Optimal Scheduling of Wind–Solar Power Generation and Coalbed Methane Well Pumping Systems

Abstract

With the integrated development of new energy and oil and gas production, introducing wind–solar–storage microgrids in coalbed methane well screw pump discharge systems enhances the renewable energy proportion while promoting green development. However, the cyclical, volatile, and random characteristics of wind and photovoltaic generation create scheduling challenges, with insufficient green power consumption reducing renewable energy utilization efficiency and increasing grid dependence. This study establishes an operation scheduling optimization model for coalbed methane well screw pump discharge systems under wind–solar–storage microgrids, minimizing daily operation costs with screw pump rotational speed as decision variables. The model incorporates power constraints of generation units and production constraints of screw pumps, solved using particle swarm optimization. Results demonstrate that energy storage batteries effectively smooth wind and photovoltaic fluctuations, enhance regulation capabilities, and improve green power utilization while reducing grid purchases and system operation costs. At different coalbed methane extraction stages, the model optimally adjusts screw pump rotational speed according to renewable generation, ensuring high pump efficiency while minimizing operation costs, enhancing green power consumption capacity, and meeting daily drainage requirements.

1. Introduction

With the introduction of the national “dual carbon” goals, the oil and gas industry—as a major energy consumer—urgently needs to accelerate the transformation of its energy structure, represented by renewable energy, and strengthen the integration of oil and gas production with new energy sources. The state has also introduced numerous relevant policies to actively promote the integration of oil and gas exploration and development with new energy, constructing integrated “source-grid-load-storage” projects in oil and gas fields, and striving to create “low-carbon” and “zero-carbon” oil and gas well sites. In recent years, researchers have integrated renewable energy technologies such as wind, solar, and geothermal power into oil and gas production systems, establishing novel integrated energy management systems to reduce production costs and carbon emissions. Reference [1] validated the economic viability and sustainability of incorporating wind power into offshore oil and gas production systems, establishing a robust optimization model for the new energy system. Test results indicate that integrating wind power into platforms not only reduces carbon emissions by 39.91% but also lowers the system’s total annual cost by 2.57%. Reference [2] established an integrated offshore energy management system encompassing oil production platforms, floating wind farms, and green hydrogen production/storage facilities, employing a novel hybrid optimization method to adjust system operation plans. Results indicate that the optimized scheme reduces costs by 16% while decreasing natural gas consumption and carbon emissions by 16%. For onshore oilfields, reference [3] investigates the synergistic peak-shaving capabilities of thermal power plants and demand response within integrated oilfield energy systems incorporating photovoltaics. It establishes a synergistic peak-shaving optimization model targeting the minimization of overall oilfield energy consumption costs. Results indicate that source-load coordinated peak shaving effectively enhances the oilfield grid’s integration capacity for photovoltaic power. Additionally, reference [4] investigates the feasibility of repurposing abandoned oil and gas wells for geothermal energy production within closed-loop geothermal systems. Reference [5] indicates that geothermal energy can be tapped for heating applications within oil and gas gathering and transportation systems, while geothermal power generation technology can supply electricity for oil and gas production. These studies demonstrate that current research has integrated technologies such as wind, solar, and geothermal energy into oil and gas production systems, establishing novel integrated energy management systems that effectively reduce production costs and lower carbon emissions.

In recent years, some scholars have integrated specific oil and gas production equipment with new energy power generation, primarily focusing on optimizing the integration of pumping units with wind and solar power generation. Reference [6] investigated an optimization model for capacity allocation in wind–solar–storage microgrids at production well sites of pumping unit clusters, providing insights for microgrid construction and planning at oil and gas well sites. Reference [7] established an optimization model for peak-shaving and intermittent scheduling of pumping unit clusters under a photovoltaic microgrid without energy storage, utilizing combined power supply from photovoltaic units and the high-voltage grid. The optimization model comprehensively considered production constraints such as pumping unit output, well switching times, and gathering pipeline pressure on the oil and gas production side. Reference [8] idealized the power curve of pumping units as a quasi-sinusoidal function and established a two-layer optimization scheduling model for microgrids incorporating PV, energy storage, and gas turbines. During oil and gas production, the cyclical variations, instability, and intermittent characteristics of production processes—such as mechanical extraction, water injection, and gathering/transportation—combined with the intermittency and randomness of renewable energy generation, form a complex new energy supply-demand system. Therefore, establishing a coupled mathematical optimization model to coordinate renewable energy generation with the energy demands of oil and gas production equipment, while accounting for production constraints on the oil and gas production side, will become a critical issue requiring urgent resolution in the research of multi-energy microgrid scheduling optimization for oil and gas fields [9].

Coalbed methane development is a continuous process of drainage and pressure reduction that spans a long duration. Different coalbeds at various extraction stages require distinct drainage and extraction regimes. As the primary tool for coalbed methane drainage and extraction, screw pumps face challenges in actual operation, including high operational and maintenance costs and unstable economic returns. Their fixed operating parameters also lead to reduced pump efficiency and increased energy consumption. Furthermore, with the integration of wind and solar power generation technologies into drainage systems, screw pump operations now face challenges related to green electricity consumption. Therefore, it is necessary to optimize screw pump operating parameters based on the demand for different drainage stages and predicted wind and solar power generation data to achieve economically efficient drainage. Research on screw pump parameter optimization has been scarce in recent years, with limited accessible domestic and international literature primarily focusing on screw pump speed optimization. Overseas studies on screw pump speed optimization have yielded initial results. For instance, companies like Baker Hughes in the U.S. and Phoenix in the UK. have developed optimal speed optimization models during their research. Researchers developed speed optimization models by integrating signals from downhole pressure and temperature sensors, surface flow sensors, and theoretical calculations (e.g., outlet pressure, bottomhole flow pressure). Subsequently, intelligent control systems were employed to regulate variable frequency drives and adjust motor speeds, achieving the goal of extending screw pump economic service life while ensuring a well production-consumption balance.

