基于哈密尔顿系统与辛算法的暂态稳定约束最优潮流

Transient Stability Constrained Optimal Power Flow Based on Hamiltonian System and Symplectic Algorithm

提出了一种暂态稳定约束最优潮流的哈密尔顿模型,采用哈密尔顿系统的辛算法(symplectic algorithm)进行求解。将发电机转子运动方程转换为哈密尔顿系统的正则方程,用四阶辛Gauss-Legendre Runge-Kutta(GLRK)方法对其离散化,实现了大规模系统暂态稳定约束最优潮流的快速求解。辛GLRK方法具有很好的数值稳定性和保结构特性,相同精度时,计算步长可达隐式梯形法的6倍;大步长计算时仍具有较高的数值精度。某省3301节点,236机等5个系统的仿真结果表明:所提模型在高阶离散辛框架下具有很高的数值稳定性,即便采用大步长也可保持较高的数值精度,能提高计算速度10倍以上,具有很好的应用前景。

A Hamiltonian system model for transient stability constrained optimal power flow is proposed and solved by symplectic Gauss-Legendre Runge-Kutta （GLRK） algorithm suitable for Hamiltonian system. The rotor motion equation of generator is transformed into regular equation of Hamiltonian system and discretized by four order symplectic GLRK method to implement the fast solving of transient stability constrained optimal power flow in large-scale power grid. The symplectic GLRK method possesses satisfied numerical stability and structure preserving, and its calculation step length can reach to six times of that by hiding-trapezium method under the same calculation accuracy, and higher calculation accuracy can be obtained by large step length. Simulation results from five different examples with various system scales and structures, such as WSCC 3-machine 9-bus system, New England 39-bus system, IEEE ll8-bus system, IEEE 300-bus system and a certain provincial power grid X-3301 system with 236 machines, show that the proposed model possesses high numerical stability under discrete high-order symplectic framework, and higher numerical accuracy can be ensured even if under large step length. Using the proposed model, the calculation speed can reach to ten times and higher.