Improved Lagrangian Relaxation Active Power Dispatching Strategy Considering Valve-point Effect of Generator

Jianhua CHEN; Dong DING; Xijuan YU; Hong DING; Yu XIN

doi:10.7500/AEPS20201123004

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Improved Lagrangian Relaxation Active Power Dispatching Strategy Considering Valve-point Effect of Generator

Application Research | 更新时间：2025-06-16

- Improved Lagrangian Relaxation Active Power Dispatching Strategy Considering Valve-point Effect of Generator
- Automation of Electric Power Systems Vol. 45, Issue 24, Pages: 115-121(2021)
- 作者机构：
  
  1.国网冀北电力有限公司，北京市100053
  2.国网北京市电力公司，北京市100031
  3.国网北京市电力公司电力科学研究院，北京市100075
- 作者简介：
- 基金信息：
- DOI：10.7500/AEPS20201123004
  CLC：
- Received：23 November 2020，
  
  Revised：2021-05-26，
  
  Published Online：19 November 2021，
  
  Published：25 December 2021
- 稿件说明：
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陈建华,丁冬,于希娟等.考虑发电机阀点效应的改进拉格朗日松弛有功调度策略[J].电力系统自动化,2021,45(24):115-121.

CHEN Jianhua,DING Dong,YU Xijuan,et al.Improved Lagrangian Relaxation Active Power Dispatching Strategy Considering Valve-point Effect of Generator[J].Automation of Electric Power Systems,2021,45(24):115-121.
陈建华,丁冬,于希娟等.考虑发电机阀点效应的改进拉格朗日松弛有功调度策略[J].电力系统自动化,2021,45(24):115-121. DOI： 10.7500/AEPS20201123004.

CHEN Jianhua,DING Dong,YU Xijuan,et al.Improved Lagrangian Relaxation Active Power Dispatching Strategy Considering Valve-point Effect of Generator[J].Automation of Electric Power Systems,2021,45(24):115-121. DOI： 10.7500/AEPS20201123004.

摘要

发电机阀点效应导致的非凸非光滑特性增加了有功经济调度模型的复杂度，从而增大了求解难度。文中提出一种考虑发电机阀点效应影响的改进拉格朗日松弛有功调度算法。首先，提出一种二次多项式分段拟合算法，从而将发电机阀点效应成本分解为多个分段二次多项式形式；其次，将拟合后的表达式代入拉格朗日松弛子问题中，从而将原问题转化为分段二次规划问题，并采用比较对称轴及优化变量上下限的方法快速求解，避免了引入整数变量造成的求解效率偏低问题。同时，为防止多个局部最优解导致的优化过程不收敛问题，提出一种基于近端梯度法的增广求解策略，通过在目标函数中引入辅助变量及惩罚项来加强子问题的凸性，加快收敛速度。最后，基于40机和48机测试系统对所提方法的有效性进行了测试。

Abstract

The non-convex and non-smooth characteristics caused by valve-point effect of generators increase the complexity of active power economic dispatching models

which increases the difficulty in solving the model. An improved Lagrangian relaxation active power dispatching algorithm considering the influence of valve-point effect of generators is proposed. Firstly

a quadratic polynomial piecewise fitting algorithm is proposed to decompose the cost of valve-point effect of generators into multiple piecewise quadratic polynomials. Secondly

the fitted expression is brought into the Lagrange relaxation subproblem

so that the original problem is transformed into a piecewise quadratic programming problem

which is solved rapidly by comparing the axis of symmetry and the upper and lower limits of optimization variables

so as to avoid the problem of low solution efficiency caused by the introduction of integer variables. At the same time

in order to prevent the convergence stagnancy of the optimization process caused by multiple local optimal solutions

an augmented solution strategy based on the proximal gradient method is proposed. The convexity of the subproblem is strengthened by introducing auxiliary variables and penalty terms into the objective function to accelerate the convergence speed. Finally

the effectiveness of the proposed method is tested based on 40-machine and 48-machine test systems.

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references

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