Enhancing Distribution Networks with Optimal BESS Sitting and Operation: A Weekly Horizon Optimization Approach

Abstract

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.

1. Introduction

The interest in Renewable Energy Sources (RES) has greatly increased in the last years as a result of environmental concerns, the price volatility of fossil fuel reserves, advances in technology that have lowered the costs of renewable energy and the rapid growth of electrical demand. In this sense, new investigations have considered the optimal sitting and operation of Battery Energy Storage System (BESS) to harvest the benefits of RES [1]. The optimal operation and sitting of BESS contribute to sustainability by enhancing the integration and utilization of RES, reducing reliance on fossil fuels, and minimizing greenhouse gas emissions [2]. Strategically placed and operated BESS can store excess energy during periods of high renewable generation and release it during peak demand, smoothing out the variability in renewable sources [3,4]. Moreover, the optimal sitting of BESS close to demand centers minimizes energy losses, further promoting energy efficiency and enhancing sustainability. Integrating Photovoltaic Energy (PV) and Wind Power Generation (WPG) into power networks is essential for the energy transition. However, since these resources rely on environmental conditions such as wind and solar radiation, the operation of the electrical system needs careful management [5]. As stated by [6], some precautions need to be taken to avoid quality of service issues when considering scenarios with high penetration of RES. For example, impacts on frequency regulation [7], voltage unbalance [8], and overloaded components [9]. In this context, the integration of carbon-free Conventional Generation (CG) and RES in the power system can be facilitated by well-designed BESS which may result in lower power losses [10,11], frequency regulation [12], lower operational costs [13], enhanced voltage regulation [14], lower peak demand [15] and higher energy efficiency [16].

1.1. Literature Review

Energy storage systems have been the focus of several studies. In 1988, Chiang et al. [17] proposed a preliminary model for a residential application that considered the daily generation of PV, the associated load, and BESS. The results illustrate the effectiveness and potential of combining these resources. Subsequently, further studies of BESS have been conducted, including the best strategies for planning and operating these systems within power systems. In [18], the authors propose a risk-averse approach for deploying electrical and thermal energy storage systems in a residential microgrid. The method considers uncertainties and demand-side management. Along with determining the optimal size and location of the hybrid energy system, the approach also identifies the best investment phase by maximizing the system’s equivalent daily profit. A two-stage model for energy storage systems was developed in [19]. This model is integrated into a predictive control framework and includes selective operational modes that allow for chronological power scheduling. Furthermore, the authors propose a new algorithm to assess future worst-case cost expectations. A temporally-coordinated operation method of a multi-energy microgrid (thermal and power energy) is proposed in [20]. In this case, the authors consider uncertainties of energy prices, renewable sources and power loads. The authors of [21] assess the role of long-duration energy storage technologies using real-world historical demand and hourly weather data. Furthermore, in [22] the authors explore the need for compressed air energy storage to compensate for the variability in solar and wind energy. A case study for California is presented using real historical demand and weather data.

Finding the optimal sitting and operation strategy of BESS in modern networks is a challenging task [23]. The optimization models developed to tackle this problem can be solved either through Meta-heuristics (MT-H) techniques or exact methods. MT-H is designed to find near-optimal solutions by exploring the solution space using strategies inspired by natural phenomena or other heuristics. These methods are typically non-deterministic and provide no guarantee of finding the optimal solution. On the other hand, exact methods, such as linear programming, branch and bound, Dynamic Programming (DP), etc., are designed to find the optimal solution by exhaustively exploring the solution space. In [16], the optimal operation of multiple sources such as batteries, CG, PV and WPG in distribution grids is proposed. The model was implemented using an exact method through A Mathematical Programming Language (AMPL); nonetheless, the allocation of BESS was not optimized. In [24], the authors proposed an approximate dynamic programming (ADP) approach to the control of a BESS, with the objective of minimizing the end user’s electricity bill. This was achieved by considering energy charges and monthly peak demand charges. To address the issue of time-varying uncertainty, a periodic autoregressive (PAR) model was employed to model the net demand. The model was evaluated in a real-world community in Queensland, Australia, and compared to two established policies. The findings indicated that the proposed method results in a greater reduction in the average monthly peak demand than the benchmark policies; however, the study does not optimize the location of the battery, and the simulations were developed on a daily basis. A Mixed Integer Non-Linear Programming (MINLP) was developed in [25] to integrate BESS and pumped hydro storage units incorporating demand response; however, the model did not consider the sitting of BESS as a decision variable.

