3.1. Forecasting the Electrical Loads of the Compressor Gas Compressor Station in Order to Improve the Efficiency of Demand Response, Taking into Account the Use of Energy Storage Systems
In order to predict the loads of an enterprise of a mineral resource complex, this article considered the power consumption of a compressor gas pumping station.
The characteristics of the load graph are presented in
Table 1:
From the results obtained, it could be concluded that the electricity consumption was uneven and the load graph was subject to significant fluctuations (the fill factors of the schedule and the unevenness of the weekly load schedule were <0.5).
To predict the loads, an additive autoregressive model was applied, taking into account the nonlinearity of the trend. The value of the predicted value at a certain point in time was determined by the following equation [
51]:
where:
—the value of the predicted value at time t;
—trend function that simulates non-periodic changes in a time series value;
—reflects periodic changes in the time series (for example, weekly and annual seasonality);
—the effects of holidays that occur with potentially irregular schedules over one or more days;
—any changes in the predicted value that are not adapted to the model (stochastic error that is not accounted for by the model).
Characteristics of the dataset for training the model:
Depth of study: 854 days (2.3 years).
Forecast horizon: 120 days (~ 4 months).
Values: hourly load.
Forecast score metric: mean absolute error.
The use of the ARIMA autoregressive model for forecasting power consumption, as well as methods for determining the quality of the forecast, were described in [
52]. The Prediction Interval Coverage Probability (PICP) was used to determine how much the predicted values diverged from the actual over the entire forecast horizon, which was determined by the following formula [
43]:
where:
—lower and upper bounds of the prediction interval;
—fact value of consumption;
N—number of observations.
With an uneven graph of power consumption, individual spot values had a strong deviation from the average level of the series, which was used as a trend in the forecast.
To level this type of error, the forecast confidence interval was used, which took into account the possibility of predicting a value in a certain interval with a given probability. The higher the probability, the wider the confidence interval. The confidence interval was determined using the following expression [
53]:
where:
—forecast of the value of the time series at time n + 1;
—the value of the Student’s t-statistic for the time series;
—MAE value.
To determine the width of the confidence interval with a given PICP, it was necessary to determine the value of
using tables [
54].
Figure 4 shows a graph with the results of predicting power consumption with PICP = 0.95.
The mean absolute error for this model was 2104 kWh. The forecast profile had a clearly pronounced monthly seasonality, but the irregularity of the load schedule was not taken into account.
The deviation of the confidence interval was 64.4% of the average power consumption.
A study was conducted of the linear correlation according to Spearman’s criterion of exogenous parameters with the load of the enterprise (
Table 2):
Based on the results obtained, we could conclude that the planned production volume affected the volume of electricity consumption to the greatest extent.
The introduction of an additional regression series into the additive autoregressive model was described in article [
55].
The next step was to introduce exogenous parameters into the model. The business plan for the volume of gas compression at the compressor station, which was the main production process, was used as an external factor.
The forecast result of this model is shown in
Figure 5.
The mean absolute forecast error was 1324 kWh.
The deviation of the confidence interval was 41.2% of the average electricity consumption.
From the graph, we could conclude that exogenous parameters made it possible to take into account, with a certain degree of efficiency, the unevenness of the schedule, based on the micro-factors of the enterprise, but seasonality was still taken into account and worsened the model.
Since the coefficient of unevenness of the weekly load schedule was below 0.4, it could be concluded that for an effective forecast, it was not necessary to take into account historical data, as well as previous observations. This is the main reason why LSTM neural networks are not effective for predicting workloads of this kind: a neural network with long-term and short-term memory uses the previous values of the time series among other external factors.
To determine the value of the load from the influencing factors, a linear regression model was used.
The mean absolute error was 962 kWh, which was almost 30% lower than when using the autoregressive model.
The deviation of the confidence interval was 20.8% of the average power consumption.
According to
Table 2, the linear correlation was higher than 0.5 only for the “Production volume” parameter. It was necessary to test the hypothesis that the dependence of the consumption schedule on other characteristics was a non-linear function.
To take into account the nonlinearity of the graph, we used gradient boosting for regression. A gradient-boosting model is a machine learning technique that uses a feature-based decision tree for training and prediction.
The purpose of the forecasting algorithm is to reduce the error between the predicted and real value. The error was defined by the following expression [
53]:
where:
—real target value;
—predicted target value.
The learning task is to determine the minimum of the loss function:
The loss function was the vector and its result was the scalar value of the prediction error.
