Research on Optimal Operation Model of Virtual Electric Power Plant Considering Net-Zero Carbon Emission

Abstract

“World Energy Outlook 2021” has mentioned the fact that with the current pledges announced, the 2050 net-zero carbon emission target would not be realized. To further improve energy efficiency, energy integration will be important. Therefore, this paper introduced virtual power plant (VPP) and power to gas (P2G) technology to analyze the improvement of energy integration. Firstly, the structure of VPP connected with P2G is proposed, and the physical output model is constructed. Secondly, combined with carbon emission and economic operation objectives, a multi-objective operation optimization model of VPP considering electrical interconnection is constructed, and the solution idea of the model is put forward. Finally, through the case study, the contribution of P2G, DR and GST is proven. With DR, P2G involved in VPP, the goal of carbon emission reduction can be achieved. In addition, the example also proves that carbon trading has a positive effect on energy efficiency and generation uncertainty improving.

1. Introduction

The centralized development of fossil energy has brought a large number of greenhouse gas emissions, resulting in prominent global environmental contradictions. Energy transformation has gradually become the main task of energy planning in various countries. In order to construct a power system with efficiency, safety, green and low-carbon development, the large-scale and efficient utilization of renewable energy is significant. In recent years, the prospect of the renewable energy popularization is preferable, with an increasing installed capacity year by year. And the curtailment phenomenon has been alleviated to a certain extent. However, due to scale limitation and high generation costs, the development of distributed renewable energy is limited. Therefore, realization of the integrated and efficient utilization of renewable energy is also an important direction of energy development in the future.

Compared with other forms of aggregation, a virtual power plant (VPP) emphasizes the functions and effects presented outside, aggregating diversified distributed energy to meet the system power requirements [1,2]. VPP can efficiently integrate distributed renewable power sources, energy storage and demand response, and flexibly adjust the output intermittency and fluctuation to improve the stability of grid connection. Different from microgrid (MG) and integrated energy systems (IES), VPP pays more attention to the space–time complementary characteristics with distributed energy components. Through advanced measurement, communication and control technology, long-distance scheduling can be optimized, and thus the integrity of multiple distributed units remains [3].

Scholars at home and abroad have done research on the efficient integration of VPP. Literature [4] connects electric vehicles (EVs), constructing an optimal dispatching model of VPP considering the access of EVs, and analyzes the economy of system dispatching. Considering the time of use (TOU) price, Literature [5] establishes the operation optimization model of VPP with energy storage, and optimizes the capacity allocation in combination with the output of each unit. In literature [6], combined with the operation characteristics of distributed generators and energy storage, a coordinated dispatching model of VPP based on revenue maximization is constructed, analyzing the contribution of energy storage and demand response. Literature [7] aggregates EVs, controllable loads and combined generation systems as VPP, and studies the load frequency control function. Literature [8] proposed a control strategy of aggregated home temperature control considering users’ comfort constraints to maintain voltage stability and provide system rotation standby assistance. In addition, to further ensure the operation safety and stability of the VPP, a VPP consisting of energy storage system, controllable load and demand response is designed. Literature [9] establishes a model of VPP by combining wind, thermal, hydro, and energy storage together. Considering the uncertainty of the power system, literature [10] proposed an optimal dispatching model of VPP based on the combination of wind, solar, thermal power, power storage and demand response. In literature [11], focused on the thermoelectric coupling property, a thermal-electric scheduling model of VPP is proposed, which is solved by the adaptive immune genetic algorithm. Literature [12] established a double-layer inverse robust optimal scheduling model of VPP considering the uncertainty of wind power output and EVs’ grid-connection. Literature [13] considers the benefits and risks of VPP, and constructs the optimal dispatching model. In literature [14], based on the real-time balance and risks between the source, network and the load, a bi-level scheduling optimization model considering risk is proposed and solved by an artificial bee colony algorithm. By using the scene sampling method and reduction technology to deal with the uncertainty of wind and photovoltaic (PV) output, literature [15] forms a classic scene with probability information and combines the cooperative game theory to reach economic objectives and benefits allocation under multiple scenarios.

The control modes of VPP include the centralized control mode, the decentralized control mode and the fully decentralized control mode [16]. The centralized control mode is applied in literature [17], which contains micro-CHP (combined heat and power) units, wind power, PV and other renewable energy. In literature [18], combined with different control modes of VPP and considering the uncertainty of power generation and the load, a multi-objective optimal operation model under multiple scenarios is constructed. The VPP composed of renewable energy, an energy storage system, a thermal generator and a demand side is designed in literature [19]. Each unit adopts the decentralized control mode, and a daily dispatching model is established. Compared with the centralized control mode, the decentralized control mode can modularize the VPP and improve the problems of communication congestion and poor compatibility. The fully decentralized control mode improves the VPP with better expansibility and openness, and is more suitable for market trading.

The existing research has focused on the operation mode and control optimization of VPP and considered the uncertainty of renewable energy output in optimal dispatching, but the current policy development requirement is not well-combined. Therefore, combined with the current policies—China’s “carbon neutralization target” in 2060, the “power to gas” (P2G) technology is introduced in this paper. By combining P2G with VPP, an operation optimization model of VPP is constructed. Considering the operating characteristics of various components in VPP, this paper established an optimal operation model focusing on how to get a regional (among the VPP components) zero carbon emission by letting a P2G device get involved, based on consideration of economics and carbon emission. Additionally, simulations were made to compare the power volume differences with consideration of component differences. Thus, this paper provides certain reference for the future development of VPP under China’s carbon emission target.

