1. Introduction

2. Italian Electricity Markets

2.3. Intra-Day Market

The Intraday Market (MI) allows participants to adjust their schedules set in the Day-Ahead Market (DAM) through additional buy or sell bids. Trading in the MI occurs via three MI-A auction sessions (CRIDA) and a continuous trading session, MI-XBID.

2.3.1. MI-A Auction Sessions

During the MI-A auction sessions, alongside the trading of buy and sell bids, intraday interconnection capacity is allocated between all zones of the Italian market and interconnected geographical areas involved in Market Coupling. The specifics of each MI-A session are as follows:

• MI-A1 Session: Opens at 12:55 PM on the day before the delivery day and closes at 3:00 PM on the same day. Results are communicated by 3:30 PM on the day before the delivery day.
• MI-A2 Session: Opens at 12:55 PM on the day before the delivery day and closes at 10:00 PM on the same day. Results are communicated by 10:30 PM on the day before the delivery day.
• MI-A3 Session: Opens at 12:55 PM on the day before the delivery day and closes at 10:00 AM on the delivery day. Results are communicated by 10:30 AM on the delivery day.

The selection of buy and sell bids follows the same criteria as described for DAM. However, unlike the DAM, accepted buy bids are valued at the zonal price.

2.3.2. MI-XBID Continuous Trading Session

The MI-XBID continuous trading session is divided into three phases, wherein buy, and sell bids are traded and intraday interconnection capacity is allocated between all zones of the Italian market and interconnected geographical areas active in XBID. The schedule for each phase is:

• Phase I: Opens at 3:30 PM on D-1 and closes at 9:40 PM on D-1.
• Phase II: Opens at 10:30 PM on D-1 and closes:
• For relevant periods corresponding to the first twelve hours of day D, one hour before each relevant period begins (h-1).
• For relevant periods corresponding to the second twelve hours of day D, at 9:40 AM on day D.
• Phase III: Opens at 10:30 AM on day D and closes one hour before each relevant period begins (h-1).

Buy and sell bids can be submitted by unit and by portfolio. For each phase of continuous trading in MI-XBID, the GME organizes a trading book segmented by geographical and/or virtual zones.

2.3.3. Sequential Conduct of Sessions

The MI-A auction sessions and the phases of the MI-XBID continuous trading session are conducted sequentially and non-overlapping in the following order:

a)

MI-A1

b)

Phase I MI-XBID

c)

MI-A2

d)

Phase II MI-XBID

e)

MI-A3

f)

Phase III MI-XBID

Figure 3. Sequential Conduct of MI Sessions.

Figure 3. Sequential Conduct of MI Sessions.

The GME acts as the central counterparty. This research will focus only on the operations on the MI-XBID Continuous Trading Session and not on the MI-A auction sessions.

3. System Modelling

3.1. BESS Model

The numerical model of the BESS aims at accurately representing the operation of the BESS while participating in the markets. The model receives and conveniently processes real-world input data, such as electricity market prices and quantities. To optimally represent a real BESS, the model must provide accurate estimates even when the BESS operates at its limits, i.e., power and SOC saturation limits. This will enable the coherent evaluation of the gap between the performance requested from the grid-side and the actual provision of the BESS (e.g., in terms of energy provided on energy requested). Given these premises, the proposed layout of the model [15] is presented in Figure 4.

Input comes from the bidding strategy and is fed to the BESS model. The model considers the presence of electric loads acting as auxiliaries of the operation as described in Figure 5. As can be seen, the electric demand depends on the ambient temperature and the BESS power.

The input is a power setpoint fed to the BESS empirical model. The setpoint is transformed considering η_BESS (considering both the PCS and battery pack), illustrated in Error! Reference source not found., and capability curves (representing the maximum charging and discharging power achievable for each SOC) in Error! Reference source not found.. SOC is updated accordingly, as described in Equation . The outputs are the power requested DC-side and the and the updated SOC. These are fed to a simplified battery management system (BMS) that modifies the inputs conveniently for staying within the operational boundaries (safe operating area [2]). The main outputs of the model are the SOC and the power provided AC-side. This process is repeated for each timestep of the simulation. The outputs are elaborated for supporting the analysis of the results.

$${SOC}_i^{BESS}={SOC}_{i-1}^{BESS}+p_i^{cha}\times {\displaystyle \frac{samplin{g}_{time}\times {\eta }_{BESS}}{3600}}-p_i^{dis}\times {\displaystyle \frac{samplin{g}_{time}}{3600\times {\eta }_{BESS}}}$$

Figure 6. BESS Efficiency.

Figure 6. BESS Efficiency.

