Volt-VAr Optimization Problem Research Articles

Carbon-Aware Operation of Resilient Vertical Farms in Active Distribution Networks

Emerging utilization of Electric Vehicles (EVs) in Distribution Networks (DNs) decreases the power quality in the DN. The main quest of this research is to find out Can EVs and Photovoltaic (PV) systems support the DN and mitigate the voltage magnitude violations due to utilizing high penetration level EV? This article proposes a novel volt/VAR optimization (VVO) model by leveraging the reactive power support of EVs and PVs as Distributed Energy Resources (DERs) for the DN. The proposed VVO model contains the second-order conic relaxed form of the AC power flow equations. Thus, the presented VVO problem is a Mixed-Integer Second-Order Cone Programming (MISOCP) problem. To obtain the ability to support the DN, Smart Inverters (SIs) are utilized to connect EVs and PV systems to the DN. Thus, to add the PV and EV systems to the convexified form of the VVO problem, the P-Q characteristics and the model of SIs working at different operating points are presented based on experimental results. The proposed model of SIs allows the participation of DERs in the reactive power compensation to mitigate voltage issues of DN due to utilizing high penetration level EVs. Besides, the proposed model of SIs enables DERs to increase their dispatchability. The performance of the proposed model is examined in the case studies using the IEEE 33-bus system and the 123-bus system. It is illustrated in the case studies that the solar dispatchability increases by 12% when the proposed volt/VAR model is utilized for IEEE 33-bus system. Besides, it is illustrated in the case studies that the voltage profile of buses remains in the desired operating range when the proposed model is leveraged, even if the penetration level of EVs increased to 40%.

Comparative Analysis of the Particle Swarm Optimization and Primal-Dual Interior-Point Algorithms for Transmission System Volt/VAR Optimization in Rectangular Voltage Coordinates

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method.

A novel robust Volt/Var optimization method based on worst‐case scenarios for distribution network operation

The Volt/Var optimization (VVO) problem is used for scheduling the voltage regulation and reactive power compensation equipment in distribution networks to minimize power loss and voltage violation. In order to solve the VVO problem for a forthcoming time horizon, it is necessary to predict some parameters such as load demand and renewable energy production. The prediction of these parameters is always accompanied by uncertainty that robust optimization can be used to solve this concern. This paper presents a scenario-based robust Volt/Var optimization (RVO) method that significantly reduces the number of scenarios required for the worst-case approach. Solving the VVO problem with the worst-case scenarios reduces the computational burden and maintains the voltage security of the distribution network against the severe events. The proposed RVO is formulated based on a mixed-integer second-order cone programming (MISOCP) model in which Volt/Var control (VVC) equipment is scheduled over a two-stage strategy. The proposed method is validated using modified 33-bus and 69-bus IEEE test systems. The results demonstrate that the proposed RVO method maintains the network's voltage profile within the acceptable range against uncertainties.

An Efficient Primal-Dual Interior-Point Algorithm for Volt/VAR Optimization in Rectangular Voltage Coordinates

Security and reliability of electrical power supply has become indispensable to modern society, and the system operator is challenged to manage the increasingly complex modern power system in a manner that ensures the expected reliability and security of system operation. In this context, Volt/VAR optimization (VVO) plays a key role in the efficient delivery of power through the transmission system, contributing significantly to the security, reliability, quality and economy of system operation. This article presents the design and implementation of an efficient primal-dual interior-point algorithm for the solution of the VVO problem. The primal-dual interior-point method combines efficient constraint handling by means of logarithmic barrier functions, Lagrangian theory of optimization, and the Newton method to constitute one of the most efficient deterministic algorithms for large-scale nonlinear optimization. The developed algorithm also incorporates the efficient Newton-Raphson load flow computation, which ensures that the solution is feasible with respect to the power flow balance equations at each iteration of the VVO algorithm. Both the VVO and Newton-Raphson load flow problems are formulated in the rectangular coordinates of system voltages. This is a departure from most researchers, who make use of the polar formulation, and adds considerably to the efficiency of the developed algorithm. The efficiency and effectiveness of the developed algorithm has been demonstrated by means of case studies performed on the 6-bus and IEEE 14-bus, 30-bus and 118-bus test systems, which have been selected to analyse the computational efficiency and scalability of the algorithm as it is applied to systems of various sizes. The extensive analyses that have been conducted reveal the developed primal-dual interior-point algorithm’s effectiveness and efficiency, particularly in being able to successfully solve the VVO problem for systems of widely varying sizes without disproportionate increase in computational cost or deterioration in the quality of the results. The developed algorithm exhibits characteristics of fast convergence, high efficiency, and scalability to large-scale problems.

