Long-term Voltage Stability Analysis And Control Based On Receding Horizon Optimization

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.