Research on screw pump speed optimization is scarce domestically, with no relevant studies emerging in recent years and available literature being relatively outdated. Reference [10] established a nonlinear mapping relationship between screw pump speed and influencing factors using artificial neural networks, designing an online rotor speed control system based on artificial neural networks. Reference [11] constructed an optimized mathematical model for screw pump rotors and adjusted their speed using variable frequency drives and programmable controllers to achieve high efficiency and energy savings. Additionally, reference [12] analyzed the primary factors affecting screw pump speed, developed an optimization model using artificial neural network technology, and regulated motor speed through variable frequency speed control to extend the service life of screw pumps. Reference [13] proposes a method for constructing screw pump speed optimization models based on artificial neural network technology. Input parameters include crude oil temperature, viscosity, pump-end pressure differential, and stator rubber wear, with screw pump speed as the output variable. Actual operating conditions are simulated to evaluate optimization effectiveness. With the advancement of artificial intelligence technology, these studies provide new avenues for constructing screw pump speed optimization models and developing optimization testing systems. As evident from the above literature, domestic and international scholars primarily establish speed optimization models by analyzing the relationship between screw pump speed and related constraints using intelligent technologies such as artificial neural networks. However, specific mathematical models for screw pump speed optimization remain scarce. China remains in the early stages of screw pump speed optimization research, with unstable factors in the optimization process not yet comprehensively addressed. Furthermore, the failure to capture parameter data generated during oil production screw pump operation in a timely manner has hindered improvements in screw pump efficiency and timeliness. This has adversely affected overall oilfield productivity and increased the difficulty of screw pump speed optimization [14].

The aforementioned research on screw pump speed optimization remains confined to grid-powered scenarios. Literature review indicates no existing studies on parameter optimization for screw pumps used in coalbed methane extraction under renewable energy generation scenarios. Current research primarily focuses on the synergistic optimization of oil pumping units and renewable energy. In contrast, systematic studies on screw pumps, which are the core equipment for continuous coalbed methane drainage, remain limited. The inherent flexibility of these pumps in terms of speed regulation and their adaptability to varying operating conditions provide significant advantages for enhancing renewable energy utilization. When wind and solar renewable energy are introduced to power screw pump extraction systems, the intermittent nature, significant output fluctuations, and instability inherent in these renewable sources necessitate that screw pump speed optimization not only consider economic operation but also enhance the screw pump’s capacity to absorb green electricity.

This study aims to fill a research gap and establish a mathematical model for optimizing the scheduling of screw pump production systems in coalbed methane wells under photovoltaic-wind-storage microgrids. The optimization objective is to minimize the daily operating costs of the production system, considering source-side constraints such as upper and lower limits on photovoltaic and wind power generation, as well as constraints related to energy storage batteries. Load-side constraints include screw pump flow rate limitations and electrical power consumption restrictions. Based on predicted renewable energy generation, the model integrates optimization algorithms for both the wind–solar–storage system and the screw pump production system. Utilizing a particle swarm optimization algorithm, it dynamically adjusts the screw pump’s rotational speed and electricity consumption while regulating battery charging/discharging. This ensures the screw pump operates under optimal conditions, enhancing production efficiency, maximizing the utilization of renewable green electricity, improving the economic benefits of screw pump operation, and achieving automated production regulation—a “source-load interaction” mechanism.

2. Wind/Solar/Storage Microgrid-Based Screw Pump Production System for Coalbed Methane Wells

2.1. Stages of Coalbed Methane Production and Depletion

Coalbed methane production primarily involves three processes: drainage, pressure reduction, and gas extraction. The overall production cycle for coalbed methane wells typically spans 10 to 30 years, with a few wells in exceptionally favorable resource conditions potentially exceeding 40 years. Based on successful domestic and international coalbed methane development experiences, as well as variations in wellbore pressure, production characteristics, and operational parameters, the production process can generally be divided into four stages, as illustrated in Figure 1 [15,16,17].

(1)

Single-Phase Water Production Stage: In this stage, coalbed methane exists in an adsorbed state within the coal matrix, and the bottom-hole flowing pressure is higher than the critical desorption pressure. During the initial dewatering phase, a large amount of water needs to be removed to reduce reservoir pressure, resulting in very low or zero gas production. When the bottom-hole flowing pressure drops to the critical desorption pressure (usually 70% to 80% of the original reservoir pressure), the gas production begins to increase. In this stage, the optimization objective is to maximize the dewatering rate while ensuring that excessive coal fines are not produced (i.e., controlling the dewatering volume within a reasonable upper limit, such as not exceeding 90% of the reservoir’s fluid supply capacity per day), to shorten the pressure reduction time and reduce dewatering energy consumption.

(2)

Gas Production Rise Phase: As the bottom-hole pressure falls below the critical desorption pressure, coalbed methane begins to desorb and diffuse. Daily gas production rapidly increases from zero (e.g., from 0 to 1000 m³/d), while daily water production begins to decrease slowly. A two-phase gas-water flow forms in the wellbore, and the fluid density decreases. When the growth rate of daily gas production levels off (e.g., monthly growth rate < 5%) and the gas production approaches its peak, the stable gas production stage is reached.

(3)

Stable Gas Production Phase: When drainage and desorption reach a dynamic equilibrium, the daily gas production remains fluctuating within the peak range (e.g., 1000–3000 m³/d), and the daily water production decreases to a low level and remains stable. This stage lasts the longest and is the core period for generating economic benefits. When the daily gas production begins to show an irreversible and continuous decline (e.g., an annual decline rate > 10%), it marks the end of the stable production period. At this point, the bottom-hole flowing pressure is relatively stable, and the optimization objective is to minimize system operating costs through coordinated scheduling of wind, solar, and energy storage while maintaining a constant dynamic fluid level.

(4)

Declining Gas Production Phase: As the coal seam energy is depleted, the amount of desorbed gas gradually decreases. Daily gas production and daily water production show a simultaneous downward trend (gas production may drop to <500 m³/d) until it is no longer economically viable to extract. This stage is considered a low-efficiency production period, and operating energy consumption can be reduced by lowering the screw pump speed.

This study employs screw pumps for drainage operations in coalbed methane wells. Given the characteristics of each drainage and production phase, daily drainage volume significantly impacts gas production. Controlling an optimal daily drainage volume is essential to enhance coalbed methane yield. By integrating daily wind and solar power generation data with the daily liquid reduction requirements of coalbed methane wells across each drainage and production phase, the daily screw pump speed is optimized. This adjustment regulates power consumption and drainage volume to meet daily drainage demands, thereby improving drainage and production efficiency.

