# Power System Voltage Correction Scheme Based on Adaptive Horizon Model Predictive Control
## 1 Introduction  
The power system voltages should be maintained within predefined limits according to the operation requirements. Nowadays, the increasing penetration of distributed renewable energy has had significant impacts on system behavior due to its variability and uncertainty. Besides, the power systems are operated more closely to their physical limits. The risk of temporary voltage problems or even voltage collapse has increased [1]. When abnormal or unstable voltage profiles are detected, appropriate countermeasures should be taken to enhance voltage quality, power system security and operating economy. A reliable real-time optimal corrective voltage control scheme requires valid power system prediction models and feedback signals. Due to the inevitable modeling inaccuracies and measurement noise, it is impossible to build an accurate mathematical model to describe all the dynamic features of power systems, thus non-optimal or even inappropriate control decisions may be made. Model predictive control (MPC) is an appealing approach for dealing with the above issues [2], which is especially suitable for complicated systems with changeable dynamics and uncertain factors. The prediction model of a MPC-based method traces the operating state of practical system, and the control sequences are updated and corrected by real-time measurements. In order to reduce prediction complexity for real-time application, linear prediction models are commonly applied in a MPC-based voltage control scheme. In [3; 4], the coordinated voltage control is realized using tree search optimization method based on MPC. The authors of [5; 6] apply trajectory sensitivity and MPC to solve the optimal voltage control problem. In [7], the prediction model of a MPC-based real time voltage control scheme is simplified using wide area measurement information in receding horizons. In [8; 9], the search solution space of the MPC-based voltage controller is significantly reduced with the prepared control knowledge. A distributed model predictive control scheme for interconnected power systems is presented in [10]. In [11], MPC is applied in a large power system with most effective controls identified. In recent years, the increasing penetration of renewable power can introduce high variability into transmission and distribution systems, which can be well handled by MPC-based methods. A hierarchical controller based on MPC is proposed to regulate voltages in system with high penetration of wind power in [12]. Model predictive voltage control methods of wind farms are introduced in [13; 14; 15]. Reference [16] proposes a centralized controller based on MPC to mitigate voltage violations in active distribution networks (ADN) by coordinating power outputs of distributed generation units and the voltage set-point of the transformer load tap changer. The impact of the model predictive control of the ADN voltages to the transmission grid is discussed in [17]. A two-level real-time voltage correction scheme is proposed in [18]. The local level provides the fast response to a disturbance, and the central level coordinates the various distributed generation units relying on the concept of MPC. In [19], the performance of a MPC-based voltage controller is verified by the field test in a real distribution system. The length of the control horizon and prediction horizon of the existing MPC-based voltage control method has significant impact on the voltage control performances. A larger value of control horizon leads to smoother control but increased computation time. A smaller value of control horizon leads to less control steps and more aggressive control decisions, but it weakens the ability to deal with the modeling inaccuracies and measurement noise problem. The length of the prediction horizon should be equal to the length of the control horizon unless the controller is requested to consider changes happening beyond the control horizon [16].