2. Structure of Virtual Power Plant

2.1. Composition of Virtual Power Plant

VPP is the integration of power sources in a certain area, such as wind power, PV, thermal power, hydro, natural-gas and other sources, forming a unified virtual control center to dispatch energy sources [20]. Broadly speaking, by introducing the demand response, energy storage, electric vehicles, etc., and technologies like communication and control technology, the supply side and the demand side can be integrated, so as to realize the flexible linkage of source-load and the orderly access of distributed power as well.

As shown in Figure 1, the VPP is usually composed of distributed renewable energy units, distributed gas-turbine units, energy storage system (ESS), controllable loads, etc. In addition, the coordinated operation of multiple components is realized through coordination methods such as demand response (DR). Through VPP, power can be distributed again between the supply side and the demand side by transforming.

2.2. VPP Structure Considering Zero Carbon Emission of System

Based on China’s recent commitments to carbon emissions, the proportion of renewable energy in the energy structure should be greatly increased. As a typical mode of power integration, VPP is significant in power reformation. By replacing the subsidy mechanism by renewable energy quota system and relevant policies, the parity advantage of renewable energy continues to expand. In addition, “Power to Gas” (P2G) is an energy technology that can effectively reduce carbon emissions, promoting “comprehensive energy planning with zero carbon as the goal” from the power supply chain, which provides a feasible path for strengthening emissions reduction, improving energy utilization and implementing the “carbon neutralization” strategy. Therefore, connecting P2G devices in VPP can effectively control carbon emission.

By introducing P2G into VPP, the CO₂ generated by the gas turbine (GT) units can be directly transported into P2G devices for conversion, producing CH₄ and stored in a gas storage tank (GST). The CH₄ stored in the GST can be sold or directly supplied to GT by comparing the price with the external gas network. At the same time, VPP can guide P2G devices and ESS to operate/charge based on the TOU price mechanism in peak and valley periods, that is, P2G and ESS convert and store power at lower prices and release at higher-priced times to obtain price difference profits. In addition, to achieve the carbon emission reduction target to a greater extent, VPP can participate in the carbon market to obtain benefits from carbon emission utilization, which not only reduces the fuel costs, but also brings gas sales revenue. The structure of VPP with P2G devices is shown in Figure 2. Combined with P2G technology, this paper builds a multi-objective operation optimization model of VPP.

3. VPP Modeling

3.1. Component Models of VPP

3.1.1. Micro Conventional Gas Turbine

A micro conventional gas turbine (MT) has the characteristics of quick startup and shutdown times and flexible output adjusting. During the operation of VPP, MT can adjust its self-output to improve the grid connection of renewable power and can provide auxiliary services for the power market to maximize economic benefits. The output model of MT is as follows.

$$C_{MT}^f=a_{MT}+b_{MT}{g}_{MT,t}+c_{MT}{g}_{MT,t}^2$$

(1)

$$C_{MT,t}^s=\{\begin{array}{l}{u}_{MT,t}{D}_{MT,t}\\ (1-u_{MT,t})D_{MT,t}\end{array}$$

(2)

wherein, $C_{MT,t}^f$ and $C_{MT,t}^s$ represents the fuel cost of MT power generation and the start and stop cost, respectively. $g_{MT,t}$ is the output of MT. $u_{MT,t}$ is the generation state variable and is the 0–1 variable. $u_{MT,t}=1$ means the unit is operating, and $u_{MT,t}=0$ means the MT unit is shut down. $D_{MT,t}$ represents the start-up cost of the MT, which is related to the cold start and hot start status.

The operation constraints of MT include output constraints, ramping constraints and start–stop constraints, which are specifically described as follows.

$$u_{MT,t}{g}_{MT}^{\min }\le g_{MT,t}\le u_{MT,t}{g}_{MT}^{\max }$$

(3)

$$u_{MT,t}\Delta g_{MT}^{-}\le g_{MT,t}-g_{MT,t-1}\le u_{MT,t}\Delta g_{MT}^{+}$$

(4)

$$(T_{MT,t-1}^{\mathrm{on}}-M_{MT}^{\mathrm{on}})(u_{MT,t-1}-u_{MT,t})\ge 0$$

(5)

$$(T_{MT,t-1}^{\mathrm{off}}-M_{MT}^{\mathrm{off}})(u_{MT,t}-u_{MT,t-1})\ge 0$$

(6)

wherein $g_{MT}^{\min }$ and $g_{MT}^{\max }$ are the upper and lower limits of MT output. $\Delta g_{MT}^{-}$ and $\Delta g_{MT}^{+}$ are the upper and lower limits of MT ramping. $T_{MT,t-1}^{\mathrm{on}}$ is the time that the MT unit has been operating at time t. $T_{MT,t-1}^{\mathrm{off}}$ is the time that the MT unit has been off at time t. $M_{MT}^{\mathrm{on}}$ is the minimum start-up time of the MT unit.$M_{MT}^{\mathrm{off}}$ is the minimum downtime of the MT unit.

