Ensuring Power Balance in the Electrical Grid of an Oil-and-Gas-Producing Enterprise with Distributed Generation Using Associated Petroleum Gas

Abstract

The purpose of this research is to develop a multi-agent model of an electrical engineering complex for an oil-and-gas-producing enterprise to ensure power balance in its electrical grid by taking into account the increase in the incoming part of the balance by introducing small- and medium-capacity-distributed generation facilities using associated petroleum gas. Previously, the structure of a multi-agent system and the principles of agent interaction were developed to allow the dependence between the processes of generation and consumption of electric energy and the technological process during oil and gas production. In this research, the multi-agent approach is based on the application of the developed methodology to ensure power balance in the electrical grid of an oil-and-gas-producing enterprise. The fuel balance during electricity generation under various scenarios of electrical modes in electrical engineering complexes is considered. To test the operability and make an error estimation of the methodology, digital and physical models of an electrical engineering complex with low- and medium-power-distributed generation facilities were developed for an oil-and-gas-producing enterprise. One of the most important factors that determines the efficiency of a ensuring power balance in the electrical grid of an oil-and-gas-producing enterprise is the consideration in the power balance equation the value of power generated through the use of associated petroleum gas produced by oil production facilities.

1. Introduction

The United Nations currently proposes the blueprint of the Sustainable Development Goals (SDGs). In the authors’ opinion, the relevance of achieving the SDGs is conditioned for any modern oil-and-gas-producing enterprise. In particular, “Goal 12: Re-sponsible Consumption and Production” [1] can be achieved by increasing the efficiency of associated petroleum gas (APG) utilization. An important objective of the state policy in the field of energy in mining is to minimize the volume of APG flaring. According to the “Energy Strategy of the Russian Federation for the period up to 2035” [2], the challenges of the electric power industry are to increase the level of technological processes automation [3,4] and reliability improve the electric power objects at an increase in the complexity of the systems and algorithms for controlling these objects and processes. Gas turbine power stations based on an aircraft gas turbine engine in the field of APG utilization that generate electricity and thermal energy are considered [5,6]. The use of autonomous power supply sources includes the conditions of distributed generation [7,8]. The typical problems of reducing the operational characteristics of gas turbine power stations are the available electric power of gas turbine units [9], energy efficiency [10], and especially power quality [11].

Grid technologies in the electric power industry include technologies, the use of which can lead to organizational and technological changes in the management and operation of electrical complexes (ETCs) and contribute to the transition of energy to a new technological basis, including a multi-agent approach in the electric power industry [12,13].

At the moment, the concept of small-scale distributed generation (MicroGrid) is being developed in the electric power industry, and the most efficient way of APG utilization is the introduction of distributed generation (DG) based on gas turbine power plants in the ETC of an oil-and-gas-producing enterprise (OGPE) [14,15]. To ensure the reliability of operation, new approaches of control should be applied [16]. The multi-agent approach makes it possible to consider the problem of ensuring the reliability of operation as a problem of the electricity balance and fuel balance in the ETC of the OGPE [17]. Model predictive control as a method of solving problems related to optimizing constraints and increasing the efficiency of electric networks with distributed generation facilities (microgrids) is presented [18,19]. The development of multi-agent models in relation to the energy and electric complexes has already been considered [20]. The development of multi-agent models has already been considered in related technical problems, such as transport problems (optimal transport theory) [21]. Planning of the process of operation of electrical equipment using the theory of Markov processes is considered in [22]. Some practical aspects of genetic algorithms’ implementation regarding control of the electrical equipment life cycle are considered in [23].

2. Agents of the OGPE ETC with Distributed Generation

The goal of this research is the development of a multi-agent model of an electrical engineering complex with distributed generation to ensure the power balance of electric networks at oil-and-gas-producing enterprises [24]. At the first stage of the research, the functions of the agents in the multi-agent model of the OGPE ETC with DG were formed with regard to the datasets used [25]. In the second stage, research methodology was developed to ensure power balance, allowing you to take into account the possible control actions specified for the multi-agent model of the OGPE ETC with DG [26,27]. At the final stage of the work, an analysis of the following experiments was carried out:

• To estimate the error of the developed methodology for ensuring power balance in the electrical grid;
• To estimate the error of modeling the control actions in a digital multi-agent model at a real physical object;
• To estimate the error in calculating the electric power based on the APG performance in the framework of developing a methodology for ensuring power balance [28].

Table 1. Functions of agents of the OGPE ETC with DG.

