Impact of PV and EV Forecasting in the Operation of a Microgrid

Abstract

The electrification of the transport sector together with large renewable energy deployment requires powerful tools to efficiently use energy assets and infrastructure. In this framework, the forecast of electric vehicle demand and solar photovoltaic (PV) generation plays a fundamental role. This paper studies the impact of forecast accuracy on total electric cost of a simulated electric vehicles (EVs) charging station coupled with true solar PV and stationary battery energy storage. The optimal energy management system is based on the rolling horizon approach implemented in with a mixed integer linear program which takes as input the EV load forecast using long short-term memory (LSTM) neural network and persistence approaches and PV production forecast using a physical hybrid artificial neural network. The energy management system is firstly deployed and validated on an existing multi-good microgrid by achieving a discrepancy of state variables below 10% with respect to offline simulations. Then, eight weeks of simulations from each of the four seasons show that the accuracy of the forecast can increase operational costs by 10% equally distributed between the PV and EV forecasts. Finally, the accuracy of the combined PV and EV forecast matters more than single accuracies: LSTM outperforms persistence to predict the EV load (−30% root mean squared error), though when combined with PV forecast it has higher error (+15%) with corresponding higher operational costs (up to 5%).

1. Introduction

The transportation sector is a major polluter, as it accounted for 28.51% of the total greenhouse gas emissions in 2021 in Europe [1]. The evolution of current transportation fleets to electric vehicles (EVs) (10% of the road vehicle fleet is expected by 2030 [2]) will accelerate the green transition and decarbonization of Europe. This rapid increase in EV adoption will considerably affect electric grids since a large charging network is required, with a special focus on optimal planning and operation of public charging stations (CSs). Therefore, it is essential to monitor and regulate the charging process, to exploit renewable energy sources (RESs) locally, and, where needed, to include stationary storage. Implementing novel emerging technologies for the optimization of the charging process is crucial for exploiting RESs, especially solar photovoltaic (PV) production [3], and stabilizing the grid [4]. EVs charging stations powered by the grid, PV, and a battery energy storage system (BESS) are analyzed by the scientific community from the placement [5], sizing [6], implementation [7], and energy scheduling [8] points of view, among others. From this perspective, CS integration is being investigated under the lens of microgrids (MGs) [9]. In the scientific literature on MGs, several works stressed the importance of optimizing MG operation [10], as well as the relevance of using accurate forecasting methods in the optimization of MG energy management [11,12]. Forecasting and optimization techniques are also being developed considering the achievements in managing uncertainties in MGs [13].

Load forecasting plays a significant role in demand-side management (DSM) [14,15,16], where it serves as a crucial element in balancing load demand and power production.

EV load forecasting methods are categorized into traditional statistical models and artificial intelligence models [17]. Traditional models include time series analysis, autoregressive integrated moving average (ARIMA), regression analysis, Kalman filtering, and statistical methods, while artificial intelligence methods encompass artificial neural network (ANN), support vector machine, and deep learning (DL) models. Initially, statistical models were preferred due to limited EV charging data, necessitating the creation of realistic scenarios through computational algorithms [18]. However, with the greater availability of electric vehicle supply equipment (EVSE) load data, the focus has shifted to data-driven approaches, particularly ANNs, in EV power load forecasting research [19,20]. In [21], a review of EV scheduling, clustering, and forecasting, the authors report that artificial intelligence models have been the preferred approach for many researchers, as they perform better than other probabilistic models.

Long short-term memory (LSTM) recurrent neural networks (RNNs) appear to be exceptionally proficient in predicting load across diverse time series problems [22]. In [23], an LSTM model combined with feature engineering empirical mode decomposition (EMD) is benchmarked against seasonal autoregressive integrated moving average (SARIMA) obtaining a skill score up to 73% relative to 7-day persistence. The literature consistently demonstrates the superior performance of LSTM networks in the field of EVs charging forecasts. Hence, based on these findings, we have selected the LSTM model as the cornerstone of our work due to its demonstrated effectiveness and suitability for the task at hand.

Moving to the EVs charging optimization, the operation of CSs relying on PV and BESS was performed with several different methods and goals. Selected approaches generally aim to achieve cost minimization [24] or profit maximization [25] according to the use case, but also enhanced grid support through self-consumption [26] and charging scheduling [27] the effectiveness of pre-calculated schedules can be compromised by uncertainties in the arrival and departure times of EVs and fluctuations in energy demand. Therefore, real-time operation algorithms must have robustness with respect to load as well as forecast uncertainties, as described in the previous subsection.

Regarding optimization methods, probabilistic approaches are robust and reliable in uncertain environments but suffer from heavy computational time [28]. This drawback is partially solved by robust optimization (RO) [29]. Model predictive control (MPC) is extensively used for robustness and reliability obtained through the receding horizon approach but also suffers from high computational time. Therefore, MPC is often used as the later stage in a multi-stage formulation to amend the decision made by an earlier algorithm in real time. Other relevant methods are metaheuristics algorithms and fuzzy logic optimization [30,31].

