On the convexity of the system loss function
On the convexity of the system loss function
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DOI：
10.1109/tpwrs.2005.856993
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发表时间：
2005-10
影响因子：
6.6
通讯作者：
S. D. L. Torre;F. Galiana
中科院分区：
文献类型：
--
作者：
S. D. L. Torre;F. Galiana
我们证明了电力网络中的系统损耗函数在广义注入空间中被任意数目的支撑超平面有界。支撑超平面由系统损失函数在给定工作点附近的线性泰勒级数展开定义。如果扩展点足够接近平坦电压分布，则支撑超平面属性是有效的。我们在实验上评估了这个假设的有效范围，称为超平面支持范围(RHS)，表明对于典型的网络，RHS是广泛的，特别是当母线电压被控制在接近每单位1的时候。支持超平面模型也作为考虑网损的经济调度的一部分进行了测试，以证明该线性模型提供了与将网损作为非线性函数处理时相同的结果。
We show that the system loss function in a power network is bounded below by any number of supporting hyper-planes in the space of generalized injections. A supporting hyper-plane is defined by the linear Taylor series expansion of the system loss function around a given operating point. The supporting hyper-plane property is valid provided that the expansion point is sufficiently near the flat-voltage profile. We have assessed experimentally the range of validity of this assumption, called the range of hyper-plane support (RHS), showing that for typical networks, the RHS is broad, particularly when the bus voltages are controlled near 1 per unit. The supporting hyper-plane model was also tested as part of an economic dispatch with transmission losses to demonstrate that this linear model provides the same results as when the losses are treated as a nonlinear function.