By using a gradient, the direction of maximum error reduction was determined to optimize the time to find a solution:
where:
—derivative of the function f with respect to external factor
x.
The values of external signs at which the error function reached its minimum value were calculated as follows:
where:
t—iteration number.
A finite number of iterations was used to search for the minimum of the error function.
The correlation between the target value (electricity consumption) and the exogenous parameters used in the model for gradient-boosting models took into account the nonlinearity of the relationship, as well as categorical variables such as the day of the week and the hour of the day. The algorithm for determining the degree of influence of exogenous parameters on the target feature in the used gradient-boosting model was described in [
56]. Since the degree of linear correlation between electricity consumption and the business plan for gas compression was known (
Table 2), a comparative analysis of the correlation of exogenous parameters relative to the business plan was performed (the correlation between the business plan and electricity consumption was taken as 0.77 in accordance with
Table 2). The results of calculating the degree of correlation of a feature with respect to the target value are shown in
Figure 7.
From the results obtained, it could be concluded that the nonlinear correlation between features and power consumption was much higher.
The forecasting model was trained by determining the combination of external features at which the error value was minimal. With known external signs on the basis of the trained model, it became possible to predict future values of power consumption.
The mean absolute forecast error was 521 kWh.
The deviation of the confidence interval was 18.4% of the average power consumption. This result demonstrated a greater confidence in the forecast accuracy than the algorithms discussed earlier.
We could conclude from the graph that the use of gradient boosting allowed for the most accurate prediction of the power consumption of an enterprise based on exogenous and endogenous parameters. Accordingly, with an increase in the number of exogenous parameters, the forecast error would decrease.
The results of using various models to predict power consumption are shown in
Table 3:
3.2. Regulation of the Electricity Load Schedule
The metric for evaluating any forecast is the deviation of the real values from the predicted ones. The main task of forecasting is to reduce the forecast error; however, the real values depend on an infinite number of factors, and even taking into account a huge number of external factors, the deviation of the real load schedule from the planned one is inevitable.
If the declared electricity consumption is exceeded, significant penalties are inevitable for the enterprise; therefore, the next task was to compensate for deviations from the planned load schedule. The magnitude of the error in the predicted interval is shown in
Figure 9.
Based on the graph in
Figure 9, it could be concluded that the forecast deviations from the actual values were characteristic both upward and downward.
The number of excess of the fact over the forecast—1181. Average value—724 kWh.
The amount of underestimation of the fact over the forecast—979. Average value—276 kWh.
Based on the results obtained, we could conclude that the predicted values of power consumption were higher and lower than the actual values on the graph with, approximately, the same frequency due to the approximation of the predicted value to the average; however, in cases where the actual consumption was higher than predicted, the error values were much larger than when the consumption was lower than predicted. This phenomenon was due to the fact that, with an uneven electricity consumption schedule, there were significant peaks that were difficult to predict and which led to an increase in the peak consumption of the enterprise and, as a result, a significant increase in electricity costs. The purpose of this study was to compensate for peaks in power consumption using an ESS.
The algorithm for the formation of the cost of electricity and power when consumption exceeded the declared maximum had general principles in different countries. Article [
57] discusses a way to reduce consumption peaks in the Chile power system using wind generators and analyzes the existing methods of generating the cost of electricity in the country to maintain the balance of frequency and active power in the system.
The issues of regulating the parameters of the power system and the formation of the cost of electricity on the example of the power system of the Netherlands are considered in [
58].
Electric power systems built on the basis of a competitive market, due to the peculiarities of electricity as a commodity, are based on a single algorithm for the formation of the cost of electricity. The cost of electricity, determined a day before the current one, was adjusted due to the discrepancy between the planned consumption and the actual one. The main added value was formed due to the need to include new generating capacities and load less efficient and more expensive generators. Further, using the example of the enterprise under consideration, an algorithm for the formation of the cost of electricity in the balancing market was described.
In accordance with the forecast of the power system load, the system operator formed the planned peak load hours for the coming period, which were published in the public domain annually [
59].
Figure 10 shows an example of a graph of electricity consumption for all consumers in the region where the enterprise was located (power system of Siberia) for 6 August 2021, in which the maximum electricity consumption was highlighted in red (from 7:00 to 8:00).
The 8th hour (from 7:00 to 8:00) was the peak hour on this day, 6 August 2021.
