Intelligent Decision-Making for Multi-Scenario Resources in Virtual Power Plants Based on Improved Ant Colony Algorithm-Simulated Annealing Algorithm

Abstract

Virtual power plants (VPPs) integrate distributed energy sources and demand-side resources, but their efficient intelligent resource decision-making faces challenges such as high-dimensional constraints, output volatility of renewable energy, and insufficient adaptability of traditional optimization algorithms. To address these issues, an innovative intelligent decision-making framework based on the Ant Colony Algorithm–Simulated Annealing (ACO-SA) is first proposed in this paper, aiming to realize intelligent collaborative decision-making for the economy and operational stability of VPP in complex scenarios. This framework combines the global path-searching capability of the Ant Colony Algorithm (ACO) with the probabilistic jumping characteristic of the Simulated Annealing Algorithm (SA) and designs a dynamic parameter collaborative adjustment mechanism, which effectively overcomes the defects of traditional algorithms such as slow convergence and easy trapping in local optimal solutions. Secondly, a resource intelligent decision-making cost model under the VPP framework is constructed. To verify algorithm performance, comparative experiments covering multiple scenarios (agricultural parks, industrial parks, and industrial parks with energy storage equipment) are designed and conducted. Finally, the simulation results show that compared with ACO, SA, Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), ACO-SA exhibits significant advantages in terms of scheduling cost and convergence speed; the average scheduling cost of ACO-SA is 2.31%, 0.23%, 3.57%, and 1.97% lower than that of GA, PSO, ACO, and SA, respectively, and it can maintain excellent stability even in high-dimensional constraint scenarios with energy storage systems.

1. Introduction

With the rapid increase in the demand for electricity, the regulation capacity of traditional power grids is facing severe challenges. Virtual power plants (VPPs) achieve peak shaving and valley filling through unified scheduling of distributed resources, effectively improving the safety, stability, and economic scheduling capabilities of power grids [1,2]. However, the inherent output volatility of renewable energy sources such as solar and wind energy significantly increases the complexity of system operation. In this context, VPPs need to frequently adjust power generation plans or increase electricity purchases from the grid to maintain supply–demand balance, which pushes up system operation costs [3]. Therefore, the efficient scheduling of renewable energy has become a key issue that needs to be solved urgently.

Intelligent optimization algorithms such as the Genetic Algorithm (GA) and Ant Colony Algorithm (ACO) are widely used to solve complex engineering problems [4]. Deghfel et al. [5] use GA to solve the maximum power point tracking problem of photovoltaic systems under rapidly changing weather conditions. Mehrdad et al. [6] adopt PSO to achieve high-precision prediction and wide applicability. Huo et al. [7] apply ACO to plan smooth paths for mobile robots. Yusuf et al. [8] develop a new global solar radiation prediction model using the Simulated Annealing Algorithm (SA). Xue et al. [9] optimize satellite orbit trajectories using SA to maximize the common-view possibility between stations in regional satellite laser ranging networks. It is worthy of recognition that Yuvaraj et al. [10] enhance the resilience of radial distribution networks and the profitability of virtual power plants using hybrid algorithms.

Although intelligent algorithms can effectively improve complex engineering problems, they also have limitations. Wang et al. [11,12,13,14] point out that intelligent algorithms have drawbacks such as slow convergence speed, stagnation after a certain number of iterations, the need for prior access to complete cycle information, proneness to falling into local optimum, low initialization efficiency, and poor solution quality. Song et al. [15] suggest that the performance of hybrid algorithms can be improved by organically combining two algorithms with specific strategies.

ACO is a bio-inspired heuristic algorithm, whose basic idea is to simulate the cooperative behavior of ant colonies, and it is one of the commonly used intelligent algorithms for path planning problems [16]. Cui et al. [17] proposed a multi-strategy adaptive ACO that alleviates the problems of insufficient convergence and low efficiency of ACO. Wang et al. [18] proposed a Monte Carlo-improved ACO to solve the problem of a large number of redundant parts in ACO path searching.

SA draws on solid annealing principles. In thermodynamics, annealing is the physical phenomenon of an object’s gradual temperature decrease: lower temperature means lower energy, with condensation and crystallization at sufficiently low temperatures achieving the system’s lowest energy state, though rapid cooling prevents this. SA adopts this idea: a solid’s internal particles move more intensely with rising temperature (increasing internal energy), and as temperature drops, particles become ordered and internal energy decreases, eventually reaching a near-minimum internal energy thermal equilibrium [19]. Yu et al. [20] propose making improvements to PSO using the core idea of SA to address the problems of slow convergence and easy trapping in local optima of PSO. Li et al. [21] combine the improved Non-dominated Sorting Genetic Algorithm II with a radial basis function neural network to provide a reliable decision support tool for the sustainable operation of power markets. Zarei et al. [22] proposed an ant colony optimization (ACO) algorithm to efficiently solve the ESP problem. Chen et al. [23] applied ACO to optimize the parameters of the thermodynamic system in the biomass briquette chain boiler. Rafał et al. [24] employed two ACO algorithms and compared them in terms of their application to reconstructing the second kind of boundary conditions of the fractional heat conduction equation.

VPP resource decision-making is a high-dimensional, nonlinear, multi-constrained combinatorial optimization problem with a huge solution space and numerous local optimal solutions. The hybrid strategy in this study is not a simple superposition but rather enables ACO and SA to perform in-depth division of labor and collaboration. ACO utilizes its swarm search capability to quickly explore and locate promising solution regions; on the basis of ACO’s search, SA performs probabilistic perturbations on the solutions and key parameters generated by ACO, helping the algorithm jump out of the local optimal traps that ACO may fall into. This hybrid strategy overcomes both the premature convergence of ACO and the search blindness of SA. It not only possesses the directional search efficiency of ACO but also incorporates the global convergence capability of SA.

The VPP problem involves a large number of power balance and equipment operation constraints. The ACO-SA hybrid algorithm, through its strong global exploration capability, can navigate more effectively in the complex feasible solution space and find high-quality solutions that satisfy all constraints. Moreover, renewable energy sources and loads in VPP have uncertainties. The dynamic parameter collaborative adjustment mechanism designed in this paper enables ACO-SA to adapt to such changes. ACO adjusts pheromones according to search feedback, and the annealing process of SA further regulates the breadth and depth of the search, endowing the algorithm with robustness to cope with system fluctuations. For VPPs that require day-ahead or intraday planning, the speed and quality of the solution are equally important. Through the collaborative mechanism, ACO-SA can obtain scheduling schemes with lower costs at a faster convergence speed compared with single ACO or SA, which is crucial for engineering applications.

