Optimization Scheduling of Virtual Power Plants Considering Source-Load Coordinated Operation and Wind–Solar Uncertainty

Abstract

A combined approach of Latin hypercube sampling and K-means clustering is proposed in this study to address the uncertainty issue in wind and solar power output. Furthermore, the loads are categorized into three levels: primary load, secondary load, and tertiary load, each with distinct characteristics in terms of demand. Additionally, a load demand response characteristic model is developed by incorporating the dissatisfaction coefficient of electric and thermal loads, which is then integrated into the system’s operational costs. Moreover, an electricity–hydrogen–thermal power system is introduced, and a source-load coordination response mechanism is proposed based on the different levels of demand response characteristics. This mechanism enhances the interaction capability between the power sources and loads, thereby further improving the economic performance of the virtual power plant. Furthermore, the operation economy of the virtual power plant is enhanced by considering the participation of renewable energy sources in carbon capture devices and employing a tiered carbon-trading mechanism. Finally, the CPLEX algorithm is employed to solve the optimization model of the virtual power plant, thereby validating the effectiveness of the proposed models and algorithms.

1. Introduction

With the escalating energy crisis and environmental pollution concerns, the issue of fossil fuel development and utilization has garnered significant attention on the international stage, demanding urgent energy conservation and emissions reduction measures [1,2]. The rapid development of renewable energy generation technologies, represented by wind and solar power, offers new possibilities for addressing these challenges [3]. Additionally, virtual power plants (VPPs) have gained widespread application as an effective means of harnessing renewable energy sources.

However, the stochastic and volatile nature of renewable energy generation poses obstacles to its efficient utilization, necessitating the resolution of uncertainties associated with wind and solar power. For instance, a novel distributed economic model predictive control strategy is proposed in reference [4] to address the uncertainty associated with the integration of electric vehicles. To mitigate the vulnerability of load frequency control to false data injection attacks, the intrusion detection unit is integrated with the distributed economic model predictive control in the study. Furthermore, reference [5] focuses on enhancing the penetration level of renewable energy generation by integrating wind turbines into conventional load frequency control. In the context of potential false data injection attacks, an elastic model predictive control framework is constructed to reduce the generation cost of power units. Reference [6] describes wind and solar power uncertainty using interval-based uncertainty sets based on robust theory, with the lower limit of power deviation serving as the basis. Reference [7] utilizes polyhedral uncertainty sets to handle source-load uncertainty and solves a two-stage robust model using column-and-constraint generation algorithms. However, these methods rely heavily on historical wind–solar load data and prioritize system robustness, often resulting in reduced economic efficiency. References [8,9] adopt an approach combining chance constraints with sequential operations to address the uncertainty in wind and solar output, ensuring system stability through the provision of additional reserve power. However, this approach requires VPP generation units to provide a significant amount of extra reserve power, which adversely affects the economic performance of the VPP. Moreover, this method employs probability density functions to describe wind and solar uncertainty, and the accuracy of the parameters in these functions directly impacts the results. To improve upon these limitations, reference [10] employs Monte Carlo simulation methods to randomly generate wind and solar output scenarios. However, this approach suffers from drawbacks such as excessive data generation and long computational times. To address these issues, this study proposes the use of Latin hypercube sampling to generate randomized wind and solar output data, combined with an improved K-means clustering method to reduce the number of scenarios while maintaining their validity.

As a controllable resource, load demand response characteristics play a crucial role in the optimization process of VPPs [11], enhancing system operational efficiency and deferring equipment investment costs. Reference [12] constructs an energy system planning model considering load demand response, utilizing the load peak-to-valley ratio as an evaluation criterion. The analysis demonstrates that load demand response characteristics can reduce peak-to-valley differences while postponing system planning and configuration costs. Reference [13] proposes an optimization scheduling model for a thermal–electric interconnected VPP, focusing on incentive-based electric–thermal load demand response characteristics and maximizing VPP operational profits. The results indicate that the proposed demand response model can smooth the load curve and improve the economic performance of the VPP. While the aforementioned studies consider load demand response to improve energy system operation, it has been shown that the proportion of loads capable of participating in demand response is relatively small, limiting the overall system adjustment capability [9]. To address this, reference [14] introduces a dual-response model that coordinates waste-heat power generation units with demand response characteristics, further enhancing energy system operational efficiency and economic performance. However, the improvement in source-load response capability leads to increased output from gas turbines, which hinders the low-carbon operation of the system. To overcome this issue, an electric–hydrothermal system is proposed, integrating electric–thermal load demand response and establishing a source-load coordination model to enhance the economic and low-carbon performance of the VPP.

To address the aforementioned issues, this study first proposes a combined approach of Latin hypercube sampling and an improved K-means clustering method to handle the uncertainty of wind and solar power generation. Additionally, the load is divided into different levels based on their importance, each with distinct demand response characteristics. By incorporating the coefficient of unsatisfactory electric and thermal loads, a load demand response characteristic model is constructed and included in the system operating cost. Furthermore, an electric–hydrothermal system is introduced, and a source-load coordinated response mechanism is proposed based on the different demand response characteristics of the load levels. Moreover, considering the participation of wind and solar power in carbon capture and the use of a tiered carbon-trading mechanism, this paper aims to reduce system carbon emissions while improving the economic performance of VPP operation. Finally, the optimization model of the VPP is solved using the CPLEX algorithm to validate the effectiveness of the proposed model and algorithm.

2. Wind and Solar Scenario Generation and Reduction

2.1. Wind and Solar Scenario Generation Based on Latin Hypercube Sampling (LHS)

To address the impact of uncertainty in wind and solar power generation on the operation of virtual power plants, this study employs a scenario-based simulation approach to generate wind and solar output scenarios along with their corresponding probabilities. Latin hypercube sampling (LHS) is used, which is essentially a stratified sampling technique. LHS avoids the issue of clustering in the sampled scenario set, thereby saving sampling time. This method involves stratifying the probability density function and performing random sampling within each stratum, where the sampled values represent the values of that stratum. The original probability density function is then reconstructed. The specific steps of LHS can be divided into sampling and sorting [15], as follows:

(1) Sampling

Assuming that $Y_k$ is one of the k randomly generated variables, $X_1$, $X_2$,…, $X_x$, the cumulative probability distribution function can be described as follows:

$$Y_k=F_k\left(X_k\right)$$

(1)

In Equation (1), the LHS capacity is set to N, and LHS is employed to divide the intervals of the probability density function into N equal parts. Among them, by substituting the value corresponding to the mth interval into the inverse function of the probability density function, the sample value for the mth interval can be obtained.

$$x_{km}=F_k^{-1}\left(\frac{m-0.5}{N}\right)$$

(2)

Additionally, employing the same method allows for obtaining sample values from the remaining N − 1 intervals in a sequential manner, ultimately forming a sample matrix.