3.1.2. Wind Power Plant

Limited by the technical parameters of the wind power plant (WPP), the wind power output presents phased characteristics with the change of the wind speed [4,6,12].

$$g_{WPP,t}^{}=\{\begin{array}{l}0,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}0\le v_t<v_{in}, v_t>v_{out}\\ 0.5C_w\rho A_{WT}{v}_t{}^3,\hspace{1em} v_{in}\le v_t\le v_{\tau }\\ g_{WPP,t}^r,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{v}_{\tau }\le v_t\le v_{out}\end{array}$$

(7)

$$0\le g_{W,t}\le g_{WPP,t}^r$$

(8)

wherein $C_W$ is the performance parameters of WPP. $\rho$ is the air density. $A_{WT}$ is the projection of the blade swept area. $v_t$ is the real-time wind speed of the wind turbine at time t. $v_{in}$, $v_{\tau }$, and $v_{out}$ are the cut-in wind speed, the rated wind speed, and the cut-out wind speed. $g_{WPP,t}^r$ is the rated output of WPP. When the wind speed is lower than the cut-in wind speed or higher than the cut-out wind speed, the wind turbine will stop working. If the wind speed is between the rated speed ${\nu }_{\mathrm{rated}}$ and the cut-out speed ${\nu }_{\mathrm{out}}$, the wind turbine will output at the rated output. In other cases, the output depends on the wind speed. Considering that the wind speed varies at different heights, the wind speed at a specific height should be converted into the actual speed at the tower height.

$$f(v_t^{\prime })={\left(\frac{h}{h^{\prime }}\right)}^{\beta }{v}_t^{\prime }$$

(9)

wherein $v_t^{\prime }$ is the measured speed at height $h^{\prime }$. $f(v_t^{\prime })$ is the measured speed $v_t$ at tower height $h$. $\beta$ is the calculation coefficient.

3.1.3. Photovoltaic Unit

PV generation is based on the photovoltaic effect on the semiconductor surface, which directly converts the absorbed solar energy into electric power. Assuming that the PV unit is equipped with maximum power point tracking, the power output can be directly expressed as follows [4,6,12].

$$g_{PV,t}=\left[1-\gamma \left(T_{air}+\frac{T_n-20}{800}{\theta }_t-T_{ref}\right)\right]{\eta }_{PV}{\theta }_t{S}_{PV}{N}_{PV}$$

(10)

wherein, $\gamma$ is the temperature parameter, which represents the PV conversion efficiency of the panels. $T_{air}$ is the atmospheric ambient temperature. $T_n$ is the normal operating temperature. $T_{ref}$ is the reference temperature. ${\eta }_{PV}$ is the reference efficiency. ${\theta }_t$ is the radiation intensity at time t. $S_{PV}$ is the area of one panel. $N_{PV}$ is the number of the PV panels.

PV generation has the characteristics of randomness, intermittence and fluctuation. The output intensity is related to the solar radiation intensity. The beta distribution function is commonly used to describe the radiation intensity. The specific formula is as follows.

$$f\left(\theta \right)\{\begin{array}{l}\frac{{\theta }^{\alpha -1}{\left(1-\theta \right)}^{\beta -1}}{{\displaystyle {\int }_0^1{\theta }^{\alpha -1}{\left(1-\theta \right)}^{\beta -1}d\theta }},0\le \theta \le 1,\alpha \ge 0,\beta \ge 0\\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}, otherwise\end{array}$$

(11)

wherein $\theta$ is the solar radiation. $\alpha$ and $\beta$ are the shape parameters of beta distribution.

Based on the historical radiation intensity data, after obtaining the expected value and variance value, $\alpha$ and $\beta$ are calculated as follows.

$$\beta =\left(1-\mu \right)\times \left(\frac{\mu \times \left(1-\mu \right)}{{\sigma }^2}-1\right)$$

(12)

$$\alpha =\frac{\mu \times \beta }{1-\mu }$$

(13)

wherein, $\mu$ and $\sigma$ are the expected value and standard deviation of solar radiation intensity, respectively. The distribution function of solar radiation intensity is as follows.

$$P\left(\theta \right)={\displaystyle {\int }_{{\theta }_{\min }}^{{\theta }_{\max }}f\left(\theta \right)}d\theta$$

(14)

wherein ${\theta }_{\max }$ and ${\theta }_{\min }$ are the upper limit and lower limit of the radiation intensity, respectively.

3.1.4. P2G Device

The wind power output has the characteristics of fluctuation and uncertainty. By introducing P2G, the transformation and utilization of surplus wind power can be realized in the low load period. Combined with GST, stored gas can obtain more benefits in peak hours through power generation. With P2G, the source and user roles of power and gas can be replaced in the power system, realizing the network interconnection of power and gas, which can improve the system’s capacity to absorb renewable power, and reduce the system’s carbon emission.

P2G realizes power–gas conversion through electrolysis and methanation. Electrolysis is to generate hydrogen through water electrolyzed using excess power. Based on electrolysis, the methanation process promotes the reaction of hydrogen and carbon dioxide to generate methane and water with catalyst. The specific chemical reaction formula is as follows.

$$2{\mathrm{H}}_2\mathrm{O}\stackrel{electrolysis}{\to }2{\mathrm{H}}_2{+\mathrm{O}}_2$$

(15)

$${\mathrm{CO}}_2+4{\mathrm{H}}_2\to {\mathrm{CH}}_4+2{\mathrm{H}}_2\mathrm{O}$$

(16)

After the electric power is converted into CH₄, it can be transferred into the natural gas network or GST. The input and output of H₂O are the same in P2G process, and only CO₂ is consumed, which is conducive to carbon emission reduction. Figure 3 shows the technical principle of P2G.