Based on the above analysis, a hybrid algorithm combining ACO and SA is adopted in this paper for intelligent decision-making of distributed energy in virtual power plants.

This study offers the following distinctive contributions:

To address the problems of slow convergence, easy trapping in local optimal solutions of ACO, and low search efficiency of SA, a deep fusion mechanism is proposed, and an ACO-SA hybrid optimization framework based on a dynamic parameter collaborative adjustment mechanism is constructed. By balancing global exploration and local development capabilities, this framework significantly improves the global solution efficiency and solution quality for VPP resource intelligent decision-making under complex constraints.

The parameter settings of traditional intelligent optimization algorithms rely on empirical criteria and are difficult to adapt to the variable operating scenarios of VPP. For this reason, a dynamic parameter adaptive adjustment strategy is designed in this study, which effectively solves the problem of algorithm parameter sensitivity and enhances robustness to different working conditions.

To overcome the defect of insufficient flexibility in matching distributed energy and loads in existing scheduling models, a percentage-based power supply decision variable matrix x_ij(t) ∈ [0,1] is innovatively introduced, breaking through the limitation of traditional binary decisions and greatly improving the flexibility and engineering feasibility of intelligent decision-making schemes.

To overcome the limitation of single scenarios in existing studies, multi-scenario comparative experiments are systematically designed, covering three typical scenarios, including agricultural parks, industrial parks, and industrial parks with energy storage systems, to comprehensively verify the universality and stability of algorithm performance.

The remainder of this paper is structured as follows:

• Section 2 elaborates on the design of the improved ACO-SA hybrid algorithm;
• Section 3 constructs the cost model and constraint conditions for VPP resource intelligent decision-making;
• Section 4 verifies the performance of the proposed algorithm through comparative simulation experiments of three typical cases;
• Section 5 finally draws conclusions and prospects future research directions.

2. Design of ACO-SA Hybrid Algorithm

To overcome the insufficient performance of traditional optimization algorithms and the inherent defects of single intelligent algorithms, this study proposes to apply ACO and SA collaboratively for VPP resource intelligent decision-making. ACO realizes path optimization based on the pheromone positive feedback mechanism, with strong global search capability, and can effectively handle high-dimensional combinatorial optimization problems. However, ACO has defects such as slow convergence and easy trapping in local optima; moreover, its key parameters such as pheromone volatilization coefficient and pheromone heuristic factor usually rely on empirical settings and are difficult to adapt to the multi-temporal and spatial scale characteristics of VPPs. SA escapes local optima through a probabilistic jumping mechanism in the controlled temperature reduction process and has excellent global optimization capability. However, SA lacks the ability to utilize problem-specific structural information in the search process, resulting in low search efficiency. The flowcharts of the classical ACO algorithm and classical SA algorithm are shown in Figure 1 and Figure 2, respectively.

In view of this, an ACO-SA intelligent collaborative decision-making framework is designed in this paper: the swarm intelligence search capability of ACO is used to analyze the topological structure of scheduling problems; the probabilistic jumping characteristic of SA is introduced to enhance the algorithm’s ability to escape local solutions; and global exploration and local development are balanced through a dynamic parameter collaboration mechanism.

This framework gives full play to the complementary advantages of the two algorithms and provides an efficient solution for VPP resource intelligent decision-making under complex constraints.

2.1. ACO-SA Algorithm Flow

The improved ACO-SA integrates the dual advantages of ACO and SA through an intelligent collaborative decision-making mechanism, effectively solving the core defect of insufficient parameter adaptability in traditional methods: a dynamic adjustment strategy is designed to adapt to variable VPP operating scenarios for the problem that key parameters such as pheromone volatilization coefficient and pheromone heuristic factor rely on empirical settings; meanwhile, it significantly improves the solution quality of ACO and the convergence speed of SA. In particular, the decision variable x_ij(t) is proposed to make power supply decisions more flexible and specific; that is, to supply power to loads according to the percentage of power generation according to specific conditions so that the solution result is better, the algorithm search accuracy is significantly improved, the solution speed is accelerated, and the solution quality is enhanced. The operation process of the algorithm is shown in Figure 3.

The steps for solving the optimal solution of the VPP resource intelligent decision-making economic model using the improved ACO-SA are as follows:

(1)

Initial ACO parameters are randomly generated, and a complete intelligent decision-making scheme is randomly constructed;

(2)

The objective function value f is calculated according to the constructed intelligent decision-making scheme;

(3)

ACO pheromones are updated;

(4)

A set of new ACO parameters is generated by applying random perturbations in the neighborhood of the current ACO parameters;

(5)

A new intelligent decision-making scheme is reconstructed by ACO using the perturbed parameters, and the objective function value f is calculated;

(6)

Δf = f_n − f_n−1 is judged; if Δf ≤ 0, the new solution is accepted, and whether the annealing temperature T reaches the termination threshold T_end is detected;

(7)

If Δf > 0, the inferior solution is accepted with probability p = exp(−Δf/T) according to the Metropolis criterion, and whether the termination threshold T_end is reached is judged;

(8)

If the inferior solution is not accepted according to the Metropolis criterion, the original scheme is used, and whether the termination threshold T_end is reached is judged;

(9)

If T_k ≤ T_end, the optimal collaborative decision-making scheme is output; otherwise, the temperature is updated according to T_k+1 = γT_k, and the process returns to step (3) for iterative optimization until the termination temperature is reached, and the final scheme is determined.

2.2. Optimization Framework of ACO-SA Algorithm

To improve the feasibility and search efficiency of intelligent decision-making schemes, the ACO-SA framework proposed in this paper constructs an intelligent collaborative decision-making framework by integrating the swarm intelligence search mechanism of ACO with the probabilistic perturbation characteristic of SA. Based on the dynamic parameter collaboration strategy, core parameters including pheromone heuristic factor, expected heuristic factor, pheromone matrix, and heuristic information matrix are adaptively adjusted with the iteration process: in the global exploration stage, the guidance of heuristic information on path selection is prioritized to accelerate the coverage of the feasible region; in the local development stage, the feedback of pheromone accumulation on high-quality paths is gradually strengthened to improve convergence accuracy.

