考虑发电与碳排放不确定性的园区综合能源系统分布鲁棒优化

doi:10.11930/j.issn.1004-9649.202511033

摘要/Abstract

摘要：

“双碳”发展目标下，园区综合能源系统作为实现多能互补与低碳转型的重要载体，受到了广泛关注。然而，其运行过程受风电出力波动及电网间接碳排放强度等多源不确定性因素影响，给系统的经济性与低碳性带来挑战。为此，提出一种考虑发电与碳排放不确定性的园区综合能源系统分布鲁棒优化方法。基于Wasserstein距离与矩信息构建混合模糊集，利用机会约束以处理风电不确定性，并采用多面体不确定集描述碳排放强度波动，同时考虑用户侧需求响应。通过列和约束生成（column-and-constraint generation，C&CG）算法及Karush-Kuhn-Tucker（KKT）条件将模型转化为可求解的混合整数线性规划问题。算例结果表明，所提方法在保证系统鲁棒性的同时提升了经济性，有效协调了可再生能源消纳、碳排放约束与经济运行之间的关系。

关键词: 园区综合能源系统, 分布鲁棒机会约束, 碳排放强度不确定性, 列和约束生成算法, KKT

Abstract:

Under the "dual carbon" goals, the park-level integrated energy system (PIES), as an important carrier for achieving multi-energy complementarity and low-carbon transition, has attracted extensive attention. However, its operation is affected by multiple sources of uncertainty, such as wind power output fluctuations and indirect carbon emission intensity of the power grid, which poses challenges to both economic efficiency and carbon performance of the system. To this end, this paper proposes a distributionally robust optimization method for PIES considering the uncertainty of power generation and carbon emissions. A hybrid fuzzy set is constructed based on the Wasserstein distance and moment information, while chance constraints are employed to handle wind power uncertainty. Meanwhile, a polyhedral uncertainty set is used to characterize the fluctuations in carbon emission intensity, and user-side demand response is incorporated to enhance system flexibility. The proposed model is transformed into a solvable mixed-integer linear programming (MILP) problem through the column-and-constraint generation (C&CG) algorithm and Karush–Kuhn–Tucker (KKT) conditions. Case study results demonstrate that the proposed method enhances economic efficiency while ensuring system robustness, and effectively coordinates the relationship between renewable energy accommodation, carbon emission constraints, and economic operation.

Key words: park-level integrated energy system, distributionally robust chance constraint, uncertainty of carbon emission intensity, column-and-constraint generation algorithm, KKT

张啸林, 杜尔顺, 张光斗, 王佳旭, 宋亮, 刘昱良. 考虑发电与碳排放不确定性的园区综合能源系统分布鲁棒优化[J]. 中国电力, 2026, 59(2): 1-12.

ZHANG Xiaolin, DU Ershun, ZHANG Guangdou, WANG Jiaxu, SONG Liang, LIU Yuliang. Distributionally robust optimization of park-level integrated energy systems considering uncertainties in power generation and carbon emissions[J]. Electric Power, 2026, 59(2): 1-12.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202511033

https://www.electricpower.com.cn/CN/Y2026/V59/I2/1

图/表 11

图 1 PIES系统架构

Fig.1 PIES structure

图 2 模型求解流程

Fig.2 Model solving flowchart

表 1 不同场景下成本对比

Table 1 Comparison of costs under different scenarios

场景	碳排放量/t	碳交易成本/万元	需求响应成本/万元	总成本/ 万元
1	195.29	2.421	2.829	29.604
2	192.05	2.357	2.741	29.259
3	161.92	1.714	2.705	26.814
4	163.62	1.749	2.665	26.505
5	161.77	1.659	2.658	25.885

图 3 PIES电出力

Fig.3 Electrical power output of the PIES

图 4 PIES热出力

Fig.4 Thermal power output of the PIES

图 5 间接碳排放强度不确定集

Fig.5 Uncertainty set for indirect carbon emission intensity

图 6 PIES用户电负荷响应

Fig.6 Demand response of the electrical load on the user side of the PIES

图 7 PIES用户热负荷响应

Fig.7 Demand response of the thermal load on the user side of the PIES

表 2 不同半径下算例成本

Table 2 Costs of the case study under different Wasserstein radii

$ {\rho } $	模糊集设置	PIES成本/元
0.01	$ {D}_{\mathrm{W}} $	265054
0.01	$ {D}_{\mathrm{H}} $	258466
0.02	$ {D}_{\mathrm{W}} $	275134
0.02	$ {D}_{\mathrm{H}} $	262393
0.05	$ {D}_{\mathrm{W}} $	296325
0.05	$ {D}_{\mathrm{H}} $	273842
0.10	$ {D}_{\mathrm{W}} $	326037
0.10	$ {D}_{\mathrm{H}} $	293792

图 8 不同风险系数下PIES总成本

Fig.8 Total cost of the PIES under different risk aversion parameters

图 9 不确定参数对购电量和碳排放成本影响

Fig.9 Impact of uncertain parameters on electricity procurement and carbon emission cost

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