Set of Agents	Datasets Used	Agent Function
$G=\left\{{\dot{S}}_0^G,{\dot{S}}_1^G,{\dot{S}}_2^G\cdots {\dot{S}}_n^G\right\}$ n—number of generation agents	$G_n$—fuel consumption of the n-th agent, m3/h ${\dot{S}}_n^G$—generated power of the n-th agent, kVA ${\dot{S}}_0^G$—generated power without fuel processing (external power system), kVA	${\dot{S}}_n^G=f_n(G_n)+{\dot{S}}_0^G$, where $f_n(G_n)$ is the function reflecting the process of converting fuel into electricity, kVA
$R=\left\{{\dot{S}}_1^R,{\dot{S}}_2^R\cdots {\dot{S}}_i^R,G^R\right\}$ i—number of agents in the power system of the field; $G^R$—fuel balance, parameter of the technological process object responsible for the fuel balance	${\dot{S}}_i^{out}$—output power of the i-th agent, kVA ${\dot{S}}_i^{in}$—input power of the i-th agent, kVA ${\dot{S}}_i^R$—capacity of consumers’ own needs and (or) power losses in the i-th agents, kVA ${\displaystyle \sum G_n}$—total fuel consumption, m3/h ${\displaystyle \sum H_m}$—total liquid flow rate, m3/h	${\dot{S}}_i^{out}={\dot{S}}_i^{in}-{\dot{S}}_i^R$ $G^R=f_R({\displaystyle \sum H_m})-{\displaystyle \sum G_n}-G_0$ where $G_0$ is the gas flow not involved in electricity generation, m3/h $f_R({\displaystyle \sum H_m})$—function reflecting the APG separation process, m3/h
$H=\left\{{\dot{S}}_0^H,{\dot{S}}_1^H,{\dot{S}}_2^H\cdots {\dot{S}}_m^H\right\}$ m—number of consumption agents	$H_m$—liquid flow rate of the m-th agent, m3/h ${\dot{S}}_m^H$—power consumption of the m-th agent, kVA ${\dot{S}}_0^H$—power not spent directly on the extraction of the oil and gas mixture, kVA	$\left\{\begin{array}{l}{\dot{S}}_m^H=f_m(H_m)+{\dot{S}}_0^H\\ G_m=f_R({\displaystyle \sum H_m})\end{array}\right.$, where $f_m(H_m)$ is the function reflecting the process of power consumption during the production of oil and gas mixture, kVA

presents the functions of the agents in the multi-agent model of the OGPE ETC with distributed generation. The function involves the real-time processing of observed parameters; that is, working with datasets [29].

The classification of agents in the multi-agent model of the OGPE ETC with DG within the sets of agents is carried out according to a characteristic feature that takes into account the datasets used.

Generation agents are divided into two types: an agent external power system (agent PS) and an agent gas turbine power station (agent GTPS):

$${\displaystyle \sum {\dot{S}}_{n+1}^G}={\dot{S}}_0^{G1}+{\displaystyle \sum {\dot{S}}_n^{G2}}.$$

(1)

If the generation agent does not use the fuel consumption data, set $f_n(G_n)$ = 0; then, this agent corresponds to the agent PS (external power system), and its function is written as:

$${\dot{S}}_{}^{G1}=f_n(G_n)+{\dot{S}}_0^G, \mathrm{provided} f_n(G_n)=0.$$

(2)

where ${\dot{S}}_0^G$ is the is the output of power to the grid from the external power system, kVA.

The function of the generation agent corresponding to the GTPS is written as:

$${\dot{S}}_n^{G2}=f_n(G_n)+{\dot{S}}_0^G, \mathrm{provided} {\dot{S}}_0^G=0.$$

(3)

where $f_n(G_n)$ corresponds to the operating characteristics of the gas turbine, individual for each type of gas turbine, and the type of fuel used.

Consumption agents are divided into three types: production agents, process agents, and additional load agents:

$${\displaystyle \sum {\dot{S}}_m^H=}{\displaystyle \sum {\dot{S}}_b^{H1}}+{\displaystyle \sum {\dot{S}}_t^{H2}}+{\displaystyle \sum {\dot{S}}_d^{H3}}.$$

(4)

where b is the number of production facilities, t is the number of process facilities, and d is the number of additional load facilities that are not included in the OGPE ETC.

