# Incentive Price-Based Demand Response in Active Distribution Grids
## 1 Introduction
An incentive-based distributed optimization algorithm is proposed in [18] for voltage regulation by optimum control of the PV power production in LV grids. This algorithm is proposed to use primal-dual projected gradient method to compute the incentive price signals of PV systems. However, the disadvantages of this approach are (i) the PV power will be curtailed to bring the grid voltage within limits, (ii) forecasted load and generation information are not utilized for computing the incentive price signals. The above demerits can be overcome as follows (i) charging of the BESS when there is an over-voltage instead of curtailing the PV power, and (ii) use of forecasted power demand to solve the optimization problem over a prediction horizon, thereby the optimizing the utilization of BESS over a future time period. The benefits of the proposed approach will be increase in the hosting capacity of the grid, reduced operating costs for the DSO, and reduced electricity bills for the customers. A profit-sharing model or a detailed economic analysis among the players are not considered and they are beyond the scope of this paper. A limitation of the proposed method is the requirement of communication infrastructure among the LVGC and BESS controllers and the need for exchange of signals at each time-step to compute the incentive prices. However, it is assumed that in the near future, with the rollout of smart meters and other smart grid technologies the above communication requirement could be satisfied. The following are the assumptions of this work. 1. [label=(A0)]
2. Hourly load forecasts and PV generation forecasts are available that can be used by both DSO and BESS controllers. 3. The LVGC and DER controllers are able to solve the proposed distributed optimization routine at each time-step (10 min) by exchanging information such as dual variables of the optimization problem and the incentive price signals over the communication network. It is to be noted that short-term forecasts of loads and generation are important to realize a model predictive control algorithm, which is stated in assumption A1. As per assumption A2, it is assumed that the DSO install and operate the LVGC, which may be located in the LV distribution substation. Similarly, the DERs owned and operated by the customers are assumed to have the computational power and communication capability with the LVGC. In this paper, the challenge of DSOs to compute incentive price signals to customers owning flexible resources such as BESS is addressed. The major contributions of this paper are provided below. 1. Primal-dual projected gradient-based distributed optimization algorithm [18] is proposed to calculate the incentive price signals by the DSO to regulate the node voltages within limits. 2. Model predictive control algorithm for control of individual BESS to minimize the electricity costs of the corresponding customer taking into account the incentive price signals from the DSO. It is to be noted that compared to [18], a more accurate method for estimating the node voltages is employed in this paper. Although Ref. [13] also employs a model predictive control algorithm for control of individual BESS, the main difference is the distributed implementation of the above algorithm instead of a centralized control approach. This paper is organized as follows. A review and comparison of the demand response methods for the control of DERs are made in Section 2. In Section 3, linear models of the LV grid and the BESS are derived and the simulation setup used for conducting simulation studies in this paper are described. Section 4 elaborates the formulation of the proposed incentive price based demand response control method of DERs. Three simulation case studies to numerically evaluate the proposed IDR method are reported in Sections 5 and 6 concludes the paper with remarks and future works.