Optimal Scheduling of Hydro–Thermal–Wind–Solar–Pumped Storage Multi-Energy Complementary Systems Under Carbon-Emission Constraints: A Coordinated Model and SVBABC Algorithm

Abstract

This paper focuses on power system scheduling problems, aiming to enhance energy utilization efficiency through multi-energy complementarity. To support the “dual-carbon” strategic goals, this paper proposes a coordinated dispatch model for hydro–thermal–wind–solar–pumped storage integrated energy systems, aiming to enhance energy utilization efficiency and system flexibility while reducing carbon emissions. To address issues such as premature convergence and low computational efficiency in traditional optimization algorithms for multi-energy complementary dispatch, an improved Artificial Bee Colony algorithm named Super-quality Variation Burst Artificial Bee Colony (SVBABC) is developed, which incorporates elite solution guidance and an explosion variation mechanism. Simulation results based on a regional practical power system demonstrate that compared to classical methods (e.g., Artificial Bee Colony, Fireworks Algorithm, and Ant Lion Optimizer), SVBABC exhibits significant advantages in global optimization capability and convergence stability. This study provides an innovative solution for efficient dispatch of multi-energy complementary systems. Through synergistic regulation of pumped storage and thermal power, the accommodation capability of renewable energy is effectively enhanced, thereby providing critical technical support for the development of new power systems.

1. Introduction

With the advancement of the “dual carbon” policy and the continuous increase in renewable energy penetration within power systems, multi-energy complementary coordinated optimization dispatch technology has emerged as a core breakthrough for constructing new power systems [1,2]. This technology exploits the complementary characteristics of various energy sources to achieve organic coordination between renewable energy and controllable power sources, thereby significantly enhancing grid operational flexibility and control margins [3].

In recent years, research on the coordinated optimization dispatch of multi-energy complementary systems has made remarkable progress, establishing itself as a pivotal research frontier in the energy field. Existing literature has explored this issue from multiple dimensions, including market mechanisms, temporal coordination, power fluctuation mitigation, and operational optimization. For instance, Reference [4] innovatively established a two-layer optimization framework for cascade hydro-wind-solar-pumped storage systems participating in power markets. By synergistically optimizing day-ahead bidding models and real-time adjustment mechanisms, it achieved a balance between economic benefits and dispatch accuracy. Regarding temporal coordination [5], a method was proposed for generating medium-to-long-term dispatch rules that account for short-term operational risks. Through nested modeling of risk constraints, it effectively reduced the probability of system curtailment and load loss. For power fluctuation mitigation [6], an intraday optimization model was established targeting source-load matching and maximizing clean energy utilization, based on the fluctuating characteristics of renewable generation. This validated the regulatory role of cascade hydropower in balancing wind and solar output fluctuations. At the operational optimization level, Reference [7] pioneered a multi-objective short-term dispatch model prioritizing pumped storage regulation. By incorporating multi-physical constraints spanning hydraulic, mechanical, and electrical systems, it achieved synergistic optimization of economic efficiency and low-carbon performance. Reference [8] introduced a capacity-dispatch co-optimization theory, employing intelligent algorithms to simultaneously solve dispatch rule functions and PV capacity planning, establishing a new research paradigm for integrated planning and operation of hydro-solar complementary systems. However, a theoretical gap remains in existing research regarding the deep co-optimization of cascade hydropower, new energy with thermal power, and pumped storage. Therefore, conducting research on the co-scheduling of hydro, thermal, wind, solar, and pumped storage multi-energy sources not only fills this theoretical void but also provides a crucial methodological foundation for building new power systems.

The construction of multi-energy complementary system dispatch models centers on minimizing comprehensive operating costs. However, the strong coupling characteristics and output uncertainty of renewable energy pose significant challenges to the model solution. Against this backdrop, meta-heuristic algorithms have garnered significant attention due to their outstanding optimization performance. Existing research confirms that various improved intelligent algorithms demonstrate remarkable advantages in this field. Reference [9] applied the chimpanzee optimization algorithm to solve the joint scheduling problem of wind, solar, thermal, and pumped storage, significantly enhancing power generation economic efficiency. Reference [10] improved the solution efficiency of the traditional krill algorithm in integrated energy systems by integrating a linear decay strategy with the particle swarm optimization algorithm. Reference [11] innovatively proposed an adaptive enhanced prey search mechanism, effectively maintaining the population diversity of the whale population algorithm. Reference [12] employed a wavelet mutation strategy to enhance the whale optimization algorithm, achieving breakthroughs in system economic optimization. Reference [5] significantly improved the convergence speed and stability of the moth search algorithm by introducing a greedy strategy and adaptive mutation operators. Reference [13] innovatively applied deep learning technology to the short-term optimization scheduling of water–wind–solar multi-energy complementary systems, achieving maximized power generation revenue. Notably, despite the Artificial Bee Colony algorithm’s outstanding performance in multi-variable function optimization, its application in multi-energy complementary system scheduling remains unexplored, providing a significant opportunity for algorithmic innovation in this paper. A comparison of relevant hybrid metaheuristics for energy system dispatch is shown in

Table 1. Comparison of relevant hybrid metaheuristics for energy system dispatch.