Figure 7. Capability Curves.

Figure 7. Capability Curves.

3.2. Day-Ahead Market Model

The main goal of the DAM model is to develop an efficient strategy to make energy arbitrage. The term energy arbitrage refers to the possibility of storage systems exploiting DAM spread to generate profits. To achieve this control, the algorithm identifies, by means of a predictive tool based on deep learning model, the minimum and maximum prices of the market each day to set up the proper control logic. To enhance the chances of achieving a positive economic profit, the procedure has a feedback control that checks whether the predicted daily profit is greater than zero, if not considering the Levelized Cost of Storage (LCOS), in case it is not the BESS will not submit any bid for that day.

The LCOS is a metric used to evaluate the overall cost of storing energy over the lifetime of an energy storage system. It is a valuable measure for comparing the economic viability of different energy storage technologies. LCOS is calculated as the total cost of the storage system divided by the total amount of energy stored and released by the system over its lifetime, as expressed in Equation (4):

$$LCOS={\displaystyle \frac{CAPEX+\sum OPEX}{\sum _{VU}{E}_{tot}^y}}$$

(4)

This control logic heavily impacts the arbitrage provision. Algorithm 1 describes the structure of the energy arbitrage on the day-ahead market algorithm in detail.

Algorithm 1 Day-Ahead Market Energy Arbitrage

If the outcome is profitable, offers on DAM are structured as follows:

• Selling at a significantly reduced price to secure acceptance of the offer.
• Buying at a substantially higher price to ensure acceptance of the offer.

As already mentioned, the energy arbitrage strategy is based on predicted zonal prices via a neural network model that will be described in the following section.

3.2.1. Deep Learning P_z Prediction Tool

The DL model implemented is a hybrid neural network model that leverages both Long Short-Term Memory (LSTM) and Convolutional Neural Networks (CNN) to capture the temporal dynamics and spatial features of the data. The 83 features used for training the model are listed in Table 1.

The architecture includes layers of bidirectional LSTM, useful for capturing long-term relationships in sequential data [21], and CNN, used to extract local features from sequential data. Batch normalization [22] and dropout layers [23] are added to prevent overfitting and improve generalization.

A distinctive feature of this model is the incremental training of the model. Each day of the simulation, the training set is expanded with newly available data, continuously improving the model’s predictive capability. This incremental process allows the model to quickly adapt to changes in the energy market. The process is shown in Figure 8.

The model was trained using mean squared error (MSE) (see Equation (5)) as the loss function, with the Adam optimizer [24]. Early stopping was implemented to prevent overfitting [25], and a learning rate scheduler was used to improve convergence [26].

To assess the model's efficiency, various metrics are monitored during the tool's utilization. Additionally, the model's performance is compared with a Persistence Model, evaluating both against the actual P_z values. In particular, the metrics evaluated are the Mean Squared Error MSE (Equation (5)), the Root Mean Squared Error RMSE (Equation (6)) and R² factor (Equation (7)).

$$\mathrm{Mean}\mathrm{Squared}\mathrm{Error}–\mathrm{MSE}\text{:}MSE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2$$

(5)

$$\mathrm{Root}\mathrm{Mean}\mathrm{Squared}\mathrm{Error}–\mathrm{RMSE}\text{:}RMSE=\sqrt{MSE}$$

(6)

$${\mathrm{R}}^2\mathrm{Factor}\text{:}{R}^2=1-{\displaystyle \frac{\sum _{i=1}^n{(y_i-\widehat{y_i})}^2}{\sum _{i=1}^n{(y_i-\overline{y_i})}^2}}$$

(7)

3.3. Intra-Day Market – Continuous Trading Market XBID

XBID represents a new opportunity for energy resources, since it occurs slightly before real-time, and it is characterized by continuous trading where a bid is awarded at bid price as soon as it is accepted by another resource. This opens to various bidding strategies. This is a new market, gone live in many EU Member States in 2021: therefore, a statistical analysis of its early stage could be beneficial. It is presented in the next paragraph.

3.3.1. Comprehensive Statistical Analysis

Particular emphasis has been placed on studying and modeling the continuous trading session of the Intra-Day Market. Initially, an extensive statistical analysis of XBID data for the Italian wholesale market has been conducted, reviewing all the public offers submitted. As of the time of authoring this article, these offers total almost fifty million. This analysis is crucial for the subsequent modeling of XBID and the development of a strategy for the participation of the BESS in this market. The analysis involves a detailed examination of various statistical measures, including means μ and standard deviations σ of the bid prices, described in Equation (9) and Equation (10), to understand the central tendencies and variability in the data. Additionally, acceptance rates of offers by price range (Equation (8)) were analyzed to identify the price ranges for successful transactions. Distributions of accepted offers by price were also constructed using Kernel Density Estimation KDE to visualize the frequency and likelihood of different prices being accepted and to better understand the underlying distribution pattern (Equation (11)).