2.2.1. Cost-Driven Path Selection Mechanism

In the ACO-SA hybrid optimization framework, the economy of the path selection strategy directly determines the cost-effectiveness of the VPP intelligent decision-making scheme. To achieve efficient exploration of the solution space, a cost-driven path decision mechanism is constructed in this paper, whose core is to quantify the economic cost increment in the state transition process and convert the scheduling objective into heuristic rules for ant colony search.

When distributed energy i supplies power to load j at time t, the total cost change ΔC_ij(t) (CNY) caused by this decision at time t consists of adjustment cost ΔC_gen(t) (CNY), grid interaction cost ΔC_grid(t) (CNY), and incentive compensation cost ΔC_adj(t) (CNY); that is,

$$\Delta C_{ij}(t)=\Delta C_{gen }(t)+\Delta C_{grid }(t)+\Delta C_{adj }(t)$$

(1)

where the adjustment cost ΔC_gen(t) is the adjustment cost of energy, such as photovoltaic and wind energy, and the charge–discharge cost when energy storage equipment is adjusted; that is,

$$\Delta C_{gen}(t)=LCO{E}_i{x}_{ij}(t)P_{gen,i}(t)+x_{ij}\left(t\right)\mu P_{gen,i}^{out}\left(t\right)+\mu P_{gen,i}^{in}\left(t\right)$$

(2)

where LCOE_i (CNY/MWh) is the levelized cost of electricity for photovoltaic or wind power i, which comprehensively considers the full lifecycle cost of distributed energy and is allocated to unit power generation; x_ij(t) represents the decision variable, the proportion of energy i supplying power to load j at time t, satisfying x_ij(t) ∈ [0,1]; P_gen,i(t) (MW) represents the power generation of photovoltaic or wind power i at time t; μ (CNY/MWh) is the cycle life loss cost per unit charge–discharge power of energy storage; $P_{gen,i}^{out}\left(t\right)$ (MW) represents the discharge power of energy storage unit i at time t; and $P_{gen,i}^{in}\left(t\right)$ (MW) represents the charge power of energy storage unit i at time t.

When energy i supplies power to load j at time t, compared with completely relying on grid power supply, this will reduce the electricity purchased by VPP from the grid (or increase the electricity sold to the grid), and the resulting change in the grid interaction cost is as follows:

$$\Delta C_{grid}(t)=C_{buy}\left(t\right)P_{grid,in}(t)-C_{sell}\left(t\right)P_{grid,out}(t)$$

(3)

where C_buy(t) (CNY/MWh) represents the electricity price at which VPP purchases electricity from the grid at time t; P_grid,in(t) (MW) represents the electricity purchased by VPP from the grid at time t; P_grid,out(t) (MW) represents the electricity sold by VPP to the grid at time t; and C_sell(t) (CNY/MWh) represents the electricity price at which VPP sells electricity to the grid at time t;

When energy i supplies power to load j at time t, the incentive compensation cost ΔC_adj is as follows:

$$\Delta C_{adj}(t)=C_{adj,j}\Delta L_j(t)$$

(4)

where ΔC_adj(t) represents the adjustment cost of incentive compensation for adjustable load j at time t; ΔL_j(t) (MW) represents the adjustment amount of adjustable load j at time t.

In the above formulas, i ∈ I, j ∈ J, t ∈ T, I is the set of schedulable distributed energy sources, J is the set of adjustable loads, and T is the set of scheduling periods.

To integrate formulas, simplify calculations, and enhance the distinguishability of heuristic information, and avoid configuration scheme selection deviations caused by dimension differences, normalization is performed:

$$d_{ij}={\displaystyle \frac{\max \left(0,-\Delta C_{ij}\right)}{{\max }_{s\in allowed }\left(-\Delta C_{is}\right)+\epsilon }}$$

(5)

where ΔC_is reflects the cost change caused by energy allocation from the current energy node i to the selectable state s; ε is a very small positive number used to avoid zero denominator; d_ij is inversely proportional to the cost reduction amplitude, i.e., the greater the cost reduction, the smaller d_ij, and the higher the probability of selecting this path.

The heuristic information is η_ij, whose design follows the principle of cost minimization: the greater the cost reduction amplitude, the higher the heuristic information value η_ij, and the higher the probability of the corresponding path being selected:

$${\eta }_{ij}={\displaystyle \frac{1}{d_{ij}}}$$

(6)

where η_ij represents the expected cost reduction degree brought by selecting path (i,j), which is the path heuristic information.

After ant Q completes all path construction, i.e., constructs a complete intelligent decision-making scheme, the total cost C_Q corresponding to this scheme is calculated. Pheromones are updated according to the cost value. For path (i,j), the pheromone update equation is as follows:

$${\tau }_{ij}(t+1)=(1-\rho ){\tau }_{ij}(t)+{\displaystyle \sum _{Q=1}^m\Delta }{\tau }_{ij}^Q$$

(7)

where Δ${\tau }_{ij}^Q$ is the pheromone increment after selecting (i,j); the pheromone increment Δ${\tau }_{ij}^Q$ reflects the relationship between the quality of the intelligent decision-making scheme constructed by ant Q and its selection of path (i,j). The lower the total cost C_Q, the greater the pheromone increment Δ${\tau }_{ij}^Q$ released by ant Q on path (i,j):

$$\Delta {\tau }_{ij}^Q=\left\{\begin{array}{ll}{\displaystyle \frac{1}{C_Q}}\hfill & choose\left(i,j\right)\hfill \\ 0\hfill & otherwise\hfill \end{array}\right.$$

(8)

where C_Q is the cost; pheromone update will affect subsequent path selection and then affect the decision-making of equipment participating in scheduling.

In summary, ant Q selects the next energy–load pair (i,j) to be matched according to the following path selection probability equation:

$$P_{ij}^Q={\displaystyle \frac{{\left[{\tau }_{ij}\right]}^{\alpha }{\left[{\eta }_{ij}\right]}^{\beta }}{{\displaystyle {\sum }_{s\in allowe{d}_Q}{\left[{\tau }_{is}\right]}^{\alpha }{\left[{\eta }_{is}\right]}^{\beta }}}}$$

(9)

where α is the pheromone importance factor, β is the heuristic information importance factor, τ_ij is the pheromone concentration, η_ij is the heuristic information value, allowed_Q represents the set of states that ant Q can select in the next step, s represents a specific optional state node in the set allowed_Q, τ_is represents the pheromone value of the next state (i,s) selected by the ant, and η_is represents the heuristic information value of the next state selected by the ant. A complete intelligent decision-making scheme is constructed through continuous selection, and finally, a decision variable matrix x_ij(t) is formed.