The maximum predicted hourly consumption was calculated as the maximum consumption of electricity by the consumer per hour of the day from certain hours of the maximum load of the power system. Based on these data, the system operator determined the price that would develop in the balancing market and at which the participants would sell or buy deviations of the actual consumption from the planned one. Due to the calculation method of these parameters, the so-called imbalance of the balancing market arose—the preliminary requirements of the sellers (generation) were higher than the preliminary obligations of the buyers. Thus, to satisfy generation bids, the difference between requirements and obligations was attributed to each kW purchased or sold on the balancing market in terms of the volume of buyers (i.e., it decreased the selling price for buyers and increased the purchase price). Additionally, the cost of each kW increased by an amount determined as the weighted average cost of starting up the generating equipment to maintain the balance of active power in the system when the schedule deviated from the specified one.
The final cost of electricity in the balancing market was calculated using the following formula [
60]:
where:
—price of 1 kW of electricity for a consumer in the balancing market;
—price determined for settlements in the day ahead market;
—increase in the price of electricity in the balancing market;
—unbalance price.
The resulting price was usually significantly higher than the day-ahead market price of electricity. Therefore, in order to reduce the cost of purchasing electricity, it was necessary to reduce the amount of deviations from the planned consumption schedule.
For this purpose, various methods were used:
Changing the mode of production equipment.
Changing the operating mode of air conditioning, heating and water supply systems.
Using our own sources of small generation.
Using rechargeable batteries to redistribute consumption peaks.
Methods 1 and 2 could be detrimental to production, and the lost revenue could be higher than the savings in the cost of electricity.
Methods 3 and 4 could be used both to optimize the consumption schedule and to participate in the demand response system.
In this paper, an algorithm for the use of energy storage systems was considered as a way to reduce deviations of the actual schedule of electricity consumption from the planned one.
3.3. Using Energy Storage Systems to Improve the Efficiency of Power Supply
The use of energy storage systems in order to flatten the load curve is relevant for the power systems of many developed and developing countries due to the increasing share of the use of renewable energy sources, which are dependent on external factors and are characterized by low maneuverability, such as wind turbines and solar panels. The use of energy storage systems in the Chinese power system is discussed in [
61]. The use of energy storage systems in the Chilean Power System is discussed in [
62].
The use of storage batteries for leveling the electricity consumption schedule of enterprises is described in [
63]. The article presents the results of modeling an electrical complex using a hybrid ESS; however, the choice of the optimal power of an ESS is not considered.
The use of an ESS to reduce the peaks in consumption of various types of consumers in Belgium is described in [
64]. The use of an ESS to optimize the power supply system of enterprises is considered in [
65].
The structural diagram of the use of an ESS in the enterprise is shown in
Figure 11.
Next, an algorithm was proposed for selecting the capacity of energy storage systems (batteries) to reduce the difference between the actual and predicted load values.
Figure 12 shows a graph of the distribution of the forecast error over time using the example of one day.
An evolutionary genetic algorithm was used to find the optimal value of the SNE capacity at known values of the forecast error.
The task of optimizing the maximum working capacity of the energy storage system was reduced to determining the optimal value of the capacity, at which the following value of the maximum power consumption was achieved on the calculated day:
where:
i—hour of the day in which the maximum power consumption was controlled due to coincidence with the peak load of the power system;
—the actual value of the power consumption of the enterprise;
—the predicted value of the power consumption of the enterprise;
n—the size of the sample under consideration (forecast horizon), based on the results of which a decision was made on the choice of the optimal capacity.
Limitations for the operation of the algorithm:
where:
—capacity value of the ESS per hour of day, kWh;
—power supplied by the ESS to the network at time, kW;
—minimum working capacity, kWh;
—actual temperature of the ESS;
—permissible maximum energy supplied by the ESS to the network.
A limitation of the minimum charge–discharge cycles per day was also imposed.
The program code that implemented the genetic algorithm was implemented in the Python 3.8 programming language in the PyCharm software environment. The functioning of the algorithm together with the forecast of power consumption to determine the optimal capacity is shown in
Figure 13.
Obviously, the maximum error reduction would be achieved with the maximum battery capacity, but, often, the cost of installing the ESS exceeded the possible penalties for exceeding the specified power consumption schedule. Therefore, to determine the efficiency of the battery for a specific load schedule, the following formula was used:
where:
—ESS performance.
—reduction in power consumption.
C—battery capacity.
The result of choosing the optimal capacity of the ESS is shown in
Figure 14:
The results shown in
Figure 14 allowed us to conclude that the efficiency of using an ESS could be increased by up to 75% (from 0.22 to 0.385).
Algorithm results:
The optimal effective capacity of ESS—200 kW.
Average reduction in power consumption—77 kW.
Efficiency of ESS operation—38.5%.