A Genetic Algorithm (GA) was implemented in [26] for the optimal sitting of BESS in a radial distribution network to minimize power losses. The model was developed within a 24-h period taking into account variations in load and the output of PV generators. The proposed approach resulted in a reduction in power losses by 62% in comparison to the base case; nevertheless, the suggested methodology is not appropriate for implementation in large-scale applications. In [27], a Particle Swarm Optimization (PSO) algorithm is implemented for the optimal placement of BESS considering demand response. Nevertheless, the study does not provide a detailed analysis of the optimization process for the allocation of storage units.

In unbalanced three-phase distribution systems, an Optimal Power Flow (OPF), as proposed in [28], represents an effective method for managing BESS; nonetheless, the optimal placement of these devices is not considered in the model. In [29], the authors put forth a Mixed-Integer Linear Programming (MILP) for the optimal sitting and sizing of batteries, taking into account their lifetime cycle; nonetheless, the proposed method was not validated in weekly operation. In [30], the authors describe a two-stage model for the sitting and sizing of BESS, which is designed to enhance the operational performance of the grid operator. Validation of the model is based on tests conducted on the 33-bus and rural test system from Finland. A key benefit of this study is its use of actual data on loads, market prices, and frequency deviations. However, the study was limited to a 24 time horizon. As reported in [31], the simultaneous sitting and operation of BESS is a non-convex optimization problem that involves discrete and continuous decision variables associated with the location and operation of BESS systems, respectively.

Notably, a recent examination of published literature reveals a growing interest in the optimal planning and operation of BESS in modern distribution networks, which serves to highlight the relevance and importance of this topic. A comparison of the various optimization approaches used to site and operate BESS systems is presented in

Table 1. Optimization approaches applied to optimal sitting and operation of BESS with RES.

Ref.	Method	RES	Sitting	Operation	Horizon
[1]	MOPF	x	x	x	day
[16]	MOPF	x		x	day
[24]	DP	x		x	day
[25]	MINLP	x		x	day
[26]	MT-H	x	x	x	day
[27]	MT-H	x	x	x	day
[28]	OPF	x		x	day
[29]	MILP	x	x	x	day
[30]	Two-stage	x	x	x	day
This Paper	MOPF	x	x	x	week

. It is noteworthy that several studies focus on either the operational aspects of the subject under consideration, or both the operational aspects and the location of the site in question. This problem is of a complex nature, arising from the challenge of implementing the model on a weekly basis and the substantial number of variables that must be taken into account during the optimization process. The variables in question encompass load flow constraints, battery charging and discharging operations, voltage constraints, and the number of BESS installations to be allocated.

The following research question is, therefore, proposed for investigation. “Is it possible to simultaneously sit and optimize the operation of BESS with high penetration of PV generation within an MOPF framework considering the weekly time horizon?”

1.2. Research Gap and Contributions

The literature survey evidences the interest of BESS in modern distribution systems. Nonetheless, one of the main challenges is related to their optimal sitting and operation considering PV, load variability, and network constraints. In this context, we propose a MOPF for the sitting and operation of storage systems in distribution grids. This approach draws inspiration from [1,16], although it diverges from these works in several ways. In contrast with [1], our investigation is conducted over a weekly time frame. Consequently, the proposed MOPF must now observe a larger number of variables in order to achieve optimal performance. Furthermore, unlike the study presented in [16], the proposed formulation involves the simultaneous sitting and operation of BESS in coordination with RES. The essential features and contributions of this paper can be summarized as follows:

• The simultaneous sitting and operation of BESS considering the high penetration of PV generation.
• In addition to the daily operation, the proposed approach also incorporates a weekly operation.
• The BESS is designed to provide active power output in accordance with the requirements of the grid, the interaction between PV and load, and the typical production curves.
• The objective function takes into account the constraints of the systems and the charge/discharge capacities of the BESS. This function is formulated to minimize active power losses over a 168-h time horizon.
• The methodology, which requires only generation and demand forecasts, can be applied to both short-term planning (such as day-ahead) and longer periods (such as weeks and months).

