A sample-based approach for computing conservative linear power flow approximations
A sample-based approach for computing conservative linear power flow approximations
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DOI：
10.1016/j.epsr.2022.108579
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发表时间：
2022-11
影响因子：
3.9
通讯作者：
Paprapee Buason;Sidhant Misra;D. Molzahn
中科院分区：
文献类型：
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作者：
Paprapee Buason;Sidhant Misra;D. Molzahn
非线性潮流方程的非凸性给电力系统优化和控制问题的求解带来了挑战。线性近似通常用于通过权衡建模精度和易处理性来解决这些挑战。潮流线性化的精度取决于电力系统的特性和线性化应用的运行范围。然而，而不是利用知识的这些特性为一个特定的系统，许多现有的潮流线性化的基础上广泛的系统类别的一般假设，从而限制了他们的准确性。此外，由于现有的线性化不一致地高估或低估感兴趣的量，如电压幅值和线路流量，基于这些线性化的算法可能会导致约束违反时，应用于系统。相反，本文计算潮流方程的保守线性近似，即，线性近似，其旨在高估或低估感兴趣的量，以便实现避免约束违反的易处理算法。使用基于样本的方法，我们通过求解约束线性回归问题来计算这些保守线性化。我们分析和改进的保守线性近似通过迭代采样方法，优化功能的数量感兴趣的，和样本的复杂性分析。考虑到电压幅值与有功和无功功率注入之间的关系，我们表征了一系列测试用例的保守线性近似的性能。
Non-convexities induced by the non-linear power flow equations challenge solution algorithms for many power system optimization and control problems. Linear approximations are often used to address these challenges by trading off modeling accuracy for tractability. The accuracy of a power flow linearization depends on the characteristics of the power system and the operational range where the linearization is applied. However, rather than exploiting knowledge of these characteristics for a particular system, many existing power flow linearizations are based on general assumptions for broad classes of systems, thus limiting their accuracy. Moreover, since existing linearizations do not consistently overestimate or underestimate quantities of interest such as voltage magnitudes and line flows, algorithms based on these linearizations may lead to constraint violations when applied to the system. In contrast, this paper computesconservative linear approximationsof the power flow equations, i.e., linear approximations that intend to overestimate or underestimate a quantity of interest in order to enable tractable algorithms that avoid constraint violations. Using a sample-based approach, we compute these conservative linearizations by solving a constrained linear regression problem. We analyze and improve the conservative linear approximations via an iterative sampling approach, optimizing over functions of the quantities of interest, and a sample-complexity analysis. Considering the relationships between the voltage magnitudes and the active and reactive power injections, we characterize the performance of the conservative linear approximations for a range of test cases.