(2) Sorting

A sequence matrix L, consisting of K × N elements, is selected to represent the order of the original matrix X. The final position of each row in the sample matrix X is determined by referencing the corresponding number in L. This is represented in conjunction with a K × K correlation coefficient matrix p. The degree of correlation can be expressed as follows:

$${\rho }_{rms}^2=\frac{{\displaystyle {\sum }_{j=2}^K{\displaystyle {\sum }_{k=2}^{k-1}{\rho }_{kj}^2}}}{\frac{\left(N-1\right)N}{2}}$$

(3)

The sample matrix can be described as follows:

$$x_{kn}=F_k^{-1}\left(\frac{l_{kn}-0.5}{N}\right)$$

(4)

The conventional LHS method does not account for the temporal aspect of wind and solar power output. To address this limitation, we propose an enhanced approach by constructing a sample matrix that considers the temporal sequence of wind and solar generation. This enables multi-period simulation and analysis of the wind and solar generation profiles. The sample matrix that incorporates the time series aspect can be described as follows:

$$x_{k_{i}n}=F_{k_i}^{-1}\left(\frac{l{k}_{i}n-0.5}{N}\right)$$

(5)

In Equation (5), $k_i$ represents the sample matrix for the ith time period, taking into account the temporal sequence.

2.2. Wind and Solar Scenario Reduction

The use of the LHS method results in a large number of wind and solar output scenarios, which can lead to computational challenges such as excessive solution space and prolonged computation time when used for optimization purposes. To address this issue, this paper proposes an improved K-means clustering-based scenario reduction method that reduces the number of scenarios while ensuring their effectiveness. The improved K-means clustering approach achieves scenario reduction by eliminating scenarios with close distances and small probabilities based on the computed distances between initial scenarios and their respective probabilities.

The methodology of the improved K-means clustering-based scenario reduction [16,17] is as follows: Initially, the data point with the highest density is selected as the first initial cluster center, denoted as. Subsequently, the data point with a relatively distant distance and high density from the first cluster center is chosen as the second cluster center, denoted as. This process continues iteratively to determine all initial cluster centers. The remaining data points are partitioned using the moment distance and spatial distance formulas to obtain the initial cluster scenarios.

Assuming the desired number of reduced scenarios is M, the N initial scenarios generated are subject to reduction. Let P denote the original scenario set, where each scenario has an equal probability, denoted as $p_i=1/N$. Let $P^{opt}$ represent the set of reserved scenarios, and $S^{opt}$ denote the number of scenarios in $P^{opt}$. The steps of the improved K-means clustering-based scenario reduction are as follows:

(1) The scenario is defined as a sequence, and the sequence of the Sth scenario is denoted as:

$$w_s=\left(w_{s,1},w_{s,2},\cdot \cdot \cdot ,w_{s,r},w_{s,R}\right)$$

(6)

(2) The improved K-means clustering-based scenario reduction approach gradually selects M scenarios ${\lambda }_l{{}_{,}}_{1,\mathrm{\dots },T,p_i,M}$ from P and adds them to the set of reserved scenarios $P^{opt}$. The probability array of the reserved scenario set is denoted as $P_{\gamma }=p_i$, and the remaining scenarios are denoted as $P^R=P-P^{opt}$.

(3) The moment distance (the maximum value of the squared difference between the qth central moments of the original and retained scenes) $f_m$ and spatial distance (the difference between the minimum value of the difference between the probability values of the original scene sequence and the difference between the original scene sequence and the retained scene sequence) $f_s$ between each cluster and their respective cluster centers $P^{opt}$ are computed separately. The formulas for calculating $f_m$ and $f_s$ are given by Equations (7) and (8) as follows:

$$f_m=\max \left\{{\left(\frac{1}{T}{\displaystyle \sum _{t=1}^T\left(M_{q,t}\right)-\frac{1}{T}{\displaystyle \sum _{t=1}^T\left(\stackrel{-}{M_{q,t}}\right)}}\right)}^2\right\}$$

(7)

$$f_s=\frac{1}{T}{\displaystyle \sum _{{\lambda }_l{{}_{,}}_{1,\mathrm{\dots },T}\in \left\{P-P^{opt}\right\}}{p}_l}-\underset{{\stackrel{-}{\lambda }}_m{{}_{,}}_{1,\mathrm{\dots },T,M}\in P^{opt}}{\min }\left|{\lambda }_l{{}_{,}}_{1,\mathrm{\dots },T}-{\stackrel{-}{\lambda }}_m{{}_{,}}_{1,\mathrm{\dots },T,M}\right|$$

(8)

$$M_{q,t}={\displaystyle \sum _{s=1}^S{p}_s}{\left({\lambda }_{s,t}-{\displaystyle \sum _{s=1}^S{p}_s{\lambda }_{s,t}}\right)}^2$$

(9)

$${\stackrel{-}{M}}_{q,t}={\displaystyle \sum _{\stackrel{-}{s}=1}^{\stackrel{-}{S}}{\stackrel{-}{p}}_s}{\left({\stackrel{-}{\lambda }}_{s,t}-{\displaystyle \sum _{\stackrel{-}{s}=1}^{\stackrel{-}{S}}{\stackrel{-}{p}}_s{\stackrel{-}{\lambda }}_{s,t}}\right)}^2$$

(10)

$${\displaystyle \sum _{s=1}^S{p}_s}=1$$

(11)

$${\displaystyle \sum _{\stackrel{-}{s}=1}^{\stackrel{-}{S}}{\stackrel{-}{p}}_s}=1$$

(12)

Among them, ${\lambda }_s{{}_{,}}_{1,\mathrm{\dots },T}$ represents the time-series scenarios in the original scenario set P, ${\stackrel{-}{\lambda }}_s{{}_{,}}_{1,\mathrm{\dots },T,M}$ represents the time-series scenarios in the set of reserved scenarios $P^{opt}$, and $p_s$ and ${\stackrel{-}{p}}_s$ denote the probabilities corresponding to scenario ${\lambda }_s{{}_{,}}_{1,\mathrm{\dots },T}$ and ${\stackrel{-}{\lambda }}_s{{}_{,}}_{1,\mathrm{\dots },T,M}$, respectively. ${\lambda }_s{{}_{,}}_t$ and ${\stackrel{-}{\lambda }}_s{{}_{,}}_t$ represent the scenario values at time t, while $M_{q,t}$ and ${\stackrel{-}{M}}_{q,t}$ represent the qth-order central moments of scenario set P and $P^{opt}$ at time t.

If $f_m<{\epsilon }_m$ and $f_s<{\epsilon }_s$, the scenario selection is completed, and the corresponding scenario set $P^{opt}$ becomes the optimal set of reserved scenarios. Otherwise, proceed to step (3).

(4) Select a new scenario ${\lambda }_l{{}_{,}}_{1,\mathrm{\dots },T,p_j}$ from each cluster class and remove it from the remaining scenario set P. Calculate the distances between each scenario ${\lambda }_l{{}_{,}}_{1,\mathrm{\dots },T,p_j}$ in the cluster class and each scenario $P^{opt}$ in the cluster class, and take the minimum value c. The specific calculation is given by Equation (13) as follows:

$$c=\underset{{\stackrel{-}{\lambda }}_{m,t}\in P^{opt}}{\min }{p}_j{\displaystyle \sum _{t=1}^T\left|{\lambda }_{j,t}-{\stackrel{-}{\lambda }}_{m,t}\right|}$$

(13)

If $c>{\epsilon }_d$, the scenario is added to $P^{opt}$, and the scenario probability $P_{\gamma }$ is updated according to Equation (14).

$$P_{\gamma }=P_{\gamma }\cup \left\{p_j\right\}$$

(14)

At this point, the process of scenario reduction is complete.