Excess power in valley hours is used to electrolyze water and produce CH₄ through methanation.

$$Q_{pg,t}=P_{pg,t}{\eta }_{pg}$$

(17)

$$P_{pg,t}^{GST}=Q_{MT,t}^{GST}{\eta }_{MT}$$

(18)

wherein $Q_{pg,t}$ is the amount of gas generated by P2G. $P_{pg,t}$ is the power consumption during P2G. ${\eta }_{pg}$ is the power–gas conversion efficiency. $P_{pg,t}^{GST}$ is the power generated by using gas in GST. $Q_{MT,t}^{GST}$ is the gas consumption amount from GST. ${\eta }_{\mathrm{CGT}}$ is the gas generation efficiency of MT.

GST is used to store the natural gas synthesized by P2G and distributes the gas reasonably based on the real-time price. During peak hours, the stored gas can be used for generation or sale. The operating status of natural gas in GST is as follows.

$$S_{\mathrm{GST},t}^{}=S_{GST,T_0}^{}+{\displaystyle \sum _{t=1}^T\left(Q_{GST,t}^{pg}-Q_{MT,t}^{GST}-Q_{GN,t}^{GST}\right)}$$

(19)

wherein $S_{\mathrm{GST},t}^{}$ is the stored gas amount of GST at time $t$. $S_{GST,T_0}^{}$ is the origin state of GST. $Q_{GST,t}^{pg}$ is the gas amount after P2G reaction. $Q_{GN,t}^{GST}$ is the sold amount of GST at time $t$ with external gas network. $Q_{MT,t}^{GST}$ is the gas amount transferred to MT at time $t$. Meanwhile, GST is set not to store and release gas together.

3.1.5. Demand Response

Demand response (DR) can guide the autonomous change of load by adjusting power consumption behavior on the load side in order to provide positive impact on generation scheduling of VPP. In this paper, incentive-based demand response (IBDR) is introduced, taking the interruptible load as the response resource. The cost of DR is the VPP power sales revenue difference before and after implementing DR, which is expressed as follows.

$$R_t^L={\lambda }_t^{load}{P}_t^{load}$$

(20)

$$R_t^{IL}={\lambda }_t^{load}(P_t^{load}-P_t^{IBDR})-a{(P_t^{IBDR})}^2-b{P}_t^{IBDR}$$

(21)

wherein $R_t^L$ and $R_t^{IL}$ are the system revenue before and after implementing the interruptible load. ${\lambda }_t^{load}$ is the price of the internal system load. $P_t^{load}$ can be seen as the total load of the system. In real-time operation, the IBDR does not happen every time, so it is listed only to calculate the cost of IBDR. $P_t^{IBDR}$ is the output of the interruptible load, which is a decision variable. $a$ and $b$ are the coefficients of the quadratic term and the primary term of the compensation function. The cost of DR is shown as follows.

$$C_t^{DR}=R_t^L-R_t^{IL}=a{(P_t^{IBDR})}^2+(b+{\lambda }_t^{load})P_t^{IBDR}$$

(22)

3.1.6. Energy Storage System

In VPP, an energy storage system (ESS) can provide a better balance guarantee for the operation of distributed generation. Due to the reverse distribution of renewable energy output, excess power can be stored in ESS in valley hours, and ESS discharges the power in peak hours, which can reduce the generation pressure of conventional units and improve power curtailment as well. The operation process of the ESS is shown in Figure 4.

The operation of ESS is expressed as follows.

$$SOC(t)=SOC(t-1)+\frac{{\eta }_{chr}{P}_{chr}(t)}{E_n}\cdot \Delta t$$

(23)

$$SOC(t)=SOC(t-1)+\frac{P_{disc}(t)}{{\eta }_{disc}{E}_n}\cdot \Delta t$$

(24)

wherein $SOC(t)$ is the charging state of the ESS at time $t$. ${\eta }_{chr}$ and ${\eta }_{disc}$ represent the charging and discharging efficiency of the ESS. $P_{chr}(t)$ and $P_{disc}(t)$ represent the charge/discharge power of ESS at time $t$. $E_n$ is the rated capacity of ESS.

During operation, the ESS should meet the following technical constraints.

$$SO{C}_{\min }\le SOC(t)\le SO{C}_{\max }$$

(25)

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

(26)

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

(27)

$$0\le P_{charge,t}^{ESS}\le {\phi }_{ESS}{P}_{charge,\max }^{ESS}$$

(28)

$$0\le P_{discharge,t}^{ESS}\le {\phi }_{ESS}{P}_{discharge,\max }^{ESS}$$

(29)

wherein ${\phi }_{ESS}$ is the charge and discharge state of the ESS, which is a 0-1 variable; that is, the charge and discharge state cannot exist at the same time.

3.2. Optimal Operation Model for VPP Considering System Net-Zero Emission

(1)

Carbon emission reduction objective function

In the system operation, the VPP works as a whole. In a 24-h cycle, all CO₂ generated in the system can be transformed into CH₄, meaning a net-zero emission. In addition, combined with the carbon trading in the carbon market, the system net-zero emission goal of the VPP can be achieved easier, which can be expressed as follows.

$$CE=CP+CT$$

(30)

wherein $CE$ is the actual carbon emission of VPP, which mainly comes from the combustion of fossil fuels, that is, the MT unit in VPP. $CP$ is the carbon emissions absorbed by P2G. $CT$ is the amount of carbon trading.

$$CE=Q_{MT}^{gas}{\eta }_{gp}{\varphi }_{}$$

(31)

wherein $Q_{MT}^{gas}$ is the gas amount of MT. ${\eta }_{gp}$ is the gas–power conversion efficiency of MT. ${\varphi }_{}$ is the CO₂ emission coefficient per kWh generated by MT.