2.2.2. Parameter Perturbation and Annealing Convergence Control

ACO can generate a preliminary intelligent decision-making scheme under the cost-driven path selection mechanism, but its performance is highly dependent on parameter configuration. Empirical parameter settings are difficult to adapt to the complex scenarios of VPP with multiple temporal and spatial scales, which easily leads to a decrease in convergence speed or trapping in local suboptimal solutions. To overcome this defect and integrate the global exploration advantages of SA, a parameter perturbation mechanism and an annealing convergence control strategy are introduced in this section, which constitute the second core mechanism of the ACO-SA hybrid optimization framework.

New ACO parameters are generated in the neighborhood of the current ACO parameters through certain perturbation rules, i.e.,

$$\left\{\begin{array}{l}\rho \prime =\rho +\Delta \rho \Delta \rho \in \left[-0.05,0.05\right]\\ \alpha \prime =\alpha +\Delta \alpha \Delta \alpha \in \left[-0.5,0.5\right]\\ \beta \prime =\beta +\Delta \beta \Delta \beta \in \left[-0.5,0.5\right]\\ m\prime =m+\Delta m \Delta m\in \left[-50,50\right]\end{array}\right.$$

(10)

The objective function value change is calculated; the current ACO parameters and newly generated ACO parameters are substituted, respectively, to obtain the corresponding objective function values f_n and f_n−1, and the objective function value change Δf = f_n − f_n−1 (CNY) is calculated.

If Δf ≤ 0, this indicates that the new solution is better than or equal to the current solution, and the newly generated ACO parameters are directly accepted; if Δf > 0, the newly generated ACO parameters are accepted with probability p = exp(−Δf/T) according to the Metropolis criterion; a random number k in the interval [0,1] is generated; if k < P, the newly generated ACO parameters are accepted; otherwise, the current ACO parameters are retained.

Whether the current temperature T_k reaches the termination temperature T_end is checked; if not, iteration continues; if the termination temperature is reached, the final scheme is determined.

The temperature is updated according to the cooling rate γ, i.e., the exponential cooling strategy T_k+1 = γT_k is adopted. As the temperature decreases, the probability of the algorithm accepting inferior solutions gradually decreases, and the search gradually focuses on local optimal solutions.

Whether the current temperature T_k reaches the termination temperature T_end is checked. If not, return to the “generate new solution” step to continue iteration; if the termination temperature is reached, stop SA.

A matrix related to x_ij(t) is generated according to the final result, which is actually matching energy and loads in VPP; the finally determined intelligent collaborative decision-making is a better intelligent decision-making scheme and the final cost.

This mechanism realizes dynamic and adaptive optimization of key parameters by performing guided random perturbations in the ACO parameter space and combining with the probability acceptance criterion of SA, thereby effectively improving the robustness and optimization efficiency of the algorithm under complex constraints.

3. VPP Resource Intelligent Decision-Making Cost Model

3.1. Objective Function

The cost of VPP resource intelligent decision-making mainly consists of the power generation cost of distributed energy sources, the interaction cost between VPP and the grid, and the adjustment cost of adjustable loads:

$$\begin{array}{c}f=\min C_Q\\ ={\displaystyle {\sum }_{t\in T}{\displaystyle {\sum }_{j\in J}{\displaystyle {\sum }_{i\in I}\left(\begin{array}{l}{x}_{\mathit{ij}}\left(t\right){\mathit{LCOE}}_i{P}_{\mathit{gen},i}\left(t\right)\\ {+x}_{\mathit{ij}}\left(t\right){\mu P}_{\mathit{gen},i}^{\mathit{out}}\left(t\right){+\mu P}_{\mathit{gen},i}^{\mathit{in}}\left(t\right)\end{array}\right)}}}\\ +{\displaystyle {\sum }_{t\in T}\left(\begin{array}{l}{C}_{buy}(t)P_{grid,in}(t)-C_{sell}(t)P_{grid,out}(t)\\ +{\displaystyle {\sum }_{j\in J}\left(C_{adj,j}\left|\Delta L_j(t)\right|\right)}\end{array}\right)}\end{array}$$

(11)

The solution dimensionality of the objective function C_Q is determined by the number of decision variables, which directly reflects the scale and complexity of the optimization problem. The dimensionality of the objective function is given by the product of I, J, and T. The total cost C_Q is composed of three parts, each of which depends on a series of physical and economic parameters. The distributed energy generation cost is primarily influenced by LCOE. In addition, this component is also affected by the unit cycle life loss cost μ of the energy storage equipment. The grid interaction cost is entirely driven by the time-of-use electricity price mechanism, with the key input parameters being C_buy(t) and C_sell(t). These electricity price parameters are time-varying, and their specific values are determined by the external electricity market. The incentive compensation cost for adjustable loads depends on the incentive electricity price and the adjustable potential of the loads. The adjustable potential of the loads is a critical input parameter that defines the upper and lower limits by which each load can increase or decrease its electricity consumption in each time period. In summary, the objective function is dependent upon 15 parameters.

3.2. Constraints

Constraints mainly include VPP power balance constraints, energy storage equipment charge–discharge power balance constraints, distributed energy output constraints, adjustable load adjustment amount constraints, and energy storage equipment power constraints.

(1)

VPP capacity balance constraints

The real-time balance of power supply and demand of VPP in each scheduling period t shall be ensured. In each period t, the power generation of distributed energy sources, the charge–discharge power of energy storage equipment, the interaction amount with the grid, and the adjustment amount of adjustable loads shall satisfy the following capacity balance relationship, i.e., the total power generation when energy storage discharges are equal to the total load demand considering load adjustment and energy storage charging:

$$\begin{array}{l}{\displaystyle \sum _{j\in J}{\displaystyle \sum _{i\in I}{x}_{ij}(t)P_{gen,i}}(t)}+P_{grid}(t)+{\displaystyle \sum _{j\in J}{\displaystyle \sum _{i\in I}{x}_{ij}(t)P_{gen,i}^{out}\left(t\right)}}+P_{gen,i}^{in}\left(t\right)\\ ={\displaystyle \sum _{j\in J}\left(L_j^0(t)+\Delta L_j(t)\right)} \forall t\in T\end{array}$$

(12)

where $L_j^0$(t) (MW) represents the original load demand of adjustable load j at time t.