3. Source-Load Coordinated Response Model

The proposed source-load coordinated response in this study aims to maximize the reduction of VPP operational costs and enhance energy utilization by coordinating the characteristics of electric-storage hydrogen systems on the source side and demand response on the load side. The source-load coordinated response model consists of electric-storage hydrogen systems and demand response characteristics, which are modeled as follows.

(1) Electric-Storage Hydrogen Systems

Hydrogen energy, as a clean and efficient energy source, has been gradually applied in various fields, such as hydrogen-powered vehicles and hydrogen fuel cells (HFCs). Electrolysis cells, which play a key role in hydrogen production from electricity, typically include alkaline electrolysis cells, solid oxide electrolysis cells, and proton exchange membrane electrolysis cells. Among these types, alkaline electrolysis cells are widely used in practical applications. In this study, alkaline electrolysis cells are employed for hydrogen production, and the operating model of the electrolysis cell is as follows [18]:

$$\left\{\begin{array}{l}{P}_{EL,t}={\eta }_{EL}{P}_{e,EL,t}\\ P_{e,EL,\min }\le P_{e,EL,t}\le P_{e,EL,\max }\\ {\tau }_{EL,\min }\le P_{e,EL,t+1}-P_{e,EL,t}\le {\tau }_{EL,\max }\end{array}\right.$$

(15)

In the equation, $P_{e,EL,t}$ represents the electrical energy consumed by the electrolysis cell during time period t, $P_{EL,t}$ represents the hydrogen gas generated by the electrolysis cell during time period t, ${\eta }_{EL}$ represents the efficiency of the electrical-to-hydrogen conversion in the electrolysis cell, $P_{e,EL,\max }$ and $P_{e,EL,\min }$ represent the upper and lower limits of the electrical energy consumed by the electrolysis cell during time period t, and ${\tau }_{EL,\max }$ and ${\tau }_{EL,\min }$ represent the upper and lower limits of the electrolysis cell ramping.

A portion of the hydrogen gas generated by the electrolysis cell is stored in hydrogen storage tanks, while another portion is directly supplied to the fuel cell. Previous literature studies have indicated that the sum of the electrical and thermal efficiency coefficients of hydrogen fuel cells can be considered a constant, and the electrical and thermal efficiency of hydrogen fuel cells can be adjusted. In this study, it is assumed that the required hydrogen gas for the fuel cell is solely produced by the electrolysis cell, and the output model of the fuel cell is as follows [19]:

$$\left\{\begin{array}{l}{P}_{H,HFC,t}=P_{EL,H,t}-E_{H,in,t}+{\eta }_E{E}_{H,out,t}\\ P_{HFC,e,t}={\eta }_{e,HFC}{P}_{H,HFC,t}\\ P_{HFC,h,t}={\eta }_{h,HFC}{P}_{H,HFC,t}\\ P_{H,HFC,\min }\le P_{H,HFC,t}\le P_{H,HFC,\max }\\ {\tau }_{HFC,\min }\le P_{H,HFC,t+1}-P_{H,HFC,t}\le {\tau }_{HFC,\max }\\ {\lambda }_{HFC,\min }\le P_{HFC,h,t}/P_{HFC,e,t}\le {\lambda }_{HFC,\max }\end{array}\right.$$

(16)

In the equation, $P_{H,HFC,t}$ represents the hydrogen gas consumed by the fuel cell during time period t, $P_{HFC,e,t}$ and $P_{HFC,h,t}$ represent the electrical power and thermal power generated by the fuel cell during time period t, ${\eta }_{e,HFC}$ and ${\eta }_{h,HFC}$ represent the electrical and thermal efficiency of the fuel cell during time period t, $P_{H,HFC,\max }$ and $P_{H,HFC,\min }$ represent the upper and lower limits of the fuel cell output during time period t, ${\tau }_{HFC,\max }$ and ${\tau }_{HFC,\min }$ represent the upper and lower limits of the fuel cell ramping, and ${\lambda }_{HFC,\max }$ and ${\lambda }_{HFC,\min }$ represent the upper and lower limits of the fuel cell thermal-to-electric ratio.

The hydrogen storage tank plays a crucial role in providing a stable and time-shifted hydrogen gas supply to the fuel cell, ensuring its stable and continuous operation. The physical model of the hydrogen storage tank involves processes such as hydrogen compression, storage, and release. In this section, the storage and discharge characteristics of the hydrogen storage tank are characterized, and the model can be described as follows:

$$\left\{\begin{array}{l}{E}_{H,t+1}=E_{H,t}+{\eta }_H{P}_{H,in,t}-P_{H,out,t}\\ E_{H,\min }\le E_{H,t}\le E_{H,\max }\\ P_{H,in,\min }\le U_{H,in,t}{P}_{H,in,t}\le P_{H,in,\max }\\ P_{H,out,\min }\le U_{H,out,t}{P}_{H,out,t}\le P_{H,out,\max }\\ 0\le U_{H,in,t}+U_{H,out,t}\le 1\\ E_{H,T}=E_{H,1}\end{array}\right.$$

(17)

In the equation, $E_{H,t}$ denotes the storage capacity of the hydrogen storage tank during time period t. The charging and discharging power of the hydrogen storage tank are represented by $P_{H,in,t}$ and $P_{H,out,t}$, respectively. The upper and lower limits of the storage capacity are denoted by $E_{H,\max }$ and $E_{H,\min }$. The charging and discharging of the hydrogen storage tank are represented by $U_{H,in,t}$ and $U_{H,out,t}$, respectively. The hydrogen efficiency during charging and discharging is denoted by ${\eta }_H$. The upper limits of the charging and discharging power of the hydrogen storage tank are represented by $P_{H,in,\max }$ and $P_{H,out,\max }$, while the lower limits are denoted by $P_{H,in,\min }$ and $P_{H,out,\min }$. Finally, $E_{H,1}$ and $E_{H,T}$ represent the initial and final capacity of the hydrogen storage tank within one scheduling period.