If a consumption agent uses a dataset of fluid flow rate $f_m(H_m)$, then this agent corresponds to an artificial lift object, and its function is written as:

$$\left\{\begin{array}{l}{\dot{S}}_b^{H1}=f_m(H_m)+{\dot{S}}_0^H\\ G_m=f_R({\displaystyle \sum H_m})\end{array}\right., \mathrm{provided} f_R({\displaystyle \sum H_m})=0.$$

(5)

If the object of artificial lift is the installation of an electric submersible pump (ESP), then the term $f_m(H_m)$ will be equal to the active power supplied to the pump, which is necessary to maintain the specified technological parameters [30].

$${\dot{S}}_b^{H1}=P_b^{H1}+{\dot{S}}_0^{H1}=\frac{{\mathsf{\rho }}_l\cdot g\cdot \left(\frac{P_{\mathrm{buf}}}{{\mathsf{\rho }}_{\mathrm{l}}\cdot g}+H_{ESP}\right)\cdot Q_{ESP}}{\mathsf{\eta }\cdot K_{\mathsf{\eta }\mathsf{\nu }}\cdot \mathrm{86,400}}+{\dot{S}}_0^{H1}.$$

(6)

where $P_b^{H1}$ is the active power consumed by the ESP, kW; ${\dot{S}}_0^{H1}$ is the total power not spent directly on the extraction of the oil and gas mixture, kVA, ${\mathsf{\rho }}_l$ is the density of the lifted liquid, kg/m³; g is the free-fall acceleration, assumed to be 9.81 m²/s; $P_{\mathrm{buf}}$ is the buffer pressure, Pa; $H_{ESP}$ is the dynamic level of fluid in the well, m; $Q_{ESP}$ is the specified flow rate of the pump, m³/day; η is the efficiency of the pump at a given operating point, p.u.; and $K_{\mathsf{\eta }\mathsf{\nu }}$ is the coefficient for taking into account the change in pump efficiency when operating on viscous liquids, p.u.

If the consumption agent uses the fuel consumption dataset $G_m$, then this agent corresponds to the process object, and its function is written as:

$$\left\{\begin{array}{l}{\dot{S}}_t^{H2}=f_m(H_m)+{\dot{S}}_0^H\\ G_m=f_R({\displaystyle \sum H_m})\end{array}\right., \mathrm{provided} f_m(H_m)=0.$$

(7)

where ${\dot{S}}_0^H$ is the power supplied to an object designed to work with certain volumes of the oil and gas mixture, kVA, and $f_R({\displaystyle \sum H_m})$ is the function that reflects the gas separation process. In a simplified form, this dependence can be expressed as:

$$G_m=J\cdot H_m.$$

(8)

where J is the gas factor, the amount of gas dissolved in oil, m³/m³.

If the agent of consumption does not use the datasets about the liquid flow and fuel consumption $H_m=0$, $G_m=0$, then this agent corresponds to the additional load:

$$\left\{\begin{array}{l}{\dot{S}}_d^{H3}=f_m(H_m)+{\dot{S}}_0^H\\ G_m=f_R({\displaystyle \sum H_m})\end{array}\right., \mathrm{provided} f_m(H_m)=0, f_R({\displaystyle \sum H_m})=0.$$

(9)

Agents of the set R are divided into two types: agents of the electrical grid (agent EG) and agents of the technological process responsible for the fuel balance. Agents EG use input ${\dot{S}}_i^{in}$ and output ${\dot{S}}_i^{out}$ power datasets:

$${\dot{S}}_i^{out}={\dot{S}}_i^{in}-{\dot{S}}_i^R.$$

(10)

Agents of the technological process use a dataset on the total liquid flow rate, $f_R({\displaystyle \sum H_m})$, total fuel consumption, ${\displaystyle \sum G_n}$, and gas flow $G_0$ not involved in electricity generation:

$$G^R=f_R({\displaystyle \sum H_m})-{\displaystyle \sum G_n}-G_0.$$

(11)

3. Methodology for Ensuring Power Balance in the Electrical Grid of an Oil-and-Gas-Producing Enterprise

A methodology has been developed to ensure power balance, which makes it possible to take into account the possible control actions provided in the multi-agent model of the OGPE ETC with DG [31,32].

The power balance equation in the electrical grid of the OGPE is as follows:

$${\displaystyle \sum {\dot{S}}^G}={\displaystyle \sum {\dot{S}}^H}+{\displaystyle \sum {\dot{S}}^R}$$

(12)

where ${\displaystyle \sum {\dot{S}}^G}$ is the total generated power, kVA, ${\displaystyle \sum {\dot{S}}^H}$ is the total power of consumers, kVA, and ${\displaystyle \sum {\dot{S}}^R}$ is the power spent on the operation of the electrical grid (losses, own needs, etc.), kVA.

