IFAC PapersOnLine 50-1 (2017) 4374–4381 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2017.08.881 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Delayed reaction, frequency control, optimal switching, power systems, stochastic optimal control. 1. INTRODUCTION The worldwide deregulation of electricity markets has changed the operation of power systems and drawn atten- tion to development of new operational strategies. A power system should be securely operated at all times whilst the operating conditions change over time. There are several states to keep track of which makes it challenging, in real- time, to monitor and perform countermeasures to prevent leaving the secure region of operation. In particular, a power system must, at all times, be operated close to its nominal frequency where the system inertia together with fast controlling reserves are able to decelerate fre- quency deviations following disturbances. A complicating factor is the random nature of power consumption and volatile production that brings stochastic variations into the frequency. With the increased integration of renewable production the challenge only seems to grow in the near future. The deregulation has also often led to a more inflexible generation control as independent system operators do not, themselves, operate the production units. In many systems, regulating power is instead traded on a market, called the regulating market. A bid to the regulating market is a block-bid on alteration of injected power at a given price per MW of produced power, that is binding in a specific operation period. One example is the Nordic market with operating periods of one hour, where the regulating market for each operating period closes 45 ⋆ This work was supported by the Swedish Research Council through the grant NT-14, 2014-03774 and by the Swedish Energy Agency through grant number 42982-1. minutes before the start of the period. During operation, the system operator can control the system frequency by and purchasing the energy specified During operation, the system operator has the opportunity to, at any time, contact actors responsible for bids on the regulating market to purchase the power specified in the contract. This is referred to as calling-off the bid. Furthermore, the system operator can reverse any prior call-offs. Call-offs can does be made of several bids simultaneously and each bid can, due to the possibility of reversing call-offs, be called-off several times during one operation period. In this setting the problem of finding an economically efficient frequency control scheme can be formulated as a multi-modes optimal switching problem. This problem is further complicated by the reaction times which, combined with ramp rates of power plants, lead to execution delays. The general optimal switching problem (sometimes re- ferred to as starting and stopping problem) has been thoroughly investigated in the last decades after being popularised in Brennan and Schwartz (1985). In Djehiche et al. (2009) existence of a solution to the multi-modes optimal switching problem was proved for constant switch- ing costs. In El Asri and Hamad´ ene (2009) this result was extended to switching costs which depend on the state variable and uniqueness of the viscosity solution to the Bellman equation was shown. Since then, results have been extended to problems with negative switching costs in El- Asri and Fakhouri (2012), partial information in Li et al. (2015) and execution delays in Perninge (2016). * Department of Physics and Electrical Engineering, Linnaeus University,V¨axj¨ o, Sweden (e-mail: magnus.perninge@lnu.se). ** Department of Market and System Development, Swedish National Grid, Sundbyberg, Sweden. (e-mail: robert.eriksson@svk.se) Abstract: The system frequency of a power systems is a good indicator of the networks resilience to major disturbances. In a completely deregulated setting, for example in the Nordic power system, the system operator controls the system frequency manually by calling-off bids handed in to a market, called the regulating market. In this paper we formulate the problem of optimal bid call-off on the regulating market, that the system operator is faced with each operating period, as an optimal switching problem with execution delays. As general optimal switching problems with execution delays are computationally cumbersome we resort to a recently developed suboptimal solution scheme, based on limiting the feedback information in the control loop. Magnus Perninge * Robert Eriksson ** Optimal Tertiary Frequency Control in Power Systems with Market-Based Regulation ⋆