Demand-Side Management Optimization Using Genetic Algorithms: A Case Study

Abstract

This paper addresses the optimization of contracted electricity demand (CD) for commercial and industrial entities, focusing on cost reduction within the Brazilian time-of-use electricity tariff scheme. Leveraging genetic algorithms (GAs), this study proposes a practical approach to determining the optimal CD profile, considering the complex dynamics of energy demand on a city-like load. The methodology is applied to a case study at the Federal University of Pará, Brazil, where energy efficiency and demand response initiatives as well as renewable energy projects are underway. The findings highlight the significance of tailored demand management strategies in achieving energy-related cost reduction for large-scale consumers, with implications for economic efficiency in energy consumption.

1. Introduction

1.1. General Considerations

Energy efficiency and renewable energy are a global commitment to the energy transition. Energy efficiency has recently been called the “invisible” energy, because avoided energy consumption is carbon-free and does not compromise economic growth. When energy efficiency (EE) is compared to renewable energies, it can be considered a cheaper solution because it ranges from a change in human behavior and energy management to the old/non-efficient equipment substitution.

However, despite the benefits of these actions, energy efficiency still has a wide field of action: according to the International Energy Agency [1], 68% of the final use of global energy is not covered by energy efficiency standards. Among the challenges to the implementation of energy efficiency actions globally are the absence of public policies, technological innovation, as well as economic incentives for end users.

Within energy efficiency, there is the well-known demand-side management (DSM), which includes the demand response (DR). Despite the multiple definitions found in the literature for DSM, it can be explained as any action aimed at reducing energy consumption/demand/emissions and costs, including efficiency actions, energy in buildings, the replacement of non-efficient equipment, changes in behavior, and others [2,3,4,5]. The demand response can be defined as any intentional action by the final consumer that modifies the response in demand or consumption based on economic signals but only includes non-permanent actions in demand [2,3,6,7].

1.2. Literature Review

In order to create the foundations of this work, a bibliometric analysis was conducted using the Scopus platform, with the keywords demand-side management AND genetic algorithms. After filtering the documents by category and field of study, 263 documents were used to create a thematic map of keywords presented in Figure 1. In the clustering performed, it is noted in the red circle the strong relationship between demand-side management and genetic algorithms in energy optimization applications. It is also observed that with the growth of renewable energies and smart grids, genetic algorithms are a tool used to optimize and manage these distributed energy resources.

Globally, DSM has been the subject of extensive research and applications to adjust the load shapes (peak clipping, load shifting, valley filling, strategic load growth, flexible load shapes, and strategic conservation) aiming at optimizing energy consumption, demand, and costs [5,8]. Works analyzing its applications have been presented in [2,4,5,6,7], including literature reviews [3,9,10]. The studies include the classification, strategies, and modalities considering the proliferation of smart-grids and renewable energies in distribution systems [11,12,13].

The works [14,15] contribute to demand-side management using optimization techniques. In [14], a genetic algorithm-based energy management approach is presented that focuses on optimizing the demand response and unit commitment in a factory power system with uncertain PV generation. The uncertainty in PV generation is mitigated using a point estimation method integrated with the genetic algorithm approach. On the other hand, ref. [15] introduces a decentralized robust control algorithm to optimize electric vehicle (EV) charging in the presence of grid constraints. The algorithm considers cost, robustness, and constraint violation and demonstrates its scalability with an increasing number of EVs. The problem is formulated as a quadratic programming problem, and an extended Jacobi-Proximal Alternating Direction Multipliers Method algorithm is used to efficiently optimize the charging schedules. In this way, both contribute significantly to demand-side management, providing solutions for optimal resource utilization, grid stability, and overall system efficiency.

In recent years, one of the techniques to alter electricity use is the demand response (DR), which can be classified as the price-based demand response and incentive-based demand response [16,17]. At first, the final consumer is encouraged to change the patterns of consumption in response to electricity values that include the fixed price (FP), time of use (TOU), critical peak pricing (CPP), and real-time pricing (RTP). After, the consumer receives an incentive from the energy provider to reduce the loads in operation at indicated times based on market conditions, concerning costs and energy production [16,18].

Computational intelligence approaches have also been applied in [19,20,21,22,23] with a focus on cost reduction, peak energy demand, energy saving, and DSM. Aiming at solving optimization problems, several studies have proposed genetic algorithms, including [24,25,26,27,28,29,30]. The results justify the applicability of the genetic algorithms for power utilization reduction, minimizing the electricity cost and peak-to-average ratio considering shifting and non-shifting loads via appliance scheduling.