Reference	Main Hybrid Strategy	Advantages	Limitations	SVBABC Contribution
[9]	Chimp Optimization Algorithm	Good convergence	Limited constraint handling	Elite guidance + explosion mutation for complex constraints
[10]	Improved Krill Algorithm	Enhanced efficiency	Premature convergence	Dynamic mutation maintains diversity
[11]	Adaptive Whale Algorithm	Maintains diversity	Complex parameters	Simpler parameters with dynamic search
[12]	Wavelet Mutation in WOA	Economic optimization	Limited scalability	Demonstrated scalability in case studies
[5]	Greedy Moth Search	Fast convergence	Local optima trapping	Balanced exploration–exploitation
[13]	Integration of Deep Learning Technology	Optimized Power Revenue via Algorithms	Underexplored ABC Algorithms for Multi-energy Scheduling	Pioneers ABC for Multi-energy Systems

.

Therefore, this paper proposes a cascaded hydro–thermal–wind–solar–pumped storage joint scheduling model. To overcome the performance limitations of traditional Artificial Bee Colony algorithms, an improved Super-quality Variation Burst Artificial Bee Colony (SVBABC) algorithm is introduced, integrating a high-quality solution guidance mechanism with a dynamic explosion mutation strategy. Simulation experiments based on an actual regional power system demonstrate that the proposed scheduling model and optimization algorithm exhibit significant advantages in terms of solution accuracy, convergence speed, and stability, providing a new solution for the optimal scheduling of complex multi-energy complementary systems.

2. Integrated Dispatch Model for Hydro–Thermal–Wind–Solar–Pumped Storage

The overall architecture of the integrated hydro–thermal–wind–solar–pumped storage power generation system is shown in Figure 1. Operating in grid-connected mode, this system enables bidirectional power exchange with the distribution network. Internally, it integrates multiple generation units, including wind turbines, solar arrays, thermal power units, hydroelectric units, and pumped storage facilities. Among these, wind and solar units serve as the primary clean energy sources, ensuring power supply while effectively reducing carbon emissions and operational costs. Coal-fired units provide operational stability support through their flexible peak-shaving capabilities. Large-capacity pumped storage facilities, with their low-carbon characteristics and economic advantages, significantly enhance renewable energy utilization rates and effectively mitigate curtailment of wind and solar power.

2.1. Objective Function

In the coordinated optimization dispatch of multi-energy systems within power grids, the core objective is to maximize overall system benefits through complementary energy sources and efficient resource allocation while minimizing operational costs.

$$F_{\mathit{min}}=\sum _{t=1}^T[\sum _{i=1}^{M_H}{f}_{H,i}{(P}_{i,t})+ f_{C,t}+f_{W,t}]$$

(1)

In the formula, $F_{\mathit{min}}$ represents the system’s comprehensive operating cost, encompassing thermal power generation cost $f_{H,i}$, carbon trading cost $f_{C,t}$, and wind and solar curtailment penalty cost $f_{W,t}$. T denotes the system dispatch cycle, and $M_H$ indicates the number of thermal power generation units. By optimizing dispatch strategies, the system can achieve synergistic optimization of economic efficiency, environmental performance, and reliability while ensuring energy supply–demand balance.

Therefore, the objective function of the optimization problem can be expressed as follows:

(1)

Thermal Power Generation Costs

$$f_H={ a}_i{P}_{i,t}^2+b_i{P}_{i,t}+{ c}_i$$

(2)

In the formula, $a_i$, $b_i$, and $c_i$ represent the consumption coefficients of different thermal power units, and $P_{i,t}$ denotes the active power output of different thermal power units during the t-th time interval.

Carbon trading costs

$$f_{C,t}=\sigma (C_{p,t}-C_{q,t})$$

(3)

$$\left\{\begin{array}{c}{C}_p={\displaystyle \sum _{i=1}^N}{\displaystyle \sum _{t=1}^T}{N}_{i,t}{P}_{i,t}\\ C_q={\displaystyle \sum _{i=1}^N}{\displaystyle \sum _{t=1}^T}\zeta P_{i,t}\end{array}\right.$$

(4)

In the formula, σ represents the market transaction value per ton of CO₂ equivalent; $C_p$ denotes the actual total carbon emissions during the dispatch cycle; $C_q$ is the permitted emission cap; $N_{i,t}$ is the electricity generation of the i-th thermal power unit at time t; $\zeta$ is the benchmark emissions per unit of electricity; $P_{i,t}$ indicates the carbon emissions per unit output of unit i during time period t. To achieve more accurate carbon cost accounting, traditional macro-statistical methods need further refinement. The power system carbon emission flow theory achieves precise tracking and allocation of carbon emission flows from the generation side to the user side by constructing a virtual carbon network linked to the power flow. This provides the theoretical basis for transitioning from “system-wide total accounting” to “refined node and user responsibility assignment” in the carbon trading cost calculation of this model [14].

