Comparison of Optimum Reactive Power Schedule with Different Objectives Using LP Technique

Three algorithms for reactive power optimization are proposed in this paper with three different objective functions. The objectives in the proposed algorithm are to minimize the sum of the squares of the voltage deviations of the load buses, minimization of sum of squares of voltage stability L-indices of load buses (:3L2) algorithm, and also the objective of system real power loss (Ploss) minimization. The approach adopted is an iterative scheme with successive power flow analysis using decoupled technique and solution of the linear programming problem using upper bound optimization technique. Results obtained with all these objectives are compared. The analysis of these objective functions are presented to illustrate their advantages. It is observed comparing different objective functions it is possible to identify critical On Load Tap Changers (OLTCs) that should be made manual to avoid possible voltage instability due to their operation based on voltage improvement criteria under heavy load conditions. These algorithms have been tested under simulated conditions on few test systems. The results obtained on practical systems of 24-node equivalent EHV Indian power network, and for a 205 bus EHV system are presented for illustration purposes.

Reactive power and voltage control in grid connected wind farms

Wind power, as an alternative to fossil fuels, is plentiful, renewable, widely distributed, clean, produces no greenhouse gas emissions during operation, and uses little land. In operation, the overall cost per unit of energy produced is similar to the cost for new coal and natural gas installations. However, the stochastic behaviour of wind speeds leads to significant disharmony between wind energy production and electricity demand. Wind generation suffers from an intermittent characteristics due to the own diurnal and seasonal patterns of the wind behaviour. Both reactive power and voltage control are important under varying operating conditions of wind farm. To optimize reactive power flow and to keep voltages in limit, an optimization method is proposed in this paper. The objective proposed is minimization of the voltage deviations of the load buses (Vdesired). The approach considers the reactive power limits of wind generators and co-ordinates the transformer taps. This algorithm has been tested under practically varying conditions simulated on a test system. The results are obtained on a system of 50-bus real life equivalent power network. The result shows the efficiency of the proposed method.

A multi-winding transformer based power converter topology for a growing DC Micro-grid structure

A DC micro-grid essentially consists of power ports, bidirectional power converter and a controller structure that enables the control of dynamic power flow. In this paper, a prototype of a micro-grid structure using a recently proposed multi-winding transformer based power converter has been implemented. The power converter topology is further extended to multiple transformer cores in order to form a growing micro-grid structure. Additionally, modifications have been made in order to incorporate a battery charge controller with the main power circuit. All the other advantages of the power converter and its control scheme are still preserved.

Investigation of schemes for incorporating generator Q limits in the fast decoupled load flow method

Fast Decoupled Load Flow (FDLF) is a very popular and widely used power flow analysis method because of its simplicity and efficiency. Even though the basic FDLF algorithm is well investigated, the same is not true in the case of additional schemes/modifications required to obtain adjusted load flow solutions using the FDLF method. Handling generator Q limits is one such important feature needed in any practical load flow method. This paper presents a comprehensive investigation of two classes of schemes intended to handle this aspect i.e. the bus type switching scheme and the sensitivity scheme. We propose two new sensitivity based schemes and assess their performance in comparison with the existing schemes. In addition, a new scheme to avoid the possibility of anomalous solutions encountered while using the conventional schemes is also proposed and evaluated. Results from extensive simulation studies are provided to highlight the strengths and weaknesses of these existing and proposed schemes, especially from the point of view of reliability.

Flexible implementation of power system corrective topology control

This paper proposes a novel decision making framework for optimal transmission switching satisfying the AC feasibility, stability and circuit breaker (CB) reliability requirements needed for practical implementation. The proposed framework can be employed as a corrective tool in day to day operation planning scenarios in response to potential contingencies. The switching options are determined using an efficient heuristic algorithm based on DC optimal power flow, and are presented in a multi-branch tree structure. Then, the AC feasibility and stability checks are conducted and the CB condition monitoring data are employed to perform a CB reliability and line availability assessment. Ultimately, the operator will be offered multiple AC feasible and stable switching options with associated benefits. The operator can use this information, other operating conditions not explicitly considered in the optimization, and his/her own experience to implement the best and most reliable switching action(s). The effectiveness of the proposed approach is validated on the IEEE-118 bus test system. (C) 2015 Elsevier B.V. All rights reserved.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

An integrated design approach to power systems : from power flows to electricity markets

Power system is at the brink of change. Engineering needs, economic forces and environmental factors are the main drivers of this change. The vision is to build a smart electrical grid and a smarter market mechanism around it to fulfill mandates on clean energy. Looking at engineering and economic issues in isolation is no longer an option today; it needs an integrated design approach. In this thesis, I shall revisit some of the classical questions on the engineering operation of power systems that deals with the nonconvexity of power flow equations. Then I shall explore some issues of the interaction of these power flow equations on the electricity markets to address the fundamental issue of market power in a deregulated market environment. Finally, motivated by the emergence of new storage technologies, I present an interesting result on the investment decision problem of placing storage over a power network. The goal of this study is to demonstrate that modern optimization and game theory can provide unique insights into this complex system. Some of the ideas carry over to applications beyond power systems.

Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

Power system parameters forecasting using Hilbert-Huang transform and machine learning

A novel hybrid data-driven approach is developed for forecasting power system parameters with the goal of increasing the efficiency of short-term forecasting studies for non-stationary time-series. The proposed approach is based on mode decomposition and a feature analysis of initial retrospective data using the Hilbert-Huang transform and machine learning algorithms. The random forests and gradient boosting trees learning techniques were examined. The decision tree techniques were used to rank the importance of variables employed in the forecasting models. The Mean Decrease Gini index is employed as an impurity function. The resulting hybrid forecasting models employ the radial basis function neural network and support vector regression. A part from introduction and references the paper is organized as follows. The second section presents the background and the review of several approaches for short-term forecasting of power system parameters. In the third section a hybrid machine learningbased algorithm using Hilbert-Huang transform is developed for short-term forecasting of power system parameters. Fourth section describes the decision tree learning algorithms used for the issue of variables importance. Finally in section six the experimental results in the following electric power problems are presented: active power flow forecasting, electricity price forecasting and for the wind speed and direction forecasting.