Furthermore, to capture the nuances of the market, these statistics were categorized based on several factors:

• Type of day – D_t: Weekday or Holiday, to account for variations in market behavior due to differences in demand and operational patterns.
• Hour of the day – h_D: electricity consumption and prices can vary significantly throughout the day, necessitating a time-based analysis.
• Season – S: Different seasons impact electricity demand and supply conditions, which was factored into the analysis
• Hours in advance of the offer publication – h_A: the timing of offer submissions was examined to understand its effect on offer acceptance.
• Type of offer - o_t: Selling or buying, to distinguish the different dynamics in the market for sellers and buyers.

$${AR}_{range}={\displaystyle \frac{\sum o_{range}^{ACC}}{\sum o_{range}^{TOT}}}$$

(8)

$$\mu ={\displaystyle \frac{1}{N}}\sum _{i=1}^N{Price}_i^{ACC}$$

(9)

$$\sigma =\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{({Price}_i^{ACC}-\mu )}^2}$$

(10)

$$\widehat{f}\left(x\right)={\displaystyle \frac{1}{Nh}}\sum _{i=1}^{N}K\left({\displaystyle \frac{x-x_i}{h}}\right)$$

(11)

Where:

$K$	is the kernel function.
$h$	is the bandwidth.
$x_i$	Are the data points.

This detailed and multifaced analysis provides a thorough understanding of market dynamics, enabling the development of an informed and strategic approach to participating in the XBID market. It allows for the identification of optimal times and conditions for submitting offers and helps in tailoring strategies to maximize the efficiency and profitability of a BESS in the electricity market and it is central in the strategy of price formation for the bidding strategy.

3.3.2. Deep Learning Acceptance Probability Prediction Tool

To model a realistic bidding strategy, as already mentioned, a tool for the acceptance probability prediction has been developed.

The implemented deep learning model is a neural network that combines Bidirectional Long Short-Term Memory (BiLSTM) layers and Convolutional Neural Networks (CNN). This hybrid architecture effectively captures both temporal dynamics and spatial features present in the data.

The dataset used for training the model includes various features such as historical offer data, market data, and categorical data, with detailed descriptions provided in Table 2.

The model architecture leverages the following components:

• Bidirectional LSTM Layers: by processing data bidirectionally, the BiLSTM layers enhance the model’s ability to understand complex temporal patterns.
• Conv1D Layer: the convolution operation helps in identifying significant patterns and trends within smaller windows of the data sequence.
• Batch Normalization and Dropout: Batch normalization layers stabilize and accelerate training by normalizing the input of each layer, as described in Equation (12). Dropout layers randomly deactivate a fraction of neurons during training, making the model more robust.

$$\mathrm{Batch}\mathrm{Normalization}\text{:}\widehat{h_t}={\displaystyle \frac{h_t-\mu }{\sqrt{{\sigma }^2+\epsilon }}}·\gamma +\beta$$

(12)

Where:

$h_t$	This is the input value for batch normalization at time t.
$\mu$	This is the mean of the batch of input ht.
${\sigma }^2$	This is the variance of the batch of input ht.
$\epsilon$	A small positive value added to avoid division by zero during normalization.
$\gamma \mathit{and}\beta$	These are parameters learned during training and optimized during training

(4)

Dense Layer: The output layer is a dense layer with a sigmoid activation function, used for binary classification. This layer outputs the probability of offer acceptance and can be represented by Equation (13) that encapsulates the fundamental operation of a neural network layer:

$$\widehat{y}=\sigma (W·h_t+b)$$

(13)

Where:

$\widehat{y}$	This is the output of the neural network layer after applying the activation function σ.
$\sigma$	This is the activation function, in this case Sigmoid: $\sigma \left(x\right)={\displaystyle \frac{1}{1+e^{-x}}}$, this function squashes the input to a range between 0 and 1
$W$	This represents the weight matrix. It contains the weights that are learned during the training process.
$h_t$	This is the input vector to the layer at time t.
$b$	This represents the bias vector.

The model utilizes Binary cross-entropy loss function (Equation (14)) as metric to optimize that is one of the metrics most suitable for binary classification tasks and model accuracy is monitored during training process.

$$L=-{\displaystyle \frac{1}{N}}\sum _{i=1}^N[y_i\log \left(\widehat{y_i}\right)+(1-y_i)\log (1-\widehat{y_i})$$

(14)

The model undergoes training over multiple epochs with a large batch size, utilizing the dataset's full potential to ensure stable updates and efficient convergence. Validation data is used to monitor the model's performance and make necessary adjustments to prevent overfitting.