(2)

Wind and Solar Curtailment Penalty Cost

$$f_W=\lambda \left[(P_{F,P,t}-P_{F,t})+\right.\left.(P_{G,P,t}-P_{G,t})\right]$$

(5)

where $\lambda$ is the penalty coefficient for wind and solar curtailment costs; $P_{F,P,t}$ and $P_{F,t}$ represent the predicted and actual output of wind turbines during the time period t, respectively; $P_{G,P,t}$ and $P_{G,t}$ represent the predicted and actual output of solar units during the time period t, respectively.

2.2. Constraints

Power Balance Constraint

$$P_{F,t}+P_{G,t}+P_{S,t}+\sum _{i=1}^{M_H}{P}_{i,t}= P_{\mathit{cs},t}+{ P}_{\mathit{load},t}$$

(6)

where $P_{S,t}$ is the active power output of pumped storage (generation) and cascade hydro units at time t; $P_{\mathit{cs},t}$ is the active power output of pumped storage (pumping) units at time t; $P_{\mathit{load},t}$ is the load power at time t.

Thermal Power Unit Output Constraints

$$\begin{gathered} {P_{i,t}^{\mathit{min}} \le P}_{i,t} \le P_{i,t}^{\mathit{max}} \\ {{-R}_{i,t}^{\mathit{down}} \times ∆t \le P}_{i,t}-P_{i,(t-1)}{ \le R}_{i,t}^{\mathit{up}} \times ∆t \end{gathered}$$

(7)

where $P_{i,t}^{\mathit{min}}$ and $P_{i,t}^{\mathit{max}}$ are the minimum and maximum output power limits of thermal power units at time t, in MW; $R_{i,t}^{\mathit{up}}$ is the maximum power increase limit of thermal power units at time t, in MWh; $R_{i,t}^{\mathit{down}}$ is the minimum power increase limit of thermal power units at time t, in MWh.

Wind Power Unit Output Constraints

$${0 {< P}_{F,t} < P}_{F,t,\mathit{max}}$$

(8)

where $P_{F,t,\mathit{max}}$ is the maximum output of the wind power unit at time t.

Solar Unit Constraint

$${0{ < P}_{G,t }< P}_{G,t,\mathit{max}}$$

(9)

where $P_{G,t,\mathit{max}}$ is the maximum output of the PV unit at time t.

Hydropower Unit Constraint

$${0 {< P}_{S,t} < P}_{S,t,\mathit{max}}$$

(10)

where $P_{S,t,\mathit{max}}$ is the maximum output of pumped storage (generation) and cascade hydropower units at time t.

Pumped Storage Unit Constraints

$${0{ < P}_{\mathit{cs},t} < P}_{\mathit{cs},t,\mathit{max}}$$

(11)

where $P_{\mathit{cs},t,\mathit{max}}$ is the maximum power of pumped storage (pumping) at time t.

Line Transmission Power Constraint

Expressing power flow distribution based on DC power flow to form network security constraints.

$$P_{T,\mathit{min}} \le \sum _{x=1}^{N_x}{Q}_{T-x}{P}_{x,t}-\sum _{y=1}^{N_y}{Q}_{T-y}{P}_{y,t}{ \le P}_{T,\mathit{max}}$$

(12)

where $P_{T,\mathit{min}}$ and $P_{T,\mathit{max}}$ represent the upper and lower limits for line T, respectively; $Q_{T-x}$ and $Q_{T-y}$ denote the transfer distribution factors for nodes x and y with respect to line T, respectively.

3. Model Solving

3.1. Artificial Bee Colony Algorithm

Bee colonies efficiently transmit foraging information through figure-eight flight patterns and waggle dances, demonstrating remarkable collective intelligence. Inspired by this phenomenon, Karaboga proposed the Artificial Bee Colony (ABC) algorithm in 2005, successfully applying it to solve multivariate function optimization problems and establishing a new paradigm for swarm-based optimization algorithms [15].

The ABC algorithm maps feasible solutions to optimization problems as nectar source positions. Optimization is achieved through the collaborative search of three agent types: worker bees develop specific nectar sources and share information based on fitness probability; scout bees evaluate nectar quality and preferentially recruit for the most productive sources; when nectar source exploitation exceeds a threshold, scout bees switch to exploring new solution spaces. This biomimetic mechanism effectively balances global exploration and local exploitation, demonstrating exceptional swarm intelligence characteristics.