(2)

Energy storage equipment charge–discharge power balance constraints

Within the scheduling cycle, the total discharge energy and total charge energy of energy storage equipment shall satisfy the balance relationship to ensure the charge–discharge balance of energy storage equipment within a day:

$${\displaystyle \sum _{t=1}^{t=24}{P}_{gen,i}^{out}\left(t\right)}={\displaystyle \sum _{t=1}^{t=24}{P}_{gen,i}^{in}\left(t\right)}$$

(13)

(3)

Distributed energy capacity constraints

The power generation of distributed energy i at each period t shall be within its allowable minimum and maximum power generation ranges to limit the operation range of distributed energy and ensure the feasibility of the intelligent decision-making scheme:

$$P_{gen,\min ,i}\le {\displaystyle {\sum }_{j\in J}{x}_{ij}(t)P_{gen,i}(t)}\le P_{gen,\max ,i} \forall i\in I,t\in T$$

(14)

where P_gen,min,j (MW) is the minimum power generation of distributed energy i, and P_gen,max,j (MW) is the maximum power generation of distributed energy i.

(4)

Adjustable load adjustment amount constraints

The adjustment amount of adjustable load j at each period t shall be within its allowable minimum and maximum adjustment amount ranges to limit the operation range of adjustable loads and ensure the feasibility of the intelligent decision-making scheme:

$$\Delta L_{\min ,j}\le {\displaystyle {\sum }_{i\in I}{x}_{ij}(t)}\Delta L_j(t)\le \Delta L_{\max ,j} \forall j\in J,t\in T$$

(15)

where ΔL_min,j (MW) is the minimum adjustment amount of adjustable load j, and ΔL_max,j (MW) is the maximum adjustment amount of adjustable load j.

(5)

Energy storage equipment power constraints

The discharge power of energy storage equipment i at each period t shall meet the minimum and maximum discharge power limits; its charge power shall meet the minimum and maximum charge power limits to limit the operation range of energy storage equipment and ensure the feasibility of the intelligent decision-making scheme:

$$P_{gen,\min ,i}^{cn}\le P_{gen,i}^{out}\left(t\right)\le P_{gen,\max ,i}^{cn} \forall i\in I,t\in T$$

(16)

$$P_{gen,\min ,i}^{cn}\le P_{gen,i}^{in}\left(t\right)\le P_{gen,\max ,i}^{cn} \forall i\in I,t\in T$$

(17)

where $P_{gen,min,i}^{cn}$ (MW) is the minimum charge–discharge power of energy storage equipment i, and $P_{gen,max,i}^{cn}$ (MW) is the maximum charge–discharge power of energy storage equipment i.

The core of applying the ACO-SA algorithm to VPP scheduling lies in mapping complex scheduling problems to ant colony optimization path search problems. Within this framework, the process of solution construction by an ant represents the generation of a complete day-ahead scheduling scheme, whose path is composed of a series of decision variables x_ij(t), indicating the proportion of power supplied from distributed energy source i to load j during time period t. Pheromones τ_ij are deposited on the “energy–load” pairing relationships, characterizing the superiority or inferiority of such decisions in historical experience; heuristic information η_ij is directly driven by the cost model and is inversely proportional to the cost variation, thereby guiding ants to preferentially select power supply paths that can reduce the total cost. Ant colonies collaboratively explore the solution space through state transition rules, quickly locating regions of high-quality scheduling schemes.

Meanwhile, the Simulated Annealing mechanism, as a high-level optimization strategy, injects adaptive perturbation capability into the algorithm by perturbing key parameters of ACO and probabilistically accepting new parameter sets according to the Metropolis criterion. This design effectively prevents ant colonies from falling into local optima due to the premature concentration of pheromones and significantly enhances the global exploration performance of the algorithm under complex high-dimensional constraints. The deep integration of ACO and SA enables the algorithm to not only utilize the directional search efficiency of ant colonies but also stably converge to the global optimal solution by virtue of the probabilistic jumping characteristics of the annealing mechanism, thus providing an efficient solution for economical and highly reliable scheduling of VPP.

4. Case Verification and Analysis

To verify the effectiveness and universality of the ACO-SA hybrid algorithm in VPP resource intelligent decision-making, multi-scenario comparative experiments are designed in this study. Cases are constructed based on real operation data, covering agricultural and industrial load characteristics and complexity with/without energy storage systems. Through comparison with benchmark algorithms such as ACO, SA, GA, and PSO, algorithm performance is comprehensively evaluated from three dimensions: convergence speed, solution quality, and calculation efficiency. All case data are derived from actual systems to ensure the reproducibility and engineering reference value of the experimental results. The following will discuss scenario modeling, parameter configuration, and comparative analysis. To validate the effectiveness and applicability of the proposed model, China’s Lankao Energy Revolution Pilot was selected as the object for case study analysis in this paper.

4.1. Agricultural Park VPP Model

This case (Case 1) takes a typical agricultural park in North China as the research object; its distributed energy structure is dominated by renewable energy such as wind power and photovoltaic, and the load composition mainly includes agriculture, resident, and factory. The core reason for selecting this scenario is that the agricultural park load has significant diurnal time-sharing characteristics, and the output of distributed energy and the agriculture cycle have temporal and spatial coupling, which can effectively verify the algorithm’s performance in handling the “source-load” dynamic matching problem. The following will analyze four aspects: output characteristics of distributed energy, load demand curve, adjustable load characteristics, and algorithm parameters.

Figure 4 shows the predicted output of wind power plant (WPP) and photovoltaic (PV) on a typical day in the agricultural park, where the photovoltaic LCOE is 336 CNY/MWh and the wind power LCOE is 231 CNY/MWh.

As shown in Figure 4, the predicted output of WPP and PV on a typical day shows significant differences. Wind farm output characteristics: the output is high from 20:00 to 9:00 the next day and remains stable from 9:00 to 19:00; this characteristic is derived from the inertial characteristics of atmospheric movement, and its continuity makes the wind power output change smoothly without significant step changes. Photovoltaic output characteristics: the output is zero from 17:00 to 7:00 the next day; it shows a single-peak curve after 7:00 and reaches the peak at 13:00. This phenomenon is determined by the periodic change in solar radiation caused by the Earth’s rotation: after sunrise, the increase in the solar altitude angle enhances irradiance, and the output power of photovoltaic modules increases monotonically; the irradiance reaches the peak around noon; and the power decreases exponentially in the afternoon as the solar altitude angle decreases. The complementary characteristics of wind and solar output provide natural temporal and spatial regulation resources for VPP scheduling.