To evaluate the efficiency of the model, relevant metrics are stochastically monitored. Evaluated metrics include Accuracy, that measures the fraction of correctly predicted instances out of total instances (Equation (15)), the Precision, that measures the fraction of true positives among all positive predictions (Equation (16)), Recall (or Sensitivity), that measures the fraction of true positives that were correctly identified (Equation (17)), and lastly the F1-score, that is the harmonic mean of precision and recall and balances these two metrics (Equation (18)).

Accuracy:	$Accuracy={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}$	(15)
Precision:	$Precision={\displaystyle \frac{TP}{TP+FP}}$	(16)
Recall:	$Recall={\displaystyle \frac{TP}{TP+FN}}$	(17)
F1-Score:	$F1Score=2·{\displaystyle \frac{Precision\times Recall}{Precision+Recall}}$	(18)

Given the future strategy of using predicted probabilities for decision-making, it is crucial to evaluate the model in a manner that aligns with this operational context. This involves conducting multiple simulations of stochastic predictions, which mimics how the model would function in the XBID simulation. By measuring the variation in metrics across these simulations, we can gauge the model's resilience to fluctuations in predicted probabilities.

The optimal number of simulations to assess metrics is determined through an iterative process where the number of stochastic simulations is incrementally increased. This continues until a specified metric variation (Equation (19)), falls below a predefined tolerance (ε). This iterative approach ensures that the metrics stabilize sufficiently amidst the variability introduced by different stochastic predictions. Ultimately, it strikes a balance between computational efficiency and the thoroughness needed for robust metric evaluation.

Condition:

$Metri{c}_{variation}={\sigma }_{Accuracy}+{\sigma }_{Precision}+{\sigma }_{Recall}+{\sigma }_{F1-score}\le \epsilon$

(19)

Where:

${\sigma }_i$:

Standard Deviation of the metric values calculated for each simulation

This methodical evaluation is essential for ensuring the reliability and effectiveness of the model in practical applications, where decisions hinge on probabilistic predictions.

3.3.3. XBID Offer Price Decision Mechanism

With data from the statistical analysis and with the prediction tool, a model of a bidding strategy on XBID has been developed.

Through the historical data analyzed in the previous statistical analysis an appropriate price for the bid is established; for each hour, considering the season and the year, the optimal bid submission interval is identified. Subsequently, the corresponding average price is determined. Using the previously constructed distributions, the price with the highest probability of acceptance is evaluated. In fact, knowing that the Kernel Density Estimation for a given data set ${\left\{x_i\right\}}_{i=1}^N$ is defined as in Equation (3.9), to determine the optimal discharging price, the price range where the probability density is maximized has to be identified. This involves integrating the KDE over different intervals and finding the interval with the maximum integrated density.

The initial lower bound is set equal to the mean price of the selected submission interval augmented of the LCOS and the price ranges are identified as:

$${PriceRange}_i={(lower}_{bound}^i,{lower}_{bound}^i+\delta )$$

where delta is set to 10 €/MWh and ${lower}_{bound}^{i+1}={lower}_{bound}^i+\delta$.

The KDE is integrated over each price range, as described in Equation (20):

$$Area={\int }_{{Price}_{range}^i}\widehat{f}\left(x\right)dx$$

(20)

and from the price range with the highest Area, the optimal discharging price is obtained as in Equation (21):

$${Price}_{offer}={\displaystyle \frac{{Price}_{range}\left({Area}_{max}\right)}{2}}$$

(21)

Before submitting the offer, profit control is introduced, securing a profit downstream from the strategy. This is possible introducing the hypothesis that, for charging offers, the battery acts as price-taker accepting the offer with the price closest to the average present on XBID order book for the hour selected for charging. Furthermore, if the spread between ${Price}_{offer}$ and ${Price}_{charge}$ results non profitable, the ${Price}_{offer}$ is adjusted as in Equation (22):

$${Price}_{offer}=\left\{\begin{array}{cc}{Price}_{offer}\hfill & if{Price}_{offer}>({Price}_{charge}+{\displaystyle \frac{LCOS}{\eta }})\hfill \\ {Price}_{charge}\hfill & if{Price}_{offer}<\left({Price}_{charge}+{\displaystyle \frac{LCOS}{\eta }}\right)\mathit{and}\mathit{LCOS}=0\hfill \\ {Price}_{charge}+{\displaystyle \frac{LCOS}{\eta }}\hfill & if{Price}_{offer}<\left({Price}_{charge}+{\displaystyle \frac{LCOS}{\eta }}\right)\mathit{and}\mathit{LCOS}\ne 0\hfill \end{array}\right.$$

(22)

The flow of the bidding strategy can be seen in Figure 9.

