Model Predictive Control with and without Terminal Weight: Stability and Algorithms

This paper presents stability analysis tools for model predictive control (MPC) with and without terminal weight. Stability analysis of MPC with a limited horizon but without terminal weight is a long-standing open problem. By using a modified value function as an Lyapunov function candidate and the principle of optimality, this paper establishes stability conditions for this type of widely spread MPC algorithms. A new stability guaranteed MPC algorithm without terminal weight (MPCS) is presented. With the help of designing a new sublevel set defined by the value function of one-step ahead stage cost, conditions for checking its recursive feasibility and stability of the proposed MPC algorithm are presented. The new stability condition and the derived MPCS overcome the difficulties arising in the existing terminal weight based MPC framework, including the need of searching a suitable terminal weight and possible poor performance caused by an inappropriate terminal weight. This work is further extended to MPC with a terminal weight for the completeness. Numerical examples are presented to demonstrate the effectiveness of the proposed tool, whereas the existing stability analysis tools are either not applicable or lead to quite conservative results. It shows that the proposed tools offer a number of mechanisms to achieve stability: adjusting state and/or control weights, extending the length of horizon, and adding a simple extra constraint on the first or second state in the optimisation

A Cyber-Physical Systems Approach for Implementing the Receding Horizon Optimal Power Flow in Smart Grids

Two Major challenges in securing reliable Optimal Power Flow (OPF) operations are: (i) fluctuations induced due to renewable generators and energy demand, and (ii) interaction and interoperability among the different entities. Addressing these issues requires handling both physical (e.g., power flows) and cyber aspects (computing and communication) of the energy grids, i.e, a cyber-physical systems (CPS) approach is necessitated. First, this investigation proposes a receding horizon control (RHC) based approach for solving OPF to deal with the uncertainties. It uses forecasts on renewable generation and demand and an optimization model solving a predictive control problem to secure energy balance while meeting the network constraints. Second, to handle the interoperability issues, a middleware using common information model (CIM) for exchanging information among applications and the associated profiles are presented. CIM profiles modelling various components and aspects of the RHC based OPF is proposed. In addition, a middleware architecture and services to collect information is discussed. The proposed CPS approach is illustrated in a distribution grid in Steinkjer, Norway having 85 nodes, 700 customers, 3 hydrogenerators, and various industrial loads. Our results demonstrate the benefits of CPS approach to implement OPF addressing also the interoperability issues.acceptedVersio

A Cyber-Physical Systems Approach for Implementing the Receding Horizon Optimal Power Flow in Smart Grids

Two major challenges in securing reliable Optimal Power Flow (OPF) operations are: (i) fluctuations induced due to renewable generators and energy demand, and (ii) interaction and interoperability among the different entities. Addressing these issues requires handling both physical (e.g., power flows) and cyber aspects (computing and communication) of the energy grids, i.e, a cyber-physical systems (CPS) approach is necessitated. First, this investigation proposes a receding horizon control (RHC) based approach for solving OPF to deal with the uncertainties. It uses forecasts on renewable generation and demand and an optimization model solving a predictive control problem to secure energy balance while meeting the network constraints. Second, to handle the interoperability issues, a middleware using common information model (CIM) for exchanging information among applications and the associated profiles are presented. CIM profiles modelling various components and aspects of the RHC based OPF is proposed. In addition, a middleware architecture and services to collect information is discussed. The proposed CPS approach is illustrated in a distribution grid in Steinkjer, Norway having 85 nodes, 700 customers, three hydrogenerators, and various industrial loads. Our results demonstrate the benefits of CPS approach to implement OPF addressing also the interoperability issues