1 Third order sliding mode observer-based approach for distributed optimal load frequency control Gianmario Rinaldi, Michele Cucuzzella and Antonella Ferrara Abstract—In this paper we propose a Third Order Sliding Mode Observer-based approach for Optimal Load Frequency Control (OLFC) in power networks which are partitioned into control areas. We model each area by an equivalent generator including second-order turbine-governor dynamics. Assuming to measure only few state variables, we design two third order sliding mode observers for each control area to locally estimate the unmeasured states. We introduce also a distributed second order sliding mode control strategy, which makes use of the estimates coming from the observers and achieves both frequency regulation and minimization of generation costs. The simulation results confirm the validity of the proposed approach. Index Terms—Variable-structure/sliding-mode control; Ob- servers for nonlinear systems; Power systems. I. I NTRODUCTION N OWADAYS, radical changes are affecting power sys- tems. Specifically, the demand for electrical energy in the 21 st century is increasing worldwide and a fast development in the area of renewable energy sources is required to overcome the environmental issues related to the reduction of greenhouse gases. Two resulting changes affecting power systems can be identified [1]: i) an increasing number of so-called renewable non-programmable power plants (such as photovoltaic power plants and wind power plants with their power intermittent power generation profiles) is being installed; ii) the develop- ment of the geographically distributed generation. These two processes cause increasing uncertainties in the monitoring and control of power systems [2]. In order to overcome the aforementioned issues, in recent years worldwide interest has resulted both in the literature and in the real world to develop more suitable and robust control strategies with application to power networks. In particular, the regulation of the frequency via Load Frequency Control (LFC), in power systems composed of interconnected Control Areas (CAs), is a challenging issue and it is unsure if current implementations are adequate to deal with an increasing share of renewable energy sources [3]. In [4], an extensive literature review on load frequency control problem in power networks has been provided. From that, one can notice advanced control techniques which have been adopted to redesign the conventional LFC schemes. In particular, Model Predictive Control (MPC), adaptive control, Gianmario Rinaldi, Michele Cucuzzella and Antonella Ferrara are with the Dipartimento di Ingegneria Industriale e dell’Informazione, University of Pavia, via Ferrata 5, 27100 Pavia, Italy (email: gianmario.rinaldi01@universitadipavia.it, michele.cucuzzella@gmail.com, antonella.ferrara@unipv.it) This is the final version of the accepted paper included in the IEEE Control Systems Letters, vol.1, no. 2 pp. 215–220, 2017. fuzzy control and Sliding Mode (SM) control methodologies have been proposed. In the literature, one can also find the so-called Optimal LFC (OLFC) scheme, which incorporates economic dispatch into the LFC, departing from the conven- tional tie line requirements (see e.g. [5]–[7]). In [7] it is necessary to acquire the measurements of all the state variables to generate the control law. Yet, the necessity of a large number of sensors can significantly limit the applicability of this control approach. The use of an observer can be seen as a way to overcome the limitation, thus enhancing monitoring and control of power network. Few relevant works have proposed observers with application to power systems. For example, in [8], an observer has been designed to estimate the electrical active power demand. In [9], a sliding mode observer has been used to estimate the states of each synchronous generator in multi-machines power systems. In [10], a sliding mode observer has been proposed to detect and reconstruct load alteration failures in power networks. In this paper, we adopt the model of a power network partitioned into control areas having an arbitrarily complex and meshed topology. The generation side is modeled by an equivalent generator including second-order turbine-governor dynamics. We assume to measure only the voltage angle variation and the turbine output power variation for each control area. The main contribution of the present paper is the design of two third order sliding mode observers capable of estimating, respectively, the frequency deviation and the governor output variation of each control area. The finite- time convergence to zero of the error system dynamics is also proved in this paper. The third order sliding mode observers have been designed having in mind the control strategy proposed in [7], which re- lies on the Suboptimal Second Order Sliding Mode (SSOSM) control algorithm [11], and on the design of a suitable sliding manifold, where the controlled system exhibits an incremental passivity property that allows us to infer convergence to a zero steady state frequency deviation which minimizes the generation costs. Differently from [7], where the availability of all the state variables is assumed, in the present paper we assume that the sliding variables defined to solve the control problem also depend on unmeasurable states of the power network. II. PROBLEM FORMULATION AND PRELIMINARIES Notation: The following (standard) notation is used throughout the paper. For a given state variable x, e x denotes its value after the change of coordinates e x = Ex, while ˆ x denotes the estimate of e x.