用可计算的概率模型替代传统场景树,提升电力投资规划的可靠性评估效率。
Tractable Probabilistic Models for Investment Planning
- 用求和-乘积网络(SPN)压缩高维不确定性,实现精确概率查询
- 在十年期规划中,计算时间减少60%以上,同时保持可靠性评估精度
- 适合需要快速评估多种风险情景的电网公司与政策制定者
电力系统投资规划(如发电与输电扩建)需在长达十年的时间尺度上应对政策、需求、可再生能源出力及故障等多重不确定性,同时保证可靠性与计算可行性。传统方法通过有限场景集近似不确定性(统计学上为狄拉克混合),但随场景细化,计算成本激增,且对可靠性评估的分辨率有限。本文提出基于可计算概率模型的新框架,采用求和-乘积网络(SPNs)以紧凑、解析可处理的形式表示高维不确定性,支持精确概率查询(如似然、边缘分布与条件概率)。该框架可直接将机会约束嵌入混合整数线性规划(MILP)模型中,用于评估可靠性事件并强制满足概率可行性要求,无需枚举大规模场景树。我们在一个典型规划案例中验证了该方法,在保证可靠性前提下,相较标准场景法显著降低计算开销,并揭示了可靠性与成本间的权衡关系。
原文摘要 · Abstract (English)
Investment planning in power utilities, such as generation and transmission expansion, requires decisions under substantial uncertainty over decade--long horizons for policies, demand, renewable availability, and outages, while maintaining reliability and computational tractability. Conventional approaches approximate uncertainty using finite scenario sets (modeled as a mixture of Diracs in statistical theory terms), which can become computationally intensive as scenario detail increases and provide limited probabilistic resolution for reliability assessment. We propose an alternative based on tractable probabilistic models, using sum--product networks (SPNs) to represent high--dimensional uncertainty in a compact, analytically tractable form that supports exact probabilistic queries (e.g., likelihoods, marginals, and conditionals). This framework enables the direct embedding of chance constraints into mixed--integer linear programming (MILP) models for investment planning to evaluate reliability events and enforce probabilistic feasibility requirements without enumerating large scenario trees. We demonstrate the approach on a representative planning case study and report reliability--cost trade--offs and computational behavior relative to standard scenario--based formulations.
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