The power balance can be estimated by the volume of the power unbalance:

$$\Delta \dot{S}={\displaystyle \sum {\dot{S}}^G}-{\displaystyle \sum {\dot{S}}^H}-{\displaystyle \sum {\dot{S}}^R}$$

(13)

The power balance equation within the framework of the multi-agent model describes the rules for the interaction of agents; that is, the environment for the interaction of agents. The general equation for the interaction environment of agents is written as:

$$({\dot{S}}_{}^{G1}+{\displaystyle \sum {\dot{S}}_n^{G2}})=({\displaystyle \sum {\dot{S}}_b^{H1}}+{\displaystyle \sum {\dot{S}}_t^{H2}}+{\displaystyle \sum {\dot{S}}_d^{H3}}+{\displaystyle \sum {\dot{S}}_i^R)}$$

(14)

where ${\dot{S}}_{}^{G1}$ is the power coming from the external power system, kVA, ${\dot{S}}_n^{G2}$ is the generated power of the n-th generation agent, kVA, ${\dot{S}}_b^{H1}$ is the power spent on the production of the oil and gas mixture by the b-th production agent, kVA, ${\dot{S}}_t^{H2}$ is the power spent on providing the technological process by the t-th agent technological process, kVA, ${\dot{S}}_d^{H3}$ is the power consumed by the d-th agent of the additional load, kVA, and ${\dot{S}}_i^R$ is the power spent on the operation of the electrical grid by the i-th agent of the electrical grid, kVA.

Taking into account the fuel balance equation when using APG to generate electricity, the equation for the interaction environment of agents can be written as:

$${\dot{S}}_{}^{G1}={\displaystyle \sum {\dot{S}}_b^{H1}}-{\displaystyle \sum {\dot{S}}_b^{G2}}+{\displaystyle \sum {\dot{S}}_t^{H2}}+{\displaystyle \sum {\dot{S}}_d^{H3}}+{\displaystyle \sum {\dot{S}}_i^R}$$

(15)

where ${\dot{S}}_b^{G2}$ is the power generated through the use of APG produced by the b-th production agent, kVA. Taking into account the topology of the electrical grid of the OGPS with DG, the following restrictions on active power are added to the equation of the interaction environment of agents:

$$\left\{\begin{array}{l}{\displaystyle \sum P_b^{G2}}-{\displaystyle \sum P_b^{H1}}-{\displaystyle \sum P_d^{H3}-{\displaystyle \sum P_i^R}}\ge 0,\\ P_{}^{G1}-{\displaystyle \sum P_t^{H2}}\ge 0.\end{array}\right.$$

(16)

Restrictions mean that in order to provide the required category of power supply to the process facilities, power must be supplied from an external power system, while the power supply of artificial lift facilities, auxiliary needs of the electrical grid, and additional load is allowed from the DG facilities [33].

The task of ensuring power balance is reduced to the task of finding the minimum of the function:

$$\left\{\begin{array}{l}{\dot{S}}_{}^{G1}+{\displaystyle \sum {\dot{S}}_b^{G2}}-{\displaystyle \sum {\dot{S}}_b^{H1}}-{\displaystyle \sum {\dot{S}}_t^{H2}}-{\displaystyle \sum {\dot{S}}_d^{H3}}-{\displaystyle \sum {\dot{S}}_i^R\to \mathit{min},}\\ \mathrm{provided} \dot{S}=\sqrt{P^2+j{Q}^2},\\ {\displaystyle \sum P_b^{G2}}-{\displaystyle \sum P_b^{H1}}-{\displaystyle \sum P_d^{H3}-{\displaystyle \sum P_i^R}}\ge 0,\\ P_{}^{G1}-{\displaystyle \sum P_t^{H2}}\ge 0,\\ P_{\mathit{max}}^{G1}\ge {\displaystyle \sum P_{}^{G1}}\ge P_{\mathit{min}}^{G1},\\ P_{\mathit{max}}^{G2}\ge {\displaystyle \sum P_n^{G2}}\ge P_{\mathit{min}}^{G2},\\ P_{\mathit{max}}^{H1}\ge {\displaystyle \sum P_b^{H1}}\ge P_{\mathit{min}}^{H1},\\ P_{\mathit{max}}^{H2}\ge {\displaystyle \sum P_t^{H2}}\ge P_{\mathit{min}}^{H2},\\ P_{\mathit{max}}^{H3}\ge {\displaystyle \sum P_d^{H3}}\ge P_{\mathit{min}}^{H3},\\ P_{\mathit{max}}^R\ge {\displaystyle \sum P_i^R}\ge P_{\mathit{min}}^R,\end{array}\right.$$

(17)

where $P_{\mathit{min}}^{G1},P_{\mathit{min}}^{G2},P_{\mathit{min}}^{H1},P_{\mathit{min}}^{H2},P_{\mathit{min}}^{H3},P_{\mathit{min}}^R$ are the the minimum allowable values of active power under the conditions of the normal electrical mode of the ETC.