The remainder of this paper is organized as follows. The formulation of the problem is outlined in Section 2. Section 3 details the solution approach. The results, evaluated in various scenarios, are discussed in Section 4. Section 5 presents the discussion and future challenges. Finally, Section 6 presents the conclusions of the study.

2. Problem Formulation

The suggested MOPF constitutes a complex optimization problem with variables of different nature, which complicates solving the problem with iterative methods [32]. The objective function, given by Equation (1), consists of minimizing the total active energy losses within a 168-h period (one week), indicated as T. In this case, $f\left(x\right)$ represents the active power losses of the system, $N_L$ is the number of circuits, $I_i$ is the electric current circulating in branch i and $R_i$ is the resistance of each line or circuit [16]. This objective function is subject to several constraints as indicated below.

$$\begin{array}{c}\hfill \begin{array}{c}\hfill minf\left(x\right)=\sum _{t=1}^T\sum _{i=1}^{N_L}{R}_i{\left(I_i^t\right)}^2\end{array}\end{array}$$

(1)

2.1. Power Balance Constraints

Active and reactive power balance constraints in every node of the network are enforced by Equations (2) and (3). In this case, ${\beta }_k$ is a binary variable used to indicate the sitting of a BESS at bus k. If it is 0, it does not allocate BESS at bus k; otherwise, if it is 1, it allocates BESS at bus k. $P_k^t$ and $Q_k^t$ are the active and reactive power provided by the substation k at time t; ${P_{PV}}_k^t$ represents the active power generated by PV generators at bus k in time t; $P_{Lk}^t$ and $Q_{Lk}^t$ are the active and reactive loads at bus k in time t; $G_{km}$ and $B_{km}$ are the real and imaginary components of the admittance matrix at position $k,m$; $V_k^t$ and $V_m^t$ indicate the voltage magnitudes at buses k and m at time t, respectively. Finally, ${\Omega }_{\kappa }$ is the set of buses connected to bus k.

$$\begin{array}{c}\hfill P_k^t+{P_{PV}}_k^t+{\beta }_k{P_B}_k^t-{P_L}_k^t=V_k^t\sum _{m\in {\Omega }_{\kappa }}{V}_m(G_{km}cos{\theta }_{km}+B_{km}sin{\theta }_{km})\end{array}$$

(2)

$$\begin{array}{c}\hfill Q_k^t-{Q_L}_k^t=V_k^t\sum _{m\in {\Omega }_{\kappa }}{V}_m^t(G_{km}sin{\theta }_{km}^t-B_{km}cos{\theta }_{km}^t)\end{array}$$

(3)

2.2. Charging and Discharging Operation of BESS

The constraints associated with the charging and discharging of BESS are given by Equation (4), which represents a linear approximation based on [33]. In this case, $n_c$ and $n_d$ are charging and discharging parameters, respectively, ${B_S}_k^t$ is the energy stored at bus k at time t, and ${P_B}_k^t$ represents the charging and discharging power of the BESS.

$${B_S}_k^t=\left\{\begin{array}{c}{B_S}_k^{t-1}+n_c{P_B}_k^{t-1}\Delta t\forall {P_B}_k^t\ge 0\forall k\hfill \\ {B_S}_k^{t-1}-{\displaystyle \frac{1}{n_d}}{P_B}_k^{t-1}\Delta t\forall {P_B}_k^t<0\forall k\hfill \end{array}\right.$$

(4)

2.3. Charging and Discharging Capacities of BESS

Equation (5) indicates the capacity of the BESS to absorb or supply energy, which is dependent on battery technology. In this case, ${P_B}_k^{mi{n}^t}$ and ${P_B}_k^{ma{x}^t}$ are the minimum and maximum values of active power injected into the BESS at bus k at time t.

$$\begin{array}{c}\hfill \begin{array}{c}\hfill {P_B}_k^{mi{n}^t}\le {P_B}_k^t\le {P_B}_k^{ma{x}^t}\forall k\end{array}\end{array}$$

(5)