3.3.4. XBID Control Strategy

Energy arbitrage in the XBID market is an advanced strategy designed to profit from energy price fluctuations.

The implemented control strategy combines predictive models, statistical price analysis, and operational enhancement of the Battery Energy Storage System (BESS). By precisely managing charging and discharging operations, this strategy aims to maximize profits from energy arbitrage, effectively capitalizing on market dynamics.

The strategy introduced firstly ensures the feasibility of the battery’s program considering the constraints on the state of charge (SOC) of the battery and adhering to the schedule established in the Day-Ahead Market (DAM). In fact, if the initial SOC is too low, it is adjusted to fall within the operational range to ensure the operability of the BESS. Additionally, the charging phase following an accepted discharging phase must commence within two hours after the discharge. This ensures that the battery capacity is available throughout the day, allowing for multiple discharging phases to occur.

For each hour, the arbitrage opportunity is identified by maximizing the spread between the average price during the discharge period and the bid price during the charging period, which must occur within two hours of the discharge period, and to ensure to not overlap the operations defined on DAM. For the selected hour, a sell bid is submitted, and the probability of its acceptance is evaluated using the previously defined DL Tool. If the bid is accepted, the Battery Energy Storage System (BESS) begins the discharge phase, considering the available energy and system capacity. Simultaneously, a charge offer is accepted from the order book, assuming it is reasonable to accept an offer at an average price, and, at the identified hour, the SOC is restored to prepare the BESS for further arbitrage opportunities.

The control strategy can be summarized by Algorithm 2.

Algorithm 2 XBID Market Energy Arbitrage

4. Case Studies and Results

4.1. Day-Ahead Market – DAM

The study initially focused on the investigation and analysis of DAM simulation and the development and implementation of the Deep Learning (DL) Tool for zonal price prediction. The primary objective was to assess the effectiveness and feasibility of BESS operations in the DAM under varying market conditions and the influence of advanced price prediction methodologies.

4.1.1. Deep Learning P_z Prediction Tool

The hybrid neural network model developed for zonal price (P_z) prediction demonstrates notable improvements over the Persistence Model (D-1), although these enhancements do not fully align with the actual P_z values. The performance of the model was assessed using three primary metrics: Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the R2 factor. These metrics provide a comprehensive understanding of the model's accuracy and reliability in predicting P_z values.

The Mean Squared Error (MSE) metric served as both the loss function during the training process and a primary evaluation metric for assessing the performance of the hybrid neural network model. MSE measures the average of the squares of the errors, representing the differences between the predicted and actual zonal price (P_z) values. Lower MSE values indicate a more accurate model, as they reflect smaller discrepancies between the predicted outcomes and the actual values.

In this evaluation, the hybrid model achieved an MSE of 326.97, which is lower than the Persistence Model's MSE of 378.85. This represents a 13.69% improvement, underscoring the hybrid model's effectiveness. This substantial reduction in MSE can be attributed to several key factors. Firstly, the hybrid model leverages a comprehensive set of features, including historical P_z prices, meteorological data, gas prices, and the Global Horizontal Irradiance (GHI) index. This extensive feature set allows the model to capture the complex interactions and dependencies that influence zonal prices, leading to more accurate predictions. The continuous learning process ensures that the model remains relevant and effective, even as market conditions evolve. Despite these improvements, the remaining MSE of 326.9744 indicates that there is still room for further enhancement in the model's accuracy. While the hybrid architecture improves prediction accuracy, increasing the model's complexity can also lead to overfitting, where the model performs well on training data but less effectively on unseen data. Furthermore, zonal prices are influenced by a wide range of external factors, including regulatory changes, geopolitical events, and economic conditions, which may not be fully captured by the model.

The Root Mean Squared Error (RMSE), offers an interpretable measure of the prediction errors. The hybrid model's RMSE was 18.08, while the Persistence Model's RMSE was 19.46, reflecting a 7.1% improvement. Despite this reduction in prediction errors, the deviations between the predicted and actual values indicate that the model's predictions are not yet perfectly accurate. The slightly better behavior of the hybrid model is shown in Figure 11.