$P_{\mathit{max}}^{G1},P_{\mathit{max}}^{G2},P_{\mathit{max}}^{H1},P_{\mathit{max}}^{H2},P_{\mathit{max}}^{H3},P_{\mathit{max}}^R$ are the the maximum allowable values of active power under the conditions of the normal electrical mode of the ETC.

The power values of the agents make up the set $E_z$, which determines the electrical mode in the space E of all possible regimes:

$$E_z=\left\{{\dot{S}}_{}^{G1},{\dot{S}}_n^{G2},{\dot{S}}_b^{H1},{\dot{S}}_t^{H2},{\dot{S}}_d^{H3},{\dot{S}}_i^R\right\}$$

(18)

where z is the electrical mode number [24].

The problem in this setting is a non-linear programming problem with an inequality constraint. To solve such optimization problems, a solution method belonging to the group of indirect methods is used—the method of penalty functions [34].

If ${\dot{S}}_{}^{G1},{\dot{S}}_n^{G2},{\dot{S}}_b^{H1},{\dot{S}}_t^{H2},{\dot{S}}_d^{H3},{\dot{S}}_i^R$ are the functions that are continuous on the whole space E, then the functions $A\left({\dot{S}}_{}^{G1}\right),A\left({\dot{S}}_n^{G2}\right),A\left({\dot{S}}_b^{H1}\right),A\left({\dot{S}}_t^{H2}\right),A\left({\dot{S}}_d^{H3}\right),A\left({\dot{S}}_i^R\right)$ are the penalty functions, under the following conditions for each:

$$A\left(\dot{S}\right)=0 \forall \dot{S}\in E_z,$$

(19)

$$A\left(\dot{S}\right)\ne 0 \forall \dot{S}\notin E_z.$$

(20)

The generalized function is introduced (k = 1, 2, …):

$$F\left(\dot{S}, k\right)=\dot{S}+k\cdot A\left(\dot{S}\right),$$

(21)

where k is the penalty coefficient denoting the scenario for the transition of the ETC from one electrical mode to another, and the function $A\left(\dot{S}\right)$ determines the control action of a certain agent. The algorithm for ensuring power balance, taking into account the possible control action provided for in the multi-agent model of the OGPE ETC with DG, is shown in Figure 1.

4. Results

Using the physical model of the OGPE ETC with DG, the following experiments were carried out:

• Evaluate the error of the developed methodology for ensuring power balance in an electrical grid;
• Evaluate the error of modeling the control actions in a digital multi-agent model on a real physical object;
• Evaluate the error of the electric power calculation based on the heat output of APG when developing a methodology for ensuring power balance in the electrical grid.

Taking into account the operating factors in specific technological conditions (changes in the configuration and topology of the power system, changes in the operating modes of the supply grid, the load’s specifics, etc.) at the stage of testing these objects will allow the operator to understand the technical and technological limitations at the stage of the operation. On the other hand, it will be an opportunity to formulate requirements for equipment operation modes, maintain a database of parameters of the power system’s elements from the test stages, and formulate requirements for equipment maintenance and repair measures.

4.1. Evaluate the Error of the Developed Methodology for Ensuring Power Balance in the Electrical Grid

On the laboratory stand, the adequacy of the developed methodology for ensuring power balance in the electrical grid was checked. As generation agents, a system on one shaft “Induction motor—Synchronous generator” with a power of 1.5 kW [35] was used. As agents of consumption, the following load was used: motor (AC machines 120 W and 220 W/380 V/1500 rpm) and active (resistance block at 270 Ohm, 360 Ohm, 550 Ohm, and 1100 Ohm). As agents of the electrical grid, the “Electrical Machines” module and an active load unit with resistance connection terminals were used.

The experiment was carried out to determine the power of consumption agents in different operating modes of the ETC and scenarios for the transition between them. First, the steady-state electrical modes were modeled, and then the scenarios for connecting and disconnecting the load, followed by a change in the power output to the grid by the generation agent. The appearance of the laboratory stand and the block diagram of the multi-agent model are shown in Figure 2.

The conformity assessment of the developed mathematical and physical models was carried out. It is assumed that the nature of the change in performance characteristics (load factor, power factor, efficiency) of the real motor load and laboratory motors is the same. It is also assumed that the nature of the change in operating characteristics (excitation current, efficiency) of a real GTPS generator and a laboratory one is the same.