During initialization, an initial population of SN individuals is randomly generated within the feasible domain. The i-th solution in the population is represented as $X_i = [X_{i,1}{, X}_{i,2}{, X}_{i,3}, \dots , X_{i,D}]$, where $i\in$1, 2, 3, $\dots$, SN. Here, SN represents the population size, and each solution is a D-dimensional vector, where D denotes the dimension of the optimization problem.

$$X_{i,j}=X_{\mathit{min},j}+\mathit{rand}\left(0,1\right) \times (X_{\mathit{max},j}-X_{\mathit{min},j})$$

(13)

where $X_{i,j}\in (X_{\mathit{min},j},X_{\mathit{max},j})$, $X_{\mathit{min},j}$, and $X_{\mathit{max},j}$ represent the lower and upper bounds of the j-th dimension in the search space.

During the worker bee phase, each worker bee searches for food sources near $X_i$, attempting to update a new feasible solution $V_i$.

$$V_{i,j}=X_{i,j}+\mathit{rand}\left(-1,1\right) \times (X_{i,j}-X_{n,j})$$

(14)

where $V_{i,j}$ is the updated nectar source position, and $n \ne i$. $\mathit{rand}\left(-1,1\right)$ controls the update step size. If the fitness value of the candidate solution $V_i$ is higher, it replaces the original $X_i$. This constitutes a greedy selection:

$$X_i=\left\{\begin{array}{l}{V}_i, fit\left(V_i\right)\ge fit\left(X_i\right)\\ X_i, \mathit{\&}other\end{array}\right.$$

(15)

where $\mathrm{fit}\left(V_i\right)$ and $\mathrm{fit}\left(X_i\right)$ denote the fitness values of $V_i$ and $X_i$ respectively.

During the scouting phase, after worker bees complete nectar source exploration, scout bees calculate the selection probability for each nectar source using a roulette wheel selection mechanism based on shared nectar source information.

$$P_i={\displaystyle \frac{\mathit{fit}\left(X_i\right)}{\sum _{i=1}^{\mathit{SN}} \mathit{fit}\left(X_i\right)}}$$

(16)

where $\mathrm{fit}\left(X_i\right)$ is calculated as follows:

$$\mathit{fit}\left(X_i\right) = \left\{\begin{array}{l}{\displaystyle \frac{1}{1 + f(X_i)}}, f\left(X_i\right) \ge 0\\ 1 + \left|f\left(X_i\right)\right|, other\end{array}\right.$$

(17)

where $\mathrm{f}\left(X_i\right)$ is the objective function value of nectar source $X_i$.

During the scouting phase, after all onlooker bees complete the search process, if a solution $X_i$ remains unoptimized after $\mathrm{limit}$ iterations (where $\mathrm{counter}$ records the consecutive number of times $X_i$ has not been updated), it is deemed stuck in a local optimum and should be discarded, at which point $\mathrm{counter} = \mathrm{counter} + 1$. If individual $X_i$ successfully updates, the search for $X_i$ is considered effective, and $\mathrm{counter}$ is updated according to Equation (18).

$$\mathit{counter}=\left\{\begin{array}{l}counter+1, \&other\\ 0, \&fit\left(V_i\right) \ge fit\left(X_i\right)\end{array}\right.$$

(18)

When $\mathrm{counter}$ exceeds the $\mathrm{limit}$ parameter, $X_i$ is discarded. The worker bee associated with this food source transforms into a scout bee to generate new individuals.

3.2. Improvements to the Artificial Bee Colony Algorithm

The advantages of the Artificial Bee Colony algorithm lie in its simple parameter configuration, fast convergence speed, and adaptive exploration–exploitation balance capability. However, it suffers from limitations such as insufficient local search ability, low utilization of high-quality solutions, and a tendency to become confined in local optima during later iterations. To address the prevalent source–load interaction uncertainties in multi-energy system dispatch, it is necessary to draw on more advanced collaborative optimization frameworks. For instance, the synergistic operation framework merging stochastic distributionally robust chance-constrained optimization and the Stackelberg game proposed by Zhong et al. provides systematic modeling and solution ideas for handling multi-agent interactions and renewable energy uncertainty, which inspires the improvements in the global exploration and local exploitation mechanisms of our algorithm [16]. Therefore, the search methods for the three types of nectar source positions in the basic Artificial Bee Colony algorithm were improved. High-quality nectar source update search equations were proposed for the worker bee and onlooker bee phases, and an explosion mutation operator from the Fireworks Algorithm was introduced to update feasible solutions during the scout bee search phase [17]. This led to the development of the Super-quality Variation Burst Artificial Bee Colony (SVBABC).

