Accumulators, crucial components in the MG energy ecosystem, play a pivotal role in the ε-variables method [6]. Introduce an evolution operator for accumulators, dependent on their capacity and the directed flows, further emphasizing their role in the overall energy dynamics. The integration of if/else statements into the ε-variables framework enhances the practicality of managing MG systems, allowing for dynamic adjustments in response to changing conditions without extensive re-modifications. This paper explores the ε-variables methodology in depth, shedding light on its theoretical foundations, practical applications, and contributions to the field of energy systems engineering. Through an analysis of the integration of if/else statements and a hybrid approach, we aim to demonstrate the adaptability and simplicity afforded by ε-variables in managing Microgrid systems. Ultimately, this research contributes to the ongoing discourse on innovative strategies for enhancing the efficiency, resilience, and sustainability of contemporary power systems.

Methodology

The Implementation of ε-variables for the MG

The main idea behind the ε-variable method is that every asset is symbolized by a node, and every flow of matter/energy is symbolized by an edge in the complicated MG system. Using this theory, this power system’s analysis, management, and operation can be simplified. This method states that any hybrid power system consists of three key factors: converters, accumulators, and flows. Converters are used to convert the energy/matter to matter/energy, the accumulators accumulate energy/matter, and the flows symbolize the flow of energy/matter. Lastly, the control statements are the evolution operators based on the logical operators, illustrating the different types of energy management systems (EMSs) exploited by the multi-vector system [3]). According to the graph theory, the converters are the PV array, load (LD) , and utility grid (GR) ; the battery (BAT ) can be considered as an accumulator, and power can be regarded as flows. The assets of the MG system can be split into two sets as follows:

The implementation of the if/else statement method

As shown in Figure 1, the if/else statement implementation consists of several steps in the MATLAB. Initially, the loop calculates the net values of equal PV power minus load demand. The condition of SOC is then evaluated to determine whether it is greater or less than the minimum/maximum values of SOC. At that time, both negative and positive values are examined. This technique operates based on the four distinct situations formulated within ε-variables, as shown in Figure 1’s large rectangular area. These conditions include:

The results of the if/else statement are evaluated based on these four conditions. Using logical operators, including AND and OR, the results are binary variables (0 or 1). Finally, the power flows are calculated by incorporating the battery’s SOC constraint. Concerning the feedback line, the if/else statement’s results are compared to those obtained by the if/else statement. As depicted in Figure 1, despite the fact that we get the same results with ε-variables, the if/else statement is neither straightforward nor practical. To make it clear, supposing that we decide to change the value for the initial SOC or remove one of the power flows, the controller is required to be re-modified. Nevertheless, in the ε-variables, we do not need to re-modify too many things in this controller, supposing that we decided to change something in this controller. Therefore, ε-variables are primarily used to make the MG system more practical and simpler to implement, particularly hybrid MG systems.

The Implementation of hybrid if/else statement-ε- variables technique

As depicted in Figure 2, the ’data’ utilized as input data by the hybrid if/else statement-ε-variables technique are initially obtained using the if/else statement method. In Figure 2, the ’data’ are , GR_LD , PV_LD , PV_BAT and BAT_LD . The evolution operators are then computed using the state of the accumulators and converters. To be more specific:

Results and Discussions

Simulation results of hybrid the if/else statement-ε- variables technique

Figure 3 depicts the PV and load data obtained from a building in the UK during the autumn season. Energy generation starts at the beginning of the morning (different morning times depending on sunlight) during these days. Also, peak energy generation occurs at 1 PM and 2 PM. On the other hand, there is no PV generation during the non-sunlight times. Regarding the load demand, it fluctuates due to several parameters such as the number of occupants, special days, and colder/warmer days, e.g., For instance, the load demand peaks on the first day between 7 PM and 8 PM since the occupants may return from their works or special day along with Christmas or Easter days. When sunlight is insufficient, or there is excessive load-generation mismatch, especially on nights, the battery (as a priority), then the utility grid is utilized. On the other hand, if the PV generates excess energy after covering the load-generation mismatch, the energy is exploited in order to charge the battery. The following figures will effectively demonstrate energy usage using the if/else statement and the if/else statement-ε variables.

Initially, the if/else statement is implemented, and then the ε-variables is merged to compare each strategy’s results. According to our results, the standard the if/else statement and the merged the if/else statement-ε-variables have the same results. Moreover, our results indicate that the proposed method does not alter the fundamental goals and behavior of the if/else statement. It is simple to extend the use of ε-variables to more complex systems and control constraints by modifying their logical operators. If the initial value of SOC is chosen as 55%, the energy from the battery to the load BAT LD ε → is increasing initially. The SOC of the battery is dramatically decreasing during the first day (see Figure 4b), but it does not pass critical value due to the evolution operator of BAT LD ε → . After the first day, the binary variables of BAT LD ε → are converted from 1 to 0. Therefore, the value starts to decrease as demonstrated in Figure 4. On the contrary, the utility grid works instead of the battery. In this case, the logical operators of the GR LD ε → are turned from AND to OR. By doing that, the binary variables of GR LD ε → are converted to 1. Hence, energy imported from the utility grid GR→ LD is increased, whereas energy imported from the battery is decreased BAT → LD . In summary, the MG system is re modified when changing the initial value of SOC of the battery because of ε-variables. To meet the load-generation mismatch, the utility grid runs much more than before rather than the usage of the battery.

Conclusion

In conclusion, the ε-variables method emerges as a promising and comprehensive approach to address the intricate dynamics of MG systems. By leveraging graph theory and categorizing assets into converters, accumulators, and flows, this methodology provides a systematic framework for analyzing, managing, and operating hybrid power systems. The integration of if/else statements enhances the practicality of the approach, allowing for dynamic adjustments without necessitating extensive remodifications. Through the exploration of the theoretical foundations and practical applications of the ε-variables methodology, this research contributes to the evolving discourse on innovative strategies for enhancing the efficiency, resilience, and sustainability of MG systems. The demonstrated adaptability and simplicity of ε-variables, particularly through the integration of if/else statements and a hybrid approach, underscores its potential impact on the field of energy systems engineering. As we move forward, the ε-variables method stands as a valuable tool for researchers, engineers, and practitioners engaged in the development and optimization of MG systems. The insights gained from this methodology not only advance our understanding of complex energy systems but also pave the way for more adaptive, practical, and sustainable solutions in the ever-changing landscape of contemporary power systems.

Conflict of Interest

There is not any economic interest, or any conflict of interest exists.

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