(2) Demand Response of Electric Heating Loads

This paper posits that all electric heating loads possess the capability for demand response. Electric heating loads can be classified into fixed loads, shiftable loads, and interruptible loads. Furthermore, to meet practical application requirements, electric heating loads are categorized into three levels of importance: Level 1 load, Level 2 load, and Level 3 load. Among these, Level 1 loads have the smallest proportion and do not possess demand response capability. Level 3 loads have the largest proportion and exhibit demand response capability. Level 2 loads fall in the middle and have the characteristic of load shifting. The cost of load interruption can be described as [20]:

$$\left\{\begin{array}{l}{C}_{IL,t}=\left(\begin{array}{l}{\alpha }_e{P}_{e,i,IL,t}^2+{\gamma }_e{P}_{e,i,IL,t}+\\ {\alpha }_h{P}_{h,i,IL,t}^2+{\gamma }_h{P}_{h,i,IL,t}\end{array}\right)\\ T_{IL,i,k,t}\le T_{IL,i,k,\max }\\ \left({\displaystyle {\sum }_{t=1}^T{\delta }_{IL,i,k,t}}\right)/T_{IL,i,k}\le y_i\left(k\right)\\ 0\le P_{IL,i,k,t}\le P_{IL,i,k,\max }\end{array}\right.$$

(18)

Equation (18) is as follows: where $C_{IL,t}$ represents the demand response cost of electric heating loads during time period t; ${\alpha }_e$ and ${\gamma }_e$ are coefficients for load dissatisfaction and interruption compensation cost, respectively; ${\alpha }_h$ and ${\gamma }_h$ are coefficients for heat load dissatisfaction and interruption compensation cost, respectively; $T_{IL,i,k,\max }$ represents the maximum duration of continuous interruption for the kth category and ith level load; ${\delta }_{IL,i,k,t}$ is a state variable indicating whether the kth category and ith level load is interrupted; $y_i\left(k\right)$ represents the maximum number of interruptions for the kth category and ith level load; and $P_{IL,k,t}$ and $P_{IL,i,k,\max }$ are the interrupted power and its upper limit for the kth category and ith level load.

Unlike the interruptible loads, shiftable loads allow for the adjustment of load demand between time periods without altering the overall load quantity. Both Level 2 and Level 3 loads possess the capability for load shifting. Considering constraints such as response time, response capacity, and response frequency for shiftable loads, a mathematical model can be formulated as follows:

$$\left\{\begin{array}{l}{P}_{TSL,i,k,in,\min }\le {\mu }_{TSL,i,k,in,t}{P}_{TSL,i,k,in,t}\le P_{TSL,i,k,in,\max }\\ P_{TSL,i,k,out,\min }\le {\mu }_{TSL,i,k,out,t}{P}_{TSL,i,k,out,t}\le P_{TSL,i,k,out,\max }\\ T_{TSL,i,k,in,\min }\le {\displaystyle {\sum }_{t=1}^T{T}_{TSL,i,k,in,t}\le T_{TSL,i,k,in,\max },t\in \left[t_{TSL,i,k,in,s},t_{TSL,i,k,in,e}\right]}\\ T_{TSL,i,k,out,\min }\le {\displaystyle {\sum }_{t=1}^T{T}_{TSL,i,k,out,t}\le T_{TSL,i,k,out,\max },t\in \left[t_{TSL,i,k,out,s},t_{TSL,i,k,out,e}\right]}\\ {\displaystyle {\sum }_{t=1}^T{\mu }_{TSL,i,k,out,t}{P}_{TSL,i,k,out,t}={\displaystyle {\sum }_{t=1}^T{\mu }_{TSL,i,k,in,t}{P}_{TSL,i,k,in,t}}}\\ {\displaystyle {\sum }_{t=1}^T\left({\mu }_{TSL,i,k,in,t}+{\mu }_{TSL,i,k,out,t}\right)\le N_{TSL,i,k,\max }}\end{array}\right.$$

(19)

In Equation (19), k represents the type of shiftable load, and i denotes the importance level of the load. $P_{TSL,i,k,in,t}$ and $P_{TSL,i,k,out,t}$ correspond to the power intake and power off-take of the kth category and ith level load, respectively. ${\mu }_{TSL,i,k,in,t}$ and ${\mu }_{TSL,i,k,out,t}$ represent the state variables indicating the power intake and power off-take status of the kth category and ith level load. $T_{TSL,i,k,in,\max }$ and $T_{TSL,i,k,in,\min }$ denote the lower and upper limits of the time interval for load intake, respectively. $t_{TSL,i,k,in,s}$ and $t_{TSL,i,k,in,e}$ represent the start and end times for load intake, respectively. $N_{TSL,i,k,\max }$ signifies the total number of permissible load intake and off-take occurrences within a scheduling cycle.

(3) Comprehensive Satisfaction Index

Following the approach proposed in reference [9], a comprehensive satisfaction index for electric heating loads is introduced to depict the overall level of load satisfaction. The comprehensive satisfaction index can be described as follows:

$$\left\{\begin{array}{l}{U}_{s,e,i,t}=\left(1-\frac{P_{e,IL,i}}{P_{e,i,0,t}}\right)\times 100\%\\ U_{s,h,i,t}=\left(1-\frac{P_{h,IL,i}}{P_{h,i,0,t}}\right)\times 100\%\\ U_{C,t}=\frac{{\displaystyle {\sum }_{i=1}^I\left(U_{s,e,i,t}+U_{s,h,i,t}\right)}}{N_k}\end{array}\right.$$

(20)

In Equation (20), the satisfaction index of each level of electric heating load during time period t is denoted by $U_{C,t}$. $N_k$ represents the load type, and i represents the load level.

(4) Source-Load Flexibility and Dual Response Mechanism

The proposed source-load dual response operating characteristics are achieved through the coordinated operation of the source-side electric–hydrogen system and the multi-level load demand response on the load side. This flexible coordination enables the regulation of the operational economics and low carbon emissions of the virtual power plant (VPP). To further illustrate the coordinated operation between the source and load, this section presents two scenarios of VPP operation, as follows:

(1)

During periods when wind and solar power generation is high, electricity demand is low, and heat load is high (typically referring to nighttime periods), the electric–hydrogen system increases the power absorption from wind and solar sources, enhances the thermal output power of the fuel cell, and reduces the thermal output power of the gas boiler during this period. Additionally, a portion of the heat load is shifted to this period, alleviating the heating cost in other periods. Furthermore, due to the thermal–electric coupling characteristics of the fuel cell units, increasing the thermal power output also results in increased electrical power generation. Therefore, a portion of the electrical load is shifted to this period, consuming the surplus electricity generated by the coupling characteristics and relieving the power supply pressure in other periods.

(2)

During periods when wind and solar power generation is low, electricity demand is high, and heat load is low (typically referring to peak daytime periods), the electric–hydrogen system decreases its power output, reducing the power generation of the fuel cell. Wind and solar power sources are prioritized to supply electricity to meet the demand, while a portion of the electrical load is shifted to other periods. Simultaneously, the gas turbine is activated to supply electricity to the load, thereby alleviating the power supply pressure in this period. Due to the decreased thermal output power of the fuel cell, a portion of the heat load is shifted to other periods, reducing the heating cost of the VPP’s gas boiler.

The coordinated source-load response strategy improves the energy utilization efficiency and economics of the VPP. To further clarify the process of source-load coordination, Figure 1 is presented. Figure 1 presents a flowchart depicting the coordinated response strategy between the source and load in a virtual power plant. The strategy is divided into two categories by incorporating wind and solar power generation capacities and peak-load power.