2.4. BESS Storage Capacity Limits

The storage capacity limits are given by Equation (6) and must be considered throughout the operation period. In this case, ${B_S}_k^{mi{n}^t}$ and ${B_S}_k^{ma{x}^t}$ indicate, respectively, the minimum and maximum capacities of BESS at bus k at time t.

$$\begin{array}{c}\hfill \begin{array}{c}\hfill {B_S}_k^{mi{n}^t}\le {B_S}_k^t\le {B_S}_k^{ma{x}^t}\forall k\end{array}\end{array}$$

(6)

2.5. Voltage Magnitude Limits

In distribution systems, voltage must be kept within specified minimum and maximum limits to ensure the safe and efficient operation of electrical equipment and to maintain power quality for consumers. The constraint given by Equation (7) indicates the minimum $V_k^{mi{n}^t}$ and maximum $V_k^{ma{x}^t}$ voltage magnitude limits of bus k in the network at time t.

$$\begin{array}{c}\hfill \begin{array}{c}\hfill V_k^{mi{n}^t}\le V_k^t\le V_k^{ma{x}^t}\end{array}\end{array}$$

(7)

2.6. Number of BESS Allocated

The number of BESS devices ($N_{BESS}$) to be installed in the system is given by Equation (8), where $N_{bus}$ is the set of candidate buses for BESS sitting.

$$\begin{array}{c}\hfill \sum _{k=1}^{N_{bus}}{\beta }_k=N_{BESS}\end{array}$$

(8)

In this study, the PV generations and load demand will be input data considering the upcoming days. The modeling of these resources is beyond the scope of this research.

3. Solution Approach

AMPL is a platform used to model and solve complex optimization problems. It provides a high-level, algebraic representation of optimization models, making it easier to formulate complex problems involving linear, nonlinear, and integer programming [34]. An AMPL framework is proposed to tackle the optimization problem described in this paper. This software is used to minimize or maximize a given objective function containing discrete or continuous variables. AMPL offers a wide range of solvers including Baron (nonlinear integral), CBC (linear and integer linear), CPLEX (linear, quadratic, integer linear, integer quadratic), Gurobi (linear simplex and interior, quadratic, integer linear, integer quadratic) and Knitro (nonlinear integer). Knitro, a commercial solver developed by Zienna Optimisation LLC [35], is the solver version 12.0.0 used in this study in combination with AMPL. Knitro is specifically designed to handle non-linear optimization problems and is well suited to highly complex scenarios such as the one described in the case of the present study. In this case, the model considers the allocations of BESS and periods of time as discrete variables, while the BESS operation, PV generation and loads are considered as continuous variables that may assume any value within a given minimum and maximum range.

The structure of the presented MOPF to address the optimal placement and operation of BESS is shown in Figure 1. The solution vector includes ${\beta }_i^A$ (considering $N_{bus}$ potential buses for BESS placement) and $X_i^S$ (representing the optimal operation of batteries). In this study, all network buses are considered potential candidates for BESS placement, corresponding to binary variables for each bus. The charge and discharge operations for each allocated BESS are optimized over a 168-h timeframe. This problem is classified as MINLP. During the optimization, the MOPF determines the most suitable bus for BESS placement by considering load, PV generation, and the number of storage units in the network. Then, the operation of BESS is evaluated hourly for each allocated storage unit. Finally, the algorithm presents the ideal operational power losses.

4. Test and Results

This section presents the results of the methodology when applied to a 33-bus test system, which data can be consulted in [36]. All simulations were conducted on a computer with an Intel^® Core™ i7 CPU @ 3.4 GHz, 16 GB of RAM, and the Windows 11 Home 64-bit operating system. The 33-bus test system is presented in Figure 2. The system operates with a voltage of 12.66 kV (3.715 MW peak active load consumption). The maximum voltage considered was 1.05 p.u., and the minimum was 0.90 p.u. The system was modified such as buses 8, 12, 16, 18, 20, 27, and 30 present PV generation that adds up to 4600 kW. In line with [16], the storage system has a capacity of 5 MW and a charge and discharge capacity of 1 MWh with efficiency indexes ($n_c$ and $n_d$ ) of 1.