1.3. Motivation and Contributions

Despite several studies evaluating DSM, their main focus is on the implementation of actions from load shifting, power scheduling, time-based pricing, load forecasting, and others. However, there are applications in which, given the diversity of factors involved, such as temperature, renewable energies, class period, class hour schedule, strikes, and others, it is not possible to create a valid model and it is necessary to choose viable alternatives that can be quickly implemented given the costs they represent, such as the energy demand agreement.

The primary objective of this paper is to present a practical approach to the reduction in customer energy costs without the need for high-cost implementations. Instead, the focus is on providing a methodology that can be implemented quickly with minimal financial outlay. By focusing on the management of the utility contract, we aim to provide a practical solution that will have an immediate impact on the customer’s bottom line. Therefore, this study proposes an optimization algorithm that determines the optimal profile to be contracted in commercial/industrial companies considering the Brazilian time-of-use electricity tariff scheme, including the optimal time period to reduce or increase the contracted demand based on the cost–benefit ratio. The work has been carried out by taking as a case study the Federal University of Pará, in Belém, Pará, Brazil.

2. Problem Formulation

Federal University of Pará: Case Study

The Federal University of Pará (UFPA) is located in the Amazon region of Brazil. Its population is made up of more than 50,000 people, making it larger than a small city. Within the University campus can be found loads such as banks, hospitals, dental clinics, laboratories, motors, restaurants, administrative offices, and classrooms, which undoubtedly represent a small city, which lends itself as a validation model of different types of studies.

Within the University, there are different sustainable projects and initiatives, as part of research and development projects, carried out by the Center of Excellence in Energy Efficiency in the Amazon (CEAMAZON), including renewable energies generation, storage systems, and electric buses [31,32].

One of the projects under development is the Power Management and Energy Efficiency Project in which energy diagnoses in buildings located in the Federal University of Pará are carried out aiming at opportunities for energy efficiency in lighting systems, air conditioning, and motor drive systems, from which was possible a reduction in consumption and demand as a result of the energy efficiency actions and use of renewable energy [33,34,35,36,37,38]. Figure 2 presents the main actions described. For this study, a real-time energy monitoring platform system has been developed [39], which allows for following the consumption and demand of the buildings in the UFPA as well as power quality analysis.

The University has an energy pricing scheme that combines TOU pricing with a separate demand charge for peak consumption, called the “green rate”, as shown in Figure 3. For example, in this pricing scheme, the first block of energy, called the off-peak hours, is divided into two sub-blocks, from 00:00 a.m. to 06:29 p.m. and from 09:30 p.m. to 11:59 p.m., with charges for the weekdays. The second block is called the peak period, which goes from 06:30 p.m. to 09:29 p.m., and also has weekday rates, where a kwh during the peak period has a value almost ten times the value of a kwh during the off-peak period. The weekend and holiday rates are the same as the weekday off-peak rates.

The core challenge addressed by our research revolves around the other aspect of the “green rating” energy consumption pricing: the pivotal decision-making process concerning the contracted demand of a significant consumer. This critical decision holds substantial implications for the university’s financial expenditures, because the contracted demand represents approximately 18% of the UFPA energy-related expenses.

The main reason why the CD choice represents an optimization problem is related to the price scheme applied in Brazil, in particular, demand-related charging. First, the contracted value is always charged no matter the demand value measured; the only compensation is the tax exemption applied to the difference between the contracted demand and the measured demand. Then, choosing a higher CD incurs an additional cost. On the other hand, if the measured demand surpasses 105% of the CD, an additional charge is applied to the difference between the measured demand and CD corresponding to two times the current tariff. Therefore, choosing a lower CD also incurs a cost increase.

Choosing a CD may not be highly complex in some cases, e.g., an industrial plant, because the maximum power required is well known and a load controller may be used to turn off non-essential loads so the CD is not surpassed. However, a customer like the UFPA faces a much more complex choice, with dozens of buildings, some that could be medium voltage consumers themselves, like banks, hospitals, restaurants, administrative, and educational buildings, similar to a city.

In addition to the high complexity of the loads, because their behavior depends on the users activities, the introduction of several photovoltaic micro-generation sites in the campus may increase the seasonal characteristic of the yearly demand profile. Therefore, the strategy adopted was to establish a seasonal contracted demand for the campus, because the CD can be increased by the customer at any time in the year with a one-month delay after a formal request.