Improved Direct Power Control of Grid Connected DC/AC Converters

This paper proposes new direct power control (DPC) strategies for three-phase DC/AC converters with improved dynamic response and steady-state performance. As with an electrical machine, source and converter flux which equal the integration of the respective source and converter voltage are used to define active and reactive power flow. Optimization of the look-up-table used in conventional DPC is outlined first, to improve the power control and reduce the current distortion. Then constant switching frequency DPC is developed where the required converter voltage vector within a fixed half switching period is calculated directly from the active and reactive power errors. Detailed angle compensation due to the finite sampling frequency and the use of integral controller to further improve the power control accuracy, are described. Both simulation and experimental results are used to compare conventional DPC and vector control, and to demonstrate the effectiveness and robustness of the proposed control strategies during active and reactive power steps, and line inductance variations.

A Wavelet-Prony Method for Modeling of Fixed-Speed Wind Farm Low-Frequency Power Pulsations

The increasing penetration of wind generation on the Island of Ireland has been accompanied by close investigation of low-frequency pulsations contained within active power flow. A primary concern is excitation of low-frequency oscillation modes already present on the system, particularly the 0.75 Hz mode as a consequence of interconnection between the Northern and Southern power system networks. In order to determine whether the prevalence of wind generation has a negative effect (excites modes) or positive impact (damping of modes) on the power system, oscillations must be measured and characterised. Using time – frequency methods, this paper presents work that has been conducted to extract features from low-frequency active power pulsations to determine the composition of oscillatory modes which may impact on dynamic stability. The paper proposes a combined wavelet-Prony method to extract modal components and determine damping factors. The method is exemplified using real data obtained from wind farm measurements.

Application of PMUs to Coordinate Hydroelectric and Wind Power Plant Operation

It is acknowledged that wind power is a stochastic energy source compared to hydroelectric generation which is easily scheduled. In this paper a scheme for coordinating wind power plant and hydroelectric power plant is presented by using PMUs to measure and control the state of wind and hydro power plants. Hydroelectric generation is proposed as a method of energy reserve and compensation in the context of wind power fluctuation in order to avoid full or partial curtailment of wind generation to benefit wind providers. The feasibility of this proposed scheme is investigated by power flow calculation and stability analysis using the IEEE 30-bus power system model.

Analysis of Fixed-Speed Wind Farm Low-Frequency Power Pulsations using a Wavelet-Prony Method

The increasing penetration of wind generation on the Island of Ireland has been accompanied by close investigation of low-frequency periodic pulsations contained within the active power flow from different wind farms. A primary concern is excitation of existing low-frequency oscillation modes already present on the system, particularly the 0.75 Hz mode as a consequence of the interconnected Northern and Southern power system networks. Recently grid code requirements on the Northern Ireland power system have been updated stipulating that wind farms connected after 2005 must be able to control the magnitude of oscillations in the range of 0.25 - 1.75 Hz to within 1% of the wind farm's registered output. In order to determine whether wind farm low-frequency oscillations have a negative effect (excite other modes) or possibly a positive impact (damping of existing modes) on the power system, the oscillations at the point of connection must be measured and characterised. Using time - frequency methods, research presented in this paper has been conducted to extract signal features from measured low-frequency active power pulsations produced by wind farms to determine the effective composition of possible oscillatory modes which may have a detrimental effect on system dynamic stability. The paper proposes a combined wavelet-Prony method to extract modal components and determine damping factors. The method is exemplified using real data obtained from wind farm measurements.

The Impact of Wind Farm Power Oscillations on the Irish Power System

The impact of power fluctuations arising from fixed-speed wind turbines on the magnitude and frequency of inter-area oscillations has been investigated. The authors introduced data acquisition equipment to record the power flow on the interconnector between the Northern Ireland and Republic of Ireland systems. Through monitoring the interconnector oscillation using a fast Fourier transform, it was possible to determine the magnitude and frequency of the inter-area oscillation between the two systems. The impact of tower shadow on the output power from a wind farm was analysed using data recorded on site. A case study investigates the effect on the system of the removal of a large fixed-speed wind farm. Conclusions are drawn on the impact that conventional generation and the output from fixed-speed wind farms have on the stability of the Irish power system.

Small Signal Stability Performance of Power System during High Penetration of Wind Generation

The small signal stability of interconnected power systems is one of the important aspects that need to be investigated since the oscillations caused by this kind of instability have caused many incidents. With the increasing penetration of wind power in the power system, particularly doubly fed induction generator (DFIG), the impact on the power system small signal stability performance should be fully investigated. Because the DFIG wind turbine integration is through a fast action converter and associated control, it does not inherently participate in the electromechanical small signal oscillation. However, it influences the small signal stability by impacting active power flow paths in the network and replacing synchronous generators that have power system stabilizer (PSS). In this paper, the IEEE 39 bus test system has been used in the analysis. Furthermore, four study cases and several operation scenarios have been conducted and analysed. The selective eigenvalue Arnoldi/lanczos's method is used to obtain the system eigenvalue in the range of frequency from 0.2 Hz to 2 Hz which is related to electromechanical oscillations. Results show that the integration of DFIG wind turbines in a system during several study cases and operation scenarios give different influence on small signal stability performance.