电力系统非线性模型预测紧急电压控制方法研究
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摘要
为提高电力系统电压稳定性的调控能力，进一步提升电压控制手段的时空协调性，建立并求解能够全局调动无功支撑和电压控制潜力的紧急电压控制模型是亟待解决的问题。本文着眼于电力系统长期电压稳定性,将非线性模型预测控制理论引入电力系统紧急电压控制，主要解决紧急电压控制模型的建立及其稳定高效求解问题。
以准稳态假设为基础，基于模型预测控制理论建立长期电压稳定的紧急电压控制模型。该模型是一个滚动动态优化问题，旨在协调各种电压控制手段，从而以维持系统的长期电压稳定性。该滚动动态优化问题的目标函数综合考虑了电压偏移和控制成本，等式约束包括了连续-离散时间微分-代数方程组。为对该滚动动态优化模型进行有效求解，采用Radau排列法将该模型转化为非线性规划问题，并应用非线性原对偶内点算法进行求解。
针对滚动优化模型的求解问题，为了提高计算效率和保证计算的收敛性，本文提出了针对大规模非线性规划问题的可行性恢复算法。该算法借助Radau排列方法首先将滚动优化模型转化为非线性规划问题，然后对此非线性规划问题采用线搜索过滤方法进行计算，即将目标函数和约束条件作为两个优化目标分别进行优化，当该方法遇到迭代困难时，算法进入可行性恢复阶段，即通过放宽约束条件，找到一个位于约束边界内且满足目标函数下降条件的新迭代点，并使优化进程可以由该迭代点继续进行下去。该算法是一种兼顾迭代稳定性和计算效率的优选方案。
本文还以电力系统详细模型为基础，建立模型预测控制的动态优化模型。为了降低在线反馈延时，采用非线性规划灵敏度技术求解该滚动优化问题。其基本思想是：将滚动优化问题转化为非线性规划问题，在当前控制周期内，预测下一周期的状态值，并根据此预测值求解非线性规划问题，并同时给出Karsh-Kuhn-Tucker方程对模型参数的灵敏度。在进入下一控制周期后，根据状态变量的真实值，采用灵敏度信息修正控制变量值。该方法可以大幅提高计算效率，为紧急电压控制应用于大系统创造了条件。
In order to improve the control capability of the power system voltage stability and toenhance spatial and temporal coordination of voltage control means, it is essential to establishthe model of emergency voltage control that can globally mobilize reactive power support andvoltage control potential.Focus on the long-term voltage stability of power system, the paperintroduce nonlinear MPC into emergency voltage control, settle the problem that how toestablish the model of emergency voltage control and how to solve the optimization modelstably and efficiently.
Based on quasi-steady-state approximation, the nonlinear model predictive controlmethod is applied to design emergency voltage controller. The receding dynamic optimizationmodel is established to maintain long-term voltage stability by coordinating different kinds ofvoltage control means. In this receding dynamic optimization problem, the objective functionsynthetically considers both voltage deviation and control cost, and equality constraintsinclude continuous and discrete time differential-algebraic equations. To solve this recedingmodel efficiently, Radau collocation method is used to convert this model into a nonlinearprogramming problem which can be solved using the nonlinear primal-dual interior pointmethod.
For solving receding dynamic optimization model, in order to improve computationalefficiency and to ensure the computing convergence, the paper proposes the feasibilityrestoration algorithm that can be used to solve large-scale nonlinear programming problems.The Radau collocation method is used to convert this dynamic optimization model into alarge-scale NLP directly, then solve the NLP using the line search filter method, that is satisfythe objective function and constraint violation respectively. when the line search filter methodencounters convergent difficulty during solution of the this nonlinear programming problem,the optimization process will be switched to reconstruct feasibility of original NLP, and try tofind a new iteration point so that the optimization computation can continue from this point.The algorithm is a balanced optimization program between numerical stability andcomputational efficiency.
Based on detailed models of power system, the receding optimization model oflong-term voltage stability control is established under framework of model predictive control.In order to improve the computational efficiency and reduce feedback delays，nonlinearprogramming sensitivity algorithm is proposed to solve receding optimization model. Thebasic idea of this approach is converting this model into a nonlinear programming problem using Radau collocation method firstly, calculating the NLP program according to thepredicting state variable values of next period and evaluating the sensitivity of the KKTsystem with respect to model parameters。In the next control period, it calculates the value ofcontrol variables based on sensitivity information according to the true state variable values.The proposed method can improve computational efficiency significantly which creates thecondition for the emergency voltage control application to large-scale systems.