Deterministic models, and mixed-integer linear programming (MILP) in particular, are still the most widely adopted because they can identify the global optimal solution given convexity and a continuously differentiable cost function, with computational time compatible with industrial applications. MILP models are used both in real-time operation [32] or in day-ahead scheduling as a first stage that can then be adapted in real time through an operation layer [33]. Indeed, a multiple-stage optimization considers the uncertain behavior of the PV production and EV demand providing an improved solution for real-time energy management.

While stochastic and robust optimization approaches offer a more accurate and modelically correct way to handle uncertainties, their computational complexity often makes them impractical for real-time optimization. These approaches require solving extensive scenario-based models or worst-case formulations, leading to significantly longer solution times. Therefore, despite their robustness, they are not feasible for applications needing immediate decision-making. MILP, on the other hand, strikes a balance between accuracy and computational efficiency, making it suitable for real-time applications where timely decisions are crucial.

In this context, the predict-then-optimize (PTO) framework is still the most widely adopted to optimize this kind of systems. The PTO integrates prediction and optimization processes to enhance decision-making under uncertainty. In this framework, the prediction phase involves using statistical or machine learning models to forecast future uncertain parameters, such as demand, prices, or weather conditions. These forecasts are then input into an optimization model, which aims to find the best decision that minimizes cost or maximizes profit, given the predicted values. The key interaction between these two processes lies in how the predictions inform the optimization model. Accurate predictions lead to more effective optimization, as the optimization process relies on these forecasts to construct a solution that is robust against the predicted uncertainties. This interplay ensures that the optimization model is adaptive and responsive to future scenarios, thus enhancing the overall performance of the decision-making process.

Despite works on energy management system (EMS) validation and testing conducted in several universities and research centers (Public University of Navarre [34], Aalborg University [35], Center for Renewable Energy Sources and Saving (Athens) [36,37], and in Catalonia Institute for Energy Research [38]), there is still a lack of literature on the impact of prediction errors on microgrid operations, both in simulations and experimental facilities.

The scope of this work is to evaluate the impact of EV forecasting in the optimization framework, meaning that in addition to forecast skill these methods affect the operation of the microgrid from a technical and economic point of view. This paper evaluates how different EV forecast methods affect a sequential decision-making process, which is the outcome of a two-stage optimization tool. This study is performed on a physical MG located in Politecnico di Milano, Department of Energy [39], in addition to offline computer simulations.

This work is a novel contribution because the literature has yet to adequately cover how forecasting errors affect operational costs in a true functioning microgrid. While the predict-then-optimize approach is widely recognized, only a few studies have thoroughly examined its practical limitations. Notably, it is not well understood how the accuracy of load and solar forecasts influences the operational costs for a dynamic pricing electric tariff downstream of the optimizer and control equipment. Only a few papers have explored the error impact of different electric vehicle (EV) forecasting techniques within a hierarchical predictive control strategy aimed at optimizing microgrid operations. Finally, a significant distinction of this study compared to others is its real-time experimental validation and long-term simulation using highly accurate data from MG²Lab. For instance, a significant gap in the literature is the use of true building-scale microgrids in testing. In [40], a microgrid EMS is designed and implemented in a small bench-top testbed and further implanted at a commercial building with a maximum 300 kW load; however, all of the DERs are hardware-in-the-loop simulated by power converters rather than by true batteries and solar PV modules. The results are therefore much more credible than just a software simulation but lack some of the characteristics and uncertainty when controlling true Li-ion electrochemical cells and true silicon PV cells. Attempting to cover these gaps, the paper presents a comprehensive analysis of EV forecasting techniques error impacts, a comparative analysis and experimental validation between two methodologies (LSTM and persistence), and a long numerical analysis based on historical data.

The remainder of the article is structured as follows. Section 2 presents the optimization and forecasting methodologies employed in the energy management system of the proposed case study, described in Section 3. In Section 4, the model implementation is explained, as well as how the experimental testing facility is used. Section 5 includes the relevant results of this work, which is summarized and concluded in Section 6.

2. Methodology

2.1. Optimal Dispatch

The microgrid employs a two-layer EMS, previously described in [41], based on a rolling horizon (RH) approach where the first layer of the EMS is run every 15 min. The first layer determines the optimal dispatch of the BESS over the next 24 h, taking as input the forecast of both the EV load and PV generation, to minimize the operational cost of the system. The optimizer always takes into account technical constraints. However, as power unbalances inevitably arise due to forecast errors it is necessary to adopt a second layer to correct these unbalances in real time.

