基于滚动时域优化的长期电压稳定分析与控制研究
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摘要
随着电网规模的扩大和结构的加强,电网已逐渐进入发展饱和期。现阶段负荷中心水平不断增长,但由于环境资源的限制难以新建场站和线路走廊,远距离重负荷输电的局面将会日益突出,电力系统的运行越来越接近其稳定极限。虽然电网在规划时保留了一定的电压稳定裕度,但在遭受严重扰动时仍可能发生电压不稳定事故。电压稳定问题已经成为现阶段电力系统规划和运行中的主要关注问题之一。按照时间尺度和动态演化特征电压稳定可以分为短期电压稳定和长期电压稳定,几十年来,国内外发生了多起由于长期电压失稳导致的大面积停电事故,失稳主要原因在于负荷的自恢复特性使其功率需求超出了输电和发电系统容量,需要及时采取协调控制措施防止电压崩溃。由于长期电压稳定性问题的混杂动态特性和系统行为的不确定性,预测模型的精确度和计算速度成为制约在线电压协调控制效果和可行性的重要因素。发展适合在线应用的长期电压协调控制方法,对于防止因电压崩溃而导致的大停电事故具有重要的理论意义和工程应用价值。
在上述背景下,本文的研究把握长期电压稳定动态特征,量化分析电压轨迹对于控制措施的响应特性,基于滚动时域的控制方法在线求取最优电压控制序列。针对适用于在线决策的预测模型,优化约束,控制策略等一系列问题进行了研究与探索。论文的主要研究工作和创新成果如下：
(1)电压协调控制的优化决策集规模由优化目标节点和控制器的数目决定。在实际应用中,优化目标节点和控制器数量庞大,面临决策集爆炸的难题。由于电压控制局部性的特点,与爆炸增长的原始决策变量相比,系统故障场景中求取优化解中的动作控制器数目始终维持在一个较小的规模,因此对备选决策集进行筛选是必要的。论文基于模型预测控制的思想,提出了一种滚动筛选电压协调控制决策集的方法。将电压幅值和轨迹灵敏度信息作为聚类特征指标,经过原始数据标准化后形成模糊相似矩阵,在此基础上采用模糊聚类方法确定优化目标节点。根据优化目标节点电压对于控制的响应特性,在各控制时域初始时刻滚动筛选控制措施。由于聚类特征指标均源自于模型预测计算的过程量,决策集的筛选过程几乎不消耗额外计算时间；聚类和筛选方法均考虑了电压的动态响应特性,相比传统的静态指标可以更好地计及系统的动态演化趋势。仿真结果表明,提出方法能够在取得全局协调控制效果的前提下,大幅降低备选决策集规模,有效避免电压协调控制的决策集爆炸问题。
(2)基于静态分析方法的电压协调控制无法计及系统的混杂动态特性,且依赖于系统稳定平衡点的存在；基于动态分析的电压协调控制虽然能够避免上述问题,但通常以系统代数量作为优化目标和约束,能够确保系统电压轨迹渐进稳定,并使相关代数量保持在约束范围内,但无法确保系统稳定裕度满足要求。本文提出了一种计及稳定裕度约束的电压协调控制方法,在电压值协调控制时域的初始时刻,通过增加负荷功率识别系统在稳定极限点处的分岔方式。建立相应分岔情况下的电压稳定裕度指标并推导其对于控制措施的灵敏度,并在此基础上构建当前控制时域内的电压稳定裕度约束。若优化时刻系统存在稳定平衡点,则电压协调控制模型中考虑稳定裕度约束；反之则仅针对电压幅值进行优化。优化过程以采样周期为间隔在线滚动进行,不仅能够对故障后的电压幅值进行优化,还能够确保系统维持一定的稳定裕度。
(3)电力系统在运行过程中存在很多不确定因素,且长期电压稳定时间尺度下的综合负荷难以精确建模,电压协调控制研究中使用的预测模型几乎不可能与实际系统运行状态完全匹配。采用模型预测控制方法进行电压协调控制能够在一定程度上解决上述问题,但其控制效果受控制时域参数的影响较大。在其他时域参数不变的情况下,控制时域越小,需要求取的控制步数越少,相应计算时间越少,控制决策更加激进,但有可能会进一步扩大模型不匹配误差,降低优化效率；控制时域越大,控制效果更加平滑,但计算时间也会随之增加。现有研究均根据具体算例确定控制时域参数,且控制时域参数在优化过程中恒定不变。针对上述情况,提出了一种基于自适应控制时域参数的电压协调控制策略。预测时域内通过时域仿真确定评估目标节点,并求取电压对于备选控制措施的轨迹灵敏度,取每个预测时域结束时刻评估目标节点电压对于备选控制的轨迹灵敏度建立灵敏度矩阵,在控制调节速率的约束下评估当前优化步数下的评估目标节点的累计电压最大恢复值,建立极限调压能力指标,根据该指标在优化过程中自适应调整控制时域参数,使其能够根据系统运行状态及演化趋势自适应调整：在系统故障初期,电压偏移较大,为防止大幅度调节控制器加剧模型不匹配导致的预测偏差,降低优化效率,优化会采用较大的控制时域参数。随着优化的滚动进行,预测电压幅值逐渐接近其参考值,控制时域参数逐渐减小,可减少计算时间,加快故障后电压恢复速度和优化过程的收敛。
(4)针对长期电压稳定问题,提出了一种基于分段校正模型的在线电压协调控制策略。通过广域测量信息线性近似预测周期内系统动态状态变量的轨迹,结合时标分解方法避免优化过程中使用连续动态方程,并且讨论了离散动态的处理方式。预测模型在控制周期初始时刻根据广域测量信息进行校正,使其能够跟踪实际系统的运行状态,确保预测结果的可信性。通过假设负荷自恢复动态,提出了一种针对分段校正模型节点电压对于控制响应的预测方法,根据线性系统的叠加性质转化最优电压协调控制模型。在确保控制效果的同时大幅降低了计算复杂度。
With the scale expanding and structure reinforcing of the power grid, it has gradually developed into the saturation stage. Nowadays the power consumption in load centers keeps on growing, at the same time, due to environmental reasons; it is difficult to expand the network by means of new plants and transmission lines. The problem of large capacity and long distance power transmission is increasingly outstanding, thus the power system is operated closer to its physical limits. Although a certain amount of voltage stability margin is considered at the power network planning stage, voltage instability accidents may still occur under severe system disturbance. Voltage stability has become one of the major concerns in power system planning and operation. According to the time scale and dynamic feature, voltage stability can be divided into short term voltage stability and long term voltage stability. Over the last decades, several large scale blackouts caused by long