As discussed later, increasing the number of different contracted demands through the year also increases the dimension of the optimization problem by two for each additional demand. So, a genetic algorithm was used to tackle this problem, where based on a yearly demand profile the algorithm generates an optimal CD profile, where the costs associated with demand are minimal.

3. Methodology

For the methodology, the contracted demand history from the invoices was analyzed, as well as the feasibility study to implement more than one active power demand in the year from the energy contracts with the utility company. The fitness function for this optimization problem was the cost function of the individual, so the fittest individual presents the lowest cost. The lowest cost for a single contracted demand (CD) can be easily found by applying the cost function over a search space around the maximum measured demand.

The fitness function is presented in Equation (1); it is simply the sum of the demand-related costs in the energy invoice in a 12-month period, specifically from January to December. This equation fully represents the costs in the sense that the values calculated are the same as those that would appear in a hypothetical invoice given the input contracted demand profile. So, all the taxes applied were considered, as well as the pricing “rules” applied according to the relationship between the measured and contracted demand. The descriptions for each variable are the following:

• i is the month of the year.
• D_c,i is the contracted demand agreed in the contract for the i-th month.
• D_m,i is the measured demand, the maximum active power measured in the i-th month.
• T_i is the demand tariff in the i-th month. It usually has two constant values; the first one is constant between January and July and the second from August to December, because the tariff changes every year in August.
• k_1,i is the correction factor when all taxes are applied to the final price.
• k_2,i is the correction factor when all taxes but icms are applied to the final price.
• pis and cofins are the taxes called “Social Integration Program” and “Contribution for Social Security Financing”, respectively. The tax rates used were collected from the energy bills.
• icms is a tax called “Tax on Circulation of Goods and Provision of Services”. It is not applied to idle demand, i.e., the difference between contracted and measured demand when the measured one is the smallest.
• TR is the correction factor for taxes retained on their sources, like income tax or base values for pis, cofins, and icms. It mainly reduces the final energy price.

The Equation (1) has three conditionals matching the pricing cases. The first one (from top to bottom) calculates the demand-related costs when the measured demand is lower than the contracted demand. The second one is the case where the D_m is higher than the D_c but is still within the tolerance interval. The last one is the cost when the D_m surpasses the tolerance interval and the fine is applied.

$$\begin{array}{c}\hfill c=\sum _{i=0}^{12}\left\{\begin{array}{c}(1-T{R}_i)(k_{1,i}{D}_{m,i}{T}_i+k_{2,i}(D_{c,i}-D_{m,i})T_i)\mathit{i}\mathit{f}{D}_{m,i}<D_{c,i}\\ (1-T{R}_i)\left(k_{1,i}{D}_{m,i}{T}_i\right)\mathit{i}\mathit{f}{D}_{c,i}<D_{m,i}<1.05D_{c,i}\\ (1-T{R}_i)(k_{1,i}{D}_{m,i}{T}_i+2k_{1,i}(D_{m,i}-D_{c,i})T_i)\mathit{i}\mathit{f}{D}_{m,i}>1.05D_{c,i}\end{array}\right.\end{array}$$

(1)

$$\begin{array}{c}\hfill k_{1,i}=\frac{1}{(1-pi{s}_i-cofin{s}_i)(1-icm{s}_i)}\end{array}$$

(2)

$$\begin{array}{c}\hfill k_{2,i}=\frac{1}{(1-pi{s}_i-cofin{s}_i)}\end{array}$$

(3)

$$\begin{array}{c}\hfill T{R}_i=T{R}_{IRPJ,i}+T{R}_{CSLL,i}+T{R}_{pis,i}+T{R}_{cofins,i}\end{array}$$

(4)

This is exemplified in Figure 4. It can be highlighted that the notches on the curve are located where the CD value is applied to cause any measured demand to reach the 105% limit of CD when the fine is paid. The years covered by the analysis in this paper are 2007, 2018, 2019, and 2022, limited by the available data and the exclusion of pandemic years, because they do not represent typical years for this customer.

