Real-Time State Estimation and Voltage Stability Assessment of Power Grids: From Theoretical Foundations to Practical Applications

The operators of power distribution systems strive to lower their operational costs and improve the quality of the power service provided to their customers. Furthermore, they are faced with the challenge of accommodating large numbers of Distributed Energy Resources (DERs) into their grids. It is expected that these problems will be tackled with a large-scale deployment of automation technology, which will enable the real-time monitoring and control of power distribution systems (i.e., similar to power transmission systems). For this purpose, real-time situation awareness w.r.t. the state and the stability of the system is needed. In view of the deployment of such automation functions into power distribution grids, there are two binding requirements. Firstly, the system models have to account for the inherent unbalances of power distribution systems (i.e., w.r.t. the components of the grid and the loads). Secondly, the analysis methods have to be real-time capable when deployed into low-cost embedded systems platforms, which are the cornerstones of automation. In other words, the analysis methods need to be computationally efficient. This thesis focuses on the modeling of unbalanced polyphase power systems, as well as the development, validation, and deployment of real-time methods for State Estimation (SE) and Voltage Stability Assessment (VSA) of such systems. More precisely, the following theoretical and practical contributions are made to the field of power system engineering. 1. Fundamental properties of the compound admittance matrix of polyphase power grids are identified. Specifically, theorems w.r.t. the rank of the compound admittance matrix, the feasibility of Kron Reduction (KR), and the existence of compound hybrid matrices are stated and formally proven. These theorems hold for generic polyphase power grids (i.e., which may be unbalanced, and have an arbitrary number of phases). 2. A Voltage Stability Index (VSI) for real-time VSA of polyphase power systems is proposed. The proposed VSI is a generalization of the well-known L-index, which is achieved by integrating more generic models of the power system components. More precisely, the grid is represented by a compound hybrid matrix, slack nodes by Thévenin equivalents, and resource nodes by polynomial load models. In this regard, the theorems mentioned under item 1 substantiate the applicability of the proposed VSI. 3. A Field-Programmable Gate Array (FPGA) implementation for real-time SE of polyphase power systems is presented. This state estimator is based on a Sequential Kalman Filter (SKF), which - in contrast to the standard Kalman Filter (KF) - is suitable for implementation in such dedicated hardware. In this respect, it is formally proven that the SKF and the standard KF are equivalent if the measurement noise variables are uncorrelated. To achieve high computational performance, the grid model is reduced through KR, and the SKF calculations on the FPGA are parallelized and pipelined. 4. The methods stated under items 1-3 are deployed into an industrial real-time controller, which is used to control a real-scale microgrid. This microgrid is equipped with a metering system composed of Phasor Measurement Units (PMUs) coupled with a Phasor Data Concentrator (PDC). The real-time capability of the developed methods is validated experimentally by measuring the latencies of the PDC-SE-VSA processing chain w.r.t. the PMU timestamps

A Generalized Index for Static Voltage Stability of Unbalanced Polyphase Power Systems including Th\'evenin Equivalents and Polynomial Models

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., compound hybrid parameters), and the aggregate behavior of the devices in each node by Th\'evenin Equivalents (TEs) and Polynomial Models (PMs), respectively. The proposed VSI is a generalization of the known L-index, which is achieved through the use of compound electrical parameters, and the incorporation of TEs and PMs into its formal definition. Notably, the proposed VSI can handle unbalanced polyphase power systems, explicitly accounts for voltage-dependent behavior (represented by PMs), and is computationally inexpensive. These features are valuable for the operation of both transmission and distribution systems. Specifically, the ability to handle the unbalanced polyphase case is of particular value for distribution systems. In this context, it is proven that the compound hybrid parameters required for the calculation of the VSI do exist under practical conditions (i.e., for lossy grids). The proposed VSI is validated against state-of-the-art methods for voltage stability assessment using a benchmark system which is based on the IEEE 34-node feeder

