A Andrej Jokic

Assessment of non-centralised model predictive control techniques for electrical power networks

Model predictive control (MPC) is one of the few advanced control methodologies that have proven to be very successful in real-life applications. An attractive feature of MPC is its capability of explicitly taking state and input constraints into account. Recently, there has been an increasing interest in the usage of MPC schemes to control electrical power networks. The major obstacle for implementation lies in the large scale of these systems, which is prohibitive for a centralised approach. In this article, we therefore assess and compare the suitability of several non-centralised predictive control schemes for power balancing, to provide valuable insights that can contribute to the successful implementation of non-centralised MPC in the real-life electrical power system.

On Constrained Steady-State Regulation: Dynamic KKT Controllers

This technical note presents a solution to the problem of regulating a general nonlinear dynamical system to an economically optimal operating point. The system is characterized by a set of exogenous inputs as an abstraction of time-varying loads and disturbances. The economically optimal operating point is implicitly defined as a solution to a given constrained convex optimization problem, which is related to steady-state operation. The system outputs and the exogenous inputs represent respectively the decision variables and the parameters in the optimization problem. The proposed solution is based on a specific dynamic extension of the Karush-Kuhn-Tucker optimality conditions for the steady-state related optimization problem, which is conceptually related to the continuous-time Arrow-Hurwicz-Uzawa algorithm. Furthermore, it can be interpreted as a generalization of the standard output regulation problem with respect to a constant reference signal.

Almost decentralized lyapunov-based nonlinear model predictive control

This paper proposes an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By “almost decentralized” we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control (MPC). The stabilization conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, we provide a solution for relaxing the temporal monotonicity of the CLF for the overall network. For structured CLFs defined using the infinity norm, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. A nontrivial example illustrates the effectiveness of the developed theory and shows that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.

On infinity norms as Lyapunov functions for piecewise affine systems

This paper considers off-line synthesis of stabilizing static feedback control laws for discrete-time piecewise affine (PWA) systems. Two of the problems of interest within this framework are: (i) incorporation of the S-procedure in synthesis of a stabilizing state feedback control law and (ii) synthesis of a stabilizing output feedback control law. Tackling these problems via (piecewise) quadratic Lyapunov function candidates yields a bilinear matrix inequality at best. A new solution to these problems is proposed in this work, which uses infinity norms as Lyapunov function candidates and, under certain conditions, requires solving a single linear program. This solution also facilitates the computation of piecewise polyhedral positively invariant (or contractive) sets for discrete-time PWA systems.

Price-based optimal control of power flow in electrical energy transmission networks

This article presents a novel control scheme for achieving optimal power balancing and congestion control in electrical energy transmission networks via nodal prices. We develop an explicit controller that guarantees economically optimal steady-state operation while respecting all line flow constraints in steady-state. Due to these constraints, the resulting optimal control law has a piecewise affine structure. To optimize the dynamic response of the system and to satisfy line overload constraints during the transient period, the explicit optimal controller is complemented with a hybrid MPC controller. An example illustrates the effectiveness of the proposed hybrid control scheme.

Synthesis of Trajectory-Dependent Control Lyapunov Functions by a Single Linear Program

Although control Lyapunov functions (CLFs) provide a mature framework for the synthesis of stabilizing controllers, their application in the field of hybrid systems remains scarce. One of the reasons for this is conservativeness of Lyapunov conditions. This article proposes a methodology that reduces conservatism of CLF design and is applicable to a wide class of discrete-time nonlinear hybrid systems. Rather than searching for global CLFs off-line, we focus on synthesizing CLFs by solving on-line an optimization problem. This approach makes it possible to derive a trajectory-dependent CLF , which is allowed to be locally non-monotone. Besides the theoretical appeal of the proposed idea, we indicate that for systems affine in control and CLFs based on infinity norms, the corresponding on-line optimization problem can be formulated as a single linear program.

Self-optimizing Robust Nonlinear Model Predictive Control

This paper presents a novel method for designing robust MPC schemes that are self-optimizing in terms of disturbance attenuation. The method employs convex control Lyapunov functions and disturbance bounds to optimize robustness of the closed-loop system on-line, at each sampling instant - a unique feature in MPC. Moreover, the proposed MPC algorithm is computationally efficient for nonlinear systems that are affine in the control input and it allows for a decentralized implementation.

Dispatching power and ancillary services in autonomous network-based power systems

Competition is being introduced in the electricity markets worldwide. In addition, large penetration of distributed generation introduces new players into the markets and significantly increases the uncertainties in the system. The concept of autonomous power networks is a realistic approach to deal with increased uncertainty and complexity in future power systems. An autonomous power network is the aggregation of producers and consumers presented in the overall power system as one unit. This paper formulates the autonomous network dispatching optimization problem in rather general form and illustrates its efficiency. The number of trade-offs that are included at the forward time energy and ancillary service markets are outlined and discussed

Price-based control of electrical power systems

In this chapter we present the price-based control as a suitable approach to solve some of the challenging problems facing future, market-based power systems. On the example of economically optimal power balance and transmission network congestion control, we present how global objectives and constraints can in real-time be translated into time-varying prices which adequately reflect the current state of the physical system. Furthermore, we show how the price signals can be efficiently used for control purposes. Becoming the crucial control signals, the time-varying prices are employed to optimally shape, coordinate and synchronize local, profit-driven behaviors of producers/consumers to mutually reinforce and guarantee global objectives and constraints. The main focus in the chapter is on exploiting specific structural properties of the global system constraints in the synthesis of price-based controllers. The global constraints arise from sparse and highly structured power flow equations. Preserving this structure in the controller synthesis implies that the devised solutions can be implemented in a distributed fashion.

Provision of ancillary services for balance management in autonomous networks

The main hypothesis underlying the work presented in this paper is that the future power system will rely on large amounts of distributed generation (DG) with large percentage of renewable energy based sources. Consequently, this system will be characterised by significantly increased uncertainties on generation side and therefore, its behavior in time will be more difficult to control. This paper discusses the current methods for balance management. Furthermore it considers the limitations and presents a novel approach for balance management in a future situation.