While the lowest cost of a single demand for a given year can be easily determined, because it is the minimum point of a single variable function, finding the lowest cost for a multiple demand case may require an optimization algorithm due to the higher dimensions of the target function. As the function needs the n CD values and the n − 1 months where the CD should be changed, the number of variables for a given number of CDs in a year is described by Equation (5). The variables for this equation are as follows:

• N_v is the number of variables of the function that is being optimized;
• N_cd is the number of different contracted demands in a single year.

$$\begin{array}{c}\hfill N_v=2N_{cd}-1\end{array}$$

(5)

A GA was used as the optimization technique to find the lowest cost assuming a double-demand regime. The individuals have three chromosomes: D₁ representing the first CD, i.e., the demand from January to the changing month; D₂ representing the second demand, i.e., the demand from the changing month to December; and M, the changing month itself (must be an integer). Figure 5 presents the relationship between individuals and CD curves discussed above. Three variables are necessary in this example because the demand may be altered in any month of the year, so the M variable is needed to represent the moment of change. Several runs of the algorithm were performed varying the mutation rate between 1% and 10% and varying the population between 500 and 800 individuals. The stop condition was the number of iterations, fixed at 500. The selection method chosen was the tournament method, so the fittest individual of each generation is always selected.

The applied crossover method is similar to the one implemented in [40], where the value of each child chromosome representing CD is the sum of the first parent chromosome value and a random percentage (between −1 and 1) of the difference between each parent chromosome value. For example, given parents A and B, each child chromosome value w_C is computed according to Equation (6). The chromosome representing the month of change is chosen at random between parents A and B. The variables for Equation (6) are as follows:

• w_A is the chromosome value for parent A;
• w_B is the chromosome value for parent B;
• w_C is the chromosome value for child C.

$$\begin{array}{c}\hfill w_C=w_A+(w_B-w_A)\times rand(-1,1)\end{array}$$

(6)

4. Results and Discussion

Figure 6 and Figure 7 present the single and double lowest-cost CD profiles. In the analyzed set of years, none of the single CDs found caused a fine to be paid in any month, so, for those cases, the fine did not compensate for the months where idle demand was paid. The double CD profile manages to generate less idle demand while no fine is paid also, causing higher savings.

Figure 6 and Figure 7 display the recorded demand values for the years 2017, 2018, 2019, and 2022. In Figure 6, a consistent contracted demand is considered for the entire year. With the estimated demand value, no penalties were incurred for surpassing the contracted demand. However, it is important to note that there are months during which payments were made for unused demand, particularly in the initial months of the year and the vacation period between semesters (July and part of August). Additionally, it is observed that the highest recorded demands align with the second semester of the year. The expenses associated with idle demand can be reduced by introducing a secondary contracted demand during the year, as illustrated in Figure 7. In this scenario, the proposed algorithm not only determines the optimal demand values but also identifies the most suitable month for implementing the change, causing higher savings when compared to the single contracted demand scenario.

The curve generated by applying the cost function through the search space using single contracted demand (CD), the actual value paid, the lowest value for single demand, and the lowest value for double demand, for each year, is shown in Figure 8. It is observed that the lowest cost for double CD is always smaller than the lowest cost for single CD. The differences in cost between the optimal single and double CD are shown in Figure 9. Due to the high amount of power required by this customer as well as the seasonality of the demand, using non-fixed CD, double CD in this case, generates a great amount of savings. It is also perceivable that, at the point of minimum cost, the rate of change of the demand charge is lower in the direction of an increase in CD than it is in the direction of a reduction in CD, so it is safer to slightly oversize the demand than it is to undersize it.

The savings reduction by shifting the month (from the ideal month) where the CD will be modified is shown in Figure 10. The loss in the optimal month in each year is zero because it is the best month for changing. These values can be helpful to propose a month for changing the CD every year, so Figure 11 shows the same data but now summed by month. February, March, and April present the lowest costs for this customer in this set of years.

5. Performance Analysis

This section is focused on the comparative analysis between the proposed methodology (genetic algorithms) and two other optimization approaches: Simulated Annealing (SA) and Nelder–Mead (NM). As it is suggested that the genetic algorithm (GA) tends to exhibit superior performance in higher-dimensional problems, three-demand curve optimization was tested in addition to the initially explored two-demand curve optimization. The evaluated parameters included the capability to reach global minima and the execution time for each method.

Because the execution time of the GA is strongly related to the population size, several individuals were used, which makes the algorithm faster but still ensures a reasonable result in terms of finding global minima. In the end, a population size of 40 individuals was chosen.

