Handbook of Optimization in Electric Power Distribution Systems

The voltage regulation in distribution systems refers to the primary objective of maintaining customers’ voltages within an acceptable range under all loading conditions. This function has been accomplished by the Volt/Var control—a strategy that coordinates voltage regulating devices and reactive power controls in order to reach a suitable operation of the system. As the modernization of the distribution grid has become a reality, new intelligent and updated schemes for Volt/Var control must be developed to face the recent operating scenario challenges and to make use of the technological advances in infrastructure. Under those circumstances, Volt/Var control has the task of achieving high quality power supply and, at the same time, meeting strict performance goals on the grid operation. To tackle these problems, intelligent systems are built providing a computational efficient optimization engine. In this context, this chapter presents the Volt/Var control, from basic concepts to advanced topics, laying the foundation for a complete optimization framework and introducing the Volt/Var optimization as a determinant tool to further enhance system operation objectives.

High penetration level of the renewable energy resources in the power distribution network is one of the main issues of the distribution system operator due to voltage deregulation, power losses and other control problems associated with intermittency of renewable energy resources. To resolve these problems following the increasing penetration level of distributed generators (DGs), appropriate reactive power control of DGs, that can lead to the voltage profile improvement and power loss minimization, should be addressed. This chapter proposes a consensus-based distributed algorithm for the optimal reactive power control (OPRC) of DGs in the power system. Proposed algorithm is found to be effective to optimize the multi-objective function including power loss, and voltage deviation of the distribution systems. The effectiveness and scalability of the proposed algorithm have been validated by testing it on 6-bus and 162-bus distribution systems and then comparing its results with the centralized control scheme.

This chapter presents a linear model to determine node voltages and branch currents of unbalanced power distribution systems (PDS). The model allows to obtain approximate solutions for the load flow problem trough the solution of a system of linear equations, instead of using an iterative process as in the conventional load flow. Besides, a discussion on load modeling in PDS is presented to support the proposed model. Numerical studies are presented using a modified version of the IEEE 34-node test feeder. The agreement of results obtained with our linear model with corresponding results obtained through a conventional nonlinear load flow allowed to conclude that the proposed model is not only valid but also can give accurate results.

Most of renewable energy technologies and energy storage devices are operated in dc. Indeed, solar photovoltaic generation and batteries require a dc/ac converter in order to be integrated into a conventional ac distribution grid. Dc distribution emerges a suitable alternative that reduces the losses and increases reliability in modern smartgrids. Classical methodologies such as the optimal power flow require to be adapted to this new scenario. However, just as in the case of ac grids, the power flow in dc distribution grids is non-linear non-convex. Therefore, convex approximations are required in order to guarantee convergence and global optimality. Several approximations can be proposed including second order cone optimization, semidefinite programming and linealization. These approximations are analyzed theoretically and numerically in this chapter.

This chapter addresses the Energy Storage System (ESS) sitting and sizing problem for renewable support. It is divided into four major subtitles in order to give the reader an introduction of the issue by providing fundamental information and theorical background to show the basic concepts for solving the intended problem, and discusses perspectives to encourage the reader for further research. Also, it solves two practical examples using specific optimization tools. In the first part of the chapter, ESS applications for Renewable Support is presented with general introduction to renewable energy system and its limitations. Subsequently, the ESS technologies with different characteristics are described and possible applications of ESS are presented from the perspective of the utility, medium and large-business, and off and micro-grid scale applications. The second part presents the optimization methods that is used in ESS sizing and sitting problems. These methods consider heuristic and meta-heuristic approaches with a major focus on evolutionary algorithms. An optimization formulation and ESS modelling for given power system application considering specific objective function and constraints are also presented. In the third part, future applications of the ESS, together with set of possible subjects that can expand the ESS field of research are presented. Finally, the fourth part presents two practical examples of ESS support problem using HOMER proprietary software and a Genetic Algorithms, respectively. Based on the ESS specifications and types, performance is examined for selected scenarios of network architecture. In both solution procedures, the algorithms established the size of ESS for optimal technical and economic performance for the distribution system.

The need for secure and flexible operation of distributed power systems and the decline in prices for Li-ion batteries have made energy storage deployment a viable option. The electric energy storage units’ characterization (including Li-ion batteries) currently utilized for power system operation and planning models relies on two major assumptions: the charge and discharge efficiencies are constant during such processes, and the maximum charge and discharge rates are independent of the system’s state of charge. This approach can lead to an over- or underestimation of the available power and energy for supporting services such as frequency response and load balancing; thus, threatening the overall system reliability. In this chapter, we introduce an optimal stochastic operation model for distribution systems with energy storage. We, firstly, present the power flow formulation for distribution networks and derive its equivalent second-order conic reformulation. Secondly, we introduce an ideal energy storage model and a new detailed linear model for the state-dependent characterization of the unit’s charge and discharge processes. Finally, we integrate the proposed model into a deterministic and stochastic economic operation model of a distribution power grid to illustrate the benefits of a detailed battery characterization, in comparison with the existing constant efficiency approach. The proposed energy storage models are computationally compared on a modified IEEE 33-bus electric distribution system.