The first layer adopts an MILP formulation where variables model different power flows within the system (e.g., PV production, import/export from/to the grid, charge/discharge of the BESS). The optimal operation of the microgrid over the optimization horizon is evaluated by minimizing the total operational costs:

$$OF=min\left(\sum _{t\in {\mathcal{T}}_1}{\mathsf{\Phi }}_t^{Opex}\right)$$

(1)

where:

$$\begin{array}{l}{\mathsf{\Phi }}_t^{Opex}=c_t^{purch}·P_t^{grid,purch}·{dt}_1-r_t^{sell}·P_t^{grid,sell}·{dt}_1\\ +{\displaystyle \sum _{es\in \mathcal{E}\mathcal{S}}}\left[c_{es}^{TP}·P_{es,t}^{disch}·{dt}_1+{\rho }^{dev}·{SOE}_t^{dev}\right]\\ +c^{curt}·{ND}_{nd,t}^{curt}·{dt}_1+c^{UD}·{UD}_t·{dt}_1\end{array}$$

(2)

The main components of the aforementioned and following equations are explicitly stated in the Appendix A.

Meanwhile, the total operational cost ${\mathsf{\Phi }}_t^{Opex}$ associated to each timestep t is given by the sum of four main components:

• $c_t^{purch}·P_t^{grid,purch}·{dt}_1-r_t^{sell}·P_t^{grid,sell}·{dt}_1$ represents the cost and revenue (negative cost) coming from the withdrawal and injection of power from/into the grid;
• $\sum _{es\in \mathcal{E}\mathcal{S}}\left[c_{es}^{TP}·P_{es,t}^{disch}·{dt}_1+{\rho }^{dev}·{SOE}_t^{dev}\right]$ is the sum of the BESSs’ throughput-based O&M cost, and penalty cost associated with their state of energy (SOE) deviations;

$c^{curt}·{ND}_{nd,t}^{curt}·{dt}_1+c^{UD}·{UD}_t·{dt}_1$ are penalty costs for curtailment of RES generation and unmet demand.

Forecasted PV production is an input to the EMS and can be curtailed if necessary. The BESSs are modeled on an energy basis with self-discharge efficiency, and separate charge/discharge efficiencies which are a function of battery power, that are evaluated through piecewise linear interpolation. To avoid damage, constraints are imposed to limit the state of charge (SOC) between lower and upper bounds and the maximum power that can be charged/discharged by the BESS. In addition, there is a constraint to ensure a balanced SOC between the two BESSs. Interaction with the electrical grid is constrained by setting a maximum value on the power that can be imported/exported by the microgrid. Details about the mathematical formulation of the constraints and detailed nomenclature can be found in Appendix A: Energy Management System.

The second layer is a heuristic approach taking as input BESS and grid setpoints determined by the first layer as well as discrepancies between the PV and EV load forecasts and the actual values. Depending on the signs and magnitude of these errors, the microgrid can be either in “power excess”, where the inbound power flows are higher than the outbound ones, or in “power deficit”. The logic adopted is to keep the first layer setpoint of power exchanged with the electrical grid. First, either the unmet demand or PV curtailment is reduced in the case of “power excess” and “power deficit”, respectively. If that this is not enough, or if unmet demand and PV curtailment set by the first layer are equal to zero, the BESSs intervene to reduce the power balance. When the BESSs cannot correct the unbalances then the setpoint of the power exchanged with the grid is modified. Lastly, in the extreme case of unbalance even after all the previous points, either PV curtailment or unmet demand is increased in the case of “power excess” and “power deficit”, respectively.

2.2. EV Forecasting

2.2.1. LSTM with Attention

The EV charging power forecast is performed by an LSTM encoder–decoder with attention, inspired by Bahdanau [42]. The mathematical formulation of the LSTM and attention mechanism is described in Appendix B: EV Charging Forecaster. Each encoder and decoder is a single-layer LSTM of 24 hidden units, a value chosen by hyperparameter optimization. Training is performed with the Adam optimizer and early stopping to limit overfitting. The input vector is the most recent 3 days of EV charging power measurements and time-keeping variables such as day of week and time of day. The output vector is the next three days of charging power values. Power is always a 15 min interval average power time series. The training data subset is the EV charging load data in Section 4.2, less than 8 weeks—from each winter, spring, summer, and autumn—which are used for the test data subset. The model is trained using an early stopping criterion which monitors the validation loss, calculated on the final 20% of the training subset.

2.2.2. Persistence

The benchmark forecast model is naive persistence, which estimates any timestep $t$ as equal to the past timestep $t-l$, where $l$ is the lag value or the number of timesteps in the past. In a modified version sometimes called seasonal persistence, the lag value $l$ is chosen to match an appropriate seasonality in the data, often daily or weekly for electric consumption. In the present case study, the EV charging data present a strong weekly seasonality; therefore, the value of lag is chosen equal to 672 steps (7 days). The timestep $t$ is forecasted with the measurement from $t-7d$ or $t-168$ if the time series interval is 1 h. This is described in Equation (3), where $y_{forecast}$ is the forecasted value and $y_{true}$ the measured one.

$$y_{forecast}\left(t\right)=y_{true}\left(t-l\right)$$

(3)

While it is possible to use persistence for a day-ahead solar PV forecast, the benchmark would not be very useful. Weather conditions in many climates, including the humid subtropical designation of the solar plant in this study, can change dramatically between consecutive days, so even very poorly trained solar PV forecast models could outperform 1-day persistence. Persistence is more common for solar nowcasting where the time horizon is 1 to 60 min.

