Reactive power compensation with Capacitor Banks (CBs) is one of the most successful approaches used in distribution systems, mainly due to their versatility, long-term acceptance in the power industry, and reduced costs. Most allocation methods, however, lack specific strategies to handle the limited discrete nature of CBs sizes seeking to improve the overall optimization and computational performance. We present an algorithm for the Optimal Placement of Capacitor Banks (OPCB) in distribution systems by means of a hybrid Flower Pollination Algorithm (FPA)–Exhaustive Search (ES) approach. The pollination process itself determines the sets of buses for placement, while CBs sizes and the final fitness values of each pollen are selected after a full-search is conducted in the sizing space. As the sizing phase works on the limited search space of predetermined discrete bank values, the computational effort to find the optimum CB capacity is greatly reduced. Tests were performed on distribution systems of 10, 34, and 85 buses with respect to the objective function, final losses, and voltage profile. The algorithm offers an excellent compromise between solution quality and computational effort, when compared to similar approaches.

The ever-growing participation of Renewable Energy Sources (RES) in modern distribution networks is replacing an important portion of Conventional Generation (CG), which brings along new challenges in the planning and operation of distribution grids. As RES such as Photovoltaic Energy (PV) and Wind Power Generation (WPG) increase in distribution networks, studies regarding their integration and coordination become more important. In this context, the purpose of this paper is to propose a Multi-period Optimal Power Flow (MOPF) model for the optimal coordination of Battery Energy Storage Systems (BESSs) with PV, WPG, and CG in modern distribution networks. The model formulation was developed in A Modeling Language for Mathematical Programming (AMPL) and solved through the Knitro solver within a time horizon of 24 h. A distinctive feature and one of the main contributions of the proposed approach is the fact that BESSs can provide both active and reactive power. The proposed optimization model reduces power losses and improves voltage profiles. To show the applicability and effectiveness of the proposed model, several tests were carried out on the 33-bus distribution test system and a real distribution system of 141 buses located in the metropolitan area of Caracas. Power loss reductions of up to 58.4% and 77% for the test systems of 33 and 141 buses were obtained, respectively, when BESSs provided both active and reactive power. The results allow us to conclude that the proposed model for optimal coordination of BESSs with RES is suitable for real-life applications, resulting in important reductions of power losses and flattening of voltage profiles.

The optimal sitting and operation of Battery Energy Storage Systems (BESS) plays a key role in energy transition and sustainability. This paper presents an optimization framework based on a Multi-period Optimal Power Flow (MOPF) for the optimal sitting and operation of BESS alongside PV in active distribution grids. The model was implemented in AMPL (A Mathematical Programming Language) and solved using the Knitro solver to minimize power losses over one week, divided into hourly intervals. To demonstrate the applicability of the proposed model, various analyses were conducted on a benchmark 33-bus distribution network considering 1, 2 and 3 BESS. Along with the reduction in power losses of up to 17.95%, 26% and 29%, respectively. In all cases, there was an improvement in the voltage profile and a more uniform generation curve at the substation. An additional study showed that operating over a one-week horizon results in an energy gain of 1.08 MWh per day compared to single daily operations. The findings suggest that the proposed model for optimal sitting and operation of BESS in the presence of Renewable Energy Sources (RES) applies to real-world scenarios.

This paper presents a Multi-Period Optimal Power Flow (MOPF) modeling applied to the minimization of energy losses in Distribution Networks (DNs) considering the reactive power control of Photovoltaic Generation (PVG) that can be applied to both short-term and long-term operation planning. Depending on the PV Power Factor ($P{V}_{pf}$) limitations, PVG may provide both active and reactive power. The optimal power factor control on the buses with PVG contributes to an economical and safe operation, minimizing losses and improving the voltage profile of the DN. The proposed MOPF was modeled in order to minimize active energy losses subject to grid constraints and $P{V}_{pf}$ limitations. The variations of loads and PVG were discretized hour by hour, composing a time horizon of 24 h for day-ahead planning; nonetheless, the methodology can be applied to any other time period, such as a month, year, etc., by simply having generation and load forecasts. To demonstrate the effectiveness and applicability of the proposed approach, various tests were carried out on 33-bus and 69-bus distribution test systems. The analyses considered the DN operating with PVG in four different cases: (a) $P{V}_{pf}$ fixed at 1.0; (b) $P{V}_{pf}$ fixed at 0.9 capacitive; (c) hourly $P{V}_{pf}$ optimization; and (d) optimization of $P{V}_{pf}$ for a single value. The results show that a single optimal adjustment of $P{V}_{pf}$ minimizes losses, improves voltage profile, and promotes safe operation, avoiding multiple $P{V}_{pf}$ adjustments during the operating time horizon. The algorithm is extremely fast, taking around 2 s to reach a solution.

A multi‐period mixed‐integer non‐linear programming model is proposed to optimally allocate battery energy storage systems (BESSs) in networks with photovoltaic generation. The solution methodology employs modified grey wolf optimisation (MGWO) to address the discrete part of the problem and a mathematical programming to handle its continuous part, resulting in a hybrid approach labelled as MGWO‐H. The methodology considers the possibility of using BESSs to provide both active and reactive power. The proposal is based on generation and network load forecasts and is solved considering a 24‐h time horizon to minimise energy losses. To demonstrate the applicability and effectiveness of the proposed model, several tests were carried out on two benchmark test systems. The results obtained using the proposed MGWO‐H are compared with two additional proposals: a hybrid approach similar to MGWO‐H that uses the original GWO, labelled as GWO‐H, and a multi‐period optimal power flow. In the two benchmark test systems of 33 and 141 buses, the results indicated that power losses were reduced by up to 30% and 13%, respectively, when BESSs provide only active power, and by 42% and 16.74% when BESSs provide both active and reactive power.

Uma nova metodologia híbrida para resolução do problema de alocação ótima de bancos de capacitores / A new hybrid methodology to resolve the problem of optimal allocation of capacitor banks