a three phase asymmetric model of the system and precise modeling of three phase and/or single phase measurements. This approach leads to an enhanced hybrid SE approach that combines the current SCADA type data with three phase phasor measurements. The performance of the hybrid state estimator is demonstrated with visualization techniques that clearly demonstrate the superiority of the three phase modeling and hybrid data sets. The performance is demonstrated with data from an actual electric power network. Numerical experiments on this system have quantified the performance gains of the three phase hybrid state estimator.

Advanced contingency selection methodology

This paper describes the development and implementation of contingency ranking and selection algorithms, as part of a power system security assessment program. The work concentrates on performance-index-based algorithms and uses a contingency control variable for precise contingency representation. The ranking is based on the value of the sensitivity of the performance index with respect to the contingency control variable for each outage. The computation of the sensitivities is performed using the very efficient co-state method. Furthermore an approach for improving the accuracy of performance-index-based contingency ranking methods is introduced. This approach is based on state rather than performance index linearization with respect to the contingency variable and it provides more accurate results in contingency ranking and selection. The effectiveness of the proposed method in identifying critical contingencies is illustrated using some small test systems. The ultimate goal is to achieve fast and accurate contingency selection, without having to solve the full load-flow problem for each contingency (as is the current utility practice).

Visualization and Characterization of Stability Swings via GPS-Synchronized Data

This paper provides a methodology to characterize the accuracy of PMU data (GPS-synchronized) and the applicability of this data for monitoring system stability via visualization methods. GPS-synchronized equipment (PMUs) is in general higher precision equipment as compared to typical SCADA systems. Conceptually, PMU data are time tagged with precision better than 1 microsecond and magnitude accuracy that is better than 0.1%. This potential performance is not achieved in an actual field installation due to errors from instrumentation channels and system imbalances. Presently, PMU data precision from substation installed devices is practically unknown. On the other hand, specific applications of PMU data require specific accuracy of data. Applications vary from simple system monitoring to wide area protection and control to voltage instability prediction and transient stability monitoring. The paper focuses on the last application, i.e. transient stability monitoring. We propose an approach that is based on accurate evaluation of the system energy function (Lyapunov indirect method) and extraction of stability properties from the energy function. Specifically, we provide a methodology for determining the required data accuracy for the reliable real time estimation of the energy function. When the data meet these requirements, the estimated energy function can be visualized and animated providing a powerful visual tool for observing the transient stability or instability of the system

A Genetic Algorithm Solution to the Governor-Turbine Dynamic Model Identification in Multi-Machine Power Systems

Speed governors are key elements in the dynamic performance of electric power systems. Therefore, accurate governor models are of great importance in simulating and investigating the power system transient phenomena. Model parameters of such devices are, however, usually unavailable or inaccurate, especially when old generators are involved. Most methods for speed governor parameter estimation are based on measurements of frequency and active power variations during transient operation. This paper proposes a genetic algorithm based optimization technique for parameter estimation, which makes use of such measurements. The proposed methodology uses a real-coded genetic algorithm. The paper estimates the parameters of all system generators simultaneously, instead of every machine independently, which is fully in line with the interest to treat the electric power system as a whole and study its comprehensive behaviour. Moreover, the methodology is not model-dependent and, therefore, it is readily applicable to a variety of model types and for many different test procedures. The proposed methodology is applied to the electric power system of Crete and the results demonstrate the feasibility and practicality of this approach.

Quadratized model of nonlinear saturable-core inductor for time-domain simulation

This paper presents the nonlinear, time-domain model of a saturable-core inductor. The model is capable of accommodating high-order nonlinearities by representing the current-flux characteristic of the inductor by an analytical (closed form) polynomial function of high degree. An automated procedure is developed to transform the highly nonlinear model to a fully-equivalent quadratic model, without introducing any approximations. Subsequently, using the quadratic equivalent model, the algebraic companion form is developed based on the trapezoidal and the quadratic integration rules. The presented model can be utilized in transformer or surge arrester modeling to capture nonlinear phenomena that may occur, as for example, during energization of transformers. Such condition may appear during cold load pick-up after severe disturbances and transients in distribution feeders.

On Three-Phase State Estimation in the Presence of GPS-Synchronized Phasor Measurements

The paper presents a comparative study among several state estimation formulations, in the presence of GPS-synchronized phasor measurements. The presented approach is based on a hybrid state estimation formulation, which uses both traditional SCADA measurements as well as phasor measurements. Three different formulations are presented that use: (a) Cartesian representation of state and measurements, (b) Cartesian representation of state and measurements with the addition of pseudomeasurements, and (c) polar representation of state and measurements. A physically-based three-phase model of a power system is utilized. The three formulations are compared in terms of error and confidence level analysis, via a simple introductory example.

Characterization Of State Estimation Biases

Control and operation of electric power system is based on the ability to determine the state of the system in real time. State estimation (SE) has been introduced in the 60s to achieve this objective. The initial implementation was based on single phase measurements and a power system model that is assumed to operate under single frequency, balanced conditions and symmetric system model. These assumptions are still prevalent today. The single frequency, balanced and symmetric system assumptions have simplified the implementation, but have generated practical problems. The experience is that the state estimation problem does not have 100% performance, i.e. there are cases and time periods that the SE algorithm will not converge. There are practical and theoretical reasons for this and they are explained in the paper. Recent mergers and mandated RTOs as well as recent announcements for formation of mega RTOs will result in the application of the SE in systems of unprecedented size. We believe that these practical and theoretical issues will become of greater importance. There are scientists that believe that the SE problem is scalable meaning that it will work for the mega RTOs the same way as it performs now for medium-large systems. There are scientists that they believe this is not true. The fact of the matter is that no-one has investigated the problem, let alone perform numerical experiments to prove or disprove any claims. This paper identifies a number of issues relative to SE of mega RTOs and provides some preliminary results from numerical experiments for the relation between the SE algorithm performance and the power system size.