基于图论的复杂能源枢纽矩阵建模方法研究

MatrixModeling Method of Complex EnergyHub Based on Graph Theory

针对复杂能源枢纽多能流耦合关系建模问题,提出一种基于图论的多能流耦合矩阵建模方法。将能源枢纽中的设备与能流抽象为节点-支路的二元关系,通过引入公共虚拟节点和广义损耗能流支路,构建了复杂能源枢纽的多能流平衡网络模型;基于路径矩阵定理,提出一种以星型网络为基础的支撑树构建方法,利用节点支路关联矩阵子阵和设备效率参数,建立以连支能流为独立变量的多能流耦合矩阵方程,并论证了高斯消去过程中相关矩阵的非奇异性。相较于已有的矩阵建模方法,所提方法可实现以最少能流变量列写多能流耦合线性矩阵方程,该方法基于图论的标准化数据结构也有助于实现多能流耦合矩阵的自动生成。以多个能源枢纽互联的多能流系统优化运行为例进行分析,验证了所提模型和方法的有效性。

In order to solve the problem of multiple energy flow coupling relationship modeling in complex energy hub,a multiple energy flow coupling matrix modeling method based on graph theory was proposed.The equipment and energy flow in the energy hub was generalized as a node-branch binary relationship,the common virtual node and generalized loss energy flow branch were introduced,and the multiple energy flow balance network model of complex energy hub was built.Based on the path matrix theorem,a support tree construction method based on star network was proposed.By means of the sub-matrix of node branch association matrix and the equipment efficiency parameters,the multiple energy flow coupling matrix equation was established,and the non-singularity of the correlation matrix in Gaussian elimination process was proved.Compared with the existing matrix modeling methods,the proposed method can write the multiple energy flow coupling linear matrix equation with the least energy flow variables.The standardized data structure based on graph theory of the proposed method can be helpful to realize the automatic generation of multiple energy flow coupling matrix.The effectiveness of the proposed model and method can be verified by an example of optimal operation of multiple energy flow system connected by multiple energy hubs.