4. VPP Optimization Model

The VPP is optimized with the objective function of minimizing the typical daily operating cost. The objective function can be described as follows:

$$\min C_{IEO}=C_{buy}+C_{car}+C_{pen}+C_{IDR}-C_{sell}$$

(21)

In Equation (21), $C_{buy}$ represents the cost of electricity and gas procurement for the VPP, $C_{car}$ represents the cost associated with carbon emissions for the VPP, $C_{pen}$ represents the cost of curtailed renewable energy for the VPP, $C_{IDR}$ represents the cost incurred from load demand response guided by the upper-level VPP, and $C_{sell}$ represents the revenue generated from electricity sales by the VPP. The calculation formulas for the aforementioned costs can be described as follows:

(1) Energy Procurement Cost

The virtual power plant (VPP) entails the costs associated with purchasing electricity and gas. Specifically, electricity procurement is based on time-of-use pricing, while gas procurement is based on time-of-use gas pricing. The VPP’s energy procurement cost can be represented by Equation (22).

$$C_{buy}=\frac{q_{g,t}}{Q_{LHV}}\left(\frac{P_{GT,t}}{{\eta }_{GT}}+\frac{P_{GB,t}}{{\eta }_{GB}}\right)+{\omega }_{rt\_price,t}{P}_{grid,e,t}$$

(22)

In Equation (22), $q_{g,t}$ represents the time-of-use gas price, $Q_{LHV}$ represents the gas calorific value, and ${\eta }_{GT}$ and ${\eta }_{GB}$ represent the operational efficiency of the gas turbine and gas boiler, respectively. $P_{GT,t}$ and $P_{GB,t}$ represent the output power of the gas turbine and gas boiler, respectively. Finally, ${\omega }_{rt\_price,t}$ represents the time-of-use electricity price, and $P_{grid,e,t}$ represents the power purchased by the VPP from the grid.

(2) Carbon-Trading Cost

The carbon emissions of the virtual power plant (VPP) are calculated using a tiered carbon pricing approach, and the carbon-trading cost $C_{{\mathrm{CO}}_2}$ can be expressed by Equation (23) [21].

$$C_{{\mathrm{CO}}_2}=\left\{\begin{array}{l}{\displaystyle {\sum }_{t=1}^{T}c\left(E_{{\mathrm{CO}}_2,t}-E_{c,t}-E_{CCS,t}\right)},\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}0\le E_{{\mathrm{CO}}_2,t}-E_{c,t}-E_{CCS,t}\le \nu \\ {\displaystyle {\sum }_{t=1}^{T}c\nu +c\left(1+\alpha \right)\left(E_{{\mathrm{CO}}_2,t}-E_{c,t}-E_{CCS,t}-\nu \right)},\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\nu \le E_{{\mathrm{CO}}_2,t}-E_{c,t}-E_{CCS,t}\le 2\nu \\ {\displaystyle {\sum }_{t=1}^{T}c\left(1+\alpha \right)\nu +c\left(1+2\alpha \right)\left(E_{{\mathrm{CO}}_2,t}-E_{c,t}-E_{CCS,t}-2\nu \right)},\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}2\nu \le E_{{\mathrm{CO}}_2,t}-E_{c,t}-E_{CCS,t}\end{array}\right.$$

(23)

In Equation (23), $E_{{\mathrm{CO}}_2,t}$, $E_{c,t}$, and $E_{CCS,t}$ represent the system’s carbon dioxide emissions, carbon quotas, and carbon capture, respectively. $\nu$ represents the length of each tiered carbon emission interval.

(3) Wind and Solar Curtailment Cost

$$C_{pen}={\displaystyle {\sum }_{t=1}^T{\xi }_{pen}\left(P_{WT,pen,t}+P_{PV,pen,t}\right)}$$

(24)

In Equation (24), ${\xi }_{pen}$ denotes the penalty factor for wind and solar curtailment, and $P_{WT,pen,t}$ and $P_{PV,pen,t}$ represent the curtailed wind and solar power, respectively.

(4) Demand Response Cost

The cost of demand response for electric heating loads consists of two components. Firstly, there is the cost associated with the dissatisfaction caused by load interruption, which is quadratic in relation to the magnitude of the interrupted load. Secondly, there is the cost of load interruption itself, which is linearly dependent on the magnitude of the interrupted load. The specific formulation is as follows.

$$C_{IDR}={\displaystyle {\sum }_{t=1}^T\left(\begin{array}{l}{\alpha }_e{P}_{e,i,IL,t}^2+{\gamma }_e{P}_{e,i,IL,t}+\\ {\alpha }_h{P}_{h,i,IL,t}^2+{\gamma }_h{P}_{h,i,IL,t}\end{array}\right)}$$

(25)

In Equation (25), $P_{e,i,IL,t}$ and $P_{h,i,IL,t}$ represent the interrupted power of the ith category of electric and heating loads, respectively.

(5) Equipment Operation and Maintenance Cost

The operation and maintenance (O&M) cost of the BE-IES equipment is divided into two parts: the O&M cost of the energy supply equipment and the O&M cost of the energy storage equipment. These costs are expressed as the product of the O&M cost coefficient and the equipment’s output power. The specific formulation can be described as follows:

$$C_{EOM}={\displaystyle {\sum }_{t=1}^T\left({\alpha }_{EOM,x}{P}_{x,t}+{\beta }_{EOM,y}{P}_{x,y}\right)}$$

(26)

In Equation (26), ${\alpha }_{EOM,x}$ represents the O&M cost coefficient for the energy supply equipment x, $P_{x,t}$ represents the output power of the energy supply equipment x, ${\beta }_{EOM,y}$ represents the O&M cost coefficient for the energy storage equipment y, and $P_{x,y}$ represents the energy storage power (charging or discharging) of the energy storage equipment y.

The operation of electric energy storage is similar to that of thermal energy storage; the thermal storage tank is utilized to store heat during periods of low thermal load and release heat during periods of high thermal load, thereby facilitating the transfer of heat and alleviating the heating pressure on the equipment during peak thermal load periods, and the operational constraints include storage and discharge constraints, capacity constraints, and state constraints. These constraints are described in detail in reference [22].

$$\left\{\begin{array}{l}0\le P_{z,DC,t}\le U_{z,DC,t}{P}_{z,DC,\max }\\ 0\le P_{z,DC,t}\le U_{z,CH,t}{P}_{z,CH,\max }\\ 0\le U_{z,DC,t}+U_{z,CH,t}\le 1\\ S_{z,\min }\le S_{z,t}\le S_{z,\max }\\ {\eta }_{z,CH}{P}_{z,CH,t}-P_{z,DC,t}/{\eta }_{z,DC}=S_{z,t}-S_{z,t-1}\end{array}\right.$$

(27)

In Equation (27), ${\eta }_z$ represents the operational efficiency of the zth category of energy storage device, $S_{z,t}$ denotes the capacity of the zth category of energy storage device, and $P_{z,CH,\max }$ and $P_{z,DC,\max }$ represent the upper limits of charging and discharging power for the zth category of energy storage device. Furthermore, $U_{z,CH,t}$ and $U_{z,DC,t}$ represent the state variables for charging and discharging of the zth category of energy storage device, which are binary variables ranging from 0 to 1.