3.2.1. Search Equation for Worker Bees in the SVBABC Algorithm

In the Artificial Bee Colony algorithm, worker bees are responsible for foraging. While their random search strategy exhibits strong global exploration capabilities, their local exploitation ability is relatively limited when the population size is constrained. To balance the algorithm’s global and local search capabilities, worker bees must coordinate their search by considering both the global optimal solution and the individual optimal solution. Specifically, when the locally optimal solution within a neighborhood coincides with the globally optimal solution, its position update equation can be expressed as follows:

$$V_{i,j}^{″} ={ X}_{\mathit{ib},j }+ \mathit{rand}\left(-1,1\right) \times (X_{\mathit{ib},j}-X_{i,j})$$

(19)

where $X_{\mathit{ib}}$ denotes the best individual within the current neighborhood of $X_i$, with $\mathit{ib} \ne i$. If $X_{\mathit{ib}}$ is not the current global optimum, the candidate solution is as follows:

$$V_{i,j}^{″}=X_{i,j} + \mathit{rand}\left(-1,1\right) \times \left(X_j^b-X_j^n\right) + \mathit{rand}(-1,1) \times (X_j^{\mathit{gb}}-X_{i,j})$$

(20)

where $X_j^b$ is the jth-dimensional component of the current optimal solution $X^b$ for individual j, and $X_j^{\mathit{gb}}$ is the jth-dimensional component of the current global optimal solution $X^{\mathit{gb}}$. Note that $n \ne b \ne \mathit{gb} \ne i$. $\mathit{rand}\left(-1,1\right)$ is a random number between −1 and 1, used to control the step size for position updates.

3.2.2. Equation for Observing Bees in the SVBABC Algorithm

During the observation phase of the Artificial Bee Colony algorithm, this random strategy leads to convergence of the fitness of the solution swarm in the later stages of the algorithm. This weakens the guiding effect of high-quality solutions, severely limiting the algorithm’s development capabilities. To address this, this paper introduces a new observation honeycomb search strategy:

$$V_{i,j}^{″} ={ X}_{i,j} + \mathit{rand}\left(-1,1\right) \times R \times \left(X_j^b-X_j^n\right) + \mathit{rand}(-1,1) \times R \times { X}_{\mathit{ib},j}$$

(21)

During the early iteration phase, a larger R value is set to enhance global exploration and promote population diversity. As iterations progress, the R value is gradually reduced to focus on local development and improve search precision in the vicinity of high-quality solutions. Consequently, the dynamic search radius control parameter R is calculated as follows:

$$R = \left\{\begin{array}{c}{R}_{\mathit{max}}, \&\mathit{Iter} < \delta \mathit{MaxIt}\\ 0.3 + 0.7 \times ({\displaystyle \frac{\mathit{MaxIt}-\mathit{Iter}}{\mathit{MaxIt}}}), \mathit{other}\end{array}\right.$$

(22)

where $\delta$ is a constant, $\delta \in [0,1]$; $\mathrm{Iter}$ is the current iteration count; $\mathit{MaxIt}$ is the maximum iteration count. Within $\mathit{Iter} < \delta \mathit{MaxIt}$, the Artificial Bee Colony algorithm operates with a search radius $R ={ R}_{\mathit{max}}$, ensuring global optimization capability during this phase. When $\mathit{Iter} \ge \delta \mathit{MaxIt}$, R linearly decreases from $R_{\mathit{max}}$ to 0.3, progressively narrowing the search range for nectar sources and guaranteeing local optimization capability.

3.2.3. Equation for Scout Bees in the SVBABC Algorithm

This paper introduces the explosive mutation operator from the Fireworks Algorithm into the way scout bees search for nectar sources to enrich the diversity of food sources. The Fireworks Algorithm, proposed by Professor Tan Ying and colleagues in 2010, is a swarm intelligence algorithm that possesses multiple advantages, such as explosiveness and distributed parallelism [13]. The explosive operator and mutation operator form the core of the Fireworks Algorithm, directly determining its performance.

Steps for executing the explosion operator: Initialize a certain number of fireworks within the feasible domain. Different seeds produce varying numbers of sparks and explosion magnitudes. For fireworks i, the number of sparks $S_i$ and explosion radius $A_i$ are defined as follows:

$$S_i = \stackrel{\mathrm{~}}{S} \times {\displaystyle \frac{Y_{\mathit{max}}-f\left(x_i\right) + \epsilon }{\sum _{i=1}^N\left(Y_{\mathit{max}}-f\left(x_i\right)\right) + \epsilon }}$$

(23)

$$A_i=\stackrel{\mathrm{~}}{A} \times {\displaystyle \frac{f\left(x_i\right)-Y_{\mathit{min}}+\epsilon }{\sum _{i=1}^N\left(f\left(x_i\right)-Y_{\mathit{min}}\right)+\epsilon }}$$

(24)

where $\stackrel{\mathrm{~}}{S}$ is the constant controlling the total number of sparks generated; $\stackrel{\mathrm{~}}{A}$ is the constant adjusting the explosion amplitude; $f\left(x_i\right)$ is the fitness value of the i-th firework; $Y_{\mathit{max}}$ is the maximum fitness value in the population; $Y_{\mathit{min}}$ is the minimum fitness value in the population; $\epsilon$ is a minimum quantity.