Induction motor analyses including non-sinusoidal excitation

The electromagnetic theory of induction motors has been developed taking into account both the space and time harmonic spectrums. Three different approaches of analyses have been presented: a rigorous approach that deals directly with the system of partial differential equations of the field problem, a simplified approach that uses the transmission-line concept for solving the field problem, and a third approach that lies between the simplicity of the transmission-line approach and the comprehensive use of the boundary conditions of the rigorous approach. All of the analyses have been presented in their most general forms. This permits the solution of any general field problem of any machine configuration;It is concluded that some design parameters have a significant effect on the machine performance, and can be used to get an optimal machine design

Milestones, hotspots and trends in the development of electric machines

As one of the greatest inventions of human beings, the electric machine (EM) has realized the mutual conversion between electrical energy and mechanical energy, which has essentially led humanity into the age of electrification and greatly promoted the progress and development of human society. This paper will briefly review the development of EMs in the past two centuries, highlighting the historical milestones and investigating the driving force behind it. With the innovation of theory, the progress of materials and the breakthrough of computer science and power electronic devices, the mainstream EM types has been continuously changing since its appearance. This paper will not only summarize the basic operation principle and performance characteristics of traditional EMs, but also that of the emerging types of EMs. Meanwhile, control and drive system, as a non-negligible part of EM system, will be complementarily introduced. Finally, due to the background of global emission reduction, industrial intelligentization and transportation electrification, EM industry will usher again in a golden period of development. Accordingly, several foreseeable future developing trends will be analyzed and summarized

Fourier Analysis for Harmonic Signals in Electrical Power Systems

The harmonic content in electrical power systems is an increasingly worrying issue since the proliferation of nonlinear loads results in power quality problems as the harmonics is more apparent. In this paper, we analyze the behavior of the harmonics in the electrical power systems such as cables, transmission lines, capacitors, transformers, and rotating machines, the induction machine being the object of our study when it is excited to nonsinusoidal operating conditions in the stator winding. For this, a model is proposed for the harmonic analysis of the induction machine in steady‐state regimen applying the Fourier transform. The results of the proposed model are validated by experimental tests which gave good results for each case study concluding in a model proper for harmonic and nonharmonic analysis of the induction machine and for “harmonic” analysis in an electrical power system

Real-time power system dynamic simulation

The present day digital computing resources are overburdened by the amount of calculation necessary for power system dynamic simulation. Although the hardware has improved significantly, the expansion of the interconnected systems, and the requirement for more detailed models with frequent solutions have increased the need for simulating these systems in real time. To achieve this, more effort has been devoted to developing and improving the application of numerical methods and computational techniques such as sparsity-directed approaches and network decomposition to power system dynamic studies. This project is a modest contribution towards solving this problem. It consists of applying a very efficient sparsity technique to the power system dynamic simulator under a wide range of events. The method used was first developed by Zollenkopf (^117) Following the structure of the linear equations related to power system dynamic simulator models, the original algorithm which was conceived for scalar calculation has been modified to use sets of 2 * 2 sub-matrices for both the dynamic and algebraic equations. The realisation of real-time simulators also requires the simplification of the power system models and the adoption of a few assumptions such as neglecting short time constants. Most of the network components are simulated. The generating units include synchronous generators and their local controllers, and the simulated network is composed of transmission lines and transformers with tap-changing and phase-shifting, non-linear static loads, shunt compensators and simplified protection. The simulator is capable of handling some of the severe events which occur in power systems such as islanding, island re-synchronisation and generator start-up and shut-down. To avoid the stiffness problem and ensure the numerical stability of the system at long time steps at a reasonable accuracy, the implicit trapezoidal rule is used for discretising the dynamic equations. The algebraisation of differential equations requires an iterative process. Also the non-linear network models are generally better solved by the Newton-Raphson iterative method which has an efficient quadratic rate of convergence. This has favoured the adoption of the simultaneous technique over the classical partitioned method. In this case the algebraised differential equations and the non-linear static equations are solved as one set of algebraic equations. Another way of speeding-up centralised simulators is the adoption of distributed techniques. In this case the simulated networks are subdivided into areas which are computed by a multi-task machine (Perkin Elmer PE3230). A coordinating subprogram is necessary to synchronise and control the computation of the different areas, and perform the overall solution of the system. In addition to this decomposed algorithm the developed technique is also implemented in the parallel simulator running on the Array Processor FPS 5205 attached to a Perkin Elmer PE 3230 minicomputer, and a centralised version run on the host computer. Testing these simulators on three networks under a range of events would allow for the assessment of the algorithm and the selection of the best candidate hardware structure to be used as a dedicated machine to support the dynamic simulator. The results obtained from this dynamic simulator are very impressive. Great speed-up is realised, stable solutions under very severe events are obtained showing the robustness of the system, and accurate long-term results are obtained. Therefore, the present simulator provides a realistic test bed to the Energy Management System. It can also be used for other purposes such as operator training

