DC电网对输电线路扰动的长期响应
Long-Range Response to Transmission Line Disturbances in DC Electricity Grids
摘要：
我们考虑一个直流电网组成的输电线路连接发电机和消费者在其节点。直流电网由基尔霍夫定律导出的非线性方程描述。对于初始分布的消耗和产生的功率，并给定的传输线电导，我们确定的地理分布的节点处的电压。调整焦耳热损失的发电功率，然后计算通过传输线的电功率流。接下来，我们研究了电网的两个站点之间的一个额外的传输线的响应，并计算由此产生的潮流分布的变化。发现这种变化在空间中以距离附加线的距离的幂缓慢衰减。当增加一个链路时，我们发现功率传输的地理分布。在有限的概率下，当增加传输线时，电网中的最大负载变得更大，这种现象被称为Braess悖论。我们发现，这种现象是更明显的直流电网所描述的非线性方程从基尔霍夫定律比在一个线性化的流动模型研究以前在参考文献\cite{witthaut2013}。我们还观察到，由于增加线路而引起的传输线负载的增加与焦耳加热具有相同的数量级。有趣的是，对于一个固定的系统大小的负载线的增加与消费者和生产者的地理分布的无序程度。
英文摘要：
We consider a DC electricity grid composed of transmission lines connecting power generators and consumers at its nodes. The DC grid is described by nonlinear equations derived from Kirchhoff's law. For an initial distribution of consumed and generated power, and given transmission line conductances, we determine the geographical distribution of voltages at the nodes. Adjusting the generated power for the Joule heating losses, we then calculate the electrical power flow through the transmission lines. Next, we study the response of the grid to an additional transmission line between two sites of the grid and calculate the resulting change in the power flow distribution. This change is found to decay slowly in space, with a power of the distance from the additional line. We find the geographical distribution of the power transmission, when a link is added. With a finite probability the maximal load in the grid becomes larger when a transmission line is added, a phenomenon that is known as Braess' paradox. We find that this phenomenon is more pronounced in a DC grid described by the nonlinear equations derived from Kirchhoff's law than in a linearised flow model studied previously in Ref. \cite{witthaut2013}. We observe furthermore that the increase in the load of the transmission lines due to an added line is of the same order of magnitude as Joule heating. Interestingly, for a fixed system size the load of the lines increases with the degree of disorder in the geographical distribution of consumers and producers.
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