term voltage instability have occurred throughout the world, which stems from the attempt of load dynamics to restore power consumption beyond the capability of the combined transmission and generation system. The voltage decay features relatively slow dynamics, generally lasts from several seconds to a few minutes, thus allowing the necessary online optimization procedure to take place and be applied so that the voltage collapse can be averted. Because the long term voltage stability problem features hybrid dynamic and uncertainty in system behavior, the accuracy of prediction model and the optimization speed have become the main factors that restrict the performance and feasibility of on-line coordinated voltage control. In order to avert large scale blackouts caused by long term voltage instability, it is theoretically and practically necessary to develop coordinated long term voltage control scheme for on line application.
As mentioned above, the research in this paper captures the key dynamic feature of long term voltage stability. The response feature of the system voltage with respect to the control actions is quantitatively analyzed, and the optimal voltage control sequences are obtained based on receding horizon control method. Prediction models, optimization constraints and control schemes for online coordinated voltage control are proposed in this paper. The main contributions and innovations are described as follows:
(1) The scale of the optimization decision set in coordinated voltage controls is determined by the number of target optimization node and the candidate control actions. In practical applications, decision set explosion may happens because of the huge number of the target node and controls. Since that voltage controls has locality feature, the number of manipulated control variables in the optimal voltage control sequences are much less than the original candidate control variables, thus it is necessary to select the key decision set of optimal voltage control problems. Based on the principle of model predictive control, a candidate decision set rolling selection method for coordinated voltage control is proposed. The voltage magnitude and trajectory sensitivity are used as the clustering feature index. The fuzzy similarity matrix is then formulated by the data standardization process, based on which the target optimization nodes are determined using fuzzy clustering method. The controllers engaged in the optimization are selected at the beginning of each control horizons according to the response feature of the voltage magnitudes with respect to control actions. Since that the clustering feature index is the byproduct of the model prediction process, the selection of the decision set requires little computation time; the clustering and selection method considers the dynamic response feature of voltage, thus the dynamic evolution of the system is better considered compared with the traditional static index. Simulation results indicate that the proposed method significantly decreases calculation scale under the premise of global control performance; calculation burden and time consuming is remarkably reduced, and void online computation difficulty caused by decision set explosion.