The R2 factor, representing the proportion of the variance in the dependent variable that is predictable from the independent variables, further validates the model's performance. The hybrid model achieved an R2 of 0.624, compared to the Persistence Model's R2 of 0.5643, indicating a 10.58% improvement. While the higher R2 value demonstrates that the hybrid model captures more of the underlying patterns and temporal dynamics in the data, the gap between the model predictions and actual values suggests that some variance remains unexplained.

The hybrid model consistently outperformed the Persistence Model across all evaluation metrics as can be seen in Table 4.

The significant reduction in MSE and RMSE values highlights the enhanced predictive capability of the hybrid model. Additionally, the higher R2 values indicate that the hybrid model provides a better fit to the data, capturing more variance and offering more accurate predictions. However, the improvements, while significant, do not completely align the predicted values with the actual P_z values, indicating that further refinement is necessary.

The results obtained from the hybrid neural network model have several important implications for energy market forecasting and decision-making. The inclusion of meteorological data, such as temperature, precipitation, and wind speed, significantly enhances the model's predictive accuracy. These factors, which influence energy demand and supply, are crucial for accurate P_z predictions. The model's ability to integrate and learn from these diverse data sources underscores its comprehensive approach to forecasting.

Another significant insight from the analysis is that while the DL model does not perfectly predict the exact zonal price values, it identifies trends and price peaks on the DAM. The peaks are crucial for devising an effective arbitrage strategy on the DAM. Indeed, the price predictions will be used to define the charging/discharging times of the BESS, while the bid price will not be influenced by the price model. This is better clarified in the following.

4.1.2. Energy Arbitrage Strategies

To analyze the scenarios on DAM, the energy purchased and sold during the simulation period was examined along with the resulting cycles completed within the same period. Additionally, the profits generated were considered, considering also any energy purchases required to meet the power demanded by auxiliaries in cases where the SOC was insufficient.

To provide a more comprehensive financial analysis, we introduce the Net Present Value (NPV) analysis for the scenarios under discussion. This metric is used to evaluate the profitability of the investment and represents the difference between the present value of cash inflows and the present value of cash outflows over the service life of the BESS. NPV is a widely used tool in capital budgeting and investment planning because it accounts for the time value of money, allowing for the comparison of different investment scenarios. NPV can be calculated using Equation (24):

$$NPV=-CAPEX+{\sum }_{i=1}^{SL}\left({\displaystyle \frac{Revenues\left[\frac{\mathrm{€}}{year}\right]-OPEX}{{(1+i)}^t}}\right)$$

(24)

Where:

SL	It is the service life of the BESS and can be calculated as $SL={\displaystyle \frac{{n°cycles}_{BESS}^{max}}{{n°cycles}_{BESS}^{yearly}}}$
i:	It is the discount rate, considered fixed and it is hypothesized to be 5% [4]

As previously mentioned, the two cases analyzed were:

• Negligible LCOS: LCOS = 0
• Significant LCOS: LCOS = 53.14 €/MWh

The initial conditions were kept constant for both scenarios and are summarized in the table below.

Table 5. Initial Conditions for DAM Simulations.

Table 5. Initial Conditions for DAM Simulations.

	CASE A	CASE B
Simulation Period	From 2023/04/01 to 2024/03/31
Pnom	10 MW
Enom	30 MWh
SOCmin	5%
SOCmax	95%
SOCinitial, 0	5%
LCOS	0 €/MWh	53.14 €/MWh

The two simulations yielded significantly different results, highlighting the substantial impact of LCOS on DAM market strategy. Specifically, the profits decreased by 92.86% due to the effect of LCOS. This is shown in Table 6 and Table 7.

This decrease with the introduction of the LCOS constraint is primarily attributable to the zonal price trends on the DAM, which do not present favorable conditions for battery application. During the simulation period, the average daily spread between the highest and lowest prices was 70.9 €/MWh, with peaks of 159.44 €/MWh on 22 April 2023, and a low of 9.48 €/MWh on November 12, 2023. This trend is even more pronounced when considering price trends in 2024, where the average spread reaches only 54.94 €/MWh. The reduced profitability under the LCOS constraint underscores the critical influence of price volatility on the economic viability of battery storage in the DAM market. Furthermore, a high number of inactive days increase the relevance of auxiliaries’ power on the profit loss; this can be seen in Figure 13 and Figure 14.

In these graphs, the red lines represent sessions where the profit is negative, clearly illustrating the aforementioned trend.

The resulting NPV, -8.4 M€ for Case A and -10.03 M€ for Case B, is widely negative and demonstrates the unprofitability of energy arbitrage on DAM with considered prices. This is due to the limitations caused by low volatility in DAM zonal prices, as the discounted revenues and operating costs do not cover the initial investment in the battery.