This chapter introduces the Network Reconfiguration (NR) concept in Distribution Networks (DNs) as an efficient scheme to face various operational issues like reliability improvement and loss reduction. Furthermore, the potential for utilizing NR to perform voltage profile improvement under high DG or Renewable Energy Sources (RESs) penetration is presented. Finally, the coordination of the NR along with the optimal siting and sizing of DG units aiming to maximize their impact on loss reduction is also analyzed. The basic aim of this chapter is to demonstrate how specific automation upgrade in modern DNs regarding the replacement of manual switching equipment by automated controlled sectionalizers or tie-switches could allow Distribution System Operators (DSOs) to integrate real time management techniques of the DN under relatively low investment plans. Specific examples regarding both real and benchmarked DNs are included and the proposed algorithms are explained in detail.

It is a daunting task to find optimum number and placement of sectionalizing switches in Distribution Automation (DA) feeders. Switch optimization is the most essential component of evaluating economic feasibility of a DA project and one has to consider the trade-off between reliability and economics to arrive at the answer. This chapter presents a novel iterative algorithm for the optimal switch number and placement problem. The proposed iterative algorithm can determine the solution faster compared to traditional switch optimization techniques by minimizing the total interruption costs at each step of the analysis. The proposed algorithm does not rely on varying switch capital investment and customer interruption cost data that are usually based on outdated utility surveys. The proposed method has been successfully implemented on Mon Power’s, a FirstEnergy company, distribution system as part of the US Department of Energy (DOE) funded project, West Virginia Super Circuit (WVSC). The proposed method is also validated using IEEE 34-bus and 123-bus test feeders to demonstrate the effectiveness of the proposed approach. The mathematical model is developed in Matlab and the results show that the proposed iterative algorithm can drastically reduce the search space, and can find optimal number and placement of the switches with minimum computational effort.

This chapter presents a deterministic and an adaptive robust model for the short-term network expansion planning in electric distribution networks, considering siting and sizing of voltage regulators, capacitor banks, renewable energy generation, energy storage systems, and existing overloaded feeders reinforcement. The objective function to be minimized consists of investment and operation costs. Conventional expansion models in distribution networks are stated as a mixed-integer non-linear mathematical programs. In this chapter, we introduce the standard formulation and transform it into a mixed-integer linear programming form. This formulation is used to solve a deterministic short-term electric distribution network expansion planning case. Based on the deterministic formulation, we expand the formulation to a two-stage tri-level adaptive robust problem for considering load consumption and renewable-based DG uncertainties. By using Karush–Kuhn–Tucker conditions, this model is transformed into a two-stage bi-level adaptive robust optimization problem. A column and constraint generation framework is used to solve the problem. Computational results are obtained from a 123-node distribution system under different conditions to assess the performance of the proposed approach. Results show the effectiveness of the proposed methodology.

Phase balancing is an optimization problem which can reduce power losses in modern power distribution grids. The problem consists on phase swapping of the loads at the feeder level in order to reduce the unbalance of the grid. Despite being a classic problem, it is still relevant since unbalance is a common phenomena in power distribution grids and can be intensified by the uncoordinated use of distributed resources such as renewable energies and electric vehicles, among other single phase loads. Being a combinatorial problem, phase balancing requires heuristic algorithms whose codification must be carefully designed. In addition, high penetration of renewable energies makes the problem stochastic. This chapter shows a genetic algorithm which solves efficiently the problem, considering a detailed model of the power flow. A novel codification is proposed based on the identification of symmetries on the intrinsic structure of the problem by using the concept of group, an algebraic structure that can be easily combined with the conventional genetic algorithm. Simulations results on the IEEE test systems demonstrate the efficiency of the proposed method.

Distribution network conventionally have been designed and operated as some passive and radial networks. However, the presence of distributed energy resources (DERs) has changed these networks’ vision into some active ones. In this regard, new operational studies in the distribution level such as energy management problem has brought into existence. In this regard, this chapter mainly investigates the problem of energy management in distribution systems penetrated by DERs. To reach this goal, different classes of energy management problem, i.e., deterministic and stochastic models are carefully put under investigation. Extracting the mathematical model of these algorithms, it has been discussed that which algorithms should be applied to effectively solve the associated optimization problem. At the end, two examples associated with stochastic modeling of energy management problem, implemented on a sample case study, are provided to show how this problem can be applied in active distribution networks.