Figure 5 shows the typical daily demand curves of multiple types of loads in the region, and Figure 6 shows the corresponding time-sharing electricity price distribution.

As shown in Figure 5, the daily demand curves of the three types of loads show significant differences. Industrial load maintains high operation from 6:00 to 18:00, reaches the peak from 9:00 to 15:00, and drops to the base load level from 00:00 to 06:00; its quasi-stable characteristics are derived from the continuous production process and the operation inertia of industrial equipment. Residential load shows a typical double-peak structure, with a high load demand from 6:00 to 9:00 and 18:00 to 22:00. Agricultural load demand increases significantly from 9:00 to 12:00, which is highly coupled with the operation periods of irrigation systems, greenhouse environment control, and processing equipment. This load temporal and spatial distribution characteristic forms a supply–demand linkage pattern with the time-sharing electricity price mechanism shown in Figure 6.

Figure 7 shows the typical daily adjustable characteristics of multiple types of loads in the agricultural park, and Figure 8 shows the corresponding incentive compensation electricity price mechanism.

As shown in Figure 7, the adjustable amount of agricultural load is positive from 7:00 to 21:00, and load reduction is achieved through peak-shifting irrigation and optimal start–stop of greenhouse equipment; the adjustable amount is negative from 22:00 to 06:00, and water storage irrigation and heat preservation operation are carried out using off-peak electricity prices. Residential load has significant positive adjustment characteristics from 7:00 to 21:00, which is achieved through temperature control setting adjustment and shutdown of non-essential electrical appliances; it has prominent negative adjustment capability from 22:00 to 06:00, mainly contributed by timed start–stop electric water heaters and smart home appliances. The positive adjustment amount of industrial load is positive from 7:00 to 21:00, and the negative adjustment from 22:00 to 06:00 is supported by continuous production equipment and energy storage systems. This adjustment characteristic is coordinated with the time-sharing electricity price in Figure 6; positive adjustment is concentrated in peak electricity price periods, and negative adjustment responds to off-peak electricity prices, effectively realizing peak shaving and valley filling.

4.2. Industrial Park VPP Model

After completing the analysis of the agricultural park VPP model, to explore the operation characteristics of VPP in heterogeneous industrial scenarios, this section focuses on the industrial park VPP model (Case 2). Its load structure shows significant differences; industrial load is dominant, with characteristics such as strong continuity, high stability, and high energy density. The load driving mechanism is different from the natural condition dependence of agricultural scenarios, mainly dominated by production processes, equipment operation cycles, and production scheduling strategies. By constructing this model, the impact of distributed energy configuration and scheduling strategies on system economy and reliability can be quantitatively evaluated. The following will analyze the dimensions of distributed energy output, load demand characteristics, adjustable load potential, and algorithm parameters, combined with the wind and solar output characteristics of the predicted output of WPP and PV on a typical day in an industrial park shown in Figure 9; the LCOE is the same as that in Case 1.

As shown in Figure 9, the wind and solar output on a typical day in the industrial park show complementary characteristics; WPP has a high output from 17:00 to 7:00 the next day and remains stable from 8:00 to 16:00; PV has zero output from 19:00 to 6:00 the next day and shows a single-peak curve after 6:00, with the theoretical peak at 13:00.

Figure 10 shows the daily demand characteristics of multiple types of industrial loads in the region, and Figure 11 shows the corresponding time-sharing electricity price mechanism; both jointly constitute the input boundary conditions of the industrial VPP scheduling model.

As shown in Figure 10, the multi-energy loads in the industrial park show typical characteristics; the power load has a significant single-peak distribution, reaching the peak at 12:00 noon, maintaining a high level during the day, and dropping to the base load at night. This change is mainly driven by the start–stop of production equipment and the temporal distribution of lighting loads. Cooling load and heating load continue to rise from 9:00 to 18:00, which is strongly positively correlated with solar irradiance, reflecting the dynamic response of temperature control equipment to outdoor thermal disturbances. Heating load operates stably throughout the day, with a slight increase at noon due to the utilization of process waste heat, reflecting the dominant role played by thermal inertia in industrial processes. This load characteristic forms supply–demand coupling with the time-sharing electricity price in Figure 11, driving the optimization of VPP scheduling strategies.

Figure 12 shows the typical daily adjustable potential of multiple types of loads in the industrial park, and Figure 13 shows the corresponding distribution of incentive compensation electricity prices; both jointly constitute the core parameter set of demand response strategies.

As shown in Figure 12, the adjustable potential of multi-energy loads in the industrial park shows different characteristics; the power load reaches the peak at around 12:00, and non-critical equipment loads can be reduced, lighting and air conditioning power can be modulated, and smart home demand response can be implemented through production scheduling optimization. Although cooling load and heating load account for a small proportion, they have continuous adjustment capabilities, and load reduction can be achieved through the process of thermal inertia optimization and temperature control setting adjustment. This adjustment behavior is driven by the incentive electricity price shown in Figure 13; the compensation electricity price is high in peak periods, which effectively guides load shifting. The user response mechanisms include industrial users that optimize the start–stop sequence of production equipment and operate high-energy-consuming equipment in off-peak periods; commercial users that automatically adjust the operation power of heating, ventilation, and air conditioning systems to reduce peak demand; and residential users that delay the start–stop of high-energy-consuming electrical appliances based on demand response programs.

4.3. Industrial Park VPP Model with Energy Storage

After completing the analysis of VPP models for agricultural parks and industrial parks, an industrial park VPP model with energy storage (Case 3) is further constructed in this study to explore scheduling characteristics in high-dimensional constraint scenarios. As a key element of VPP, energy storage systems can effectively suppress the intermittency and volatility of wind and solar output through their charge–discharge characteristics, significantly enhancing system stability and reliability. In this model, energy storage systems mainly improve economy by arbitraging through peak-valley electricity price differences, and they also have auxiliary functions such as providing power support in the case of faults and suppressing frequency fluctuations caused by industrial impact loads. This case comprehensively considers parameters such as energy storage capacity and charge–discharge efficiency and combines industrial process thermal inertia and production scheduling constraints to construct a multi-time scale economic scheduling model. The key parameters of energy storage are shown in

Table 1. Energy storage equipment parameters.