This led to the exploration of new revenue opportunities in the Intra-Day market, particularly with a focus on XBID.

4.2. Intra-Day Market – XBID

The Intra-Day market, and more specifically the XBID market, presents a promising alternative for generating revenue. The XBID market allows for continuous trading and takes advantage of real-time price fluctuations, providing opportunities to capitalize on higher price volatility. This market’s Pay-As-Bid remuneration system further enhances the potential for profitability, as it enables more strategic bidding and better alignment of revenues with the actual market conditions.

4.2.1. Comprehensive Statistical Analysis

The Intra-Day Market has established itself as a crucial tool for operators in planning their production schedules, reaching an all-time high in traded volumes in 2023 (29.1 TWh, up by 3.1 TWh from 2022). As in 2022, these trades were mainly concentrated in auction trading (22.3 TWh, up by 0.4 TWh from 2022), particularly in the MI-A1 segment. However, it was the XBID market that drove overall growth, with over 3.5 million matched trades (more than double from 2022) and nearly 6.8 TWh traded (up by 2.8 TWh). Within the Intra-Day Market, XBID has become the second most liquid segment, accounting for 23% of the total volume (up by 8 percentage points). Regarding the different zones, the modest increase in auction trading volumes was concentrated in both purchasing and selling in the North, which remains the most significant zone in terms of traded quantities, and in the Central North. On the other hand, XBID saw substantial growth on both sides of the market across all zones.

The dynamics and average global price levels on XBID are consistent with those observed on DAM, as shown in Figure 15 and Figure 16.

However, more interesting results that can leverage the potential of this market can be observed by examining the variance of accepted prices. By considering the classification described in 3.3.1, and focusing on the year 2023, which is more useful for simulation purposes and more representative compared to 2022 (which shows abnormal trends), the results are shown in Figure 17.

From this initial analysis, it is evident that the variance already suggests additional earning potential. Furthermore, the analysis indicates that, in all examined cases, the most optimal submission intervals to exploit this advantage are (0, 2] and (2, 4] hours. These intervals consistently show higher deviations, with peaks of up to 80 €, compared to other intervals, indicating greater price volatility. In the context of energy arbitrage, particularly for a BESS, this represents a significant opportunity. For further confirmation of this opportunity, the probabilities of acceptance based on the deviation from the average price were also analyzed, considering intervals of 20 €/MWh, as shown in Figure 18.

From the graphs just shown, it is evident that there are statistical gaps that render this acceptance prediction mechanism unusable in a realistic simulation. Therefore, the price distributions of accepted offers are constructed to serve as a tool for the bidding price decision mechanism. These distributions are created for each hour based on the previously introduced classification and are reported in Figure 19 (for simplicity, they are shown only for hour 12 of each category).

This statistical analysis is an important baseline for future detailed analysis.

4.2.2. Deep Learning Acceptance Probability Prediction Tool

This Deep Learning Acceptance Probability Prediction Tool was developed to address the limitations identified in the statistical analysis described in paragraph 4.2.1. This tool leverages deep learning techniques to overcome these limitations and achieve a more accurate prediction of acceptance probability.

The training process reveals good performance, and it is evident from the results (Figure 20) that the model does not suffer from overfitting. This favorable outcome can be attributed to the incorporation of batch normalization and dropout layers in the neural network architecture. Batch normalization helps in stabilizing and accelerating the training process by normalizing the input layer by adjusting and scaling the activations. Dropout layers, on the other hand, prevent overfitting by randomly dropping units during the training process, ensuring that the network does not become overly reliant on specific nodes and promoting generalization.

The evaluated metrics are reported in Table 8. To ensure a comprehensive view of the model’s performance, the evaluation of the Area Under the ROC Curve (AUC) is added. The ROC, or Receiver Operating Characteristic curve plots the true positive rate against the false positive rate at various threshold settings, and its result is shown in Figure 21.

The evaluation metrics reveal a mixed performance of the neural network. The accuracy of 0.81 is relatively high, suggesting good overall performance. However, the precision 0.58 and recall 0.57 are moderate, indicating potential issues with false positives and false negatives, respectively. The F1-Score of 0.58 reflects a balance but also highlights that there is room for improvement in both precision and recall. Notably, the AUC value of 0.91 is very high, indicating that the model performs exceptionally well in distinguishing between the classes. This suggests that while the threshold for classification might need adjustment to improve precision and recall, the underlying model has a strong capacity for classification.

In conclusion, while the neural network demonstrates promising capabilities, particularly in its discrimination power, further refinements are necessary to enhance precision and recall. These adjustments will ensure a more robust performance across various scenarios, ultimately improving the model’s reliability and effectiveness in practical applications.