A 168-h timescale is employed in the sitting of BESS, with intervals of one hour. The total PV generation and loads over the weekly time horizon are generated empirically from the know-how of the authors as shown in Figure 3. It is important to highlight that on some days, there are times, particularly around noon, when the power generated by PV systems exceeds the load, leading to reverse power flows. In particular, the following days of the week are worthy of note: Sunday, Tuesday, Thursday, and Saturday.

The effectiveness of the proposed MOPF is demonstrated by the simulation results, which consider storage alongside PV generation for optimal planning and improving the performance of modern grids. The proposed model has undergone extensive analysis using a 33-bus test system, yielding results across various scenarios. Initially, the model focused solely on PV generation and load, without considering BESS (CASE 1). However, in the subsequent cases, the model incorporated 1, 2, and 3 storage units alongside PV generation CASE 2, CASE 3, and CASE 4, respectively. The objective was to minimize active losses by considering the fluctuating nature of both loads and PV energy production. This comprehensive approach ensures that the model accounts for the dynamic nature of the system, resulting in high-quality solutions.

In each scenario, a thorough examination was carried out on the voltage profile, active power losses, slack bus generation, and the effectiveness of the designated BESS.

4.1. BESS Sitting and Operation

• CASE 2.

Given the curves provided, the algorithm indicated the optimal location for a single BESS at Bus 16. Figure 4 illustrates the operation of the BESS over the 168-h period. Additionally, it is worth noting that on Sunday, a day with moderate load demand, the BESS stores energy to be used on Monday. This strategy allows for more efficient energy management compared to operation over 24 time periods. For this case, the algorithm converged on 166.505 s. On every day, the BESS utilized its maximum storage capacity, indicating that the storage capacity of the BESS is limited. As depicted in Figure 4, the behavior of the BESS is aligned with the PV generation and load demand, as observed in Figure 3. In this scenario, the optimal strategy is to initiate the charging process at 6:00 a.m. and conclude it at 12:00 p.m. This timing aligns with the peak production of energy and the maximum capacity of the storage equipment, maximizing the efficiency of the charging process. Subsequently, once the PV has reached 0 MW, the battery is discharged to meet the demands of the loads. The sequence of steps follows a similar pattern for the remaining days of the week. In terms of energy loss, this strategy allows for a reduction of 17.95%, with respect to the base case (CASE 1). Further details can be found in the sequence.

• CASE 3.

Considering two BESS, the algorithm indicated the sitting of one BESS at Bus 17 and the other one at Bus 30. Figure 5 illustrates the operation of the BESS at Bus 17, while Figure 6 depicts the operation of the BESS at Bus 30. In this case, the algorithm converged in 923.438 s. The BESS allocated at Bus 17 does not use its maximum capacity every day of the week, while the BESS at Bus 30 reaches its maximum capacity every day. In this instance, the batteries are empty on Sunday, initiating a charge at 6:00 a.m., after PV generation, and reaching their full capacity at noon. As can be seen in Figure 5, the BESS discharge power reaches 2 MW. In contrast, Figure 6 demonstrates that the dispatch power is below 1 MW on Monday due to the necessity to meet load requirements and the relatively low energy generation by the PV units. This same pattern is observed on other days of the week. By way of exemplification, after the week, specifically on Saturday, both batteries reach 0 MW at the 168 time horizon. The incorporation of two BESS results in a 26% reduction in power losses compared to the baseline scenario (CASE 1).

• CASE 4.

Considering three BESS, the algorithm indicated their sitting at Buses 12, 16, and 30. Figure 7 illustrates the BESS located at Bus 12, Figure 8 depicts the BESS situated at Bus 16, and Figure 9 displays the BESS installed at Bus 30. All three BESS operate continuously for a duration of 168 h. Only the BESS allocated at Bus 30 utilized its maximum energy storage capacity every day. The other BESS did not fully charge in the last few days of the week. This demonstrates that the capacity of the storage system is adequate. As with the previous analysis, it can be concluded that the battery is completely empty, indicating a power output of 0 MW. The charging process begins with the introduction of PV penetration into the system and ends when the PV source is no longer available. In this scenario, the only remaining source is the substation. The performance of individual batteries varies considerably due to their different locations within the grid.