Combined with carbon trading, the transaction cost of carbon trading in the carbon market can be expressed as follows.

$$C_{trade}^c=CT\cdot p_c$$

(32)

wherein $p_c$ is the price of carbon in the market.

(2)

Economic objectives

While achieving the goal of net-zero carbon emissions, VPP tries to minimize its cost. The total cost of VPP includes the fuel cost of MT and the cost of purchased power. Fuel cost mainly refers to gas purchasing. Therefore, this paper selects minimizing the operation cost as another optimization objective. The specific objective function is as follows.

$$F_{\mathrm{cost}}=\min [{\displaystyle \sum _{t=1}^T\left(\begin{array}{l}{C}_{MT,t}+P_{EG,t}{g}_{EG,t}+C_{ESS,t}+C_{pg,t}\\ +C_{GST,t}+C_{WPP,t}+C_{PV,t}+C_t^{DR}\end{array}\right)}+C_{trade}^c]$$

(33)

wherein $F_{\mathrm{cost}}$ is the total operation cost of VPP. $P_{EG,t}$ and $g_{EG,t}$ are the power purchase amount and power purchase price at time t of VPP. $C_{MT,t}$ is the generation cost of MT at time t, including the fuel cost and the startup–shutdown costs. $C_{pg,t}$ is the operation cost of P2G at time t. $C_{GST,t}$ is the operation cost of the GST at time t. $C_{WPP,t}$ and $C_{PV,t}$ are the generation cost of WPP and PV at time t. The cost of P2G mainly concludes the power cost of the operation and the operation cost for power converting. Considering the power driving the P2G device mainly comes from the excess wind power at nighttime, which is calculated in WPP operation cost, the power cost for P2G only means the cost of CO₂.

$$C_{pg,t}^{}={\beta }_{pg}{\phi }_{C{O}_2}^{}{Q}_{pg,t}^{}$$

(34)

wherein ${\beta }_{pg}$ is the converting coefficient of CO₂ per unit natural gas. ${\phi }_{C{O}_2}^{}$ is the cost price coefficient of CO₂ conversion.

3.3. Constraint Condition

(1)

Power supply and demand balance constraints

$$\begin{array}{l}{g}_{MT,t}+g_{WPP,t}+g_{PV,t}+\left(P_{disc}(t)-P_{chr}(t)\right)+\Delta L_{DR,t}+g_{EG,t}\\ =L_t+\Delta L_{pg,t}\end{array}$$

(35)

wherein $g_{MT,t}$, $g_{PV,t}$ and $g_{WPP,t}$ are the output of MT, WPP and PV at time t. $\Delta L_{DR,t}$ represents the output of DR at time t. $g_{EG,t}$ is the power purchase amount of VPP at time t. $L_t$ represents the load demand at time t. $\Delta L_{pg,t}$ represents the load demand of P2G at time t.

(2)

P2G operation constraints

$$0\le Q_{pg,t}\le Q_{pg}^{\mathrm{R}}$$

(36)

$$Q_{GST,t}^{pg,\min }\le Q_{MT,t}^{GST}\le Q_{GST,t}^{pg\max }$$

(37)

$$Q_{pg,t}^{\min }\le Q_{GST,t}^{pg}+Q_{GN,t}^{pg}\le Q_{pg,t}^{\max }$$

(38)

$$Q_{GST,t}^{\min }\le Q_{GST,t}^{pg}+Q_{MT,t}^{pg}\le Q_{GST,t}^{\max }$$

(39)

$$S_{GST}^{\min }\le S_{\mathrm{GST},t}^{}\le S_{GST}^{\max }$$

(40)

wherein $Q_{pg}^{\mathrm{R}}$ is the rated gas output of P2G. $Q_{pg,t}$ is the actual gas output of P2G at time t. $Q_{MT,t}^{GST}$ is the gas input to MT from GST at time t. $Q_{GST,t}^{pg,\min }$ and $Q_{GST,t}^{pg,\max }$ represent the minimum and maximum output of GST at time t. $Q_{pg,t}^{\min }$ and $Q_{pg,t}^{\max }$ are the minimum and maximum output of P2G. $S_{GST}^{\min }$ and $S_{GST}^{\max }$ represent the upper and lower limits of GST. $Q_{GST,t}^{\min }$ and $Q_{GST,t}^{\max }$ are the minimum and maximum power of the GST charging/discharging at time t.

(3)

MT operation constraints

MT operation constraints include generation constraints, ramping constraints, and startup–shutdown constraints. The constraints are listed as Equations (3)–(6)

(4)

ESS operation constraints

The operation constraints of ESS include the constraints of charging/discharging and the battery capacity, as follows.

$$g_{ESS,t}^{\min }\le g_{ESS,t}\le g_{ESS,t}^{\max }$$

(41)

$$S_{ESS,t}^{\min }\le S_{ESS,t}\le S_{ESS,t}^{\max }$$

(42)

$$S_{ESS,t+1}^{}=S_{ESS,t}^{}+\left[g_{ESS,t}^{chr}\left(1-{\eta }_{ESS,t}^{\mathrm{chr}}\right)-g_{ESS,t}^{\mathrm{dis}}/\left(1-{\eta }_{ESS,t}^{\mathrm{dis}}\right)\right]$$

(43)

wherein $g_{ESS,t}^{\max }$ and $g_{ESS,t}^{\min }$ are the maximum charging/discharging of ESS at time t. $S_{ESS,t}^{\max }$ and $S_{ESS,t}^{\min }$ are the minimum charging capacity of ESS at time t. $S_{ESS,t+1}^{}$ is the power storage capacity of ESS at time $t+1$. ${\eta }_{ESS,t}^{\mathrm{chr}}$ and ${\eta }_{ESS,t}^{\mathrm{dis}}$ are the charging and discharging power of ESS at time t.