2.2. System Architecture

Oil and gas well sites, as major energy consumers, often rely on fuel-fired gas turbines for power generation or purchase electricity from power plants to meet the power demands of production equipment. This not only increases the demand for traditional fossil fuels and raises production costs but also contributes to environmental pollution through the extensive combustion of fossil energy sources like oil and gas. Integrating renewable energy generation technologies into oil and gas production systems reduces reliance on fossil fuels and grid-purchased electricity, effectively enhancing both economic and environmental benefits of oil and gas production. This represents a crucial measure for energy conservation and emissions reduction in the oil and gas industry.

Figure 2 illustrates the topology of a wind and solar power generation system coupled with a screw pump production system. In this configuration, wind turbines, photovoltaic cells, and the high-voltage grid jointly power the screw pump. Given the random, intermittent, and unstable nature of wind and solar power generation, energy storage batteries are incorporated to perform peak shaving and valley-filling functions. This smooths fluctuations in wind and solar output, ensuring grid stability and reliability. The system dispatch platform manages power allocation, optimizing the coordination between the power system and the screw pump system based on real-time wind and solar generation conditions. By adjusting the screw pump speed, the pumping system dynamically adapts its power output to match the generation profiles of the renewable energy sources. During actual operation, the system aims to maximize green electricity utilization. It achieves this by fully leveraging wind and solar energy to optimize screw pump speed control, thereby minimizing waste of renewable power, reducing dependence on grid-purchased electricity, and simultaneously meeting specific pumping requirements.

At the control level, the system adopts a centralized control strategy. Using a 1 h scheduling time step, and based on day-ahead predicted wind and solar data, the system optimizes and adjusts the screw pump speed, energy storage battery charging and discharging strategy, and grid power purchase and sale plan for the next 24 h. Regarding the grid interaction mode, this paper assumes the system operates in “grid-connected mode.” The main power grid acts as the power balance node for the system: when there is a surplus of renewable energy within the microgrid and the energy storage is fully charged, the excess power is fed into the grid; when internal supply is insufficient, and energy storage is depleted, power is purchased from the grid. This interaction is not optional, but rather a mandatory backup measure to ensure continuous pumping operations and prevent pump blockage or liquid level control issues due to power outages.

To simplify calculations and focus on scheduling strategy research, the modeling process is based on the following key assumptions:

(1)

Day-ahead predicted data (wind speed, solar irradiance) are treated as deterministic inputs within the scheduling cycle, neglecting the impact of ultra-short-term random fluctuations.

(2)

The charging and discharging efficiency of the energy storage battery and the inverter conversion efficiency are considered constant, neglecting the nonlinear effect of temperature on battery capacity.

2.3. Source-End Device Mathematical Model

2.3.1. Photovoltaic Power Model

The power output of photovoltaic modules is primarily influenced by weather conditions, varying with changes in solar irradiance, ambient temperature, and other uncertain factors. Their output power is defined as follows [18]:

$$P_{PV}(t)=P_{STC}{\displaystyle \frac{E_c(t)}{E_{STC}}}\left[1+\mu (T(t)-T_{STC})\right]$$

(1)

In the formula, $P_{PV}(t)$ is the output power of the photovoltaic array at time t under the illumination intensity $E_c(t)$ and the photovoltaic array surface temperature $T(t)$, in kW; $P_{STC}$ is the maximum output power under standard test conditions (illumination intensity $E_{STC}$ = 1 kW/m², cell temperature $T_{STC}$ = 25 °C), determined by the parameters on the photovoltaic module nameplate; $E_{STC}$ is the illumination intensity under standard test conditions (1 kW/m²); $T_{STC}$ is the photovoltaic array temperature under standard test conditions (25 °C); $\mu$ is the temperature coefficient, which is generally taken as −0.45%/°C to −0.5%/°C for typical polycrystalline silicon modules, and −0.45%/°C is used in this paper [9].

2.3.2. Wind Power Model

The output power of a wind turbine is closely related to the wind speed at the hub height. Since meteorological stations typically measure wind speed at a height of 10 m above the ground, a power law formula is needed to correct this value to the wind turbine’s hub height. The corrected wind speed (v_t) determines the wind turbine’s power output. The mathematical relationship between wind turbine output power and wind speed can be expressed as [19]:

$$P_{WT}(t)=\left\{\begin{array}{c}0, 0\le v_t<v_{ci},v_t>v_{co}\hfill \\ {\displaystyle \frac{v_t-v_{ci}}{v_e-v_{ci}}}{P}_e,v_{ci}\le v_t<v_e\hfill \\ P_e, v_e\le v_t\le v_{co}\hfill \end{array}\right.$$

(2)

In the formula, $P_{WT}(t)$ is the output power of the wind turbine at time t (kW); $P_e$ is the rated power of the wind turbine (kW), determined by the wind turbine model; v_t indicates the wind speed at time t, in m/s; v_ci is the cut-in wind speed (m/s), representing the minimum wind speed at which the wind turbine starts generating electricity, with a typical value of 3~4 m/s (3.5 m/s in this paper); v_co is the cut-off wind speed (m/s), representing the maximum wind speed at which the wind turbine safely shuts down, usually set to 25 m/s; v_e is the rated wind speed (m/s), representing the minimum wind speed at which the wind turbine reaches its rated power, generally taken as 12~15 m/s (14 m/s in this paper).

2.3.3. Energy Storage Battery Model

The energy storage battery employs a storage battery to perform “peak shaving and valley filling.” Given that this paper focuses on short-term optimization scheduling on a daily (24 h) scale, the effects of battery aging and capacity degradation have a relatively small impact on daily operating costs and are therefore ignored in the modeling. Its mathematical model can be expressed as follows [20]:

$$SOC(t)=SOC(t-1)(1-\sigma )+{\displaystyle \frac{P_{Ba,ch}(t){\eta }_{ch}\Delta t}{E_N}}-{\displaystyle \frac{P_{Ba,dis}(t)\Delta t}{E_N{\eta }_{dis}}}$$

(3)

In the equation, $SOC(t)$ represents the state of charge (i.e., remaining capacity) of the battery at time t, expressed as a percentage; $P_{Ba,ch}(t)$ and $P_{Ba,dis}(t)$ denote the charging and discharging power of the battery at time t, respectively, in kW; ${\eta }_{ch}$ and ${\eta }_{dis}$ denote the charging and discharging efficiency of the battery, respectively; $\sigma$ denotes the self-discharge efficiency of the battery; $E_N$ denotes the rated capacity of the battery, in kWh; and $\Delta t$ denotes the time interval.

