Load Optimization of Inverter Air Conditioning Cluster Driven by Constraint Surface Projection and Spatial-Fitness Synergy
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摘要: 针对高比例新能源并网加剧电网供需不平衡的问题，聚合大规模变频空调集群作为虚拟储能参与需求响应，是提升电网灵活性的有效途径。然而，现有调度策略常面临高维寻优的维数灾难，且传统基于罚函数的软约束方法难以严格满足聚合功率的等式约束，易产生稳态误差。为此，本文提出一种基于约束面投影的位势协同自适应粒子群算法(SFA-PSO)。首先，基于等效热参数模型构建了兼顾群体热舒适度与响应公平性的多目标优化框架；其次，针对传统算法易出现功率越限的局限性，设计了约束面投影机制，将粒子的搜索路径严格限制在功率守恒超平面内，从而实现对网侧调度指令的精确跟踪；此外，针对高维空间寻优易早熟的难题，提出空间-适应度协同演化策略，通过量化粒子适应度与空间距离的认知偏差动态调节学习因子，以提升算法跳出局部最优的能力。最后，在包含多源热扰动与通信丢包等复杂动态环境下进行了连续调度仿真实验。结果表明，SFA-PSO算法在千节点级高维场景中表现出良好的鲁棒性，能够在严格满足电网侧功率管控要求的前提下，以较低的计算开销实现用户侧舒适度与公平性的有效协同。Abstract:
Objective Supply-demand imbalances in modern power distribution networks are exacerbated by the increasing penetration of distributed renewable energy and frequent extreme weather events. Consequently, large-scale inverter air conditioning (IAC) clusters are utilized for Demand Response (DR) as a viable strategy to enhance grid flexibility. However, existing dispatch strategies are often limited by the curse of dimensionality, and aggregate power equality constraints are not strictly met without compromising user comfort. In this study, an optimization framework is developed to achieve precise grid power control while thermal discomfort is minimized and fairness among heterogeneous users is maintained. Methods A multi-objective optimization framework based on an Equivalent Thermal Parameter (ETP) model is established to evaluate the thermodynamic states of heterogeneous buildings. To balance collective comfort and individual fairness, a composite fitness function is designed, in which a weighted mean square error term, a temperature variance penalty, and a violation suppression term are integrated. To address the steady-state errors inherent in traditional penalty-based methods, a Spatial-Fitness Adaptive Particle Swarm Optimization (SFA-PSO) algorithm is proposed. Particles are mapped strictly onto the power conservation hyperplane by a geometric constraint surface projection mechanism to ensure power balance. Furthermore, learning factors are dynamically adjusted by a spatial-fitness synergistic strategy based on the cognitive dissonance between a particle's fitness rank and spatial distance rank, whereby premature convergence in high-dimensional spaces is prevented. Results and Discussions Extensive continuous scheduling simulations were conducted under a complex dynamic environment, which comprehensively incorporated multi-source thermal disturbances, a 1% bidirectional communication packet loss rate, and varying part load ratios of 20%, 50%, and 80%.First, regarding the effectiveness of the proposed mechanisms, ablation experiments confirmed that the constraint surface projection guarantees power tracking accuracy. While traditional penalty-based methods (e.g., Penalty-PSO) exhibited steady-state power deviations of approximately 10-1 kW, SFA-PSO successfully restricted the aggregate power tracking errors within 10-9 kW ( Fig. 3 ). Furthermore, the introduction of the Spatial-Fitness Adaptive (SFA) strategy effectively prevented the premature convergence observed in Phy-PSO, enabling continuous fitness descent particularly in low-load scenarios with narrow feasible regions (Fig. 4 ). This is directly attributed to the dynamic evolution of the learning factors, where the cognitive factor remains high initially to encourage global exploration, and subsequently decreases while the social factor rises to enhance precise local exploitation (Fig. 5 ).Second, in terms of continuous dynamic scheduling performance, a 6-hour simulation during the peak load period (12:00 to 18:00) with 5-minute dispatch intervals, totaling 72 decision steps, was executed. Under extreme power limitations, standard algorithms like GA and WOA suffered from severe power limit violations due to poor synergy with the projection mechanism, whereas SFA-PSO maintained perfect constraint satisfaction (Fig. 7 ). SFA-PSO consistently positioned itself at the lowest fitness level throughout the real-time evolution curves, demonstrating superior robustness against environmental thermal noise and network transmission delays (Fig. 8 ). Quantitatively, compared to eight baseline algorithms including SLPSO, CSO, and DSCPSO, the proposed SFA-PSO achieved the most outstanding comprehensive performance with an average fitness of 904, a minimum fitness of 243, and the lowest standard deviation of 551 (Table 2 ).Finally, comprehensive scalability analyses across diverse cluster sizes ranging from 100 to 1,000 nodes further validated the algorithm's high-dimensional solving capability. Across all scale scenarios, SFA-PSO exhibited the strongest optimization capacity, characterized by a rapid initial descent within the first 20 iterations and sustained exploration in later stages (Fig. 9 ). Although the integration of the projection and SFA mechanisms increased the computational time by 30% to 50% compared to the basic PSO algorithm (Fig. 6 ) , the absolute optimization solving time remained highly stable at approximately 1.5 seconds even for a massive 1,000-node cluster (Fig. 9 ). This minor computational overhead is entirely negligible for minute-level control cycles, fully satisfying the stringent real-time dispatch requirements of modern smart grids.Conclusions The steady-state error limitations of traditional soft-constraint methods in aggregate power control are effectively addressed by the proposed SFA-PSO algorithm. By ensuring precise tracking of dispatch commands and mitigating high-dimensional traps, a robust and scalable solution is provided for the flexible scheduling of large-scale IAC loads in smart grids, and a practical balance between grid-side regulation and user-side comfort is maintained. Objectively, cross-algorithm generalization is restricted by the inherent algorithm dependency of the constraint projection mechanism, and additional computational overhead is introduced to guarantee high-precision tracking. Consequently, adaptive constraint processing and algorithm lightweighting technologies are primary focuses for future research. -
Key words:
- Demand response /
- Particle swarm optimization /
- HVAC cluster power
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表 1 算法通用参数
参数名称 用户
数量种群
规模最大迭代
次数独立运行
次数惯性
权重$ {J}_{\text{MSE}} $权重 $ {J}_{\text{VAR}} $权重 $ {J}_{\text{MAX}} $权重 温度
死区热扰动
基准值热扰动
随机值上行丢包
概率下行丢包
概率符号 $ D $ $ M $ $ K $ $ N $ $ \omega $ $ {\alpha }_{\text{mse}} $ $ {\alpha }_{\text{var}} $ $ {\alpha }_{\max } $ $ \delta $ $ Q_{\max }^{\text{dist}} $ $ \varepsilon _{i}^{t} $ $ {P}_{\text{loss}\_\text{up}} $ $ {P}_{\text{loss}\_\text{down}} $ 值 300 50 100 30 0.2 1 10 1 0.5 0.1 $ {\mathrm{N}(,0.02}^{2}) $ 0.01 0.01 单位 - - 次 次 - - - - °C °C °C - - 
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表 2 对比实验适应度指标
算法名称 SFA-PSO SLPSO WOA GA CSO SCMPSO DNIWPSO IDCPSO DSCPSO 平均适应度 904 2836 1038 1559 1149 1871 2339 1956 1976 最小适应度 243 752 373 610 296 623 696 601 643 最大适应度 2035 5186 2130 2751 2762 3665 4421 3805 3881 标准差 551 1232 563 609 787 901 1046 935 962
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