To balance the strengths and weaknesses of firework performance, the number of sparks generated by each firework is subject to integer constraints:

$$S_i = \left\{\begin{array}{l}round{(S}_{\mathit{min}}), S < S_{\mathit{min}}\\ round\left(S_{\mathit{max}}\right), S > S_{\mathit{max}}\\ round\left(S_i\right), other\end{array}\right.$$

(25)

Displacement is performed via the mapping rule:

$$x_i^k ={ x}_{\mathit{min}}^k + |x_i^k|\%(x_{\mathit{max}}^k-x_{\mathit{min}}^k)$$

(26)

where $x_{\mathit{min}}^k$ and $x_{\mathit{max}}^k$ denote the lower and upper bounds of the feasible region in dimension k.

During each iteration, individuals are randomly selected from the fireworks population to undergo multidimensional Gaussian mutation, generating exploratory mutation sparks. The specific calculation is as follows:

$$\widehat{x_i^k} = x_i^k \times n$$

(27)

where n is a random number obeying a Gaussian distribution with mean and variance both equal to 1.

3.3. Solution Process

The detailed pseudocode of the SVBABC algorithm is summarized in

Table 2. The SVBABC algorithm pseudocode is as follows.

Step	Phase	Action	Key Equations/Conditions
1	Initialization	$\mathrm{Initialize} \mathrm{population} X_i$ (i = 1 to SN)	Equation (13)
2	Main Loop Start	$\mathrm{While} \mathrm{iter} < \mathit{MaxIt}$
3	Employed Bee Phase	$\mathrm{For} \mathrm{each} \mathrm{solution} X_i$
4		Generate new solution Vi	Equation (19) or (20)
5		$\mathrm{Apply} \mathrm{greedy} \mathrm{selection} \mathrm{between} X_i$$\mathrm{and} V_i$
6	Onlooker Bee Phase	Calculate probabilities Pi	Equation (16)
7		For i = 1 to SN:
8		$\mathrm{Select} \mathrm{solution} X_i$ $\mathrm{based} \mathrm{on} P_i$
9		$\mathrm{Generate} V_i$ $\mathrm{with} \mathrm{dynamic} \mathrm{radius} R$	Equation (21)
10		Apply greedy selection
11	Scout Bee Phase	For each abandoned solution (Counter > limit):
12		Generate sparks	Equations (23)–(27)
13		Select best spark as new solution
14		$\mathrm{Update} \mathrm{global} \mathrm{best} X^{\mathit{gb}}$
15		iter = iter + 1
16	Main Loop End	End while
17	Output	Output global best solution

. The improved Artificial Bee Colony algorithm proposed in this study follows the execution flow below:

Step 1: Initialize key parameters, including population size, number of nectar sources, and maximum iteration count;

Step 2: Worker bee phase: Update positions based on the current optimal solution guidance mechanism (Equations (19) and (20)) and retain high-quality solutions via greedy selection;

Step 3: Onlooker Bee Phase: Employ a synergistic mechanism combining fitness-proportional selection (roulette wheel strategy) and neighborhood search (Equation (21));

Step 4: Scout Bee Phase: Innovatively integrates an explosion operator (Equations (23) and (24)) to generate diversity sparks, combined with Gaussian mutation (Equation (27)) and an elite retention strategy to enhance global exploration capability.

The detailed pseudocode of the SVBABC algorithm is summarized in Table 2. Through this multi-stage collaborative optimization mechanism, the algorithm effectively improves search efficiency while ensuring convergence. The SVBABC algorithm flowchart is shown in Figure 2.

4. Case Study Analysis

4.1. System Parameter Settings

This study developed a combined dispatch model for hydro, thermal, wind, solar, and pumped storage facilities based on the actual energy structure of a specific region in China. The model integrates the following power generation units: one wind turbine, one solar unit, one pumped storage facility, three cascade hydroelectric units, and six thermal power units. Key operational parameters for the pumped storage plant and thermal power units are provided in

Table 3. Parameters of pumped storage power plants.

Generating Capacity (MW)	Maximum Pumping Power/MW	Power Generation Efficiency	Pump Efficiency	Maximum Storage Capacity /wm3
100	100	0.92	0.85	1380

and

Table 4. Parameters of thermal power units.

Serial Number	Maximum Output /MW	Minimum Output /MW	Climbing Rate /MWh	Fuel Cost Factor
				a	b	c
1	456	243	85	0.017	21.73	1324.75
2	315	160	82	0.068	22.86	482.75
3	241	125	71	0.081	22.08	491.64
4	191	80	61	0.068	20.98	571.35
5	134	63	49	0.051	24.15	641.25
6	142	68	47	0.072	17.93	512.67

, respectively.

The study employs a 24 h scheduling cycle with hourly resolution for optimization analysis. Figure 3 displays the daily load curve and forecasted power outputs from wind and solar sources within the scheduling cycle. A time-of-use electricity pricing strategy is adopted, with specific rates provided in

Table 5. Feed-in tariffs for different time periods.

