On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems

Most techniques for power system analysis model the grid by exact electrical circuits. For instance, in power flow study, state estimation, and voltage stability assessment, the use of admittance parameters (i.e., the nodal admittance matrix) and hybrid parameters is common. Moreover, network reduction techniques (e.g., Kron reduction) are often applied to decrease the size of large grid models (i.e., with hundreds or thousands of state variables), thereby alleviating the computational burden. However, researchers normally disregard the fact that the applicability of these methods is not generally guaranteed. In reality, the nodal admittance must satisfy certain properties in order for hybrid parameters to exist and Kron reduction to be feasible. Recently, this problem was solved for the particular cases of monophase and balanced triphase grids. This paper investigates the general case of unbalanced polyphase grids. Firstly, conditions determining the rank of the so-called compound nodal admittance matrix and its diagonal subblocks are deduced from the characteristics of the electrical components and the network graph. Secondly, the implications of these findings concerning the feasibility of Kron reduction and the existence of hybrid parameters are discussed. In this regard, this paper provides a rigorous theoretical foundation for various applications in power system analysi

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

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

Invertibility Conditions for the Admittance Matrices of Balanced Power Systems

The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of invertibility. Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.Comment: 8 pages, 1 figure, submitted to IEEE Transactions on Power System

Steady state analysis of integrated A.C. and D.C. systems.

This thesis describes the development of a general method for the analysis of integrated a.c. and d.c. systems under normal, but not necessarily balanced, steady state operation. Phase component three phase system modelling is reviewed and the relationship of the well known symmetrical components to the three phase modelling is discussed. Using as a reference the single phase fast decoupled algorithm the modifications required to produce an efficient three phase fast decoupled load flow are described. It is demonstrated that the three phase fast decoupled load flow displays all the characteristics of the original single phase version. Single phase balanced convertor modelling is reviewed and several techniques for the integration of such models with the single phase fast decoupled load flow are developed and their performance is compared. The methods for single phase convertor modelling are extended to allow unbalanced convertor operation to be analysed. The integration of the unbalanced convertor model into the three phase fast decoupled load flow is described. Convergence properties are examined and detailed results given. The extension of steady state analysis techniques to the consideration of harmonic frequencies is discussed. The unbalanced convertor model is used as a basis to enable the harmonic interaction of d.c. convertors and the a.c. system to be studied

Ground fault current: Calculation of magnitude and its distribution in the neutral and ground paths

This thesis focuses on the ground fault current distribution and presents a method that enables a high accuracy in its calculation: starting from the model based on multi-conductor representation developed in Matlab, simulations are carried out to analyse which parameters influence the current distribution. These simulations, applied even on the portion of a real network, are also carried out on the commercial software Neplan and OpenDSS to validate the model

Nonlinear Modeling of Power Electronics-based Power Systems for Control Design and Harmonic Studies

The massive integration of power electronics devices in the modern electric grid marked a turning point in the concept of stability, power quality and control in power systems. The evolution of the grid toward a converter-dominated network motivates a deep renovation of the classical power system theory developed for machine-dominated networks. The high degree of controllability of power electronics converters, furthermore, paves the way to the investigation of advanced control strategies to enhance the grid stability, resiliency and sustainability. This doctoral dissertation explores four cardinal topics in the field of power electronics-based power systems: dynamic modeling, stability analysis, converters control, and power quality with particular focus on harmonic distortion. In all four research areas, a particular attention is given to the implications of the nonlinearity of the converter models on the power system