2.3. PV Forecasting

The solar PV forecast is a hybrid physical–regression method developed and validated on the Multi-Good MicroGrid Laboratory (MG²Lab) microgrid in [43]. The model outputs a day-ahead solar production time series at 15 min intervals. The model inputs are a numerical weather forecast for the location, physical plant specifications from the PV modules, and the most recent day of solar production time series. The model provides the solar production forecast based on numerical weather prediction for the week ahead at the considered locations and clear-sky radiation (CSR) of the plane of arrival to the array. The numerical weather forecast is from the European Center for Medium-Range Forecasts [44] and it is provided by a private company. The PV forecasting tool uses the global horizontal irradiance (GHI), air temperature, wind direction and speed, precipitation, humidity, and pressure. The list of the employed data is added in the following

Table 1. List of employed data.

Input	Parameters	Units of Measure
Deterministic	Global horizontal irradiance Clear-sky solar radiation	W/m2
Weather forecasts	Relative humidity	%
	Wind direction	degree
	Pressure	Pa
	Rain	mm
	Wind speed	m/s
	Ambient temperature	Celsius
	Global horizontal irradiance Solar radiation	W/m2

. A share of 80% of the whole dataset is used for the training and the remaining 20% for the validation.

The CSR model is based on reference evaluation of solar transmittance, 2 bands (REST2) that considers more variables than similar atmospheric models and is validated by the literature as one of the best-performing CSR models [45]. Finally, the GHI must be tilted to the plant-of-arrival of the solar plant, given its azimuth and tilt angles.

The ANN is trained daily on the previous day’s measured values in a supervised learning fashion, such that the weights and biases are optimized to produce a series of past outputs given past inputs. The ANN is retrained once per day to learn short-term patterns, such as a weather forecast which is consistently under estimating temperature.

2.4. Predict-Then-Optimize Approach

In this work, the predict-then-optimize framework, which integrates forecasting models and optimization techniques, has been adopted to enhance decision-making under uncertainty while maintaining computational tractability for implementation in an experimental facility. In this context, forecasts of EV load and PV generation, as described in Section 2.2 and Section 2.3, are used as inputs for the optimization process.

In particular, the EMS employs a rolling horizon (RH) approach where the first layer (where the optimization phase is performed) utilizes these forecasts within an MILP formulation to evaluate the optimal operation of the microgrid, including PV production, grid interactions, and BESS operations. The MILP model ensures that the first layer of the EMS can find a globally optimal solution under the given forecasted conditions, balancing the operational costs defined in Section 2.1. The real-time adjustments are then handled by the second layer, which corrects any discrepancies arising from forecast errors, thereby maintaining system balance and operational efficiency.

3. Error Metrics

Statistical error metrics are necessary for training forecasting models and provide a summary of forecast performance to compare to other works in the literature. In the equations below, $y$ is always a time series of true measurements or forecasted values and $n$ is the length of the series.

• Root mean squared error (RMSE) is the square root of the mean squared error (MSE), making the units of RMSE the same as the data for a helpful comparison. Since it is closely related to the MSE which is used to train the LSTM, RMSE will also closely reflect how well a model was trained;

  $$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum (y_{true}-{y_{forecast})}^2}$$

  (4)
• Mean absolute error (MAE) is also reported here because it is common in the literature and very intuitive, giving equal weight to large and small errors;

  $$MAE={\displaystyle \frac{1}{n}}\sum |y_{true}-y_{forecast}|$$

  (5)
• Symmetric mean absolute percentage error (SMAPE) is somewhat contested in the literature and there is no one single definition. However, the following definition is adequate because in this application there is no practical or theoretical problem with negative SMAPE values. Since all SMAPE definitions have terms in the denominator it is necessary to omit from the metric timesteps when the sum of $y_{true}$ and $y_{estimated}$ is zero.

  $$SMAPE={\displaystyle \frac{100}{n}}\sum {\displaystyle \frac{{|y}_{true}-y_{forecast}|}{0.5(y_{true}+y_{forecast})}}$$

  (6)

4. Experimental Setup and Case Study

This section presents the case study investigated in this work as well as the testing facility, located at Politecnico di Milano (Milan, Italy), where the experimental activities have been carried out. The MG²Lab setup available in the Department of Energy of Politecnico di Milano integrates different distributed energy resources like solar PV, combined heat and power, BESS, and hydrogen storage. Details about the microgrid, which can be operated both grid-connected or grid-islanded, can be found in [43].

4.1. Experimental Facility and Model Implementation

The selected MG²Lab’s components, as well as the structure of the EMS used for managing operation of the components, are presented in Figure 1.