The operational constraints of the virtual power plant (VPP) encompass restrictions on the operation of gas turbines, power purchase from the grid, and renewable energy generation. These constraints can be described as follows:

$$\left\{\begin{array}{l}{E}_{p,t}\le E_{p,\max },\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}p\in {\Omega }_p\\ E_{s,\min }\le E_{s,t}\le E_{s,\max },\hspace{1em}s\in {\Omega }_s\\ D_{s,\min }\le E_{s,t+1}-E_{s,t}\le D_{s,\max }\end{array}\right.$$

(28)

In Equation (28), ${\Omega }_p$ represents the set of purchased energy types for the VPP, including electricity and gas purchases. ${\Omega }_s$ denotes the set of VPP equipment types. $E_{p,t}$ and $E_{p,max}$ represent the power and upper limits of purchased energy. $E_{s,t}$ signifies the output power of the equipment, while $D_{s,\max }$ and $D_{s,\min }$ denote the upper and lower limits of the equipment’s ramping power. Figure 2 is the solution chart.

5. Case Study

This chapter validates the effectiveness and rationality of the proposed model through a case study analysis. All simulation calculations and design in this paper were conducted in the MATLAB R2017b environment, utilizing the IBM (Armonk, NY, USA) plugin and invoking the CPLEX (version 12.8) solver for optimization of the virtual power plant (VPP) model. The computer used for the computations was equipped with an Intel Core i7 (Intel, Santa Clara, CA, USA) processor running at a frequency of 1.8 GHz and 16 GB of memory.

5.1. Basic Data

This paper focuses on a park-type VPP for the case study analysis. The daily scheduling approach is employed, with a scheduling period of 24 time slots representing a day, where each time slot is 1 h long. Figure 1 presents the basic data for the VPP’s electric and thermal loads, as well as the forecasted wind and solar power. Time-of-use electricity pricing is adopted, with the low-demand periods from 1:00 to 5:00 and 22:00 to 24:00 having a price of 0.295 CNY/kWh, the normal-demand periods from 6:00 to 7:00 and 12:00 to 17:00 having a price of 0.55 CNY/kWh, and the peak-demand periods having a price of 0.804 CNY/kWh. As for the main natural gas loads, the gas turbines and gas boilers consume natural gas purchased by the VPP from the higher-level gas network, and time-of-use gas pricing is used. The low-demand gas price periods are from 1:00 to 5:00 and 23:00 to 24:00 with a price of 2.2 CNY/m³; the normal-demand gas price periods are from 6:00 to 7:00, 13:00 to 16:00, and 20:00 to 23:00 with a price of 2.99 CNY/m³; and the peak-demand gas price periods have a price of 3.82 CNY/m³.

Regarding the characteristics of the electric and thermal loads, they are categorized based on their load levels in practical applications. The loads are classified as Level 1, Level 2, and Level 3 loads. Level 1 loads do not possess demand response capabilities and account for 10% of the total load. Level 2 loads only have time-shifting characteristics but no interruptible capability, accounting for 30% of the total load. Level 3 loads have both time-shifting and interruptible capabilities, accounting for 60% of the total load. Additionally, the time-shifting power limit for Level 2 loads is 15% of their own load level, while the time-shifting power and interruptible power limits for Level 3 loads are 15% and 10% of their own load level, respectively. See

Table 1. VPP three-level load demand response parameters.

Types of Load That Can Be Reduced	Can Reduce Time Range/h	Power Reduction Ratio/%	Continuous Reduction Time/h	Reduce Compensation Prices/CNY
Third level electrical load	00:00–24:00	10	1–3 h	0.4
Third level heat load	00:00–24:00	10	1–5 h	0.4

below.

In terms of carbon emissions, the carbon-trading mechanism employs a tiered pricing system with a base price of 0.2 CNY/kg and a 25% increment in carbon price for each tier. The carbon capture equipment has a capture capacity of 3.3 kg/kW and operates at an efficiency of 0.9. The carbon emission intensity for gas turbines and gas boilers is 0.065 t/GW. Additionally, the operational parameters of the system’s various equipment are presented in

Table 2. Running parameters of VPP devices.

Device Name	Capacity/kWh	Efficiency/%	Climbing Power/kW
Gas turbine	1000	0.85	400
Gas boiler	1500	0.90	600
Fuel cell	900	0.3	350
Electric energy storage	800	0.90	/
Heat storage tank	540	0.90	/
Hydrogen storage tank	800	0.95	/
Electric tank	900	0.85	350

.Basic data of scenery and load see Figure 3 below.

5.2. Optimization Analysis of Proposed Strategies

In this section, the optimal operation plans for the power supply and heating equipment of the park-type virtual power plant (VPP) are analyzed, as depicted in Figure 4 and Figure 5. The system ensures power and thermal load power balance through the operation of the power supply and heating equipment. By analyzing the output characteristics of various energy devices, the complementarity and correlation between different energy sources are thoroughly studied. The specific analysis is as follows.

Figure 4 illustrates the optimal operation plan for the power supply equipment of the virtual power plant (VPP). It can be observed that the power balance of the VPP is primarily maintained through wind and solar power generation. During the nighttime period (1:00–5:00), the VPP purchases a portion of the power from the grid while simultaneously operating the electrolyzer for hydrogen production and charging the energy storage system. During the peak load periods (9:00–12:00, 17:00–20:00), the VPP activates the gas turbines and fuel cells to supply power to meet the demand and ensure supply-demand equilibrium. Additionally, the carbon capture equipment operates during the nighttime period to capture the carbon dioxide generated by the gas boilers, thereby maintaining a lower level of carbon emissions from the VPP.

Figure 5 illustrates the optimal operation plan for the heating equipment of the virtual power plant (VPP). It can be observed that the heating load demand is primarily maintained through the collaboration of gas boilers, fuel cells, and thermal storage tanks. During the nighttime period (1:00–7:00), when the heating load demand is high and gas prices are at a low point, the VPP provides heating to the load through the gas boilers while simultaneously charging the thermal storage tanks. During the daytime period (8:00–12:00), the VPP mainly relies on fuel cells and thermal storage tanks to meet the heating load demand. By properly managing the output power of the heating equipment, the VPP satisfies its own heating load requirements while enhancing the economic efficiency of its operation.

The introduction of flexible loads in the VPP further enhances the coordinated operation capability between the energy sources and the loads, effectively improving the operational flexibility of the VPP. In this study, the electric heating loads are classified based on their importance levels. Figure 6 and Figure 7 present the response curves of the VPP’s different priority levels of electric and heating load demands, respectively.

Figure 6 demonstrates that during the peak load period (9:00–12:00), demand response characteristics reduce the load demand by shedding and interrupting a portion of the power, exhibiting peak shaving and valley-filling characteristics. The analysis indicates that shifting the electric load to the nighttime period can consume more renewable energy and off-peak grid power, alleviate the supply pressure on the VPP during peak hours, and enhance the economic efficiency of VPP operation. Additionally, during the peak period (9:00–12:00), the second-level and third-level loads exhibit the same response characteristics, i.e., shifting a portion of the load out of this period. Conversely, during the off-peak period (1:00–5:00), the second-level and third-level loads exhibit the same response characteristics, i.e., shifting a portion of the load into this period. The analysis suggests that different-level loads achieve demand response characteristics through mutual coordination.