2.4. Mathematical Model of Load-End Screw Pump

The hydraulic characteristic curves of a screw pump primarily include the volumetric efficiency curve (Curve I), power curve (Curve II), and pump efficiency curve (Curve III), as shown in Figure 3.

In Figure 3, Curve I depicts the relationship between pump discharge pressure and displacement, typically exhibiting a decreasing trend. Before the inflection point on the curve, the pump displacement remains relatively stable. Beyond the inflection point, as discharge pressure increases, cavitation may occur, leading to a gradual decrease in displacement and a decline in volumetric efficiency.

Curve II illustrates the linear relationship between pump outlet pressure and rotor torque. As outlet pressure rises, volumetric efficiency gradually decreases, potentially causing leakage in the screw pump. Under certain conditions, dry friction between the stator and rotor may transition to lubricated friction, improving mechanical efficiency. Conversely, significant fluid leakage may shift the friction type to fluid friction, further enhancing mechanical efficiency.

Curve III depicts the relationship between pump discharge pressure and pump efficiency, typically forming a parabolic shape. As discharge pressure gradually increases, leakage volume rapidly rises, causing the screw pump’s lifting capacity to first increase and then decrease, forming a point of maximum efficiency.

The optimal operating region for a screw pump is typically located near the inflection point of Curve I. In this region, the pump exhibits high efficiency and a long lifespan. At this point, the volumetric efficiency has not yet decreased significantly, while the mechanical efficiency is close to its maximum value, resulting in the highest overall efficiency. In optimized scheduling, the operating pressure of the screw pump should be kept as close as possible to the pressure value corresponding to the inflection point to maintain system operation in the high-efficiency region.

The power consumption of a screw pump is related to its displacement, head, fluid density, and pump efficiency. The displacement is directly proportional to the rotational speed; the head is inversely proportional to the square of the displacement and can be determined from the pump characteristic curve. The mathematical model of a screw pump can be expressed as follows [21]:

$$Q_V(t)={\displaystyle \frac{6}{10^5}}\times V_C{n}_t{\eta }_v$$

(4)

$$H(t)=a-b{Q}_V(t{)}^2$$

(5)

$$P_V(t)={\displaystyle \frac{Q_V(t)H(t)\rho g}{3600\eta }}$$

(6)

In the equation, $Q_V(t)$, $H(t)$, and $P_V(t)$ represent the screw pump’s displacement (m³/h), head (m), and shaft power (kW) at time t, respectively; $V_C$ denotes the pump’s displacement per revolution, mL/r; $n_t$ indicates the screw pump’s rotational speed at time t, r/min; ${\eta }_v$ signifies volumetric efficiency, %; $\rho$ denotes the relative density of the fluid, dimensionless; g represents gravitational acceleration, 9.81 m/s²; $\eta$ indicates pump efficiency, typically 70–80%; a and b are proxy model coefficients, obtainable by fitting the actual pump characteristic curve.

Based on the principle of annular leakage, incorporating fundamental production parameters of a single screw pump, the volumetric efficiency of the screw pump can be expressed as follows:

$${\eta }_v=1-K_v{\displaystyle \frac{\sqrt{p}}{\sqrt{\rho }nT}}\sqrt{{\left[1+A{\displaystyle \frac{p}{E}}({\displaystyle \frac{{\delta }_0}{D}}{)}^{-\beta }\right]}^3\cdot {\left[({\displaystyle \frac{{\delta }_0}{D}}{)}^{\beta }\right]}^3}{\displaystyle \frac{D}{e}}\sqrt{{\displaystyle \frac{T}{L}}}$$

(7)

In the formula, ${\eta }_v$ represents the volumetric efficiency of the screw pump; $K_v$ denotes the volumetric loss coefficient; P indicates the pump pressure in MPa; $\rho$ signifies the density of the fluid in kg/m³; A is a constant value determined by the thickness of the rubber layer in the bushing; E represents the elastic modulus of the bushing rubber in N/mm²; $\beta$ is a constant value determined by the elastic modulus of the rubber. e is the screw eccentricity; D is the screw cross-sectional diameter; T is the bushing lead; L is the pump immersion depth; and ${\delta }_0$ is the initial interference fit between stator and rotor.

Equation (7) describes the loss mechanism of the screw pump’s volumetric efficiency. The main influencing factors include increased pressure P, which leads to increased leakage and decreased volumetric efficiency; increased rotational speed n, which increases the liquid flow shear force, reduces leakage, and increases volumetric efficiency; increased initial interference fit ${\delta }_0$, which enhances the sealing effect, reduces leakage, and increases volumetric efficiency; increased pump immersion depth L, which increases the leakage path length, reduces leakage, and increases volumetric efficiency; and increased screw diameter D, which increases the sealing area, but also increases the leakage gap; the overall effect requires specific analysis. e, D, T, and ${\delta }_0$ are geometric structural parameters of the screw pump, obtained from pump design drawings or product manuals; K_v, A, and $\beta$ need to be determined through experimental data fitting; E is a material property constant; P, $\rho$, n, and L are operating condition parameters.

The mechanical losses in screw pumps primarily result from power dissipation due to friction between the working parts of the screws. The mechanical efficiency can be expressed as follows:

$${\eta }_m=1-{\displaystyle \frac{\Delta P_m}{P_V}}=1-{\displaystyle \frac{M_f\cdot {\omega }_q}{P_V}}$$

(8)

In the equation, $\Delta P_m$ represents the power loss due to mechanical friction between the stationary and rotating elements of the screw pump (W); $M_f$ denotes the friction torque between the stationary and rotating elements (Nm); ${\omega }_q$ is the angular velocity of the rotating element (rad/s), ${\omega }_q=2\pi n/60$, and n are the rotational speeds of the rotating element (screw), r/min. In practical engineering applications, $M_f$ is typically determined using experimental data through regression analysis to derive an empirical formula:

$$M_f=91.3\cdot {\delta }_0-n^{0.45}+46.5$$

(9)