Specifically, the setup comprises the following units:

• Grid connection: limited to 100 kW, used for withdrawing or injecting power from/to the distribution grid;
• Non-dispatchable RES: two PV arrays, both installed on the building roofs of 23 and 25 kW_p;
• Storage: two lithium-ion BESSs (BESS1 and BESS2) of 70 and 67.5 kWh, with a C-rate (C-rate is the rate of time in which the BESS takes to charge or discharge) equal to one and a minimum and maximum SOC equal to 35% and 85%, respectively. This results in an overall storage capacity of 68.75 kWh;
• Load: simulated using a back-to-back (B2B) converter, which is a programmable load following the setpoints of an EV load dataset, scaled to a 25 kW maximum power.

The EMS consists of three different modules, namely the load forecaster, PV forecaster, and optimizer. These are implemented in Python and deployed on the microgrid PC, which communicate with each other through a MySQL database used for storing/handling data. The load forecaster module contains two different forecasting models, LSTM and persistence. The LSTM is implemented in TensorFlow, which is an open-source library by Google used to build and deploy machine learning models [46]. The LSTM and persistence models run every hour providing a load forecast for the following 1.5 days. The solar forecasting module utilizes the physical hybrid artificial neural network (PHANN) model described in [47] and implemented using TensorFlow. It runs twice a day following weather forecast updates and provides the PV forecast for the following seven days. The optimizer module is divided into the first and second layers, where the first layer is implemented in the Python-based open-source optimization library Pyomo [48]. It runs every 15 min considering an optimization horizon of 24 h. On the other hand, the second layer is used for real-time power balancing and therefore it is implemented using a programmable logic controller (PLC) with a frequency of 100 milliseconds. It communicates with the MySQL database to obtain the setpoints provided by the first layer and both the forecasted and measured values of the load and PV to perform the power balancing function. Additionally, a human–machine interface (HMI) is used to monitor the status of the microgrid and provide real-time measurements for the preliminary analysis of the results.

4.2. Case Study Description

The case study represents an EV charging station powered by the grid, PV, and BESS. The EV load is based on the records from the JPL (Jet Propulsion Laboratory) database from the adaptive charging network (ACN) [49]. This site has 52 EVSEs and is only accessible by employees, making it a good representation of a typical workplace schedule. The power curve of all 52 EVSEs is aggregated to reconstruct the whole charging station demand. However, only a subset of all the available data is considered suitable for the case study due to the anomalies associated with the COVID-19 pandemic. The considered set includes the sessions from 3 December 2018 to 4 January 2020. To accommodate the charging station demand within the MG²Lab capabilities, the aggregated load power is scaled to a maximum of 25 kW.

The cost of purchasing the electricity from the grid is assumed to be twice the Italian national unified price (Prezzo Unico Nazionale, PUN) to account for transmission and other costs, while the revenue from selling electricity to the national grid is set equal to the zonal price (Prezzo Zonale, PZ) of the North region. These costs are taken from the Italian electricity market [50] for the year 2023.

In

Table 2. Main features of the EV load and electricity prices of the considered cases in the study.

EV load	Typical week trends from the JPL dataset (scaled to 25 kW according to MG2Lab size). Energy consumption for week 1 amounts to 842.5 kWh, while for week 2 it amounts to 823 kWh. Given EV charging at a workplace, there is a substantial difference between workdays (Monday–Friday) and weekend days (Saturday and Sunday). Weekend days are also very unpredictable. Fridays are also unpredictable in terms of magnitude, while the shape remains similar.
Prices	Buy	Maximum: 0.666 €/kWh, minimum: 0.005 €/kWh, average: 0.255 €/kWh
	Sell	Maximum: 0.333 €/kWh, minimum: 0.003 €/kWh, average: 0.128 €/kWh

, values and profiles of the typical weekly EV load and prices are provided.

Both online and offline simulations are carried out to support the methods developed in this work. Online simulations means that the EMS and forecasting are implemented in the MG²Lab experimental facility under real conditions, while offline simulations are computer-based using real data as input.

Online simulations aim to demonstrate that the developed models, including the different PV and EV forecasting methods, can be deployed in real system operation. The online simulations were run for two weeks on the MG²Lab microgrid with either the persistence or LSTM models to predict the EV load. In both weeks, the same EV load was programmed for consistency. On the contrary, the PV production and forecast were from the true irradiance at the MG²Lab. Measurements from the online experiment are then used for running offline simulations with both forecasters for comparison and validation of the approach. A summary of the considered weeks is reported in

Table 3. Characteristics of the simulations performed in this work.

Simulation	Offline				Online (MG2Lab)
Goal	Assess the impact of each forecast method in the overall optimization Impact of combining PV and EV forecasting				Validate the method and demonstrate the application of the EMS with PV and EV forecasting
Weeks	Winter	Spring	Summer	Autumn	24 February 2024–1 March 2024	5 March 2024–11 March 2024
PV data	Two-week MG2Lab historical data for each season				MG2Lab PV plant
EV data	Two-week data for each season from the JPL dataset				JPL dataset: 10 December 2018–16 December 2018
PV forecaster	PHANN day-ahead (MG2Lab) and HML				PHANN Day-Ahead
EV forecaster	Persistence and LSTM and HML				Persistence	LSTM

.

