Finding the optimal size of a hybrid renewable energy system is certainly important. The problem is often modelled as an multi-objective optimization problem (MOP) in which objectives such as annualized system cost, loss of power supply probability etc. are minimized. However, the MOP model rarely takes the load characteristics into account. We argue that ignoring load characteristics may be inappropriate when designing HRES for a place with intermittent high load demand. For example, in a training base the load demand is high when there are training tasks while the demand decreases to a low level when there is no training task. This results in an interesting issue, that is, when the loss of power supply probability is determined at a specific value, say 15%, then it is very likely that most of loss of power supply would occur right in the training period which is unexpected. Therefore, this study proposes a constraint multi-objective model to deal with this issue—in addition to the general multi-objective optimization model, the loss of power supply probability over a critical period is set as a constraint. Correspondingly, the non-dominated sorting genetic algorithm II with a relaxed \(\epsilon \) constraint handling strategy is proposed to address the constraint MOP. Experimental results on a real world application demonstrate that the proposed model and algorithm are both effective and efficient.

找到混合可再生能源系统的最佳规模当然很重要。该问题通常被建模为一个多目标优化问题（MOP），在该问题中，诸如年度系统成本，电力供应概率损失等目标得以最小化。但是，MOP模型很少考虑负载特性。我们认为，在为间歇性高负荷需求的场所设计HRES时，忽略负荷特性可能是不合适的。例如，在训练基地中，当有训练任务时，负荷需求较高，而当没有训练任务时，负荷需求降低至较低水平。这就产生了一个有趣的问题，那就是当断电概率确定为特定值（例如15％）时，那么很有可能大部分电力供应损失都将在训练期间发生，这是出乎意料的。因此，本研究提出了一种约束多目标模型来解决该问题—除了一般的多目标优化模型外，还将关键时期的供电概率损失作为约束。相应地，具有宽松性的非支配排序遗传算法II提出了\（\ epsilon \）约束处理策略来解决约束MOP。在实际应用中的实验结果表明，所提出的模型和算法既有效又高效。