(5)

DR constraints

DR could effectively translate load translation. To avoid the peak-valley inversion, the demand curves of different loads need to be smoothed as possible.

$$\left|\Delta L_{DR,t}\right|\le u_{DR,t}\Delta L_{DR,t}^{\max }$$

(44)

$$u_{DR,t}\Delta L_{DR}^{Low}\le \Delta L_{DR,t}-\Delta L_{DR,t-1}\le u_{DR,t}\Delta L_{DR}^{Up}$$

(45)

$${\displaystyle \sum _{t=1}^T\Delta L_{DR,t}\le \Delta L_{DR}^{\max }}$$

(46)

wherein $\Delta L_{DR,t}^{\max }$ is the maximum variation of the load in period $t$. $\Delta L_{DR}^{Low}$ and $\Delta L_{DR}^{Up}$ are the upper limit and the lower limit of the load variation. $u_{DR,t}$ represents the state of DR.

(6)

Spinning reserve constraint

$$\begin{array}{l}{G}_{VPP,t}^{\max }-G_{VPP,t}^{}+\min \left\{\left(G_{ESS,t}^{\mathrm{dis},\max }-G_{ESS,t}^{\mathrm{dis}}\right),\left(S_{ESS,t}-S_{ESS,t}^{\min }\right)\right\}\ge \\ s_L\cdot L_t+s_{WPP}\cdot G_{WPP,t}+s_{PV}\cdot G_{PV,t}\end{array}$$

(47)

$$\begin{array}{l}{G}_{VPP,t}^{}-G_{VPP,t}^{\min }+\max \left\{\left(G_{ESS,t}^{\mathrm{chr},\max }-G_{ESS,t}^{\mathrm{chr}}\right),\left(S_{ESS,t}^{\max }-S_{ESS,t}\right)\right\}\ge \\ s_{WPP}\cdot G_{WPP,t}+s_{PV}\cdot G_{PV,t}\end{array}$$

(48)

wherein $G_{VPP,t}$ is the total output of VPP at time $t$. $G_{VPP,t}^{\max }$ and $G_{VPP,t}^{\min }$ are the upper and lower limits of the VPP output at time $t$. $G_{ESS,t}^{\mathrm{dis},\max }$ and $G_{ESS,t}^{\mathrm{chr},\max }$ are the maximum discharging and charging power of ESS at time $t$. $s_L$, $s_{WPP}$ and $s_{PV}$ are the standby rate of the load, WPP and PV, respectively.

4. Case Study

4.1. Linearization Processing

The operation model constructed in this paper contains nonlinear objective functions and constraints, and the decision variables include continuous variables and 0–1 variables, which belong to mixed integer nonlinear programming (MINLP). The power generation and wind speed of WPP are power functions, and the operating cost of MT is a quadratic equation. Based on the solving complexity and large calculation, the objective function and nonlinear factors are linearized before solving the model.

(1)

Processing methods of power function

Taking the logarithm of WPP operation model, the following equations can be obtained.

$$\ln g_{WPP,t}=\ln C_w\rho A_{WT}+3\ln v_t-0.69(v_{in}\le v_t\le v_{\tau })$$

(49)

$$y_t^{*}=3x_t^{*}+\ln C_w\rho A_{WT}-0.69$$

(50)

(2)

Processing method of the quadratic function

The operating cost of MT is a quadratic function, which can be divided into n segments and expressed as a piecewise function $F\left(g_{MT}\right)$.

For $g_{MT}\in \left[g_{MT}^{\min }+n\Delta ,g_{MT}^{\min }+\left(n+1\right)\Delta \right]$, there is $n=0,1,\dots ,N-1$. $\Delta$ is the length of each segment of the piecewise function, $\Delta =\left(g_{MT}^{\max }-g_{MT}^{\min }\right)/N$, as shown in Figure 5.

$$F\left(g_{MT}\right)=f\left(g_{MT}^{\min }+n\Delta \right)+\left(g_{MT}-g_{MT}^{\min }-n\Delta \right)\ast \left[b+\left(2n+1\right)c\Delta +2c{g}_{MT}^{\min }\right]$$

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Similarly, the IBDR cost function is the same as above.

After linearization, the objective function and constraints are transformed into a mixed integer programming (MIP) problem which is solved quickly with the help of software GAMS.

4.2. Basic Data

Taking the several specific generators in Northwest China as the research simulation object, 3 WPP with the capacity of 2 MW, 2 PV units with the capacity of 2 MW and one MT with the capacity of 4 MW, and an ESS of the capacity of 2 MW are selected to form a VPP for case study. The up–down ramping speed of the MT is 0.3 mw/h and 0.5 mw/h, respectively. The start-up and shutdown times are 0.1 h and 0.2 h, respectively, and the start-up and shutdown costs are 0.102 ¥/kWh. The cost curve is linearized in two sections according to literature [21], and the slope coefficients of the two sections are 110 ¥/MW and 362 ¥/MW, respectively. The loss efficiency of power generation is 0.052. The charge/discharge efficiency of the ESS is 0.95, and the initial stock of the system is 0.6 MWh. All parameters are shown in

Table 1. Unit’s generation parameters settings.