μ	${\mathit{P}}_{\mathit{g}\mathit{e}\mathit{n},\mathit{i}}^{\mathit{o}\mathit{u}\mathit{t}}$(t)	${\mathit{P}}_{\mathit{g}\mathit{e}\mathit{n},\mathit{i}}^{\mathit{i}\mathit{n}}$(t)	${\mathit{P}}_{\mathit{g}\mathit{e}\mathit{n},\mathit{m}\mathit{i}\mathit{n},\mathit{i}}^{\mathit{c}\mathit{n}}$	${\mathit{P}}_{\mathit{g}\mathit{e}\mathit{n},\mathit{m}\mathit{a}\mathit{x},\mathit{i}}^{\mathit{c}\mathit{n}}$
200 CNY/MWh	30 MW	30 MW	0 MW	30 MW

.

The energy storage system in this case is a lithium-ion battery energy storage system. Except for energy storage system parameters, all key VPP operation parameters in this case are consistent with those of the industrial park model in Section 4.2.

4.4. Parameter Configuration

4.4.1. Algorithm Parameter Settings

Table 2. Parameter settings of ACO-SA, ACO, and SA.

ACO-SA		ACO	SA
T0	5000		5000
Tend	0.1		0.1
γ	0.98		0.98
ρ	0.1	0.1
α	1	1
β	2	2
Nant	20	20

shows the parameter settings of ACO-SA, ACO, and SA in this study.

Table 3. Parameter settings of GA and PSO.

GA		PSO
Npop	50	Nparticle	30
Pc	0.8	C1	2
Pm	0.05	C2	2

shows the parameter settings of GA and PSO in this study.

Prior to conducting comparative experiments in this paper, parameter tuning was performed for all algorithms involved in the comparison. Multiple rounds of tests were carried out on the mentioned key parameters to identify the parameter combinations that enable each algorithm to perform relatively better on the specific problem addressed in this paper. The parameters presented in Table 2 and Table 3 of this paper are exactly the values determined after such tuning.

4.4.2. Grid Interaction Electricity Price Mechanism

Table 4. Time-sharing electricity prices for VPP to sell electricity to the grid.

Time Period	Electricity Price
0:00–8:00	109.95 CNY/MWh
9:00–10:00	209.05 CNY/MWh
11:00–15:00	323.9 CNY/MWh
16:00–18:00	209.05 CNY/MWh
19:00–21:00	323.9 CNY/MWh
22:00–24:00	209.05 CNY/MWh

shows the time-sharing electricity price mechanism for VPP to participate in the electricity market.

4.5. Convergence Characteristic Analysis

Figure 14 compares the convergence characteristics of five optimization algorithms in the scheduling of agricultural park VPP (Case 1). The horizontal axis is the number of iterations, and the vertical axis is the total scheduling cost (unit: CNY). The convergence curve shows that with iteration, the cost of each algorithm decreases monotonically and converges asymptotically; among them, the convergence curve of ACO-SA decreases the fastest and reaches the lowest cost at the same number of iterations, which is significantly better than other algorithms.

By integrating the global search capability of ACO and the local optimal escape capability of SA, ACO-SA rapidly reduces the cost in the early iteration stage, i.e., it achieves rapid convergence. ACO is prone to trapping in local optima due to the dependence of pheromone update on empirical parameters, resulting in unreliable solution quality. SA requires more iterations to reach a stable solution due to low search efficiency and lack of ability to utilize problem structure information, with a higher final cost. PSO performs well in the middle stage, but its convergence speed is lower than that of ACO-SA, and its convergence curve oscillates under complex constraints. GA relies on crossover/mutation operations, resulting in slow convergence speed and low solution quality.

Figure 15 compares the convergence performance of five algorithms in the industrial VPP scenario. It can be seen from the curve trend that with the increase in the number of iterations, the cost of each algorithm decreases gradually and finally stabilizes. Among them, the convergence curve of ACO-SA decreases the fastest and reaches the lowest cost at the same number of iterations, which is significantly better than other algorithms.

Through the dynamic parameter collaborative adjustment mechanism, the ACO-SA algorithm balances global exploration and local development under complex constraints to achieve efficient search, quickly approaches the optimal solution in the early iteration stage, and the curve decreases smoothly, indicating that its parameter adaptive mechanism effectively suppresses oscillations in the search process. ACO has a fast convergence speed but fluctuates in the later iteration stage, and its final solution quality is the lowest due to parameter dependence on empirical settings. SA has a fast cost decrease in the early stage but stagnates in the later iteration and cannot be further optimized. PSO has a fast convergence speed, but its solution quality is still lower than that of ACO-SA. GA has large fluctuations in the convergence curve due to the randomness of crossover/mutation operations, with low solution quality.

Figure 16 shows the comparison of convergence performance of five optimization algorithms in intelligent decision-making for industrial VPP resources with energy storage. It can be seen from the curve trend that with the increase in the number of iterations, the cost of each algorithm decreases gradually and finally stabilizes. Among them, the convergence curve of ACO-SA decreases the fastest and reaches the lowest cost at the same number of iterations, which is significantly better than other algorithms.

The ACO-SA algorithm basically stabilizes the cost after about 185 iterations, achieving rapid convergence, which verifies the efficiency of its two-stage optimization mechanism integrating ACO global search and SA local escape. Although ACO has a fast convergence speed, its final cost is high due to fixed parameter settings. SA decreases slowly in the early stage and is prone to trapping in local optima in the later stage, with a high cost. The convergence curve of PSO tends to be flat in the middle and later stages, but the cost value is still significantly higher than that of ACO-SA. GA has convergence oscillations due to the randomness of genetic operations (crossover/mutation), and none of the comparative algorithms reach the optimization level of ACO-SA.

4.6. Optimization Performance Comparison

Figure 17 compares and analyzes the total scheduling costs of ACO-SA, PSO, GA, SA, and ACO in three case scenarios: agricultural park VPP, industrial park VPP, and industrial park VPP with energy storage. Figure 18 compares the number of iterations required for each algorithm to reach a convergent state in different cases. Figure 19 compares the time required for each algorithm to reach a convergent state in different cases.