Offline simulations indicate the influence of EV load forecasts in different conditions by comparing the different forecasters over eight weeks, two from each season of the year. Simulations are carried out integrating the PV and EV load forecasts resulting from the JPL EV dataset and the measurements at MG²Lab’s PV field consistent with the season (i.e., for winter, two weeks of actual PV production in winter 2023 from the MG²Lab’s PV field and two winter weeks from the JPL database for EV load simulation are taken). The offline simulator, for each season, also considers different EV forecasting methods (see Table 2): persistence and LSTM forecast methods are considered. In addition, to have a benchmark case, a perfect forecast for both PV and EV is introduced, referred to as hourly mean lookahead (HML), where the perfect forecast predicts the exact average of PV and load measurements over 15 min. As the error metrics are based on forecasted data (averaged over 15 min) and measured data (discretized in 1 min intervals), statistical error metrics can never be zero even for the HML forecast, unless all measurements within the same 15 min interval are exactly equal to their average value. The case with the HML forecast for both PV and EV represents a lower bound for the simulations.

In this way, the offline simulations, besides showing the accuracy of each separate forecaster, show the combined statistical accuracy of PV and EV forecasting methods, the EV station operational costs, and quantify the impact of the forecast accuracy with respect to the ideal case.

Since the EMS adopts a rolling horizon approach, the residual SOC of the BESSs at the end of the simulation could not be imposed a priori; therefore, as different combinations of PV and load forecasts can lead to different final storage SOC, the difference between initial and final storage content is then accounted as an equivalent energy import from the grid, and it is valued at the minimum value of the import price over the entire simulation period.

For each case study, the following results have been reported:

• Statistical performances of PV;
• Load;
• Total net electrical forecast defined as

  $${\epsilon }_{tot}=\left({\widehat{PV}}_{for}-{PV}_{meas}\right)-\left({\widehat{Load}}_{for}-{Load}_{meas}\right)$$
• Total operating costs;
• Operational schedule of the system.

5. Results

In this section, the numerical and experimental results of the comparison of the different EV load forecasts implemented in the deterministic EMS approaches are presented.

5.1. Online Simulations

Measurements of the experimental campaign with the LSTM forecast are reported in Figure 2 (the case with persistence is not reported for brevity). The results are shown to demonstrate that results between the EMS operating in the microgrid with all the physical components and the simulations are consistent. Therefore, simulation results performed offline can be considered representative of the real operation of a microgrid.

Some general considerations can be noted while comparing the experimental results with the corresponding offline simulations:

• On weekdays, when the electrical load is high, the microgrid imports electric energy at night when the electricity price is lower to charge the batteries, which are then discharged during the day in the absence of photovoltaic production;
• Minor differences between the two figures occur and are related to the parasitic losses of the battery power supply systems and other equipment in the laboratory where the microgrid operates (mainly during night-time). The battery charging process measured in the experimental campaign is spread over more hours compared to the results of the simulation. Nevertheless, the quantities of electrical energy are nearly identical and the effect on the simulation results is negligible.

The overall energy and economic results for the different approaches tested in the microgrid are summarized in

Table 4. Overall results of the experiments and the corresponding simulations. Note that the persistence EV forecast is not identical among the two weeks because of small variations in the B2B converter output power.

	Week 1: 24/02/2024–01/03/2024		Week 2: 05/03/2024–11/03/2024
	Persistence Experimental	Persistence Simulated	LSTM Experimental	LSTM Simulated
EV load [kWh]	709.04	709.03	709.34	709.33
PV production [kWh]	330.28	326.68	700.63	697.04
EV forecast SMAPE [%]	39.76	41.69	54.94	52.37
PV production SMAPE [%]	111.44	111.44	195.46	195.46
Electricity purchased [kWh]	900.78	818.07	561.41	505.33
Electricity sold [kWh]	106.74	65.77	142.02	83.01
Initial SOC [kWh/%]	18.0/51.3	18.0/51.3	23.4/66.9	23.4/66.95
Final SOC [kWh/%]	22.3/63.7	13.4/38.2	24.2/69.1	21.81/62.3
Unmet demand [kWh]	0.00	0.00	0.00	0.00
Curtailment [kWh]	0.01	0.00	0.01	0.00
Purchased electricity [€]	240.24	213.35	127.44	112.92
Sold electricity [€]	18.66	10.74	19.01	12.19
Unmet demand [€]	0.00	0.00	0.00	0.00
Curtailment [€]	0.06	0.00	0.05	0.00
BESS residual [€]	−2.17	2.28	−0.46	1.13
Total [€]	219.47	204.88	108.02	96.24

. Despite the identical load data used for each online week, there are small differences between simulations and experiments as the B2B converter requires a small amount of Gaussian noise added to the programmed load profile.