A comparison of the steady-state electrical modes calculated using the multi-agent model with the grid modes obtained on the laboratory bench is presented in

Table 2. Comparison of the results of modeling modes obtained by laboratory stand and calculated with the multi-agent model.

Mode	$\mathbf{Physical} \mathbf{Model}, {\dot{\mathit{S}}}_{}^{\mathit{H}}$, VA	$\mathbf{Multi}-\mathbf{Agent} \mathbf{Model}, {\dot{\mathit{S}}}_{}^{\mathit{H}}$, VA	$\mathbf{Error}, {\mathit{\epsilon }}_{\mathit{P}}$, %	$\mathbf{Error}, {\mathit{\epsilon }}_{\mathit{j}\mathit{Q}}$, %
1.1	257 + j651	251 + j627	2.33	3.67
1.2	384 + j656	377 + j627	1.82	4.42
1.3	911 + j659	899 + j627	1.32	4.86
2.1	359 + j937	351 + j954	2.23	1.78
2.2	497 + j954	477 + j954	4.02	0.01

. The mode number consists of two parts separated by a dot—the first number means the number of the connected consumption agents from the set of motor loads (H1), and the second is the number of connected agents from the active load set in order (H2).

The error of the simulation results of steady electrical modes does not exceed 5%. A comparison of the transition scenarios parameters calculated using the multi-agent model with the parameters of possible transition scenarios obtained by laboratory stand is presented in

Table 3. Comparison of the possible modeling result transition scenarios obtained on a laboratory stand and calculated with the multi-agent model.

Scenario	Initial Mode	Final Mode	$\mathbf{Physical} \mathbf{Model}, {\dot{\mathit{S}}}_{}^{\mathit{H}}$, VA	$\mathbf{Multi}-\mathbf{Agent} \mathbf{Model}, {\dot{\mathit{S}}}_{}^{\mathit{H}}$, VA	$\mathbf{Error}, {\mathit{\epsilon }}_{\mathit{P}}$, %	$\mathbf{Error}, {\mathit{\epsilon }}_{\mathit{j}\mathit{Q}}$, %
1	1.0	1.1	245 + j622	232 + j609	5.20	2.05
2	1.0	1.2	357 + j628	343 + j613	4.06	2.31
3	1.1	1.2	375 + j636	365 + j626	2.45	1.45
4	1.1	1.3	813 + j567	768 + j537	5.54	5.29
5	1.2	1.3	848 + j572	803 + j524	5.21	5.24
6	1.2	1.0	163 + j629	171 + j637	4.95	1.33
7	1.2	1.1	254 + j678	262 + j686	3.10	1.19
8	2.0	2.1	344 + j904	331 + j891	3.70	1.41
9	2.0	2.2	457 + j903	434 + j880	4.87	2.47
10	2.1	2.2	476 + j912	459 + j895	3.49	1.82
11	2.1	2.0	249 + j946	253 + j950	1.81	0.48
12	2.2	2.0	256 + j948	262 + j954	2.29	0.63
13	2.2	2.1	463 + j915	470 + j922	1.65	0.84

. Limitations taken into account include voltage in the grid in the range of 361–399 V. The parameters of the generation agent should not exceed the passport values of the equipment. the excitation current of the synchronous generator is 2 A, and the stator current of the induction motor is 8 A.

The error of scenario modeling results does not exceed 5.54%. The proposed method for ensuring power balance, together with the proposed approach to building a multi-agent model of the OGPE ETC with DG, makes it possible to maintain the power balance in the electrical grid even with a lack of measurements, as well as under conditions of restrictions on the composition and discreteness of measurements.

Next, it is necessary to check the possibility of implementing this method on a programmable controller to show the effectiveness of automatic switching between electrical modes. Then, the generating facilities will be considered in more detail to implement the calculation of electrical energy from the APG parameters.

4.2. Evaluate the Error of Modeling the Digital Multi-Agent Model’s Control Actions on a Real Physical Object

An analysis of the experiment in manual and automatic modes results of the modules on the stand “Model of the electrical system” [36] during the development of scenario 1 is presented in

Table 4. Analysis of the experiment results in manual and automatic modes in modules of the stand “Model of the electrical system” during the development of scenario 1.