Generators	Maximum Output (MW)	Minimum Output (MW)	Ramping Speed (MW/h)	Unit Parameters
				a	b	c
MT	4	0.8	0.3/0.5	0	0.575	0.0137
WPP	2	0	1.6	0	0	0
PV	2	0	1.5	0	0	0

.

The VPP adopts the time of use (TOU) price mechanism. The peak hours are 9:00–15:00 and 18:00–21:00. Valley hours are 23:00–7:00 (the next day). The positive output price of the interruptible load is 0.55 ¥/kWh, and the negative output price is 0.25 ¥/kWh. The rated power of P2G is 0.4 MW. The energy conversion efficiency is 0.64, and the conversion cost is taken as reference [22], ${\beta }_{pg}=0.2t/\left(\mathrm{MWh}\right)$ $C_{C{O}_2}^{}=60 \yen /\mathrm{t}$. The unit carbon trading capacity is 545 m³, and the conversion price is 12.5 yuan/MWh. The rated gas storage capacity of GST is 400 m³, the upper limit of intake is 200 kcf/h. The initial gas volume in GST is 50 m³. The purchase price of natural gas is 2.5 ¥/m³ and the sale price is 2.4 ¥/m³. The line transmission constraints of the system are referenced to Literature [22]. The calorific value of natural gas is 39 MJ/m³, and the value of $\varphi$ is 0.3379. The price of the gas turbine is 243 ¥/MWh, and the prices of WPP and PV are 178 ¥/MWh and 256 ¥/MWh, respectively. The participation of various units is shown in

Table 2. Units’ generation parameters settings.

Units	Cost Price	Material Price	Conversion Efficiency	Initial Capacity
MT	243 ¥/MWh	2.5 ¥/m3
WPP	178 ¥/MWh
PV	256 ¥/MWh
P2G	-	TOU price	0.64
GST		P2G output price	0.99	50 m3
ESS	-	TOU price	0.95	0.6 MWh

.

To reflect the optimal VPP operation under complex source–load conditions, the typical daily data in summer in northern China are selected, and the time interval of data collection is 1 h. To obtain the available output, the parameters of WPP and PV are set as $v_{in}=3\hspace{0.17em}\mathrm{m}/s$, $v_{rated}=14\hspace{0.17em}\mathrm{m}/s$ and $v_{out}=25 \mathrm{m}/s$ [23], and the solar intensity parameters $\alpha$ and $\beta$ are set as 0.39 and 8.54 [24]. Combined with the set parameters, 50 groups of output scenarios are simulated. Then 10 groups of typical scenarios are obtained by the method in literature [25]. Finally, the average value is used as the output data. The output curve and system load of WPP and PV under typical days are shown in Figure 6.

4.3. Scenarios Analysis

4.3.1. Scenario Setting

Combined with the proposed VPP operation optimization model, the operation cost and output of each component is calculated under the net-zero carbon emission and economic objectives. Affected by TOU price, the VPP can purchase power during valley hours with lower power price to store or drive P2G, and release power in peak hours. The generated CO₂ can be absorbed by P2G producing CH₄, and VPP conducts carbon trading in the carbon market to ensure net-zero carbon emission. Combined with the carbon emission reduction model constructed in this paper, the optimal operation of VPP considers the adjustment of interruptible load and the excessive action of GST between P2G and MT. Therefore, different scenarios are designed to analyze the internal operation arrangement, as shown in

Table 3. Scenarios setting.

Scenarios	P2G	Interruptible Loads	GST
Scenario 1 (Basic Scenario)	√	×	×
Scenario 2 (GST Scenario)	√	×	√
Scenario 3 (Comprehensive scenario)	√	√	√

.

4.3.2. Result Analysis

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Result analysis of Scenario 1

In Scenario 1, without considering the participation of IBDR and GST, the power adjustment of VPP mainly depends on ESS and P2G, and the natural gas generated by P2G is supplied to MT or sold in a natural gas network. The output of VPP is shown in Figure 7.

It can be seen from Figure 3 and Figure 4 that the VPP purchased power from 3:00 to 10:00 to meet the load, storage and supplying to P2G. This is because the power price is relatively low, even lower than the generation cost of partial units. During the peak hours, VPP purchases less power, and the insufficient power is met through MT and ESS. However, after dealing with the excess power, there still is a carbon gap after absorbing the CO₂ generated by the system’s own operation, so the system purchases carbon in the carbon market, with a total of 5.175 tons of CO₂. At this time, the total operation cost of the system is 217, 276.79 ¥. A total of 278.1825 m³ of natural gas is produced through P2G device, some of which is transferred to MT for generation, and some of which is sold in the gas network, resulting in a gas sales revenue of 139.236 ¥. P2G operation and gas production flow are shown in Figure 8.

It can be seen from Figure 8 that the main operation time of P2G is valley hours and normal period, and most of the gas generated is directly supplied to MT. Since there is no GST, the rest of the produced gas is sold to the natural gas network, as shown in Figure 8b. On the whole, most of the natural gas generated by P2G flows into MT for “gas–power–gas” recycling. The “net-zero carbon emission” within the VPP is effectively realized.

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Result analysis of Scenario 2

In Scenario 2, GST is introduced into VPP, and the natural gas generated by P2G can be stored or supplied to MT. Figure 9 shows the optimal operation plan of the VPP with GST.

