## 2 Materials and Methods
### Multi-Agent Approach  
In this article, a multi-agent approach is proposed to enhance the energy efficiency of production processes of gas industry enterprises. The algorithm for applying the multi-agent approach can be described as follows:  
* Defining the objective function of the short-term power consumption forecasting system for the compressor station (in our case study, the energy costs; see Section 2.3.1);
* Description of the information model for short-term forecast of consumption of a compressor station (see Section 2.3.2);
* Application of Multi-agent Approach for analyzing production processes of compressor station (see Section 2.3.3):
* Identifying agents based on objects involved in the production processes of the compressor station (in our case study, GCU and ACU);
* Defining the objective functions of the agents;
* Specifying the input and output data flows of the agents;
* Establishing connections between the agents. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Units** & **Time Sampling Step, h** & **Source** \\ \hline Hourly power consumption of entire compressor station & kWh & 1 & ACEMS \\ \hline Daily power consumption of ACU 1 & kWh & 24 & ACEMS \\ \hline Daily power consumption of ACU 2 & kWh & 24 & ACEMS \\ \hline Daily power consumption of ACU 3 & kWh & 24 & ACEMS \\ \hline Total daily power consumption of ACUs & kWh & 24 & ACEMS \\ \hline Daily power consumption of GCU 1 & kWh & 24 & ACEMS \\ \hline Daily power consumption of GCU 2 & kWh & 24 & ACEMS \\ \hline Daily power consumption of GCU 3 & kWh & 24 & ACEMS \\ \hline Total daily power consumption of GCUs & kWh & 24 & ACEMS \\ \hline Production process index & - & 1 & Authors \\ \hline Wind speed & m/s & 3 & rp5.ru \\ \hline Temperature & \({}^{\circ}\)C & 3 & rp5.ru \\ \hline Atmospheric pressure & mm Hg & 3 & rp5.ru \\ \hline Humidity & \% & 3 & rp5.ru \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial data description. 2.3.1. Defining the Objective Function of the Short-Term Power Consumption Forecasting System for the Compressor Station  
The first step in creating a short-term power consumption forecasting system for the compressor station is to define its overall objective function. The objective function of this system is determined by the energy costs according to Formula (1), considering constraint (2) that represent power balance. \[S=\sum\bigl{(}P_{ext}\cdot\mathrm{T}+f\bigl{(}P_{gen}\bigr{)}\cdot k_{gen}+P_{ stor}\cdot k_{slot}\bigr{)}, \tag{1}\]  
\[P_{ext}+P_{gen}+P_{stor+}=P_{cons}+P_{stor-}+\Delta P. \tag{2}\]  
where \(S\) is the costs, \(P_{ext}\) is the power supplied by the external power system, \(T\) is the electricity tariff, \(f\bigl{(}P_{gen}\bigr{)}\) is the function of dependence between amount of used fuel and output of self-generation units, \(P_{stor+}\) is the power output of energy-storage system, \(k_{gen}\) is the utilization factor for self-generation units, \(k_{stor}\) is the utilization factor for energy-storage systems, \(P_{gen}\) is the power supplied by self-generation units, \(P_{cons}\) is the power consumption of load objects (GCU, ACU), \(P_{stor-}\) is the power consumed by energy-storage systems during charge cycle, and \(\Delta P\) is the power loss in a power supply system. 2.3.2. Description of the Information Model for Short-Term Forecast of Power Consumption of the Compressor Station  
In order to create a short-term power consumption forecasting system, it is necessary to identify the system users, the real-world objects required for forecasting power consumption, and develop an information model of the system. The information model is understood as a model consisting of a set of interconnected entities (objects). Entity is an abstraction of a real-existing object, process, or phenomenon about which information needs to be stored in a database.