(2) Coordinated voltage control schemes based on static analysis fail to capture the dynamic feature of power systems, and they are carried out on a post-contingency stable equilibrium point. However, the system may lose stability if the disturbances are severe; Coordinated voltage control schemes based on dynamic analysis can avoid the above the above problems, but their optimization target only involves the algebraic output variables of the system. Such control schemes can maintain the algebraic output variables within their limits, but a desired voltage stability margin may not be assured. To avoid post-fault power grid voltage collapse and maintain a certain stability margin, a coordinated voltage control strategy considering stability margin is proposed, in which the optimal control model is built based on model predictive control and trajectory sensitivity method. In the initial moment of each control interval the bifurcation types of the system are identified, and by means of calculating the sensitivity of voltage stability margin under corresponding bifurcation type, the stability margin constraint is constructed. If a stable equilibrium point exists at the initial moment of the control interval, the stability margin constraint is added to the optimal model to solve the optimal control sequence. Simulation results show that the proposed control strategy can ensure stability margin of power grid while post-fault voltage amplitude is effectively optimized.
(3) There are many uncertain factors in the operation process of power systems, and it is very difficult to build an accurate aggregate load in long term time scale, thus the prediction models used in coordinated voltage control have model mismatch problems. Model predictive control based control method can solve the above problem, but its control performance is related to the control horizon parameter. When the other time horizon parameters maintain constant, smaller values of control horizon parameter leads to more aggressive control and less computation time, but it may exacerbate the control error caused by the model mismatch; larger values of control horizon parameter lead to smoother control but higher settling times and increased computation time. A coordinated voltage control scheme based on adaptive control horizon parameters is proposed. The target evaluation nodes are determined by time domain simulation within the prediction horizon, the trajectory sensitivity of those nodes'voltage with respect to the candidate control actions are then obtained, based on which the voltage adjustment limit index is formulated by evaluating the maximum voltage recovery amount with the current optimization steps. The control horizon parameter is determined according to the voltage adjustment limit index, which is able to adjust itself adaptively according to the system operation state and evolution trend:at the initial stage of the system fault, the voltage deviation is relatively large, in order to avoid over aggressive control decisions that may exacerbate the prediction error caused by model mismatch, the optimization uses a large control horizon parameter. With the implementation of the control results, the voltage magnitudes gradually approach their reference values, the optimization uses smaller control horizon parameter, which can reduce computation time and accelerate the speed of voltage recovery and optimization convergence process.
(4) Focused on mid-long term voltage stability, a segmented-correction power system model for on-line coordinated voltage control is proposed. Optimal control behaviors are calculated using model predictive control method. In order to ensure reliable prediction results, the prediction model is modified at every beginning of control horizon according to wide area measurements. Dynamic load state variable trajectories are linearly approximated within prediction horizon, hybrid differential-algebraic equations of the power system model is transformed into algebraic equations with logical decisions, which avoids time domain simulation during MPC implementation. System output response trajectories with respect to control actions are derived from the prediction model based on a deformed Euler state predictor, which transforms optimal coordinated voltage control model into a tractable mixed-integer linear programming problem. Simulation results indicate that the proposed scheme is able to coordinate controls of different types and geographical locations, calculation burden and time consuming is remarkably reduced.