The efficiency of a screw pump can be expressed as follows:

$$\eta ={\eta }_v\cdot {\eta }_m$$

(10)

3. Daily Dispatch Optimization Model for Screw Pumping Storage Systems in Wind/Solar/Storage Microgrids

3.1. Objective Function

The study optimizes the system’s daily operating cost, primarily considering the daily operating costs of photovoltaic units and wind turbines, energy storage battery maintenance costs, and electricity purchase costs and sales revenues from grid interaction. The system’s daily operating cost can be expressed as follows:

$$\mathit{min}{C}_{day}=\sum _{t=1}^T\begin{array}{c}{K}_{PV}{P}_{PV}(t)+K_{WT}{P}_{WT}(t)+K_{Bat}{P}_{Bat}(t)\hfill \\ +K_{buy}(t)P_{buy}(t)-K_{sell}(t)P_{sell}(t)\hfill \end{array}$$

(11)

where $C_{day}$ is the system’s daily operating cost, yuan; $P_{Bat}(t)$ denotes the output power of the energy storage battery at time t, in kW; $P_{buy}(t)$ and $P_{sell}(t)$ represent the electricity purchased from and sold to the grid at time t, respectively, in kW; $K_{PV}$, $K_{WT}$, and $K_{Bat}$ denote the operating costs of the photovoltaic and wind power units (in RMB/kW) and the maintenance cost of the energy storage battery (in RMB/kWh), respectively; $K_{buy}(t)$ and $K_{sell}(t)$ denote the electricity prices for purchasing and selling electricity from the grid at time t, respectively, in yuan/kWh. T is the scheduling cycle, set to 24 h.

The objective function described above primarily focuses on optimizing the system’s economic operation in the short term (daily scale), specifically minimizing the direct operating and maintenance costs and electricity purchase and sale costs for the day. However, since equipment health degradation and maintenance cycle changes are typically long-term, nonlinear, and complex processes, this paper does not currently quantify them as cost items in the daily optimization objective. In future research, a full life-cycle cost model or equipment health factor could be introduced to achieve a comprehensive trade-off between short-term operational efficiency and long-term equipment degradation.

3.2. Constraints

3.2.1. Source-Side Constraints

The source-side constraints in the optimization model primarily consider the upper and lower limits of output power for photovoltaic (PV) and wind power units, the upper and lower limits of grid interaction power, as well as the state of charge (SOC) constraints and upper and lower limits of charging/discharging power for energy storage batteries.

(1) Upper and lower limits of PV unit power:

$$P_{PV}^{min}\le P_{PV}(t)\le P_{PV}^{max}$$

(12)

where $P_{PV}^{min}$ and $P_{PV}^{max}$ denote the minimum and maximum output power of the PV units, respectively.

(2) Upper and lower limits on wind turbine power:

$$P_{WT}^{min}\le P_{WT}(t)\le P_{WT}^{max}$$

(13)

where $P_{WT}^{min}$ and $P_{WT}^{max}$ denote the minimum and maximum output power of the wind turbines, respectively.

(3) Upper and lower limits on grid interaction power:

$$P_{buy}^{min}\le U_{buy}(t)P_{buy}(t)\le P_{buy}^{max}$$

(14)

$$P_{sell}^{min}\le U_{sell}(t)P_{sell}(t)\le P_{sell}^{max}$$

(15)

$$U_{buy}(t)+U_{sell}(t)\le 1$$

(16)

where $P_{buy}^{min}$ and $P_{buy}^{max}$ represent the minimum and maximum values for purchasing electricity from the grid, respectively; $P_{sell}^{min}$ and $P_{sell}^{max}$ denote the minimum and maximum values for selling electricity to the grid, respectively; $U_{buy}(t)$ and $U_{sell}(t)$ are introduced as binary decision variables to clearly define the physical flow state of the system: $U_{buy}(t)$ = 1 indicates that the system is in “power purchase mode,” in which case power cannot be sold; $U_{sell}(t)$ = 1 indicates that the system is in “power selling mode,” in which case power cannot be purchased. Equation (16) ensures that the system can only be in either the power purchase or power selling state at any given time, preventing the physically impossible situation of “simultaneous power purchase and sale”.

(4) Battery State of Charge (SOC) Constraints:

When the battery is charging:

$$SOC(t)=SOC(t-1)(1-\sigma )+{\displaystyle \frac{P_{Ba,ch}(t){\eta }_{ch}\Delta t}{E_N}}$$

(17)

When the battery is discharging:

$$SOC(t)=SOC(t-1)(1-\sigma )-{\displaystyle \frac{P_{Ba,dis}(t)\Delta t}{E_N{\eta }_{dis}}}$$

(18)

Upper and lower limits for battery SOC:

$${SOC}^{min}\le SOC(t)\le {SOC}^{max}$$

(19)

where ${SOC}^{min}$ and ${SOC}^{max}$ represent the minimum and maximum values of the battery’s remaining charge (SOC), respectively.

To ensure periodicity in power system scheduling, the initial SOC at the start of a cycle is set equal to the final SOC at the end of the cycle, expressed as follows:

$$SOC(t=0)=SOC(t=T)$$

(20)

(5) Upper and lower limits for battery charging/discharging power:

$$P_{Bat,ch}^{min}\le U_{Bat,ch}(t)P_{Bat,ch}(t)\le P_{Bat,ch}^{max}$$

(21)

$$P_{Bat,dis}^{min}\le U_{Bat,dis}(t)P_{Bat,dis}(t)\le P_{Bat,dis}^{max}$$

(22)

where $P_{Bat,ch}^{min}$ and $P_{Bat,ch}^{max}$ denote the minimum and maximum values of battery charging power, respectively; $P_{Bat,dis}^{min}$ and $P_{Bat,dis}^{max}$ denote the minimum and maximum values of battery discharging power, respectively; $U_{Bat,ch}(t)$ and $U_{Bat,dis}(t)$ are binary flags representing battery charging and discharging, respectively. $U_{Bat,ch}(t)$ = 1 indicates that the battery is performing a “charging” operation, and $U_{Bat,dis}(t)$ = 1 indicates that the battery is performing a “discharging” operation. This prevents the battery from simultaneously charging and discharging, ensuring a unidirectional flow of energy.