Hierarchical Volt-VAR Optimization Framework Considering Voltage Control of Smart Electric Vehicle Charging Stations Under Uncertainty

Smart electric vehicle charging stations (EVCSs) equipped with distributed energy resources (DERs), such as photovoltaic (PV) systems and energy storage systems (ESSs), are promising entities for maintaining voltage quality in power distribution networks through voltage regulation using the smart inverters of DERs. This study proposes a hierarchical Volt-VAR optimization (VVO) framework that reflects the voltage regulation capability of smart EVCSs, which consists of global and local voltage control stages. At the global stage, smart inverters of EVCSs cooperate with conventional voltage regulators, such as an on-load tap changer (OLTC) and capacitor banks (CBs)), and smart inverters of PV systems to minimize the total active power losses and voltage deviations along with the determination of optimal parameters for local droop control functions of the smart inverters. At the local stage, smart inverters of EVCSs and PV systems quickly mitigate local voltage violations using dynamically varying local droop control functions with their optimal parameters calculated from the global stage. Under uncertainties in PV generation outputs and driving patterns of electric vehicle users, the deterministic optimization-based VVO problem at the global stage is reformulated into the chance-constrained optimization-based VVO problem. A simulation study was performed in an IEEE 33-bus distribution system with an OLTC, CBs, PV systems, and smart EVCSs. The results demonstrate the effectiveness of the proposed framework in terms of total active power loss/voltage deviation, optimized local droop control function, and probability level of chance constraints.

Deep Reinforcement Learning Based Volt-VAR Optimization in Smart Distribution Systems

This paper develops a model-free volt-VAR optimization (VVO) algorithm via multi-agent deep reinforcement learning (DRL) in unbalanced distribution systems. This method is novel since we cast the VVO problem in distribution networks to an intelligent deep Q-network (DQN) framework, which avoids solving a specific optimization model directly when facing time-varying operating conditions in the systems. We consider statuses/ratios of switchable capacitors, voltage regulators, and smart inverters installed at distributed generators as the action variables of the agents. A delicately designed reward function guides these agents to interact with the distribution system, in the direction of reinforcing voltage regulation and power loss reduction simultaneously. The forward-backward sweep method for radial three-phase distribution systems provides accurate power flow results within a few iterations to the DRL environment. The proposed method realizes the dual goals for VVO. We test this algorithm on the unbalanced IEEE 13-bus and 123-bus systems. Numerical simulations validate the excellent performance of this method in voltage regulation and power loss reduction.

A competitive decentralized framework for Volt-VAr optimization of transmission and distribution systems with high penetration of distributed energy resources

A more efficient Volt-VAr optimization (VVO) for transmission and distribution systems can be realized with considering the interaction between distribution system operators (DSOs) and transmission system operator (TSO) and using flexibility resources such as Distributed Generations (DGs) with high penetration in distribution systems. In this paper, a competitive decentralized framework is proposed for interactive VVO of transmission and distribution systems, in the presence of high penetration of distributed energy resources (DERs). In the proposed scheme, while TSO and DSOs are self-interested and individually solve VVO sub-problem according to their own objectives and constraints, they are interactive and receive feedback from each other to understand the mutual effects of their decisions and give an appropriate response. Each optimization sub-problem minimizes power losses of its own network for each load level subjected to the network and reactive power resources constraints. The defined interactive VVO problem is solved by a new decentralized algorithm based on the decomposition of boundary bus variables between transmission and distribution systems. Furthermore, some heuristic techniques are applied to convert the sub-problems formulation to a linear or at least convex one. Some case studies on IEEE 14-bus test system connected to three IEEE 69-bus distribution systems and IEEE 118-bus test system connected to thirty IEEE 69-bus distribution systems confirm the efficiency of the proposed framework in view of power loss, voltage profile and reactive power generation of transmission and distribution networks in comparison with isolated and interactive cooperative methods.