在上述背景下,本文的研究把握长期电压稳定动态特征,量化分析电压轨迹对于控制措施的响应特性,基于滚动时域的控制方法在线求取最优电压控制序列。针对适用于在线决策的预测模型,优化约束,控制策略等一系列问题进行了研究与探索。论文的主要研究工作和创新成果如下：
(1)电压协调控制的优化决策集规模由优化目标节点和控制器的数目决定。在实际应用中,优化目标节点和控制器数量庞大,面临决策集爆炸的难题。由于电压控制局部性的特点,与爆炸增长的原始决策变量相比,系统故障场景中求取优化解中的动作控制器数目始终维持在一个较小的规模,因此对备选决策集进行筛选是必要的。论文基于模型预测控制的思想,提出了一种滚动筛选电压协调控制决策集的方法。将电压幅值和轨迹灵敏度信息作为聚类特征指标,经过原始数据标准化后形成模糊相似矩阵,在此基础上采用模糊聚类方法确定优化目标节点。根据优化目标节点电压对于控制的响应特性,在各控制时域初始时刻滚动筛选控制措施。由于聚类特征指标均源自于模型预测计算的过程量,决策集的筛选过程几乎不消耗额外计算时间；聚类和筛选方法均考虑了电压的动态响应特性,相比传统的静态指标可以更好地计及系统的动态演化趋势。仿真结果表明,提出方法能够在取得全局协调控制效果的前提下,大幅降低备选决策集规模,有效避免电压协调控制的决策集爆炸问题。
(2)基于静态分析方法的电压协调控制无法计及系统的混杂动态特性,且依赖于系统稳定平衡点的存在；基于动态分析的电压协调控制虽然能够避免上述问题,但通常以系统代数量作为优化目标和约束,能够确保系统电压轨迹渐进稳定,并使相关代数量保持在约束范围内,但无法确保系统稳定裕度满足要求。本文提出了一种计及稳定裕度约束的电压协调控制方法,在电压值协调控制时域的初始时刻,通过增加负荷功率识别系统在稳定极限点处的分岔方式。建立相应分岔情况下的电压稳定裕度指标并推导其对于控制措施的灵敏度,并在此基础上构建当前控制时域内的电压稳定裕度约束。若优化时刻系统存在稳定平衡点,则电压协调控制模型中考虑稳定裕度约束；反之则仅针对电压幅值进行优化。优化过程以采样周期为间隔在线滚动进行,不仅能够对故障后的电压幅值进行优化,还能够确保系统维持一定的稳定裕度。
(3)电力系统在运行过程中存在很多不确定因素,且长期电压稳定时间尺度下的综合负荷难以精确建模,电压协调控制研究中使用的预测模型几乎不可能与实际系统运行状态完全匹配。采用模型预测控制方法进行电压协调控制能够在一定程度上解决上述问题,但其控制效果受控制时域参数的影响较大。在其他时域参数不变的情况下,控制时域越小,需要求取的控制步数越少,相应计算时间越少,控制决策更加激进,但有可能会进一步扩大模型不匹配误差,降低优化效率；控制时域越大,控制效果更加平滑,但计算时间也会随之增加。现有研究均根据具体算例确定控制时域参数,且控制时域参数在优化过程中恒定不变。针对上述情况,提出了一种基于自适应控制时域参数的电压协调控制策略。预测时域内通过时域仿真确定评估目标节点,并求取电压对于备选控制措施的轨迹灵敏度,取每个预测时域结束时刻评估目标节点电压对于备选控制的轨迹灵敏度建立灵敏度矩阵,在控制调节速率的约束下评估当前优化步数下的评估目标节点的累计电压最大恢复值,建立极限调压能力指标,根据该指标在优化过程中自适应调整控制时域参数,使其能够根据系统运行状态及演化趋势自适应调整：在系统故障初期,电压偏移较大,为防止大幅度调节控制器加剧模型不匹配导致的预测偏差,降低优化效率,优化会采用较大的控制时域参数。随着优化的滚动进行,预测电压幅值逐渐接近其参考值,控制时域参数逐渐减小,可减少计算时间,加快故障后电压恢复速度和优化过程的收敛。
(4)针对长期电压稳定问题,提出了一种基于分段校正模型的在线电压协调控制策略。通过广域测量信息线性近似预测周期内系统动态状态变量的轨迹,结合时标分解方法避免优化过程中使用连续动态方程,并且讨论了离散动态的处理方式。预测模型在控制周期初始时刻根据广域测量信息进行校正,使其能够跟踪实际系统的运行状态,确保预测结果的可信性。通过假设负荷自恢复动态,提出了一种针对分段校正模型节点电压对于控制响应的预测方法,根据线性系统的叠加性质转化最优电压协调控制模型。在确保控制效果的同时大幅降低了计算复杂度。
With the scale expanding and structure reinforcing of the power grid, it has gradually developed into the saturation stage. Nowadays the power consumption in load centers keeps on growing, at the same time, due to environmental reasons; it is difficult to expand the network by means of new plants and transmission lines. The problem of large capacity and long distance power transmission is increasingly outstanding, thus the power system is operated closer to its physical limits. Although a certain amount of voltage stability margin is considered at the power network planning stage, voltage instability accidents may still occur under severe system disturbance. Voltage stability has become one of the major concerns in power system planning and operation. According to the time scale and dynamic feature, voltage stability can be divided into short term voltage stability and long term voltage stability. Over the last decades, several large scale blackouts caused by long term voltage instability have occurred throughout the world, which stems from the attempt of load dynamics to restore power consumption beyond the capability of the combined transmission and generation system. The voltage decay features relatively slow dynamics, generally lasts from several seconds to a few minutes, thus allowing the necessary online optimization procedure to take place and be applied so that the voltage collapse can be averted. Because the long term voltage stability problem features hybrid dynamic and uncertainty in system behavior, the accuracy of prediction model and the optimization speed have become the main factors that restrict the performance and feasibility of on-line coordinated voltage control. In order to avert large scale blackouts caused by long term voltage instability, it is theoretically and practically necessary to develop coordinated long term voltage control scheme for on line application.