4.2.3. XBID Arbitrage Strategy

Similarly to DAM simulation, two scenarios are considered and in Table 9 the initial conditions for both scenarios are provided:

In XBID simulations, the energy acquired to satisfy auxiliary power demand is considered as being bought on the DAM to ensure the satisfaction of the overall system's energy requirements. By treating auxiliary power as a separate purchase on the DAM, the simulation can accurately reflect real-world conditions, providing a more realistic assessment of the system's performance and potential market impacts.

The two scenarios’ simulations provided the results described in following tables.

Table 11. XBID Case C.

Table 11. XBID Case C.

CASE D
Operative Days	366
${\mathbf{E}}_{\mathbf{b}\mathbf{u}\mathbf{y}}^{\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{l}\mathbf{y}}$	8702.8 MWh
${\mathbf{E}}_{\mathbf{s}\mathbf{e}\mathbf{l}\mathbf{l}}^{\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{l}\mathbf{y}}$	7446.33 MWh
N° Total Cycles	269.15
${\mathbf{P}\mathbf{R}\mathbf{O}\mathbf{F}\mathbf{I}\mathbf{T}}_{\mathbf{t}\mathbf{o}\mathbf{t}}^{\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{l}\mathbf{y}}$	226517.09 €/year

In comparison to the findings for the DAM, there is an immediately noticeable increase in the number of active days in both scenarios, which span the entire simulation period. This extended activity period results in a substantial increase in the traded volumes. Consequently, the annual cycles rise significantly, reaching 268.8 and 269.15, respectively. Moreover, unlike the results observed for DAM, it appears that the most profitable scenario is Case D, where the LCOS is not negligible. The primary reason for the higher profitability in Case D is attributed to the greater risk assumed in this scenario. By taking on higher risks, the scenario leverages the potential for higher returns, resulting in a considerably higher profit margin. The Revenues from the two scenarios are represented in Figure 22 and Figure 23.

However, the NPV resulting from Case C and Case D is respectively -8.53 M€ and -8.54 M€. The persistent negative NPVs in both scenarios indicate that the project is still not financially feasible under the given conditions. These results can partly be explained by a very conservative bidding strategy in both cases, which tends to optimize the probability of acceptance with a minimal profit risk factor. This cautious approach, while increasing the likelihood of bid acceptance, significantly impacts the project's overall profitability.

To address this, a sensitivity analysis on the bid price was conducted by increasing the risk factor to evaluate its impact and the opportunities it opens for optimizing the bidding strategy on XBID. The analysis aimed to find a balance between bid acceptance probability and potential profitability. By adjusting the risk factor, we explored various scenarios to determine how higher bid prices could improve the financial outlook of the project.

Bid Price Sensitivity Analysis

The analysis considered five different scenarios to evaluate the impact of varying bid prices. The first scenario, referred to as the base case (Case D), served as a benchmark for comparison. In the subsequent scenarios, the selling bids on XBID were incrementally increased by 1 to 5 LCOS, respectively. By systematically increasing the bid prices, the analysis aimed to understand the influence of higher bid levels on the overall bidding strategy. This incremental approach allowed us to observe the corresponding changes in bid acceptance probabilities and potential profitability across different price points. The base case provided a reference point to measure the deviations and improvements observed in the other scenarios.

The results of the sensitivity analysis (Table 12) reveal a clear and consistent trend. As the bid price increases, there is a noticeable reduction in the amount of energy both bought and sold on the XBID market, with a subsequent reduction in the number of operational yearly cycles, that from 269.15 in Case D reduce to 108.38 in Case 5. This trend indicates that higher bid prices result in fewer transactions and less frequent cycling of the storage system. The reduction in operational activity can be attributed to the less frequent engagement of the system in the market at higher price points, as higher prices reduce the likelihood of bid acceptance. However, despite the decrease in operational activity, there is a significant increase in profitability with each increment in bid price. This is evidenced by the substantial rise in total yearly profit and the improvement in NPV, as the yearly profit grows from € 227k for Case D to € 839k, as shown in Figure 24, and NPV improves from -8.54 M€ to +1.54 M€.

These results highlight that while higher bid prices reduce the volume of energy traded and the number of operational cycles, they significantly enhance the financial outcomes of the project. This is likely due to the higher revenue per unit of energy sold, which outweighs the reduction in volume. Consequently, this analysis suggests that adopting a strategy with higher bid prices can make the project more economically viable. By optimizing the bid price, the project can achieve a better balance between operational activity and profitability, ensuring a positive financial return and a sustainable business model in the competitive XBID market.

5. Conclusions and Future Work

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