Finally, the operational costs of the offline simulations are in agreement with the experimental facility (i.e., Experimental), with differences below 10%. Considering that several systems and controllers present in the microgrid cannot be reasonably simulated offline, these results validate the proposed approach which can then be extended to the yearly simulations.

5.2. Offline Simulations

Once the MG²Lab approach was validated, offline simulations were conducted to assess the impact of the considered PV and EV forecasting methodologies by extending the analysis over a wider period. Results for two weeks in spring are presented, followed by the overall performance of the other three weeks.

Spring Case

For the spring season, the statistical performance indexes of the PV, load, and net load (combination of load and PV) forecasts are reported in

Table 5. Statistical performance of PV and EV forecasters (single and combined). The PV and EV forecasts are evaluated independently in the first five rows. The remaining rows are the sum of the PV and EV forecasts, which is commonly referred to as the net load. Note that the HML forecast error is nonzero because of the discrepancy between the forecast time discretization (15 min) and the experimental data sampling (1 min).

	Forecast	MAE	SMAPE	RMSE
PV	PHANN	4.10	71.91	7.49
	HML	0.72	6.85	2.13
EV	Persistence	1.58	44.89	3.23
	LSTM	1.06	44.66	1.87
	HML	0.16	7.33	0.35
PV+EV	PV HML + EV persistence	1.94	−69.67	3.87
	PV HML + EV LSTM	1.44	−30.41	2.82
	PV HML + EV HML	0.76	0.29	2.15
	PV PHANN + EV persistence	2.88	−7.73	5.27
	PV PHANN + EV LSTM	4.30	−388.93	7.63
	PV PHANN + EV HML	2.37	35.51	4.60

.

As it is possible to notice, LSTM outperforms persistence in all the statistical performance parameters. However, when coupled with the PHANN day-ahead PV forecast, it results in a higher net electrical load forecast error among all the predictors. This first result suggests the importance of considering accuracy indexes accounting for the overall forecast and not focusing on each forecaster separately. Similarly, the calibration and development of the forecast tools shall account for the whole system and not only the specific good predicted.

Results of the offline simulations for a spring week (out of the two considered) are reported in Figure 3. The operational scheduling for both methods is quite similar across the different days of the week, except for some minor quantitative differences in the net electricity imported from the grid, which appears to be slightly lower in the persistence case.

However, the major difference can be seen on 7 April: in the operational scheduling with persistence, the EMS imports electricity from the grid only in the first hours of the day to meet the load, then the BESSs are discharged in the following hours. The operational scheduling of the LSTM (right) is different, as the EMS imports electricity from the grid throughout the day without discharging the BESSs, resulting in higher operational costs, as summarized in

Table 6. Overall results of the experiments and the corresponding simulations.

PV Forecast	HML			PHANN
Load Forecast	Persistence	LSTM	HML	Persistence	LSTM	HML
EV load [kWh]	1665.24	1665.24	1665.24	1665.24	1665.24	1665.24
PV production [kWh]	3328.39	3328.39	3328.39	3328.39	3327.34	3328.39
Electricity purchased [kWh]	214.59	214.88	144.99	184.22	176.48	150.00
Electricity sold [kWh]	1830.40	1833.37	1771.80	1774.63	1740.01	1757.46
Total BESSs losses [kWh]	57.22	53.86	46.44	75.56	86.79	65.65
Initial SOC [kWh/%]	17.5/50.0	17.5/50.0	17.5/50.0	17.5/50.0	17.5/50.0	17.5/50.0
Final SOC [kWh/%]	12.56/35.9	12.90/36.9	12.45/35.6	16.09/46.0	23.39/66.8	12.52/35.8
Unmet demand [kWh]	0.00	0.00	0.00	0.00	0.00	0.00
Curtailment [kWh]	0.00	1.05	0.00	0.00	1.05	0.00
Purchased electricity [€]	50.61	48.34	29.14	47.42	51.47	35.07
Sold electricity [€]	278.30	279.24	267.79	265.40	253.35	261.38
Unmet demand [€]	0.00	0.00	0.00	0.00	0.00	0.00
Curtailment [€]	0.00	0.00	0.00	0.00	0.00	0.00
BESS residual [€]	0.40	0.37	0.40	0.11	-0.47	0.40
Total [€]	−227.29	−230.54	−238.35	−217.87	−202.35	−225.91

.