As mentioned above, the research in this paper captures the key dynamic feature of long term voltage stability. The response feature of the system voltage with respect to the control actions is quantitatively analyzed, and the optimal voltage control sequences are obtained based on receding horizon control method. Prediction models, optimization constraints and control schemes for online coordinated voltage control are proposed in this paper. The main contributions and innovations are described as follows:
(1) The scale of the optimization decision set in coordinated voltage controls is determined by the number of target optimization node and the candidate control actions. In practical applications, decision set explosion may happens because of the huge number of the target node and controls. Since that voltage controls has locality feature, the number of manipulated control variables in the optimal voltage control sequences are much less than the original candidate control variables, thus it is necessary to select the key decision set of optimal voltage control problems. Based on the principle of model predictive control, a candidate decision set rolling selection method for coordinated voltage control is proposed. The voltage magnitude and trajectory sensitivity are used as the clustering feature index. The fuzzy similarity matrix is then formulated by the data standardization process, based on which the target optimization nodes are determined using fuzzy clustering method. The controllers engaged in the optimization are selected at the beginning of each control horizons according to the response feature of the voltage magnitudes with respect to control actions. Since that the clustering feature index is the byproduct of the model prediction process, the selection of the decision set requires little computation time; the clustering and selection method considers the dynamic response feature of voltage, thus the dynamic evolution of the system is better considered compared with the traditional static index. Simulation results indicate that the proposed method significantly decreases calculation scale under the premise of global control performance; calculation burden and time consuming is remarkably reduced, and void online computation difficulty caused by decision set explosion.
(2) Coordinated voltage control schemes based on static analysis fail to capture the dynamic feature of power systems, and they are carried out on a post-contingency stable equilibrium point. However, the system may lose stability if the disturbances are severe; Coordinated voltage control schemes based on dynamic analysis can avoid the above the above problems, but their optimization target only involves the algebraic output variables of the system. Such control schemes can maintain the algebraic output variables within their limits, but a desired voltage stability margin may not be assured. To avoid post-fault power grid voltage collapse and maintain a certain stability margin, a coordinated voltage control strategy considering stability margin is proposed, in which the optimal control model is built based on model predictive control and trajectory sensitivity method. In the initial moment of each control interval the bifurcation types of the system are identified, and by means of calculating the sensitivity of voltage stability margin under corresponding bifurcation type, the stability margin constraint is constructed. If a stable equilibrium point exists at the initial moment of the control interval, the stability margin constraint is added to the optimal model to solve the optimal control sequence. Simulation results show that the proposed control strategy can ensure stability margin of power grid while post-fault voltage amplitude is effectively optimized.
(3) There are many uncertain factors in the operation process of power systems, and it is very difficult to build an accurate aggregate load in long term time scale, thus the prediction models used in coordinated voltage control have model mismatch problems. Model predictive control based control method can solve the above problem, but its control performance is related to the control horizon parameter. When the other time horizon parameters maintain constant, smaller values of control horizon parameter leads to more aggressive control and less computation time, but it may exacerbate the control error caused by the model mismatch; larger values of control horizon parameter lead to smoother control but higher settling times and increased computation time. A coordinated voltage control scheme based on adaptive control horizon parameters is proposed. The target evaluation nodes are determined by time domain simulation within the prediction horizon, the trajectory sensitivity of those nodes'voltage with respect to the candidate control actions are then obtained, based on which the voltage adjustment limit index is formulated by evaluating the maximum voltage recovery amount with the current optimization steps. The control horizon parameter is determined according to the voltage adjustment limit index, which is able to adjust itself adaptively according to the system operation state and evolution trend:at the initial stage of the system fault, the voltage deviation is relatively large, in order to avoid over aggressive control decisions that may exacerbate the prediction error caused by model mismatch, the optimization uses a large control horizon parameter. With the implementation of the control results, the voltage magnitudes gradually approach their reference values, the optimization uses smaller control horizon parameter, which can reduce computation time and accelerate the speed of voltage recovery and optimization convergence process.
(4) Focused on mid-long term voltage stability, a segmented-correction power system model for on-line coordinated voltage control is proposed. Optimal control behaviors are calculated using model predictive control method. In order to ensure reliable prediction results, the prediction model is modified at every beginning of control horizon according to wide area measurements. Dynamic load state variable trajectories are linearly approximated within prediction horizon, hybrid differential-algebraic equations of the power system model is transformed into algebraic equations with logical decisions, which avoids time domain simulation during MPC implementation. System output response trajectories with respect to control actions are derived from the prediction model based on a deformed Euler state predictor, which transforms optimal coordinated voltage control model into a tractable mixed-integer linear programming problem. Simulation results indicate that the proposed scheme is able to coordinate controls of different types and geographical locations, calculation burden and time consuming is remarkably reduced.
引文
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