带外置蒸汽冷却器热力系统热平衡通用矩阵方程

Universal Thermal Balance Matrix Equation of Thermodynamic System With External Steam Cooler

为简化带外置蒸汽冷却器(external steam cooler,ESC)热力系统热平衡通用矩阵方程的构建和求解过程,采用基于矩阵运算的数学推理和案例分析相结合的方法,推导出可一次性求解的带ESC热力系统热平衡通用矩阵方程,建立系数矩阵与热力系统结构的对应关系。该通用矩阵方程无需迭代可直接一次性求解,系数矩阵A右上角某些元素不再为0,这些非0元素的位置与ESC在热力系统中的位置对应,每个非0元素的值与对应加热器水侧焓升成正比且位于同一列的这些非0元素的和等于该段抽汽在ESC中的焓降。此规律可用于构建通用矩阵方程,并经过某1000MW机组案例验算证明是正确的。该矩阵方程及其构建方法仍然适用于无ESC热力系统,通用性强,构建和求解过程大为简化。

In order to simplify its constructing and solving process, the general matrix thermal balance equation for power plant’s thermodynamic system with external steam cooler(ESC) was established by mathematical analysis and case study based on matrix computation. And the incidence relation between the equation’s coefficient matrix and ESC was set up also. The general matrix equation can be solved directly without iteration and certain elements at up-right zone of the matrix are no longer zero. Among these non-zero elements, their positions correspond to the positions of the ESCs in the thermodynamic system and each element was proportional to water enthalpy rise in corresponding heater, and summation of the elements in same column equaled to enthalpy drop of the extracted steam in ESC. This regular can be used to build the general matrix equation of thermodynamic system with ESC and was proven right by case study on a 1000 MW unit. The matrix equation and its constructing process which simplified modelling and solving largely have strong universality and adapt to thermal system without ESC also.