以准稳态假设为基础，基于模型预测控制理论建立长期电压稳定的紧急电压控制模型。该模型是一个滚动动态优化问题，旨在协调各种电压控制手段，从而以维持系统的长期电压稳定性。该滚动动态优化问题的目标函数综合考虑了电压偏移和控制成本，等式约束包括了连续-离散时间微分-代数方程组。为对该滚动动态优化模型进行有效求解，采用Radau排列法将该模型转化为非线性规划问题，并应用非线性原对偶内点算法进行求解。
针对滚动优化模型的求解问题，为了提高计算效率和保证计算的收敛性，本文提出了针对大规模非线性规划问题的可行性恢复算法。该算法借助Radau排列方法首先将滚动优化模型转化为非线性规划问题，然后对此非线性规划问题采用线搜索过滤方法进行计算，即将目标函数和约束条件作为两个优化目标分别进行优化，当该方法遇到迭代困难时，算法进入可行性恢复阶段，即通过放宽约束条件，找到一个位于约束边界内且满足目标函数下降条件的新迭代点，并使优化进程可以由该迭代点继续进行下去。该算法是一种兼顾迭代稳定性和计算效率的优选方案。
本文还以电力系统详细模型为基础，建立模型预测控制的动态优化模型。为了降低在线反馈延时，采用非线性规划灵敏度技术求解该滚动优化问题。其基本思想是：将滚动优化问题转化为非线性规划问题，在当前控制周期内，预测下一周期的状态值，并根据此预测值求解非线性规划问题，并同时给出Karsh-Kuhn-Tucker方程对模型参数的灵敏度。在进入下一控制周期后，根据状态变量的真实值，采用灵敏度信息修正控制变量值。该方法可以大幅提高计算效率，为紧急电压控制应用于大系统创造了条件。
In order to improve the control capability of the power system voltage stability and toenhance spatial and temporal coordination of voltage control means, it is essential to establishthe model of emergency voltage control that can globally mobilize reactive power support andvoltage control potential.Focus on the long-term voltage stability of power system, the paperintroduce nonlinear MPC into emergency voltage control, settle the problem that how toestablish the model of emergency voltage control and how to solve the optimization modelstably and efficiently.
Based on quasi-steady-state approximation, the nonlinear model predictive controlmethod is applied to design emergency voltage controller. The receding dynamic optimizationmodel is established to maintain long-term voltage stability by coordinating different kinds ofvoltage control means. In this receding dynamic optimization problem, the objective functionsynthetically considers both voltage deviation and control cost, and equality constraintsinclude continuous and discrete time differential-algebraic equations. To solve this recedingmodel efficiently, Radau collocation method is used to convert this model into a nonlinearprogramming problem which can be solved using the nonlinear primal-dual interior pointmethod.
For solving receding dynamic optimization model, in order to improve computationalefficiency and to ensure the computing convergence, the paper proposes the feasibilityrestoration algorithm that can be used to solve large-scale nonlinear programming problems.The Radau collocation method is used to convert this dynamic optimization model into alarge-scale NLP directly, then solve the NLP using the line search filter method, that is satisfythe objective function and constraint violation respectively. when the line search filter methodencounters convergent difficulty during solution of the this nonlinear programming problem,the optimization process will be switched to reconstruct feasibility of original NLP, and try tofind a new iteration point so that the optimization computation can continue from this point.The algorithm is a balanced optimization program between numerical stability andcomputational efficiency.
Based on detailed models of power system, the receding optimization model oflong-term voltage stability control is established under framework of model predictive control.In order to improve the computational efficiency and reduce feedback delays，nonlinearprogramming sensitivity algorithm is proposed to solve receding optimization model. Thebasic idea of this approach is converting this model into a nonlinear programming problem using Radau collocation method firstly, calculating the NLP program according to thepredicting state variable values of next period and evaluating the sensitivity of the KKTsystem with respect to model parameters。In the next control period, it calculates the value ofcontrol variables based on sensitivity information according to the true state variable values.The proposed method can improve computational efficiency significantly which creates thecondition for the emergency voltage control application to large-scale systems.
引文
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