(6) Green Power Consumption Rate Constraint: The green power consumption rate is defined as the ratio of the total wind and solar electricity consumed by the screw pump system daily to the total daily wind and solar electricity generation. It can be expressed as follows [6]:

$$R={\displaystyle \frac{{\sum }_{t=1}^T{P}_{load}(t)-{\sum }_{t=1}^T{P}_{buy}(t)}{{\sum }_{t=1}^T{P}_{PV}(t)+{\sum }_{t=1}^T{P}_{WT}(t)}}\times 100\%\ge R_{min}$$

(23)

where R is the green electricity consumption rate, $R_{min}$ is the lower bound of the green electricity consumption rate, and $P_{load}(t)$ is the electricity consumed by the oil and gas production system at the load end. In response to the national “dual carbon” policy’s requirements for the low-carbon transformation of the fossil fuel extraction industry, and referencing the local power grid’s assessment standards for distributed energy grid connection and consumption, this paper sets R_min to 60%. This threshold ensures that the microgrid system prioritizes the use of local clean energy and interacts with the power grid only when necessary.

3.2.2. Load-End Constraints

Load-end constraints primarily include screw pump speed constraints, displacement constraints, and upper/lower bounds on power consumption.

(1) Screw Pump Speed Constraint:

$$n_{pump}^{min}\le n_{pump}(t)\le n_{pump}^{max}$$

(24)

where $n_{pump}(t)$ is the screw pump speed at time t; $n_{pump}^{max}$ and $n_{pump}^{min}$ are the maximum and minimum values of the pump speed, respectively.

(2) Daily Screw Pump Displacement Constraint:

$${\sum }_{t=0}^T{Q}_V(t)\ge L_V$$

(25)

where $L_V$ is the minimum daily displacement of the screw pump.

(3) Screw Pump Efficiency Constraint:

$$\eta \ge {\eta }_{min}$$

(26)

where ${\eta }_{min}$ is the minimum volumetric efficiency of the screw pump.

(4) Upper and lower limits for screw pump power consumption:

$$P_V^{min}\le P_V(t)\le P_V^{max}$$

(27)

where $P_V^{min}$ and $P_V^{max}$ represent the minimum and maximum output power of the screw pump, respectively.

3.2.3. Source-Load Power Balance Constraint

With photovoltaic units, wind turbines, energy storage batteries, and the power grid serving as supply-side sources, their combined output power must meet the electricity demand required for screw pump drainage. The source-load power balance constraint is expressed as follows:

$$\begin{gathered} P_{PV}\left(t\right)+P_{WT}\left(t\right)+U_{buy}\left(t\right)P_{buy}\left(t\right)-U_{sell}\left(t\right)P_{sell}\left(t\right) \\ +U_{Bat,dis}{P}_{Bat,dis}(t)-U_{Bat,ch}(t)P_{Bat,ch}(t)=P_V(t) \end{gathered}$$

(28)

4. Particle Swarm Optimization Solution

4.1. Algorithm Introduction

This paper uses the Particle Swarm Optimization (PSO) algorithm to solve the established mixed-integer nonlinear optimization model. Compared to other heuristic algorithms (such as Genetic Algorithm (GA) and Differential Evolution (DE)), PSO has the following advantages: (1) It has fewer parameters and is easy to implement, making it particularly suitable for real-time scheduling problems with complex constraints; (2) It does not require complex crossover and mutation operations, resulting in high computational efficiency and fast convergence speed; (3) It has demonstrated excellent global search capabilities and robustness in solving high-dimensional, nonlinear, and multi-constrained energy system optimization problems.

Particle Swarm Optimization (PSO) is a swarm-based metaheuristic algorithm proposed by Kennedy and Eberhart in 1995. PSO comprises three primary components: particles, the social and cognitive components of particles, and particle velocity. Within the problem space, multiple feasible solutions may exist, and the optimal solution to the problem is required. A particle represents a single solution to the problem. Particle learning originates from two sources: one is from the particle’s own experience, termed cognitive learning; the other learning source is the collective learning of the entire swarm, termed social learning. Cognitive learning is represented by the personal best value ($pBes{t}_i$), while social learning is represented by the global best value ($gBest$). The $pBes{t}_i$ solution denotes the best solution achieved by a particle in its own history, and the $gBest$ value represents the best position ever reached by the swarm [16]. The $pBes{t}_i$ and $gBest$ values jointly define the particle velocity, thereby guiding particles toward better solutions. The particle velocity calculation formula and position update formula are, respectively, as follows:

$$V_i(t+1)=\omega V_i(t)+c_1{r}_1(pBes{t}_i(t)-X_i(t))+c_2{r}_2(gBest(t)-X_i(t))$$

(29)

$$X_i(t+1)=X_i(t)+V_i(t+1)$$

(30)

where $V_i$ is the particle velocity, $X_i$ is the particle position, $pBes{t}_i$ is the best position found by each particle so far, $gBest$ is the best position found by all particles in the entire swarm; $r_1$ and $r_2$ are random numbers between (0, 1); $c_1$ and $c_2$ are learning factors. $\omega$ is the dynamic inertia weight value of the particle swarm, defined as follows:

$$\omega ={\omega }_{max}-({\omega }_{max}-{\omega }_{min})\times {\displaystyle \frac{iter}{{iter}_{max}}}$$

(31)

where ${\omega }_{max}$ is the initial inertia weight value, ${\omega }_{min}$ is the weight value after reaching the maximum iteration count, ${iter}_{max}$ is the maximum iteration count, and $iter$ is the current iteration count. The dynamic inertia weight accelerates the inertial search process during the early stages of iteration while reducing its speed in the later stages. This not only enhances the optimization speed during the initial iterations and improves the algorithm’s global search capability but also facilitates higher local search precision with smaller inertia weights in the later iterations. Dynamically adjusting the inertia weight effectively balances the demands of global exploration and local search.

4.2. Algorithm Solution Process

For the research model, the specific algorithm solution process is as follows:

(1)

Data initialization. Initialize model parameters, including preset values such as the upper limit of PV output, upper and lower limits of energy storage battery charge/discharge power, daily start/stop times for each well, number of wells, and scheduling cycle. Initialize algorithm parameters, including population size, iteration count, particle dimension, inertia weight, and learning factor. The key parameter settings for PSO are shown in

Table 1. The key parameter settings for PSO.