4.2. Voltage Profile for the Four Cases

The study sought to analyze the voltage profile of the network with the installation of the BESS, generating three graphs for cases at 6:00, 13:00, and 21:00 on Wednesday. The selected hours are based on light load behavior, peak PV generation, and maximum load. The chosen day of the week was Wednesday because it is a day of normal load. Figure 10 shows the voltage profile for the four cases at 6:00, where there was no significant variation, as there is no PV generation at this time and the BESS present little variation in charging and discharging. Figure 11 presents the voltage profile at 13:00 for the four cases. It is possible to observe a voltage increase in Case 1, in which there is no BESS allocated. In cases with BESS, due to the BESS charging, there is a slight voltage drop compared to the other cases. Figure 12 shows the voltage profile at 21:00 for the four cases. Without the presence of allocated BESS, Case 1, there is a significant voltage drop at Bus 18, which is at the end of the feeder. With the addition of BESS, the voltage profile becomes flatter, ensuring a more economical and safe operation.

4.3. Slack Generation Bus for the Four Cases

Figure 13 displays the active power generation of the slack bus (substation) for all cases. In the base case without BESS, on the first day of the week (Sunday), the 2 MW Substation shows negative generation at 12:00. This occurs because the total PV generation surpasses the demand, as shown in Figure 3, indicating a reverse power flow. In cases 2 and 3, when the BESS is in operation, the reverse flow is reduced, but it is still present. It is only the coordination of three batteries that prevents the reverse flow in the Substation. On Monday, when demand is higher than PV generation, the system is in reasonable operating conditions. On Tuesday and Thursday, the energy produced is greater than the load, leading to an increase in reverse power; however, adding batteries manages the reverse power. Wednesday and Friday, mainly due to low demand and PV generation, follow the same pattern as Monday. Low demand is observed on Saturday and high energy production from PV generators. In this scenario, a large amount of power is returned to the Substation. The coordination of cases 3 and 4 contributes to the safe operation of the network. The reduced power flow in the Substation validates the use of batteries to solve the planning and operational problem.

4.4. Active Power Losses for the Four Cases

Figure 14 shows the results of active losses taking into account all cases simulated for a period of 168 h. As can be seen, the worst-case scenario, Case 1 (without BESS), presents higher losses for all days of the week. The energy losses over a period of 24 h amounted to 3.77 MWh. In cases 2, 3 and 4 the losses are reduced to 3.09 MWh, 2.79 MWh and 2.67 MWh, respectively. The highest losses are observed on Mondays, Wednesdays, and Fridays when the demand is higher than the PV generation; in this case, the Substation complements the power required for the grid. Regarding losses, sitting 2 or 3 BESS, losses are relatively the same, in this sense 2 BESS is advantageous due to investment costs. As noted earlier, effective planning that incorporates batteries enhances system efficiency, making it an attractive solution for planners and operators, as indicated by the results.

4.5. Comparative Analysis between Weekly and Daily Operation

As many power grids exhibit different loads throughout the week in addition to PV generation, in this study, we conducted a comparative analysis considering both daily and weekly BESS operations. Thus, maintaining the network of 33 nodes with the three allocated BESS, according to the result of Case 4.

Figure 15 shows the operations of the BESS for the daily and weekly periods. In the daily operation, it was established that the BESS needs to be discharged at the end of the day. For example, on Sunday at the end of the day, the power supplied by the battery is fully discharged at 0 MW, but in weekly mode, the BESS saves energy for the next day. In weekly operation, they can store energy one day and supply it the following days. However, they must be discharged at the end of the week. It can be observed that for weekly operation, the BESS are better utilized, as they use almost their entire capacity. One point that highlights the optimized operation obtained by the algorithm is that due to the excess PV energy on Saturday, the weekly operation discharges the BESS on Friday, making the operation on Saturday identical to the daily operation.

Weekly and Daily Active Losses

Figure 16 shows the profile of active losses for daily and weekly operations. As expected, losses for weekly operations are lower. The total for daily operation is 13.5441 MWh, and for weekly operation, it is 12.4577 MWh, which results in more than 1 MWh of savings in a week, in addition to other benefits as presented in previous items. This way, it is possible to affirm that weekly operation brings benefits to the network operation. Furthermore, on days when the load exceeds the PV generation, such as (Monday, Wednesday and Friday), the active losses are worst in the case of daily BESS operation, as evidenced in Figure 16.