The search spaces for the GA and SA were the same: the contracted demand ranging from 500 kW to 8000 kW; evidently, the months of change range from 1 (January) to 11 (November). Because the NM method takes an initial guess, this value was randomly generated for each iteration of the algorithm, ensuring that it belongs to the search spaces of the other methods. In each case, every method was executed 1000 times and the results are presented as average values. The experiments were conducted on a computer with the following specifications:

• CPU—Intel Core i7-5500U 2.4 GHz.
• GPU—Nvidia GeForce 920 M.

It is shown in

Table 1. Average execution time for two-demand curve optimization.

Method	Execution Time
	2017	2018	2019	2022
GA	0.369 s	0.324 s	0.491 s	0.363 s
SA	1.076 s	0.820 s	0.872 s	1.139 s
NM	0.035 s	0.032 s	0.041 s	0.075 s

that even in the three-variable case, the GA has a better execution time than the SA and NM has a 10 times better execution time. However, as can be observed in

Table 2. Average minimum cost for two-demand curve optimization.

Method	Cost
	2017	2018	2019	2022
GA	1.983 mi BRL	2.264 mi BRL	2.457 mi BRL	2.454 mi BRL
SA	1.982 mi BRL	2.264 mi BRL	2.455 mi BRL	2.449 mi BRL
NM	2.057 mi BRL	2.367 mi BRL	2.484 mi BRL	2.509 mi BRL

, Nelder–Mead does not always get to the global minimum, having a higher value for the minimum cost.

In the five-variable case (three contracted demands), an interesting behavior appears: the average answer obtained by the Nelder–Mead method is not only worse than that of the other methods but also worse than its equivalent in the two-demand optimization because the majority of the initial guesses lead to a local minimum. The pattern of the execution times and ideal costs fins of the GA and SA is the same: NM is the fastest, followed by the GA and SA; the SA gives a slightly better answer than the GA. The results for the five-variable experiment are shown in

Table 3. Average execution time for three-demand curve optimization.

Method	Execution Time
	2017	2018	2019	2022
GA	1.052 s	0.805 s	1.405 s	1.562 s
SA	1.684 s	1.458 s	1.522 s	1.713 s
NM	0.086 s	0.071 s	0.093 s	0.088 s

and

Table 4. Average minimum cost for three-demand curve optimization.

Method	Cost
	2017	2018	2019	2022
GA	1.052 mi BRL	2.256 mi BRL	2.451 mi BRL	2.404 mi BRL
SA	1.970 mi BRL	2.251 mi BRL	2.449 mi BRL	2.404 mi BRL
NM	2.103 mi BRL	2.395 mi BRL	2.543 mi BRL	2.451 mi BRL

.

6. Conclusions

The implementation of demand-side management techniques also requires optimization in the electricity purchasing market, so that the benefits of energy efficiency and renewable energy actions can be magnified in the consumer’s energy costs. In this work, a demand optimization approach by means of genetic algorithms was presented. To this end, the seasonality was observed from the load curves, and it was identified that by contracting two active power demands during the year, greater economic benefits can be obtained.

The proposed algorithm could determine the optimal double CD profile, so the lowest cost was achieved. The results highlight significant applications in the management of energy contracts with utilities aiming to reduce the costs per contracted demand; in addition, the results revealed some important advantages of using the proposed methodology in combination with demand forecasting algorithms to increase the benefits through greater optimization of the contracted demand.

The difference between savings when choosing a month other than the month with the lowest costs was also investigated, so it can be used as an initial strategy to choose a month with the best overall savings.

The methodology outlined in this paper offers a versatile solution applicable to a wide range of customers operating under a Distribution System Use Contract [41], particularly those facing considerable demand variability through the year and lacking direct control over their demand. Moreover, the flexibility inherent in this approach extends beyond distribution system contracts, as it can be adapted to cater to entities directly connected to the energy transmission system. The power utilities, obligated to maintain a Transmission System Use Contract with the National System Operator (ONS) [42,43], can benefit from applications of this methodology to enhance their operational efficiency and ensure compliance with regulatory requirements.

7. Future Research Directions

As shown in the discussion, the decision of which demand profile is suited for this specific costumer relies on the belief that the seasonality of the demand for the next year is similar to the historical data seasonality.

Hence, to improve the results precision, a prediction of a next-year demand profile is required as an input for the algorithm. So, the next step in this research is whether to develop an Artificial Neural Network or statistical-based methodology to tackle this issue.

The main challenge of this approach is the lack of historical data available, because the primary source of data, the energy invoices, began to be collected at the beginning of the energy management project, in mid-2017.