Parameter Name	Parameter Value	Parameter Name	Parameter Value
population size	200	$c_2$	1.8
${iter}_{max}$	500	${\omega }_{max}$	1
$c_1$	1.8	${\omega }_{min}$	0.4

.

(2)

Initialize particle swarm. Randomly generate initial positions and velocities for a set of particles, ensuring each particle’s position remains within the upper and lower bounds of decision variables.

(3)

Calculate fitness. Compute the fitness value for each particle using the sum of system operating costs and penalty terms for each constraint as the fitness function output. The fitness function is defined as follows:

$$fitness=C_{day}+\phi \sum Violation$$

(32)

In the formula, Violation represents the degree of violation of all constraints (the sum of the violation amounts), and $\phi$ is the penalty factor. The penalty function method ensures that solutions violating the constraints are severely penalized, thereby guiding the population towards the feasible region.

(4)

Update individual optimal values $pBes{t}_i$. For each particle, compare its current position’s fitness value with the individual’s optimal fitness value, and update the individual’s optimal fitness value.

(5)

Update global optimal values $gBest$. Compare each particle’s optimal value with the global optimal value $gBest$ at the current iteration, and update the global optimal value.

(6)

Update particle velocity and position. Update particle velocity and position according to the particle swarm algorithm’s velocity and position update formulas. Correct particle positions exceeding the decision variable’s valid range.

(7)

Check termination conditions. Determine if the algorithm’s termination conditions are met, such as reaching the maximum iteration count or satisfying accuracy requirements. This paper adopts the maximum iteration count as the termination condition. If termination conditions are not met, return to step (3) to continue the iteration process.

(8)

Output results. Output the global optimum solution as the final optimized solution for the research model.

Combining the operations described above, the specific algorithm flowchart is shown in Figure 4.

5. Case Study

5.1. Case Parameters

This study selects a screw pump drainage system in a coalbed methane well as the scenario. The mathematical models for wind and solar power generation established in Section 2.3 are used to predict their output power, as shown in Figure 5. The installed capacity of the wind turbine is 25 kW, and that of the photovoltaic system is 40 kW. The upper limit for both purchasing and selling electricity from the high-voltage grid is 30 kW. The grid adopts a time-of-use pricing mechanism as shown in

Table 2. Storage battery parameters.

Parameter Name	Parameter Value	Parameter Name	Parameter Value
$P_{Bat,ch}^{max}$/KW	20	${\eta }_{ch}$/%	90
$P_{Bat,dis}^{max}$/KW	20	${\eta }_{dis}$/%	90
${SOC}^{max}$/%	0.9	$\sigma$/%	4.5
${SOC}^{min}$/%	0.1	$E_N$/KWh	200

, dividing the 24-h day into three periods: peak, off-peak, and normal periods, with electricity prices calculated separately for each period. During peak periods, such as daytime, electricity prices are higher due to tight supply. Conversely, off-peak periods, like nighttime, feature lower prices as demand decreases and supply becomes abundant. Parameters related to the energy storage battery and the economic cost parameters for each device are shown in

Table 3. Economic cost parameters for each unit.

Parameter Name	Parameter Value
$K_{PV}$/(yuan/KW)	0.3
$K_{WT}$/(yuan/KW)	0.2
$K_{Bat}$/(yuan/KW-h)	0.35

and

Table 4. Grid time-of-day tariffs.

Time of Use	Appointed Time	Purchased Electricity Tariff/(yuan/KW·h)	Electricity Sales Price/(yuan/KW·h)
trough hours	0:00–7:00	0.311	0.12
normal hours	7:00–9:00, 11:00–19:00	0.588	0.35
peak hours	9:00–11:00, 19:00–24:00	0.861	0.68

, respectively.

The screw pump serves as the drainage system, with its relevant parameters set as shown in

Table 5. Screw pump parameters.

Parameter Name	Parameter Value	Parameter Name	Parameter Value
$n_{pump}^{max}$/(r/min)	80	$V_C$/(mL/r)	500
$n_{pump}^{min}$/(r/min)	500	${\eta }_{min}$/%	50
$L_V$/m3	100	$\rho$	1.1

. During the initial phase of the drainage and production stage—specifically the drainage pressure reduction phase—the screw pump’s rotational speed must be increased to achieve high discharge rates. This rapidly lowers bottomhole pressure, promoting coalbed methane desorption. Accordingly, its rotational speed range is set between 80 and 500 r/min.

In the optimization scenario described herein, the scheduling cycle is 24 h, with daily schedules determined at one-hour intervals. To evaluate the performance of the optimization model for coordinating wind/solar power generation with the screw pump drainage system, the particle swarm optimization algorithm is employed for computational optimization in the example.

5.2. Case Study Results Analysis

Based on wind and solar power generation forecast data, the optimization targets were set as maximizing the green electricity consumption rate and minimizing daily operating costs. Using an optimization scheduling model and solving with a particle swarm algorithm, the optimized operational scheduling results for coalbed methane screw pumps are shown in Figure 6. Under this scheduling plan, the system’s daily operating cost is 228.1 yuan, the green electricity absorption rate reaches 86.98%, and the daily water drainage volume of the screw pump achieves 178.58 m³.

As shown in Figure 6, between 11:00 and 18:00, wind and solar power generation exceed the electricity consumption of the screw pump. During this period, the energy storage battery enters a charging state to store surplus green electricity from wind and solar sources. Due to the charging and discharging power limitations of the energy storage battery, charging cannot occur too rapidly. Excess green electricity that cannot be stored in the battery is sold to the high-voltage grid to generate revenue from electricity sales. Between 1:00 AM and 4:00 AM, and 9:00 PM and midnight, wind and solar generation cannot meet the electrical demand of the submersible screw pump. During these periods, the energy storage battery discharges to supplement the power supply. From 4:00 AM to 9:00 AM, the State of Charge (SOC) curve of the energy storage batteries (Figure 7) shows that excessive earlier discharge has depleted the remaining capacity to around 10%, the minimum level. The batteries can no longer supply power to the screw pump. Since renewable generation still fails to meet the pump’s demand, electricity must be purchased from the high-voltage grid to fulfill the pump’s power requirements. Furthermore, the period from 4:00 to 9:00 falls within off-peak and normal consumption hours, where electricity purchase costs are relatively low. Acquiring power from the grid during these times enhances the economic efficiency of system operation. In summary, throughout the system operation, the energy storage battery plays a peak shaving and valley filling role in addressing the instability and intermittency of wind and solar power generation. It smooths fluctuations in renewable energy output, ensuring system stability and reliability. This approach maximizes utilization of green electricity from wind and solar sources, prioritizing their use over grid power, thereby reducing dependence on grid purchases. This strategy lowers system operating costs and enhances the system’s capacity to absorb green electricity. As shown in the screw pump efficiency curve (Figure 8), under this scheduling plan, the screw pump’s efficiency fluctuates between 70% and 85%, ensuring it meets daily drainage requirements while maintaining high pumping efficiency.

