Polynomial Chaos Expansion Approach for Approximating Security Region Boundary of Integrated Electricity-gas Energy Systems

JIANG Tao; WANG Xuanyao; LI Xue; LI Guoqing

doi:10.13334/j.0258-8013.pcsee.241833

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Polynomial Chaos Expansion Approach for Approximating Security Region Boundary of Integrated Electricity-gas Energy Systems

更新时间：2026-10-12

- Polynomial Chaos Expansion Approach for Approximating Security Region Boundary of Integrated Electricity-gas Energy Systems
- Vol. 46, Issue 2, Pages: 620-633(2026)
- 作者机构：
  
  现代电力系统仿真控制与绿色电能新技术教育部重点实验室(东北电力大学),吉林市,吉林省,132012
- 作者简介：
- 基金信息：
- DOI：10.13334/j.0258-8013.pcsee.241833
  CLC：
- Published：2026
- 稿件说明：
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JIANG Tao, WANG Xuanyao, LI Xue, et al. Polynomial Chaos Expansion Approach for Approximating Security Region Boundary of Integrated Electricity-gas Energy Systems[J]. 2026, 46(2): 620-633.
DOI：

JIANG Tao, WANG Xuanyao, LI Xue, et al. Polynomial Chaos Expansion Approach for Approximating Security Region Boundary of Integrated Electricity-gas Energy Systems[J]. 2026, 46(2): 620-633. DOI： 10.13334/j.0258-8013.pcsee.241833.

摘要

为构建综合能源系统安全域(integrated energy system security region，IESSR)，该文提出一种基于多项式混沌展开(polynomial chaos expansion，PCE)的IESSR边界(IESR boundary，IESSRB)近似方法，借助该方法可得IESSRB的多项式逼近表达式。首先，根据IESSRB的边界拓扑特性，构建系统的IESSR边界点搜索优化模型；然后，根据PCE，对IESSR边界点搜索优化模型进行参数化处理，构建IESSRB搜索的参数化优化模型；进一步地，根据IESSRB搜索的参数化优化模型的KKT条件，将IESSRB的参数化优化模型转化为高维参数化非线性方程组；在此基础上，借助广义Galerkin投影构建关于近似IESSRB的多项式逼近系数的Galerkin投影方程组，通过求解该方程组可得IESSRB的多项式逼近系数，从而获得IESSRB的多项式逼近表达式；为进一步降低Galerkin投影方程组求解复杂度，提出多项式分段近似IESSRB方法，在提高IESSRB近似精度的同时，提升了IESSRB近似的计算效率；最后，通过IES E39-G20测试系统和IES E118-G96测试系统对所提方法进行分析、验证。结果表明，所提方法可实现IESSR的准确、有效构建。

Abstract

To form the integrated energy system security region (IESSR)

this paper develops an approximation solution for IESSR boundary (IESSRB)

which uses Polynomial Chaos Expansion (PCE) to formulate a polynomial approximation expression. First

according to the boundary topology characteristics of IESSRB

an optimization model for exploring the critical point on the IESSRB is formulated. Then

the optimization model is parameterized to a parametric optimization model of IESSRB via the PCE. Further

the parametric optimization model is transformed into a high-dimensional parameterized nonlinear equations based on its KKT condition

and the corresponding Galerkin projection equation is formulated by applying the generalized Galerkin projection on the obtained high-dimensional parameterized nonlinear equations. By solving the Galerkin projection equation

the polynomial approximation coefficients of IESSRB are determined and the polynomial approximation expression is obtained. To reduce the complexity of solving the Galerkin projection equations

the polynomial segmentation approach is proposed to approximate the IESSRB

which improves the computational efficiency and approximation accuracy for the IESSRB. Finally

the IES E39-G20 and E118-G96 test systems are employed to evaluate the performance of the proposed method

and the results confirm that the proposed method can realize the accurate and effective construction of IESSR.

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