As the PV forecasts used to perform these simulations were the same for both case studies, the higher import from the grid during the EMS–LSTM operations was only related to the accuracy of the net electrical load forecasts. This difference, which results in higher operational costs, can be attributed to two main factors:

• Purchase and sale prices fluctuate throughout the 24 h cycle, with this dynamic being particularly pronounced during the spring season. In fact, as it is possible to see from the table above, the EMS with persistence imports electricity at an average price of 0.257 €/kWh and exports to the grid at 0.15 €/kWh, while the average price for the EMS with LSTM is 0.292 €/kWh with a similar value when exporting. This is because the overall LSTM errors may be lower in absolute value compared to those of persistence, but they are more pronounced during the hours of the day when electricity prices are significantly higher (for purchases), therefore resulting in a more relevant impact;
• The accuracy of the net load forecasts is not the algebraic result of PV and EV forecasts: errors can amplify or reduce depending on the particular case. For instance, in the persistence case, errors in PV and load forecasts may exhibit opposite signs, potentially mitigating the overall inaccuracies of the individual forecasters. In fact, when considering a perfect HML PV forecast, the EMS with LSTM demonstrates slightly lower operational costs.

Overall, the optimal case for the considered two spring weeks occurs for LSTM when coupled with the HML PV forecast, while persistence performs better when coupled with the PHANN PV forecast. This is another indication of the necessity to incorporate system management costs into the error function of forecasting algorithms, to reduce the errors associated with expensive balancing costs.

6. Overall Results

Below are the overall forecast accuracy and the economic operation results, respectively, for all the seasons, as summarized in

Table 7. Accuracy of the adopted forecast tools for the combined net load of different seasons (top) and corresponding economic results (bottom). Note that the combined HML PV and HML EV forecast error is nonzero because of small differences between the input and output of the back-to-back converter.

Net Load Forecast Error (RMSE in [kW])
PV forecast	HML			PHANN
EV forecast	Persistence	LSTM	HML	Persistence	LSTM	HML
Spring	3.87	2.82	2.15	5.27	7.63	4.60
Summer	3.39	2.22	1.38	4.89	5.05	3.78
Autumn	3.64	2.25	1.25	5.16	5.71	3.80
Winter	2.87	4.40	0.93	4.68	4.48	4.23
Economic result (€)
PV forecast	HML			PHANN
EV forecast	Persistence	LSTM	HML	Persistence	LSTM	HML
Spring	−227.29	−230.54	−238.35	−217.87	−202.35	−225.91
Summer	−197.85	−199.21	−201.44	−187.02	−181.94	−191.97
Autumn	46.5	44.86	38.92	48.49	49.68	43.90
Winter	218.31	216.65	205.86	218.19	218.15	215.59

.

Looking at the tables, the following conclusions can be drawn:

• There is a good correspondence between the overall net electric errors and the economic results. The higher the accuracy of the combined forecast error the worse the operational cost; LSTM performs better when the HML PV forecast is assumed, while it is worse than persistent when the PHANN PV forecast is adopted;
• The impact of EV and PV forecasts is pretty similar on the economic results when compared to the ideal case: in both cases, the difference in operating costs between using perfect and actual forecasts is around 5%;
• The combination of PV and EV forecasts might lead to discrepancies up to 10% with respect to the ideal case.

Overall, these results suggest that the accuracy of a stand-alone forecast model is not relevant when it works in combination with other forecasters. Moreover, forecasters which have higher accuracy are outperformed by others when the accuracy of the prediction is time-relevant as this is for energy systems with varying electricity prices. Therefore, it is important to correctly predict the load or PV production when electricity prices are high and this aspect should be accounted for when training the forecast methods.

7. Conclusions

Currently, the predict-then-optimize approach remains one of the most widely adopted techniques for operational optimization in multi-energy systems. Although some conceptual limitations of this approach have been noted in the literature, few papers have attempted to investigate the impact of both load and solar forecast accuracy on the operational cost of an existing microgrid.

In this study, a detailed analysis has been conducted of the error impact of various EV forecasting techniques within a hierarchical predictive control strategy to optimize an EVs charging station microgrid operation. The analysis presented herein comprised an experimental part, during which two methodologies under investigation (LSTM and persistence) were tested within the experimental facility of the MG²Lab. Additionally, a simulation study was conducted extending the numerical analysis over a longer period, considering historical data collected in the laboratory in 2023.

The first relevant result of the study was the validated operation of a multi-good microgrid using both PHANN PV and LSTM EV load prediction combined with an EMS operated to minimize the operational costs. This confirmed that the methods developed are of interest for the quantitative results but can also be deployed in real systems.

Quantitative results showed that the accuracy of the combined forecast models matters: higher combined accuracy resulted in higher performance of the EMS with better operational results.

In addition, the accuracies of the different forecasters do not individually correlate with final performance. It was shown that LSTM has the highest accuracy in predicting the EV load; however, the EMS operating with the LSTM EV forecast can have the poorest performance when coupled with the PHANN PV forecast. Besides the interactions, LSTM is less accurate than persistence when electricity prices are high, resulting in higher operational costs.

Future works will focus on the development of new customized loss functions to train and evaluate forecasting models. These will depart from generic statistical performance metrics, aiming instead to capture downstream decision-maker dynamics, thereby providing forecasts that are optimized for the selected application. Initial investigations suggest this will result in a more integrated and cost-effective synergy between forecasting and optimization procedures.