Mode (Scenario)	Parameter	Modeling Time, s
		0	1	2	3	4	5	6	7	8	9	10
Estimated	Voltage in grid, U, V	170.0	169.0	167.5	165.0	162.5	160.0	162.5	165.0	167.5	169.0	170.0
Manual	Voltage in grid, Uman, V	170.0	166.6	162.4	147.8	143.7	119.9	157.6	155.2	173.4	180.9	170.0
	Error, %	0.0	1.4	3.0	10.4	11.6	25.1	3.0	5.9	3.4	6.6	0.0
Automatic	Voltage in grid, Uauto, V	170.0	168.8	165.4	162.3	161.8	159.6	156.8	158.9	167.9	172.8	170.0
	Error, %	0.0	0.1	1.3	1.6	0.4	0.3	3.5	3.7	0.2	2.2	0.0

. Scenario 1 involves reducing the voltage in the grid from 170 V to 160 V for 5 s and then restoring the voltage from 160 V to 170 V. As a relative error, let us set the maximum error of the unit of measuring current and voltage transformers BIT-3. According to the passport data, the measurement error of the instruments is no more than 2.5%. When simulating the manual mode (operational dispatch control mode), the system lacks all elements, except the power source of the DC motor and the exciter of the synchronous machine, which operate in manual mode; that is, during the experiment, it is necessary to turn the voltage regulator knob on the laboratory stand.

In automatic mode, the power reduction in the consumption agent went more smoothly due to the creation of an analog control signal from the National Instruments NI USB-6009 device [37]. The deviation of the voltage in the grid from the permissible did not exceed 3.7%. Figure 3 shows the interface of the NI Signal Express program with the results of modeling the scenario of a temporary decrease in the consumption agent power (load reduction) and the results of a manual control action. After the power reduction in the consumption agent, 5 s passed before it became possible to provide power balance in the grid corresponding to the parameters before the load reduction scenario.

Figure 4 shows the interface of the NI Signal Express program with the results of modeling the scenario of a temporary decrease in the consumption agent power and the results of the control action in automatic mode using the multi-agent model. The figures show that the automatic mode ensures smooth switching of electrical modes.

4.3. Evaluate the Error of the Electric Power Calculation Based on the Heat Output of APG When Developing a Methodology for Ensuring Power Balance in the Electrical Grid

At the laboratory facility, the calculation adequacy of the electric power based on the heat output of APG was checked, while ensuring the power balance in the electrical grid.

The appearance of the laboratory installation using components of a gas turbine engine with a power of 80 kW [38] is shown in Figure 5.

The experimental idea is to burn APG at fixed values of air and fuel consumption and identify the relationship between the composition of APG and its combustion temperature in a laboratory installation close to real small- and medium-power-generation facilities. APG combustion temperature directly affects the amount of electricity generated. The gas analyzer Optima-7 [39] was used as the measuring equipment; in the measurement range from +473 to +923 K, the relative error is 1%. Rotameters with a relative error of 0.5% were used to measure fuel consumption and air consumption. The fuel consumption and air consumption were recalculated to generate 80 kW of electric power (nominal parameters of the gas turbine engine) [40]. A comparison of temperature and power calculation results with the results of measurements is presented in

Table 5. Comparison of calculation results and results of the experimental measurements of gas turbine parameters.

Parameter	Calculation Results	Experiment Results	Error, %
Mass fuel consumption $G_T^M$, kg/s	0.0003	0.0003	-
Mass air consumption $G_B^M$, kg/s	0.0055	0.0055	-
Excess air ratio $\alpha$, p.u.	1.27	1.27	-
Turbine inlet temperature $T_{inCT}$, °K	725.80	737.00	1.51
Generated power $P^G$, W	738.69	730.30	1.73
Volumetric fuel consumption at rated power of gas turbine engine (80 kW) $G_T^V$, m3/h	112.90	111.62	1.74
Volumetric air consumption at rated power of gas turbine engine (80 kW) $G_B^V$, m3/h	1698.17	1717.69	1.74

.

The calculation error does not exceed 1.74%. The results of calculating the fuel consumption and air consumption during the operation of generation facilities in the nominal mode using APG of different compositions are presented in

Table 6. Fuel and air consumption in different modes of the gas turbine engine.

Object (APG Source)	Heat Output of APG, kJ/kg	Air Consumption, m3/h	Fuel Consumption, m3/h	$\mathbf{Specific} \mathbf{Fuel} \mathbf{Consumption}, \frac{{\mathbf{m}}^3}{\mathbf{kW}\cdot \mathbf{h}}$
OGGP	40,564.433	1701.85	127.58	1.60
GTPP	43,556.194	1701.70	121.97	1.52
ICS #1	29,285.120	1717.19	182.38	2.28
ICS #2	39,693.953	1714.41	127.92	1.60
ICS #3	39,359.681	1723.15	110.60	1.38

(OGGP—oil and gas gathering point, GTPP—gas turbine power plant, ICS—intermediate compressor station).