In Figure 9, from 3:00–10:00, ESS stores power and P2G converts power to gas by purchasing relatively low-cost power. During peak hours, no additional power purchase behavior happens, and the insufficient power is supplemented by ESS. However, to provide more natural gas, the system has conducted corresponding carbon purchase in the carbon market, with a total purchase of 5.263 tons of CO₂. The total operation cost of the system is 226 572.61 ¥. In the optimal operation plan of Scenario 2, a total of 310.893 m³ natural gas is generated by P2G, which is partly stored in GST, and the remainder is transferred to MT for power generation. The natural gas in GST can be supplied to MT unit for power generation at the next time, and can also be sold in the natural gas network. The operation of P2G and the change of natural gas in GST are shown in Figure 10.

From Figure 10, the gas generated by P2G is mainly supplied to MT, and the rest is stored in GST. For the GST, as shown in Figure 10b, the positive change of GST represents the input of natural gas, that is, the natural gas generated by P2G, and the negative change of GST represents the output of natural gas, that is, it flows to MT or selling to the natural gas network. Since the selling price of natural gas is lower than the market price, VPP will give priority to transferring into MT. Compared with Scenario 1, due to the access of GST, the operation efficiency of P2G is improved, resulting in more natural gas production but also bringing more operation costs and carbon purchase costs.

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Result analysis of Scenario 3

Based on Scenario 2, in Scenario 3, interruptible load (IL) is introduced, and the output of each unit can be further optimized. The “peak-shaving and valley-filling” in the system is jointly borne by ESS, P2G and the interruptible load. The VPP adjusts the cost with different controllable loads. Figure 4, Figure 5, Figure 6 and Figure 7 show the optimal operation plan of VPP considering GST and IBDR under the carbon emission reduction target.

In Figure 11, from 3:00 to 10:00, the VPP still carries out power storage and P2G by purchasing relatively low-cost power and interruptible load. To absorb excess power, P2G consumes 5.047 tons of extra CO₂ from the carbon market. Due to the participation of interruptible load, the regulating pressure of P2G and ESS reduces, and the total cost of the system decreases slightly as well. At this time, the total operation cost of VPP is about 221, 363.46 ¥.

In Scenario 3, P2G generates 258.912 m³ of natural gas. Part of the gas volume is stored in GST and the remainder is transferred to MT for generation. P2G operation and gas volume change in GST are shown in Figure 12.

Compared with the operation results in Scenario 1 and Scenario 2, the total cost in Scenario 3 is slightly higher than that of Scenario 1, but lower than that of Scenario 2. The introduction of IBDR can improve the operation efficiency and reduce the operation cost of the VPP system. The access of GST can provide additional options for the real-time P2G gas production, increasing operation flexibility, indirectly reducing the raw material cost of MT, and thus, improving the overall energy efficiency of the system.

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Impact of carbon trading price on VPP operation

During VPP operation, the “gas–power–gas” utilization cycle is realized, and it is necessary to participate in the carbon trading market to obtain relevant raw materials. The carbon trading price is directly related to the operation cost of VPP. Therefore, sensitivity analysis is carried out to calculate the operation cost of VPP under different carbon trading prices.

According to

Table 4. Analysis of the impact of carbon trading price on VPP operation.

Carbon Trading Price	Cost/¥
45	231,412.19
50	232,129.54
55	232,657.19
60	233,163.46
65	233,762.43
70	234,091.27
75	234,694.33

, when the carbon trading price is lower than 60 ¥/t, the operation cost of VPP decreases. This is because the reduction of carbon trading cost improves the utilization efficiency of P2G and more natural gas is produced; that is, MT output increases, but the corresponding WPP and PV output decreases. When the carbon trading price is higher than 65 ¥/t, the increase of carbon trading cost correspondingly drives the gas production cost. MT output depends more on the gas purchase from the natural gas network, which increases the corresponding material cost. It also brings opportunities for WPP and PV output and uncertain risk cost. At the same time, VPP only uses P2G to offset the CO₂ generated by MT operation, which greatly reduces the ability of the system to stabilize the uncertainty of renewable energy output, and increases the operation burden of ESS. The increase of the total cost is mainly reflected in the operation and maintenance cost of the ESS. The appropriate carbon price will promote VPP to increase the scheduling of P2G and the utilization efficiency of controllable load, to improve the operation stability of the system.

5. Conclusions

VPP with P2G gas can realize flexible electrical conversion, which will promote the optimal utilization of distributed energy. Based on this, this paper combines the policy orientation of “carbon emission reduction”, based on the P2G operation, enhances the neutralization effect of VPP on carbon emission, and constructs the operation optimization model based on the objective of net-zero carbon emission. By constructing a multi-objective operation optimization model of VPP considering electrical interconnection, the participation of P2G and carbon trading, the operation efficiency of VPP has been proved improved, and the carbon emission reduction goal can be achieved. In addition, the case study also proves that appropriate carbon trading can reduce the output of distributed power generation by encouraging introducing P2G, improving the utilization of the controllable load and reducing the uncertainty of VPP operation.

Besides, the zero carbon emission of this paper only stands for small regional simulation results in power dimension. The simulation of this paper is only based on the introduction of P2G devices and storage components like ESS and GST. To reach the goal of “Carbon Neutralization”, larger-scale and more components, like green hydrogen energy, carbon capture, utilization and storage (CCUS) should be taken into future research. The uncertainty of the renewable power considered in this paper has not been well overcome, and some forecasting work will be made in future studies.