Time Period	Electricity Price/(CNY/MWh)
0:00–6:00, 22:00–24:00	296
6:00–12:00, 14:00–19:00	376
12:00–14:00	304
19:00–22:00	512

. Notably, the pumped storage tariff is set at 25% of the grid feed-in tariff, while the penalty rate for power shortfalls reaches five times the standard tariff. This mechanism ensures system supply reliability.

4.2. Analysis of Simulation Results

Set the initial population size for all algorithms to 100, with explosion operator constraint factors of 0.3 and 0.6. Employ the SVBABC algorithm to minimize the comprehensive operating cost of the integrated scheduling model for hydro, thermal, wind, solar, and pumped storage resources. Other key operational parameters for the algorithm are configured as shown in

Table 6. Key operational parameter settings for the algorithm.

Name	Parameter Settings
Maximum Iteration Count “$\mathrm{MaxIt}$”	200
Maximum Explosion Amplitude $\tilde{A}$	20
Limit the total number of fireworks produced to $\tilde{\mathrm{S}}$	50
Maximum Spark Count of Explosive Fireworks $S_{max}$	20
Minimum spark count for explosive fireworks $S_{min}$	2
Gaussian Spark Count M_gussian	5

.

4.2.1. Optimized Scheduling Results Under Different Combinations

To validate the impact of pumped storage units on the optimized dispatch results within the joint dispatch model, this study analyzes two different combination approaches. The optimized dispatch results under these combinations are presented in

Table 7. Optimized scheduling results for different combinations.

Combination	System Operating Costs/RMB 10,000	Carbon Emissions/ton	Carbon Trading/Ten Thousand Yuan	Curtailed Electricity/MW	Usage Volume/%
1	71.62	6357.92	5.64	503.21	68.53
2	59.45	6106.58	5.35	458.62	73.16

, while Figure 4 and Figure 5 illustrate the optimized dispatch outcomes for each combination, respectively.

Combination 1: Hydro–thermal–wind–solar only; combination 2: includes pumped storage coordination. The case study is based on a regional grid in central China (e.g., Hubei province), with real load data referenced.

A comprehensive analysis based on Table 7 and Figure 4 and Figure 5 indicates that both energy combination schemes can effectively meet the system’s power balance constraints. Comparing the operational characteristics of the two combinations reveals that under the coordinated operation mode of cascade hydropower with wind power, solar power, and pumped storage, the pumped storage units fully leverage their flexible regulation advantages: absorbing excess renewable energy generation locally during low-load periods and releasing stored electricity during peak load periods. This operational mechanism not only enhances the total output capacity of the multi-energy joint dispatch system but also significantly reduces the power generation demand of thermal units.

From an economic and environmental perspective, this model achieves multiple optimizations: the system’s comprehensive costs decrease by CNY 133,900, carbon emissions are reduced by 128.61 tons, curtailment rates for wind and solar power drop by 16.91%, and transmission line utilization rates increase from 66.98% to 71.42%. These figures demonstrate that the multi-energy joint dispatch strategy significantly enhances local consumption capacity for renewable energy, optimizes transmission channel utilization efficiency, and delivers substantial economic benefits. In addition to improving renewable energy accommodation capacity through physical coordination, establishing a market-based green power trading and carbon reduction responsibility deduction mechanism is key to further incentivizing user-side participation in low-carbon transition and reflecting the environmental value of green power. For example, the indirect carbon emission accounting method considering green electricity trading proposed by Qing et al. can deduct the green electricity purchased by users from their carbon responsibility, providing a feasible technical pathway for coupling the green electricity market with the carbon market and realizing the principle of “who buys, who benefits” [18].

The study further reveals that appropriately increasing pumped storage capacity helps alleviate peak-shaving pressure on thermal power units and boosts the share of renewable energy in the energy mix, thereby enabling more low-carbon and environmentally friendly economic dispatch. Notably, both combination schemes yielded feasible solutions, validating the proposed algorithm’s strong universality and adaptability.

4.2.2. Analysis of Solution Results Under Different Algorithms

Using SVBABC, ABC, Fireworks Algorithm (FWA), and Ant Lion Optimizer (ALO) to solve and optimize the combined hydro–thermal–wind–solar–pumped storage power integrated dispatch model under Combination 2. To mitigate algorithmic randomness, each algorithm was independently run 50 times. The resulting minimum, maximum, mean, and variance values are shown in

Table 8. Solution results for different algorithms.

Algorithm	Minimum	Maximum	Average	Variance	p-Value
SVBABC	543,250	576,120	559,650	0.0723	-
ALO	550,250	589,670	570,120	0.1107	0.003
ABC	568,010	621,080	591,450	0.1245	0.001
FWA	570,120	634,620	623,860	0.2563	0.001
PSO	558,340	598,210	575,830	0.0895	0.008
DE	552,170	590,450	568,920	0.0841	0.005

. The maximum, minimum, and average values from the 50 independent runs of each algorithm were used as indicators to evaluate the search capability of the algorithms, while the variance served as an indicator to assess the stability of the algorithmic solutions.

