A new iterative linear programming approach to find optimal protective relay settings,International Transactions on Electrical Energy Systems

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A new iterative linear programming approach to find optimal protective relay settings
International Transactions on Electrical Energy Systems ( IF 1.9 ) Pub Date : 2020-11-25 , DOI: 10.1002/2050-7038.12639
Srimath Tirumala Pallerlamudi Srinivas ₁ , Kesanakurthy Shanti Swarup ₂

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This paper aims to present a new linearization approach to finding the optimal protective relay settings in power systems. The traditional protective relay coordination problem (CP) involving directional overcurrent relays (OcRs) is a nonconvex, nonlinear constrained optimization problem that is widely addressed in the literature. In linear programming (LP) based solution methods, the current plug settings (CPS) are fixed, and the time dial settings (TDS) are found, which though reasonably adequate but do not fetch the global solution. In nonlinear programming (NLP), both TDS and CPS are deemed to be decision variables, but NLP requires a proper initial‐point to get the best optimal solution. In this paper, the nonconvexity in CP formulation is convexified using bilinear relaxations, and global optimum is obtained. It is done by writing each bilinear term in CP formulation as a set of four linear inequalities using McCormick envelopes, and the error generated due to the linear approximations is reduced iteratively by updating the variable bounds. The proposed approach is programmed in MATLAB coding platform, and theoretical validation has been performed. The proposed approach has the advantages of being independent of initial‐point and attain the global optimum without the help of global optimization solvers.

中文翻译：

一种新的迭代线性编程方法，可找到最佳的保护继电器设置

本文旨在提出一种新的线性化方法，以找到电力系统中的最佳保护继电器设置。涉及方向性过电流继电器（OcR）的传统保护继电器协调问题（CP）是一种非凸，非线性约束的优化问题，已在文献中得到广泛解决。在基于线性编程（LP）的解决方案方法中，当前的插头设置（CPS）是固定的，并且找到了时间拨号设置（TDS），这些设置虽然合理地足够，但却无法获取全局解决方案。在非线性规划（NLP）中，TDS和CPS均被视为决策变量，但是NLP需要适当的初始点才能获得最佳的最佳解决方案。本文利用双线性松弛将CP公式中的非凸性凸出，并获得全局最优解。通过使用McCormick包络将CP公式中的每个双线性项写为一组四个线性不等式，可以完成此操作，并且通过更新变量边界来迭代地减少由于线性近似而产生的误差。该方法在MATLAB编码平台上进行了编程，并进行了理论验证。所提出的方法的优点是独立于初始点，并且无需全局优化求解器即可获得全局最优。

更新日期：2021-01-12

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