Figure 7 demonstrates that the heating load further increases the peak-to-valley difference in load. During the nighttime peak period of heating load (1:00–5:00), the load is shifted to meet the heating demand, while during the daytime valley period of heating load (9:00–12:00), the heating load is further reduced. The analysis indicates that the purpose of the heating load demand response is to reduce the operational cost of the virtual power plant (VPP) while ensuring supply–demand balance. During the nighttime period, when gas prices are at a low point, gas boilers can bear a greater portion of the heating load demand, reducing heating costs during other periods. Additionally, different-level heating loads exhibit the same demand response characteristics during peak and valley load periods, i.e., shifting simultaneously in and out.

5.3. Low-Carbon Characteristics Analysis

To further analyze the effectiveness of the proposed operation mode involving new energy participation in carbon capture equipment, this section compares it with the traditional carbon capture equipment scenario where the equipment relies solely on thermal power plants or gas units for electricity supply. Two scenarios are set: Scenario 1 adopts the traditional carbon capture equipment operation mode, while Scenario 2 adopts the operation mode with new energy participation in carbon capture. The specific analysis is as follows.

Table 3. Influence of different operation modes of carbon capture on VPP operation.

	Scene1	Scene2
Operating cost/CNY	3956.64	3919.55
Carbon emissions/kg	1921.17	1067.74
Overall Satisfaction/%	96.86	97.60
Carbon capture power/kW	176.10	470.40
Electric hydrogen production power/kW	1742.93	1417.16

presents the impact of different carbon capture equipment operation modes on VPP performance indicators. It can be observed that compared to Scenario 1, Scenario 2, with new energy participation in carbon capture, reduces the operational cost and carbon emissions of the VPP by 0.95% and 79.93%, respectively. It also improves the VPP’s load satisfaction index and carbon capture capacity by 0.76% and 62.56%, respectively. Furthermore, the participation of new energy generation in carbon capture equipment operation reduces the consumption of new energy by hydrogen production equipment, thereby lowering the power consumption of hydrogen production by 18.69%. The analysis indicates that the involvement of new energy in carbon capture operations further enhances the economic and low-carbon performance of the system.

To analyze the influence of the factors of the tiered carbon-trading mechanism on VPP operation, this section examines the sensitivity of the carbon emission interval length and its impact on VPP performance. The specific analysis is as follows.

Figure 8 and Figure 9 illustrate the impact of the carbon emission interval length on VPP operation. As the carbon emission interval length increases, the comprehensive satisfaction index of the VPP gradually increases, while the carbon capture power decreases. At the same time, the gas purchasing cost increases gradually, while the electricity purchasing cost decreases gradually. Once the carbon emission interval length reaches a certain value, these indicators reach a fixed value and no longer change. The analysis indicates that an increase in the carbon emission interval length represents a reduction in the VPP’s carbon emission cost. The VPP no longer needs to rely heavily on carbon capture equipment to reduce carbon emissions, resulting in a gradual decrease in carbon capture power. As power-consuming equipment, the decrease in power consumption of the carbon capture equipment relieves the power supply pressure on the VPP. The system no longer requires heavy reliance on load demand response to maintain operational efficiency, thereby improving the comprehensive satisfaction index of the VPP. Additionally, the reduction in carbon emission costs allows the VPP to increase the output power of gas units, reducing electricity purchasing costs from the grid during peak load periods and increasing gas purchasing costs from the natural gas network. Moreover, once the carbon emission interval reaches a certain length, the VPP’s carbon emission cost is no longer affected by further increases in the interval length, resulting in the VPP performance indicators reaching a fixed value that remains unchanged.

5.4. Comparative Analysis of Different Scenarios

(1) Comparison Analysis of Source-Load Response

In order to compare and analyze the effects of the proposed coordinated response between the source and load and the tiered carbon-trading mechanism on VPP performance indicators, this section examines five contrasting scenarios as follows:

Scenario 1: Only considering the tiered carbon-trading mechanism.

Scenario 2: Building upon Scenario 1, incorporating carbon capture equipment and considering the participation of new energy in carbon capture operations.

Scenario 3: Building upon Scenario 2, introducing the characteristics of electric heating load demand response.

Scenario 4: Building upon Scenario 2, adding an electric hydrogen production fuel cell system.

Scenario 5: Building upon Scenario 4, simultaneously considering the characteristics of load demand response as considered in this study.

Table 4. Influence of source-load response on virtual power plant operation.

	Scene1	Scene2	Scene3	Scene4	Scene5
Operating cost/CNY	5013.20	4768.23	4239.03	4183.18	3919.55
Carbon emissions/kg	2897.97	1530.80	791.94	1416.01	1067.74
Satisfaction indicators/%	100.00	100.00	97.90	100.00	97.60
Electricity purchasing cost/CNY	0.00	61.93	270.23	300.49	466.48
Cost of purchasing gas/CNY	3209.35	3226.73	2728.29	2857.06	2372.72
Abandoned wind power/kW	563.15	424.52	228.73	0.00	0.00
Carbon capture power/kW	0.00	430.05	596.81	419.94	470.40

displays the impact of different scenarios on VPP performance indicators. It can be observed that, compared to Scenario 1, Scenario 2, which considers the participation of new energy in carbon capture operations, reduces the operational cost, carbon emissions, and excess wind and solar power of the VPP by 4.89%, 47.18%, and 24.62%, respectively. The analysis indicates that the inclusion of carbon capture leads to a moderate reduction in VPP carbon emissions. Additionally, carbon capture equipment can consume the power generated by new energy sources, further reducing the VPP’s excess wind and solar power.

By comparing Scenario 3 and Scenario 4, it can be observed that Scenario 4, which only considers the electric–hydrogen system, achieves a greater reduction in VPP operational costs by 1.32%. However, due to the power consumption of the electric–hydrogen system, the output power of the carbon capture equipment is reduced. As a result, compared to Scenario 3, the VPP’s carbon emissions increase by 44.07%. Moreover, Scenario 3, relying solely on load demand response, is unable to fully absorb the wind and solar power generation. In contrast, Scenario 4, with the introduction of the electric–hydrogen system, can fully utilize the power generated by new energy sources. The analysis indicates that load demand response plays a greater role in VPP decarbonization, while the electric–hydrogen system offers advantages in VPP operational economy and new energy utilization levels.

Based on the aforementioned analysis, Scenario 5 is set to simultaneously consider load demand response and the electric–hydrogen system. Compared to Scenario 3, Scenario 5 reduces VPP operational costs by 7.54% and achieves 100% integration of new energy generation. Compared to Scenario 4, Scenario 5 reduces VPP operational costs and carbon emissions by 2.30% and 24.60%, respectively, while improving the carbon capture capacity of the carbon capture equipment by 10.73%. The analysis demonstrates that Scenario 5 better integrates the operational advantages of load demand response and the electric–hydrogen system to enhance the carbon capture capacity while ensuring the VPP operates economically and with low-carbon emissions.