5. Discussion

The simulation results showed the efficacy of the MOPF, which incorporates BESS in conjunction with PV generation for the optimal operation of distribution grids. The model was thoroughly evaluated using a 33-bus test system, producing outstanding outcomes across multiple scenarios.

5.1. Key Achievements

According to the results, a better performance of the BESS is achieved when considering a coordinated weekly operation with PV. The main advantage of this approach is the ability of the BESS to store and deliver energy from one day to another. This advantage is demonstrated in Cases 2, 3, and 4. Using the energy provided by these storage resources, the overall efficiency is improved, and the degradation of battery performance is prevented in charge and discharge operations. This means that the batteries can maintain their optimal performance for a longer period of time.

5.2. Issues and Challenges to Be Addressed

This paper investigates the optimal coordination between BESS and PV generation, considering the optimal sitting and operation of these systems in a weekly scenario. The complexity of this problem arises from the challenge of implementing the model in large-scale systems and the substantial number of variables that need to be taken into account during the optimization process. These variables include load flow constraints, battery charge/discharge operations, voltage constraints, and the number of BESS units to be allocated. Consequently, the optimal operation, which is associated with the binary variable ${\beta }_k$, may impose a significant computational burden. It is worth mentioning that MT-H may not be suitable for addressing this particular problem, since they involve exhaustive parameter adjustments, such as the number of agents, the number of interactions, and the dimension of the problem. Furthermore, the use of exact methods may result in significant demands of computational resources, including both processing time and memory sitting.

The Knitro solver offers solutions for the optimal sitting and operation of storage systems. However, due to the presence of both continuous and discrete variables in the optimization process, achieving optimal results can be challenging. The computational explosion that occurs, as a result, can make it impractical to solve medium to large-scale problems. Despite this limitation, the Knitro solver provides a reasonable solution for small-scale systems, as with the 33-bus test system. It efficiently handles the optimization process and offers satisfactory results.

5.3. Limitations and Future Work

The primary limitation of the proposed framework lies in not including real data of PV and load forecasting. To address this issue, a Monte Carlo method [37] may be employed to predict these input parameters. Another option is to use historical data of PV generation and real-world load data to create scenarios that reflect the randomness of uncertain parameters.

As mentioned before, a key challenge of the proposed optimization problem is the effective sitting and operation of BESS, using binary variables, while taking into account the load and grid requirements over a 168-h time frame. Current commercial solvers might struggle with these issues, and available MT-H algorithms do not guarantee optimal solutions. According to [38], an alternative approach is hybridization, which involves integrating the commercial solver within the MT-H framework to divide the problem into two components: sitting and operation. In this case, the MT-H addresses the discrete aspect, while Knitro focuses on the operational side. Future research will concentrate on this aspect.

BESS are currently becoming very popular and multiple directions regarding their operation can be explored. These include their sizing and sitting, which are crucial variables for making informed planning decisions. Also, producing green hydrogen through PV by electrolysis presents a promising solution for tackling global climate change. Another perspective is the integration of economic and technical analyses to assess the feasibility of incorporating batteries into the grid. The results of such studies may highlight the significance of optimal BESS planning in enhancing grid performance.

6. Conclusions

In this study, an optimization framework was proposed for the optimal operation and sitting of BESS in active distribution grids in the presence of photovoltaic generation with the aim of reducing energy losses. The formulation was based on a MOPF, developed in AMPL and solved using the Knitro solver with a 168-h planning horizon. 1, 2 and 3 BESS were deployed in the grid, leading to energy loss reductions of 3.09 MWh, 2.79 MWh and 2.67 MWh, respectively. The benefits of these devices operating at optimum capacity, i.e., charging and discharging over a 24-h period, were verified. In terms of minimizing losses, the three BESS units achieved a reduction of over 29%, equivalent to 1.0864 MWh of energy per day, providing over 400 MWh of energy per year.

The main shortcoming of the proposed framework is its failure to incorporate actual data on photovoltaic and load prediction within the model. Moreover, it would be beneficial to investigate the influence of diverse efficiency indices derived from storage units on modeling outcomes. In addition, it would be valuable to add cost analysis to the model; indicators such as net present value, net present cost, internal rate of return and payback.