The developed multi-agent model of the OGPE ETC with DG ensures the power balance in the OGPE electrical grid, taking into account the heat output of APG of various fields in the scenarios of electric modes of the OGPE during the operation of low- and medium-power-generation facilities. [41,42]. An analysis of real oil and gas fields was carried out. Systematized data based on the analysis of introducing distributed generation facilities at the real fields are summarized in

Table 7. Systematized data based on the analysis of introducing distributed generation facilities at the real fields.

Field	APG Volume, Thousand m3 per Year	GTPS Power Equivalent *, kW	Planned Load, kW	Distance from Field to Load, km	Power Supply
#1	40,000	10,811	150	2.00	Populated locality
#2	16,000	4324	1400	2.00	Populated locality
#3	2000	541	250	3.00	Populated locality
#4	1400	378	800	2.00	Populated locality
#5	6000	1622	60	3.60	Populated locality
#6	5500	1486	450	3.00	Populated locality
#7	2600	703	1500	2.00	Populated locality
#8	60,000	16,216	2500	2.75	Populated locality
#9	2400	649	650	3.70	Populated locality
#10	16,000	4324	600	3.50	Populated locality
#11	100,000	27,027	1000	3.00	Non-profit gardening partnership
			530	2.00	Booster pumping station
#12	220,000	59,459	1300	3.50	Populated locality
			200	2.00	Objects of technological process
#13	6000	1622	75	3.00	Dispensary
			387	0	Oil and gas collection point
#14	14,500	3919	275	2.00	Populated locality
			875	0	Booster pumping station

* It is assumed that generation facilities produce this power around the clock throughout the year.

.

The results of the experiment are used to build a multi-agent model of an electrotechnical complex at an oil-and-gas-producing enterprise. This allows you to accurately select the composition of the power plant based on the gas parameters of the field and its ability to generate electricity at small- and medium-power-generation facilities.

The multi-agent approach makes it possible to structure the elements of the electrotechnical complex and provides more opportunities for ensuring power balance in the electrical grid due to the clear linking of power flows to electrotechnical complex elements, right down to the process of converting the fuel flow into the incoming part of the power balance.

5. Discussion

Taking into account the territorial features, the quantitative composition and specifics of the operation of pumping units of various types (rod deep, electric centrifugal), the composition of the produced APG, and the presence of nearby settlements, 14 proposed clusters have been identified, for which it is advisable to introduce generating plants of small and medium power. The total capacity of generating units in these clusters is 13 MW, and the total volume of APG that can be used for generation is 48 million m³ per year, with a total production of 492 million m³ per year. These conclusions were made based on the results of an experiment to calculate the generated electrical energy from APG and the application of a multi-agent approach to structuring load and the generation of objects in a cluster. Previously, due to factors ensuring power balance in the electrical grid of these clusters, the possibility of introducing small- and medium-power-generation facilities was not considered. Taking into account the conversion of gas combustion energy into electrical energy at small- and medium-distributed-generation facilities will allow you to assess more accurate possible scenarios of electrical modes and, accordingly, ensure a balance of power in the facility’s electrical grid of the oil-and-gas-producing enterprise. Together with the increase in the beneficial use of the APG, the energy autonomy of remote fields and infrastructure facilities is also ensured. These factors also influence:

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The reduction in the oil-and-gas-producing enterprise dependence on the tariff policy in the electricity market;

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The reduction in the environmental load on the whole;

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The improvement of the ecological situation directly in the fields.

6. Conclusions

A mathematical multi-agent model of the OGPE ETC with DG of small and medium power has been developed and verified. The adequacy of the developed methodology for ensuring power balance in the electrical grid was checked by the physical model of the OGPE ETC with DG. Simulation of the control actions of a digital multi-agent model on a real physical object has been verified. The calculation of electrical power has also been verified based on the APG heating capacity.

The methodology for ensuring the balance of power in the electrical grid of an oil-and-gas-producing enterprise has been developed. This technique takes into account the fuel balance in electricity generation under various scenarios of transition between electrical modes. Using this method, it is possible to introduce small- and medium-sized energy projects into the electric network of an oil-and-gas-producing enterprise where previously it was impossible due to restrictions imposed by the peculiarities of ensuring a power balance. The developed method of ensuring the energy balance takes into account the electricity generated by the use of APG produced by oil production facilities, and electric loads represented by settlements located near the fields are added to the structure of the multi-agent model.