The analysis results show that the ACO-SA algorithm achieves the lowest total scheduling cost in the three cases of agricultural park VPP, industrial park VPP, and industrial park VPP with energy storage, and the standard deviation of its multiple operation results is the smallest, which fully confirms the stability advantage of the algorithm in different application scenarios.

Further comparison of industrial and agricultural park VPP case shows that in terms of scheduling cost, ACO-SA is significantly lower than the four benchmark algorithms; in terms of convergence efficiency, the number of iterations required for ACO-SA to reach a convergent state is also less than that of other algorithms, in terms of computation time, ACO-SA is also lower than the four benchmark algorithms, PSO, GA, SA, and ACO, which verifies that ACO-SA has good universality and performance stability in scenarios with heterogeneous load characteristics.

Similarly, comparing the standard industrial park VPP and the industrial park VPP with the energy storage case, the scheduling cost of ACO-SA is better than that of comparative algorithms in both scenarios. Although the charge–discharge constraints of energy storage systems significantly increase the dimension and complexity of the optimization problem, ACO-SA effectively optimizes the charge–discharge strategy of energy storage and the interaction behavior with the grid through its dynamic parameter collaborative adjustment mechanism, thereby reducing the total system cost. In contrast, it is difficult for PSO and GA to accurately meet the capacity balance constraints of energy storage systems, resulting in high costs; SA and ACO have poor cost performance due to insufficient search capabilities. In terms of convergence speed, the average number of iterations required for ACO-SA to converge in both case is less than that of other algorithms, and in terms of computation time, the average computation time required for ACO-SA to reach convergence in the two cases is less than that of other algorithms, which further reflects the excellent calculation efficiency and stability of the algorithm when facing different system complexities in the same application scenario.

Comprehensive comparison and analysis show that the number of iterations required for the ACO-SA algorithm to converge in various case is significantly less than that of comparative algorithms, which strongly verifies its advantage in efficient calculation efficiency.

This framework provides technical support for the large-scale accommodation of volatile renewable energy. At the policy level, it can assist governments in formulating more aggressive targets for high-proportion renewable energy grid integration and replace some traditional fossil energy peak-regulating units through precise VPP scheduling, directly promoting emission reduction in the power industry. Beyond the cases selected in this paper, the model and algorithm can be widely applied to energy aggregation scenarios such as urban commercial districts, data centers, and 5G base station clusters, enabling cross-regional collaborative optimization of distributed resources. Its core value lies in providing a standardized and scalable efficient decision-making tool, which can significantly improve the economy and operational reliability of new power systems and accelerate the green transformation of social energy structures.

This study validates the core performance of the ACO-SA algorithm in solving VPP economic scheduling problems. However, this research is based on an idealized communication network assumption. In practical deployment, as a cyber–physical system, the scheduling performance of VPP may be severely affected by communication delays, data packet loss, and even cyber attacks [25,26]. These network constraints could prevent scheduling commands from being executed timely and accurately, thereby compromising the system’s economy and security.

Therefore, future research will focus on the following directions: (1) Developing robust scheduling models that incorporate network uncertainties, modeling delays, and packet loss as uncertain parameters to enhance the elasticity of scheduling schemes against network disturbances; (2) designing integrated cooperative frameworks incorporating intrusion detection and security control strategies to defend against cyber attacks targeting scheduling systems, ensuring that VPP can maintain secure and stable operation even under attack; and (3) conducting further in-depth research based on the digital PID-type load frequency control scheme designed by learning from Shangguan et al. [27], which comprehensively considers the influence of data sampling, transmission delay, and nonlinearity factors and adopts a warm-up gray wolf optimization algorithm.

5. Conclusions

A two-layer optimization mechanism integrating dynamic pheromone update and annealing temperature collaborative adjustment is proposed in this paper to solve the problems of slow convergence, easy trapping in local optima of ACO, and low search efficiency of SA. Normalized heuristic information is introduced to enhance the distinguishability of path selection, effectively avoiding deviations caused by dimension differences; a percentage-based power supply decision variable is innovatively introduced to break through the limitation of traditional binary decisions, significantly improving the flexibility and engineering feasibility of energy allocation strategies. Comparative experiments based on three typical scenarios, including agricultural parks, industrial parks, and industrial parks with energy storage systems, show that ACO-SA maintains excellent stability under different load characteristics and system complexities.

Experimental verification shows that ACO-SA exhibits the following significant advantages in terms of VPP resource intelligent decision-making:

Fast convergence and efficient search: By integrating the topological analysis capability of ACO and the global optimization capability of SA, the algorithm quickly approaches the optimal solution in the early iteration stage, and its convergence efficiency is significantly improved compared with single ACO. The dynamic parameter adjustment strategy effectively reduces redundant searches and significantly shortens the average calculation time in high-dimensional constraint scenarios.

Global optimization and improved solution quality: This hybrid mechanism effectively overcomes the defect that traditional algorithms are prone to trapping in local optima. By intelligently and collaboratively optimizing the output strategy of distributed energy sources, the charge–discharge plan of energy storage, and the adjustment behavior of loads, ACO-SA achieves the lowest scheduling cost in agricultural, industrial, and energy storage scenarios, and the standard deviation of multiple independent operation results is the smallest, verifying its strong robustness and high solution stability.

Multi-scenario adaptability: In high-dimensional constraint scenarios with energy storage systems, ACO-SA can accurately meet the charge–discharge power limits and dynamic energy balance constraints of energy storage systems through the dynamic parameter perturbation mechanism; its scheduling cost is significantly lower than that of comparative algorithms such as PSO, and the number of iterations required for convergence is smaller, fully highlighting its strong adaptability to complex working conditions.

Based on the simulation results of three typical cases, the novelty of this study is reflected in three aspects: first, the proposed ACO-SA deep fusion mechanism and dynamic parameter adjustment strategy outperform existing single algorithms or simple hybrid strategies, with significantly superior convergence speed and solution quality compared to traditional algorithms, providing a more effective tool for VPP optimization under high-dimensional constraints; second, the innovative introduction of percentage-based continuous decision variables x_ij(t), which depict the flexible matching between energy and loads more precisely than binary variables, enhancing the flexibility and economy of scheduling schemes; and third, the verification of the algorithm’s universality and stability in agricultural parks, industrial parks, and industrial parks with energy storage systems, providing empirical evidence for its application in polymorphic VPPs.