## 2 Materials and Methods
### Multi-Agent Approach
#### 2.3.3 Application of Multi-Agent Approach for Analyzing Production Processes of Compressor Station  
After the objects required to create a schedule of power consumption forecast are defined, agents can be determined. Within the multi-agent approach, an agent is described by a tuple:  
\[T=\langle I_{t},O_{t},S_{t},R_{t},A_{t}\rangle, \tag{3}\]  
where \(t\) is the moment of time, \(I_{t}\) is the input data of an agent (for example, retrospective power consumption of the compressor station), \(O_{t}\) is the output data (for example, power consumption), \(S_{t}\) is the object state (for example, equipment status), \(R_{t}\) is the rules of agent's behavior (for example, emergency start-up/shutdown), and \(A_{t}\) is the list of agent actions. The proposed system of short-term power consumption forecast system is considered as the system with functions that are defined by all actions of agents aimed at achieving their goals. In the field of power system control, intellectual information systems are allowed to be used only for decision-making support due to their indeterminate nature. Thus, in this study, agents are described by the tuple without actions \(A_{t}\). Consequently, agents are described by the following tuple:  
\[T=\langle I_{t},O_{t},S_{t},R_{t}\rangle. \tag{4}\]  
The elements are defined by the following interconnections:  
\[O_{t+1}=f(I_{t},S_{t+1}), \tag{5}\]  
\[S_{t+1}=f(I_{t},S_{t}). \tag{6}\]  
The objective function of a consumer agent is the reduction in energy costs according to (1). Compressor stations can include power consumption objects, self-generation objects, and energy-storage system objects. Power consumers can be divided into those involved in the main production process and regulator consumers. A regulator consumer is a power consumer whose operating mode allows for load limitation during peak hours to smooth out the load curve. A special case of a regulator consumer can be a storage system, which can act as a consumer, generator, or storage system for electrical energy depending on economic factors and production process factors. Thus, all objects can be classified into storage agents, generator agents (in our case study, GTU) and consumer agents (in our case study, ACU and GCU). The agent decomposition for the compressor station is shown in Figure 6.  
Input and output parameters for a consumer-agent are described by (7) and (8), respectively. \[I_{t}=\Big{\langle}Power,\,T,\,Plan,\,Exp_{cons},\,Exp_{reg},\,Meteo,\,Eq,\,Cal, \,Act_{gen}\Big{\rangle}, \tag{7}\]  
where _Power_ is the retrospective power consumption, \(T\) is the forecasted electricity tariff, _Plan_ is the gas transportation plan, \(Exp_{cons}\) is the expert adjustments to schedule of power consumption forecast, \(Exp_{reg}\) is the expert adjustments to the schedule of controllable load, _Meteo_ is the weather data, _Eq_ is the equipment data (on/off, resource), \(Cal\) is the calendar-connected features (time, date, working day/day off), and \(Act_{gen}\) is the operating schedule of self-generation objects. \[O_{t}=\langle Act_{cons},\,\,Forecast\rangle \tag{8}\]  
where \(Act_{cons}\) is the schedule of controllable load consumers and _Forecast_ is the schedule of power consumption forecast. The objective functions of a generator agent and an agent-consumer are the reduction in energy costs according to (1) taking into account power balance constraints (2). Input and output parameters for a generator agent are described by (9) and (10), respectively. \[I_{t}=\Big{\langle}Power,\,Gen,\,Plan,\,Eq_{gen},\,Cal,\,Meteo,\,\,Exp_{gen} \Big{\rangle}, \tag{9}\]  
where \(Gen\) is the retrospective self-generation, \(Eq_{gen}\) is the generation equipment data (data on technical state and on/off state of generation equipment), and \(Exp_{gen}\) is the expert adjustments to operating schedule of self-generation. \[O_{t}=\big{\langle}Act_{gen}\big{\rangle}, \tag{10}\]  
Figure 6: The agent decomposition of elements of compressor station.