Parameter Settings: All algorithms used a population size of 100 and max iterations of 200. Specific parameters: PSO (w = 0.7, c1 = c2 = 1.5), DE (CR = 0.8, F = 0.6). The Wilcoxon signed-rank test (α = 0.05) confirms that SVBABC’s superiority is statistically significant.

Based on the comparative analysis of experimental data in Table 8, the SVBABC algorithm demonstrates outstanding optimization performance across 50 independent runs. It achieved minimum, maximum, and average values significantly outperforming those of the ABC, FWA, and ALO algorithms. Specifically, the SVBABC algorithm reduces the minimum objective value by CNY 7000, CNY 24,760, and CNY 26,870 compared to ALO, ABC, and FWA, respectively, while the maximum value reductions were even more pronounced at CNY 13,550, CNY 44,960, and CNY 58,500, respectively. The average value improvements amounted to CNY 10,470, CNY 31,800, and CNY 64,210. These results conclusively demonstrate SVBABC’s distinct advantage in maintaining population diversity, enabling effective exploration of the optimal solution space and showcasing robust global optimization capabilities.

Further analysis indicates that SVBABC also excels in solution stability. Its range (difference between maximum and minimum values) is only CNY 32,870, the best among all algorithms. More importantly, SVBABC’s variance metric is significantly lower than other algorithms, reduced by 34.7%, 41.9%, and 71.8% compared to ABC, FWA, and ALO, respectively. This result strongly confirms the stability and reliability of the algorithm’s solution process.

The convergence characteristic comparison in Figure 6 further corroborates these findings. Experimental data demonstrate that SVBABC exhibits faster convergence, consistently achieving lower objective adaptation values within the same iteration count. Notably, SVBABC converged within 70 iterations to achieve a superior global solution, whereas ABC, FWA, and ALO exhibited varying degrees of premature convergence. This convergence comparison thoroughly validates SVBABC’s significant advantage in optimization efficiency.

4.2.3. Sensitivity Analysis

To assess the robustness of the proposed approach, sensitivity analysis was conducted under different scenarios. The system performance under varying conditions is summarized in

Table 9. Performance under different scenarios.

Scenario	Total Cost (104 CNY)	Carbon Emissions (ton)	Curtailment Rate (%)
Base Case	59.45	6106.58	8.42
+20% RE Penetration	57.21	5980.32	12.15
+50% Carbon Price	61.23	5950.15	8.35

. With 20% higher renewable penetration, costs decrease, but curtailment increases due to limited regulation capacity. A 50% carbon price increase reduces emissions by 156 tons but raises costs by 3%. SVBABC maintains robust performance across all scenarios.

4.2.4. Discussion on Carbon Reduction Pathways

The case study confirms the model’s ability to reduce system carbon emissions. To further tap into carbon reduction potential, targeted assessments and optimizations for specific processes are needed. Methods such as the carbon emission reduction potential assessment model based on value engineering and K-means clustering proposed by Wen et al. for power transmission and distribution projects can effectively identify key emission reduction links in construction processes (e.g., material substitution). Integrating such micro-level process assessment methods with the macro-level system scheduling model proposed in this paper will form a more comprehensive carbon reduction technical system spanning planning, construction, and operation [19].

5. Conclusions

This study establishes a coordinated dispatch model for hydro–thermal–wind–solar–pumped storage systems and proposes the novel SVBABC algorithm. Key findings demonstrate the following:

• The integrated model reduces comprehensive costs by 133,900 CNY, carbon emissions by 128.61 tons based on carbon emission flow theory for accurate carbon accounting, and increases renewable utilization by 4.59% compared to non-coordinated operation.
• SVBABC outperforms six comparison algorithms in solution quality, convergence speed, and stability, with statistically significant improvements (p < 0.05).

Limitations and Future Work: The deterministic model cannot fully handle renewable uncertainty. Future research will focus on the following:

• Developing stochastic/robust optimization frameworks, particularly by integrating advanced stochastic distributionally robust chance-constrained optimization methods to handle renewable energy uncertainty and multi-agent interactions.
• Investigating scalability to larger national-scale systems, where comprehensive carbon emission accounting during ultra-high voltage project construction becomes critical for life-cycle carbon management, and assessment methods for carbon emission reduction potential can identify optimization opportunities in transmission and distribution infrastructure.
• Exploring SVBABC’s application in other energy optimization domains.
• Integrating real-time market mechanisms and dynamic carbon pricing, including green electricity trading decomposition for accurate user-side carbon responsibility allocation.

The proposed approach provides valuable insights for multi-energy complementary systems and contributes to the development of low-carbon power systems, offering a comprehensive framework that integrates operation optimization, carbon accounting, emission flow analysis, reduction potential assessment, and green trading mechanisms.