During the stable production phase or declining production phase of coalbed methane, as water production decreases, the discharge volume must be gradually reduced to match the fluid supply capacity. At this stage, the screw pump speed is set to 50–300 r/min. Within this speed range, the system’s daily scheduling plan is illustrated in Figure 9. The corresponding changes in energy storage battery SOC and screw pump efficiency are shown in Figure 10 and Figure 11. Under this scheduling plan, the system’s daily operating cost is 194.04 yuan, the green electricity utilization rate reaches 70.72%, and the screw pump achieves a daily drainage volume of 113.64 m³.

Compared to the initial drainage and pressure reduction phase of production, during the stable production period of coalbed methane, the daily drainage volume decreased from 178.58 m³/d to 113.64 m³/d—a reduction of 57.15%—due to the reduced rotational speed of the screw pump. Its pumping efficiency remained stable between 60% and 85%. The screw pump’s power consumption also decreased, reducing the system operating cost from 228.1 to 194.04 yuan, a 17.55% reduction. Compared to the dewatering and pressure reduction phase (86.98% renewable energy utilization rate) and the stable production phase (70.72%), the utilization rate decreased significantly, mainly due to a substantial decrease in load demand. During the stable production phase, the screw pump speed decreased from a maximum of 500 r/min in the dewatering and pressure reduction phase to 300 r/min, resulting in a decrease in its total daily power consumption. Since the screw pump is the main carrier for consuming wind and solar power, the reduction in its demand directly weakens the system’s absorption capacity. Therefore, although the optimized scheduling model can adapt to the working conditions of different production stages, the renewable energy utilization rate is limited by the local load level and energy storage adjustment capacity. In the stable production phase, other utilization methods (such as hydrogen production) need to be explored to improve the utilization rate of renewable energy.

Results demonstrate that the research model effectively reflects drainage demands across coalbed methane production phases. By coordinating energy storage batteries with grid electricity purchases and sales, it meets the screw pump power requirements. Optimizing screw pump speed based on wind and solar generation conditions ensures high pump efficiency while reducing production system operating costs and enhancing green electricity consumption capacity, thereby meeting daily drainage requirements.

Due to the inherent variability of actual wind and solar power output, prediction errors can have two main impacts. Economically, if actual wind and solar power are lower than predicted, it may lead to increased electricity purchase costs (requiring temporary purchases at high prices); conversely, it may lead to reduced electricity sales revenue (curtailment of wind and solar power). In terms of operational safety, in extreme cases, an insufficient state of charge (SOC) or limited grid interaction may prevent the continuous operation of the screw pump. Therefore, in subsequent research, “robust optimization” or “rolling optimization” methods can be used, combined with ultra-short-term forecasts to update dispatch instructions.

To further verify the effectiveness of the proposed optimization strategy, it was qualitatively compared with the traditional “pure grid power supply mode” and the “non-optimized wind–solar–storage operation mode.”

In the pure grid power supply mode, although power supply stability is highest, the system completely loses the ability to absorb renewable energy, and under the peak-valley electricity price mechanism, purchasing electricity from the grid around the clock results in significantly higher operating costs than in the optimized scenario, failing to meet the grid’s peak shaving and valley filling requirements. In the non-optimized wind–solar–storage operation mode (i.e., constant speed operation of the screw pump and simple battery charging and discharging strategy), due to the lack of source-load coordinated scheduling, situations often occur where the battery is fully charged when photovoltaic power generation is high, leading to curtailment of solar power, or insufficient battery power during peak load periods requiring high-priced electricity purchases. In contrast, the optimized scheduling strategy proposed in this paper dynamically adjusts the screw pump speed to match wind and solar power output fluctuations and utilizes batteries for energy time shifting. This not only significantly reduces reliance on grid power purchases (reducing operating costs) but also effectively improves the system’s green electricity absorption rate, while ensuring that the screw pump always operates in an efficient range, achieving the best balance of economy, environmental protection, and engineering reliability.

6. Conclusions

This paper addresses the insufficient green electricity absorption capacity faced by screw pump production systems in coalbed methane wells, incorporating wind and solar power generation. It proposes an optimized dispatch model for such systems under a wind–solar–storage microgrid. The conclusions are as follows:

(1)

When establishing a day-ahead scheduling optimization model for wind and solar power generation, battery energy storage, and screw pump production systems to maximize system green electricity consumption, coordinated scheduling between energy storage batteries and grid power purchase/sale can meet screw pump electricity demands and enhance the system’s green electricity consumption capacity.

(2)

Analysis of the computational example demonstrates that batteries perform peak shaving and valley filling for wind and solar power generation, smoothing fluctuations in renewable energy output. This ensures system stability and reliability while prioritizing battery supply over grid power. Consequently, it reduces dependence on grid electricity purchases, lowers system operating costs, and enhances green electricity consumption capacity. Across different coalbed methane production phases, screw pump speed can be optimized based on wind and solar generation conditions. This ensures screw pumps operate at high efficiency while meeting daily drainage requirements.

(3)

The optimization model and solution results presented in this paper have significant guiding value for practical engineering applications. The current work uses the Particle Swarm Optimization (PSO) algorithm to solve the model, achieving satisfactory results in the case study. In future research, we will, on the one hand, refine the production constraints of coalbed methane extraction (such as bottom-hole pressure control and gas production fluctuations) to adapt to the needs of more complex extraction stages; on the other hand, we will focus on improving the computational efficiency and robustness of the algorithm, for example, by improving the parameter adaptation mechanism of PSO or introducing parallel computing, to address the computational challenges brought about by the increasing scale of future models.