A Support Vector Regression Based Model Predictive Control for Volt-Var Optimization of Distribution Systems

This paper proposes a support vector regression (SVR)-based model predictive control (MPC) for the volt-var optimization (VVO) of electrical distribution systems. First, measurement data from a few days of operation of a distribution system, gathered using advanced metering infrastructure (AMI), are used to train an SVR model of the system. The trained model is then employed by the MPC in a closed-loop control scheme to control capacitor banks and tap changers of the distribution system so that the power loss is minimized, and voltage profiles are maintained within a specific range. In contrast to the many existing VVO methods, the proposed scheme does not require any circuit-based simulations for its operation, nor does it assume that the distribution system is radial. The simulation results of applying the proposed SVR-based MPC to IEEE123 bus test feeder proves that despite its measurement-based feature, the proposed approach is capable of providing close to optimal solutions to the VVO problem. The simulation results also suggest a satisfactory outcome of the proposed approach in controlling meshed grids or in the presence of distributed energy resources (DERs).

Volt-VAR Control Through Joint Optimization of Capacitor Bank Switching, Renewable Energy, and Home Appliances

Today, the evolution of smart grid, electric vehicles (EVs) with voltage to the grid mode, and deployment of renewable energy sources (RESs) are bringing revolutionary changes to the existing electrical grid. Volt-VAR optimization (VVO) is a well-studied problem, for bringing solutions to reduce the losses and demand along the distribution lines. The current VVO, however, does not acknowledge the role of elastic and inelastic loads, EVs, and RESs to reduce the reactive power losses and hence the cost of generation. We propose a mathematical model Volt-VAR and CVR optimization (VVCO)/optimal energy consumption model (OECM) to solve the VVO problem by considering load shifting, EV as the storage and carrier of the energy, and use of RES. The VVCO/OECM not only reduces the reactive load but also flatten the load curve to reduce the uncertainty in the generation and to decrease the cost. The system also considers the efficiency of the electrical equipment to enhance the lifetime of the devices. We develop a non-cooperative game to solve the VVCO/OECM problem. To evaluate the performance, we simulate the VVCO/OECM model and compare with the existing VVO solution. We found that our method took almost a constant time to produce a solution of VVO regardless of the size of the network. The proposed method also outperform the existing VVO solution by reducing the generation cost and flatten the load and minimizes the uncertainty in the power generation. Results have shown that exploiting RES will reduce the voltage drop through reducing the injection of reactive power to the system.

Optimal Voltage Control Using an Equivalent Model of a Low-Voltage Network Accommodating Inverter-Interfaced Distributed Generators

The penetration of inverter-based distributed generators (DGs), which can control their reactive power outputs, has increased for low-voltage (LV) systems. The power outputs of DGs affect the voltage and power flow of both LV and medium-voltage (MV) systems that are connected to the LV system. Therefore, the effects of DGs should be considered in the volt/var optimization (VVO) problem of LV and MV systems. However, it is inefficient to utilize a detailed LV system model in the VVO problem because the size of the VVO problem is increased owing to the detailed LV system models. Therefore, in order to formulate and solve the VVO problem in an efficient way, in this paper, a new equivalent model for an LV system including inverter-based DGs is proposed. The proposed model is developed based on an analytical approach rather than a heuristic-fitting one, and it therefore enables the VVO problem to be solved using a deterministic algorithm (e.g., interior point method). In addition, a method to utilize the proposed model for the VVO problem is presented. In the case study, the results verify that the computational burden to solve the VVO problem is significantly reduced without loss of accuracy by the proposed model.

A Framework for Volt-VAR Optimization in Distribution Systems

The possibility of leveraging the data provided by smart meters to understand the load characteristics is studied in this paper. The loads are modeled as voltage-dependent elements to increase the accuracy of volt-VAR optimization (VVO) techniques for distribution systems. VVO techniques are part of the distribution management system and may be used for purposes such as loss reduction, voltage profile improvement, and conservation voltage reduction. A deterministic framework is proposed that formulates the VVO problem as a mixed-integer quadratically constrained programming problem, which is solved efficiently using advanced branch-and-cut techniques. The proposed framework is capable of optimally controlling capacitor banks, voltage regulators, and under-load tap changers (ULTCs) for day-ahead operation planning. The results indicate that loss reductions of up to 40% and a total demand reduction of up to 4.8% are achievable under some loading conditions in a radial test system. The effect of the load voltage dependence is also demonstrated through analytical simulations.