The monitoring of induction motor starting transients with a view to early fault detection.

The aim of this work is to investigate the possibility of detecting faults in a 3 phase Induction motor by monitoring and analysing the transient line current waveform during the starting period. This is a particularly onerous time for the machine and the inter-relationships between parameters such as current, torque, speed and time are very complex. As a result two parallel paths of investigation have been followed, by methods of experimentation and computer simulation. Transient line current signals have been obtained from purpose built test rigs and these signals have been analysed in both the time and frequency domains. In order to assist with the comprehension of this data a sophisticated computer simulation of the induction motor during the starting period has also been developed. Computer simulation of the induction motor has been developed initially using the two and then three phase induction motor voltage equations which are solved by numerical integration. Using these techniques it has been possible to detect small degrees of fault level for both wound and cage rotor machines by analysing the line current waveform during the starting period. Good agreement has been found between the real and simulated data. A range of Digital Signal Processing techniques have been utilised to extract the components indicative of rotor faults. These techniques were at first wideband and highly numerically intensive, some originating from Speech Processing. The final processing techniques were far simpler and selected by analysis of the results from experimental data, both real and simulated

Connection imbalance in low voltage distribution networks

On British electricity distribution networks, the phase to which single phase loads and generators are connected is, in most cases, unknown. There is concern that large imbalances in connection will limit the capacity of the network to support distributed generation as well as the electrification of heating and transport. The roll-out of Smart Metering in Britain, expected to be completed by the end of 2020, provides Distribution Network Operators with a means to predict the phase of single phase connections and more accurately assess the impact of increased distributed generation. This thesis examines these possibilities. There are three main sections: 1. Development of a steady state LV feeder modelling program allowing for flexible definition of connection imbalance and suitable for use with a supercomputer. 2. Development of a stochastic method to assess the combined influence (on voltages, currents and losses) of connection imbalance and photovoltaic generation. 3. Creation of an algorithm for the prediction of phase connections using Smart Meter Data, based on the GB smart metering proposals. The LV feeder model uses an unbalanced load flow based on network reduction and re-expansion with nodal analysis. It was validated using PSCAD. The feeder model uses a TNS earthing arrangement; this was shown to be equivalent to TN-C-S in normal operation, allowing for simpler modelling. A metric for connection imbalance was introduced – the highest proportion of houses connected to any phase. The model is capable of varying connection imbalance by changing the phase to which each house is connected. The connection imbalance was varied by randomly allocating houses to different phases. Demand profiles were created stochastically and PV generation was added to a varied proportion of houses (0 to 100% in 10% steps). More than 19 million unbalanced load flow calculations were performed using a supercomputer. It was found that, for a typical urban feeder serving residential properties, connection imbalance is not a significant problem for DNOs until it becomes severe (>60% of houses on one phase). The phase identification algorithm combines two methods found in the literature; voltage measurement clustering and solution of the subset sum problem. It uses vii smart meter voltage profiles and active power profiles with current measured at the supply substation. It correctly predicted the phase connection for 97% of smart meters, using simulated data representing a set 100 different connection configurations, across 6 different days (different sets of demand profiles) with a measurement averaging timeframe of 30 minutes

Transient behaviour of a 3-phase slip-ring induction motor with external impedance in the rotor circuit

An investigation is described into the effect of an external rotor circuit impedance on both the steady state and the transient behaviour of a 3-phase slip-ring induction motor. The external impedance took the form of a 3-phase resistor, capacitor, or saturistor and attention is directed towards the differences in the current, torques and speeds of the motor produced by the extra circuit components. [Continues.