(2) Analysis of the Heat-to-Power Ratio of Hydrogen Fuel Cells

Figure 10 illustrates the impact of the heat-to-power ratio of fuel cell cogeneration units on the operational economy and decarbonization of the VPP. It can be observed that as the heat-to-power ratio increases, the VPP’s operational costs exhibit a gradual upward trend, while carbon emissions initially decrease and then increase. The analysis suggests that an increase in the heat-to-power ratio indicates enhanced heating capability but weakened power generation capability of the hydrogen fuel cells.

Considering the electric heating load data shown in Figure 1, it can be noted that the VPP has a significant demand for electric power. Therefore, an increase in the heat-to-power ratio indirectly increases the pressure on the power supply to meet the electric load demand, leading to the VPP purchasing more electricity from the grid and thus increasing operational costs. Additionally, an increase in the heat-to-power ratio of the hydrogen fuel cells reduces the thermal power output of the gas boilers, resulting in a decrease in VPP carbon emissions. However, as the heat-to-power ratio continues to increase, the VPP will increase the output of gas turbines and the amount of purchased electricity from the grid, thereby further increasing carbon emissions.

Furthermore, to analyze the impact of hydrogen fuel cell capacity parameters on VPP operations, this section examines indicators such as operational costs, carbon emissions, overall satisfaction, and excess wind and solar power generation. The specific analysis is as follows.

Figure 11 and Figure 12 depict the impact of hydrogen fuel cell capacity parameters on VPP performance indicators. It can be observed that as the hydrogen fuel cell capacity increases, the VPP’s operational costs exhibit a gradually decreasing trend, while carbon emissions show a gradually increasing trend, reaching a fixed value and then stabilizing. The analysis suggests that during periods of abundant energy supply, the electric–hydrogen system converts electricity into hydrogen, storing it in hydrogen tanks. During high-demand periods, the hydrogen fuel cells provide power to the VPP, reducing the need for electricity purchased from the grid or power output from gas turbines. As the hydrogen fuel cell capacity increases, the fuel cells can supply more electricity to the VPP during high-demand periods, thereby reducing operational costs. However, increasing the hydrogen fuel cell capacity leads to greater hydrogen consumption, requiring more electricity for hydrogen production, which reduces the power available for carbon capture equipment and consequently lowers the VPP’s carbon emissions.

Furthermore, increasing the hydrogen fuel cell capacity decreases the overall satisfaction indicator and excess wind and solar power. When the capacity reaches 300 kWh, the VPP achieves complete utilization of the new energy generation power. The analysis indicates that increasing the hydrogen fuel cell capacity further increases the power consumption of the electrolyzer, which, in order to maintain the VPP’s economic viability and enhance its load demand response capability, reduces the overall satisfaction indicator. Simultaneously, it increases the absorption of surplus renewable energy, thereby reducing excess wind and solar power.

(3) Analysis of Load Demand Response Ratio

To evaluate the impact of load demand response ratio on VPP operations, this section tests 11 different scenarios. In these scenarios, the load demand response ratio is adjusted to various proportions of the load’s predefined values, ranging from 0% to 50% in increments of 5%, as follows.

Figure 13 and Figure 14 illustrate the impact of the load-demand response ratio on VPP operations. It can be observed that as the load-demand response ratio increases, the VPP’s operational costs exhibit a gradually decreasing trend, while carbon emissions initially decrease and then increase. The analysis suggests that with an increase in the ratio, the VPP shifts its peak load to off-peak periods, reducing the need to purchase electricity from the grid during high-demand periods and consequently lowering operational costs. Simultaneously, an increased ratio decreases the power output of gas turbines, thereby reducing carbon emissions. As the ratio continues to increase (beyond 15%), the VPP consistently reduces its electricity purchases from the grid and increases the power output of gas turbines, resulting in higher carbon emissions.

Furthermore, as the ratio increases, the overall satisfaction indicator initially decreases and then increases, while the electricity storage utilization indicator exhibits a gradual decreasing trend. The analysis indicates that an increased ratio implies enhanced load flexibility. In the early stages of the demand response ratio (less than 35%), the load reduces its own energy procurement costs by interrupting a portion of the load, thereby decreasing satisfaction. As the ratio further increases, the load’s ability to shift in time improves, reducing the interruption power and consequently increasing satisfaction. Additionally, both electricity storage and load demand response prioritize the consumption of VPP’s low-cost energy during specific periods. As the ratio continues to increase, the VPP gradually no longer requires energy transfer through storage to maintain its economic viability, resulting in a decrease in electricity storage utilization.

In this study, the second-level and third-level loads are considered to have demand response characteristics, with the second-level load having lower power than the third-level load. The first-level load accounts for 10% of the total load, while the second-level and third-level loads together account for 90% of the load. An increase in the second-level load ratio indicates a decrease in the third-level load. To analyze the impact of variations in the second-level load power on VPP performance indicators, this section analyzes the ratio of second-level load power to total load power as a variable, as follows.

Figure 15 illustrates the impact of the proportion of second-level load to total load on VPP performance indicators. It can be observed that as the proportion of second-level load power increases, the overall satisfaction indicator of the VPP exhibits a gradual upward trend, while the carbon capture power shows a decreasing trend. The analysis indicates that the second-level load only possesses time-shifting characteristics and lacks interruption capabilities. An increase in the proportion of second-level load implies a decrease in the upper limit of power that can be interrupted by the third-level load, leading to a gradual increase in overall satisfaction. Furthermore, the gradual increase in overall satisfaction indicates an increase in load demand, which prompts the VPP to reduce the power consumption of carbon capture devices to ensure operational cost-effectiveness.

6. Conclusions

In addressing the economic and low-carbon optimization of a virtual power plant considering controllable loads, load demand response characteristics are introduced. The loads are classified based on their importance levels, and an electricity–hydrogen system is introduced to establish a source-load coordination response model for the virtual power plant. The main conclusions are as follows:

Regarding VPP’s low-carbon aspect, the participation of renewable energy in carbon capture operations reduces VPP’s operational costs and carbon emissions by 0.95% and 79.93%, respectively. It also improves VPP’s load satisfaction indicator and carbon capture capacity by 0.76% and 62.56%, respectively. Data analysis demonstrates that the participation of renewable energy in carbon capture operations can further enhance the operational cost-effectiveness and low-carbon nature of the virtual power plant.

In terms of source-load response, the consideration of load demand response and the electricity–hydrogen system reduces VPP’s operational costs, achieves 100% integration of renewable energy generation, and enhances the carbon capture capacity of the system. Data analysis shows that source-load coordination response can better integrate the advantages of load demand response and the electricity–hydrogen system, further enhancing the carbon capture capacity of the system while ensuring the economic and low-carbon operation of the VPP.

Regarding controllable loads, the analysis of the load demand response ratio parameter indicates that the response ratio directly affects the economic and low-carbon operation of the VPP. Selecting an appropriate response ratio parameter can achieve low-carbon and cost-effective operation of the VPP. Furthermore, the analysis of the proportion of second-level load power reveals that increasing the power proportion of the second-level load can enhance the overall satisfaction indicator of the VPP. However, it also imposes limitations on the carbon capture capacity, resulting in a decrease in carbon capture power.