A Semi-Analytical Framework for Faster Deterministic and Stochastic Power System Simulations

随着间歇性和可再生能源的日益普及，电力公司在互联电力系统的计算机模拟方面面临着新的挑战。这些挑战包括：(1)如何处理电网数学模型中快速增长的维数和非线性；(2)如何处理电网日常运行中不断增加的不确定性。越来越多的不确定性源于可再生能源（如太阳能和风能）的变化和不可预测的性质，甚至源于可再生能源数学模型的不准确性。所谓的电网“超实时模拟”有望在检测到干扰后立即开始，甚至在影响结束前结束，从而提高电网运营商对重大停电的实时态势感知和决策支持能力，实现实时稳定性评估和控制。然而，传统的基于数值积分的仿真方法由于其迭代计算的机制，在提高实时实现的时间性能方面收效甚微。对于可再生能源渗透率高的电网，随机模拟变得越来越重要，但传统的模拟方法并没有很好地执行。该项目将探索一个全新的方向，在确定性和随机方法中实现更快的电网模拟。所提出的半分析框架更适合于在并行计算机上进行比实时更快的模拟，也适合于涉及可再生能源的随机电力系统模拟。该项目的成功可能会激励软件供应商应用这种新的半分析方法，从而导致更快的电网模拟工具，以帮助降低电网停电的风险。这种新的电网仿真方法可以推广到其他大型非线性动态系统的快速仿真中。与传统的通过数值积分和迭代求解电网非线性微分代数方程的仿真方法不同，该方法将求解过程分解为两个基本阶段：离线阶段使用Adomian分解方法对每个状态变量推导出近似解析解，称为“半解析解”（SAS），该解在一定时间间隔内有效，并且具有时间、其他状态变量和系统条件参数等符号变量；在线阶段对每个SAS的解析表达式进行评估，将其符号变量的值按连续的时间间隔代入，直到达到期望的模拟周期，因此可以极快地给出模拟结果，而无需进行数值积分或迭代。该项目将采取四个步骤来建立这种半分析方法及其理论框架：(1)开发一个系统的程序来推导实际电网模型的SASs；(2)研究这种新方法在快速确定性和随机模拟中的最大潜力；(3)在高性能超级计算机上实现和测试该方法；(4)在最近研究的“时间平行面”框架下，将该方法与传统的数值方法结合成混合方法，以探索互联电力系统超实时仿真的最大潜力。

With the increasing penetration of intermittent and renewable resources, electric utilities are facing new challenges in computer simulation of interconnected power systems. These challenges include (1) how to handle the fast growing dimensionality and nonlinearity in mathematical models of power grids, and (2) how to deal with increasing uncertainties in daily grid operations. The increasing uncertainties stem from the varying and unpredictable nature of renewable energy sources such as solar and wind, and even from inaccuracy in the mathematical models of renewable sources. The so-called "faster-than-real-time simulation" of a power grid is expected to start as soon as a disturbance is detected and to conclude even before the impact ends so as to improve real-time situational awareness and decision support capability of the grid operator against major power outages and enable real-time stability assessment and control. However, the traditional numerical integration based simulation approach has little power to improve time performance for real-time implementation due to its mechanism of iterative computations. Stochastic simulations are becoming more important for power grids with a high penetration of renewables but have not been executed well using the traditional simulation approach. This project will explore a completely new direction to achieve faster power grid simulation in both deterministic and stochastic approaches. The proposed semi-analytical framework is a better fit for faster-than-real-time simulation on parallel computers and also for stochastic power system simulations involving renewable sources. Success of the project may inspire software vendors to apply this new semi-analytical methodology leading to faster power grid simulation tools to help reduce the risk of the power grid to blackouts. This new methodology for power grid simulation can be generalized for fast simulation of other large-scale nonlinear dynamic systems. Unlike the traditional simulation approach solving power grid nonlinear differential-algebraic equations by numerical integration and iteration, this new approach decomposes the solution process into tasks in two basic stages: the offline stage uses the Adomian decomposition method to derive an approximate, analytical solution called a "semi-analytical solution" (SAS) for each state variable, which is valid for a certain time interval and has symbolic variables such as the time, other state variables and parameters on the system condition; the online stage evaluates the analytical expression of each SAS by plugging in values of its symbolic variables for consecutive intervals until achieving the desired period of simulation, so the simulation result can be given in an extremely fast manner without any numerical integration or iteration. The project will take four steps to establish this semi-analytical methodology and its theoretical framework: (1) developing a systematic procedure to derive SASs for realistic power grid models; (2) studying the maximum potential of this new approach in fast deterministic and stochastic simulations; (3) implementing and testing this approach on a high-performance supercomputer; and (4) incorporating the approach with the traditional numerical approach into a hybrid approach under the recently studied "Parareal in Time" framework to explore the biggest potential in faster-than-real-time simulation for interconnected power systems.