Dynamics-aware Continuous-time Economic Dispatch and Optimal Automatic Generation Control Pratyush Chakraborty, Sairaj Dhople, Yu Christine Chen, and Masood Parvania Abstract— In this work, we aim to minimize the cost of generation in a power system while meeting demand in near- to real time. The proposed architecture is composed of two sub-problems: continuous-time economic dispatch (CTED) and optimal automatic generation control (OAGC). In its original form, the CTED problem incorporates generator aggregate- frequency dynamics, and it is infinite-dimensional. However, we present a computationally tractable function space-based solution method for the proposed problem. We also develop an optimization-based control algorithm for implementing OAGC. Theoretical considerations for decoupling the two problems are explored. We validate the economic efficiency and frequency performance of the proposed method through simulations of a representative power network. I. I NTRODUCTION One of the main challenges for a power system operator is to continually schedule generation to meet demand [1], [2]. The prevailing practice involves two parts: i) an offline eco- nomic dispatch (ED) problem, in which the system operator minimizes the cost of generation based on load forecasts while enforcing various operational constraints in steady state, and ii) real-time automatic generation control (AGC), which regulates system frequency to the synchronous value and fixes power interchanges between different balancing areas to their scheduled quantities. Typically, ED is per- formed (approximately on the order of) every 5 minutes to dispatch generators to meet the forecasted load. During real- time operations, the proportional-integral control-based AGC adjusts generator outputs around their ED setpoints based on deviations in frequency and tie-line flows [3], [4]. The future grid will extensively integrate renewable gen- eration, resulting in faster and less predictable frequency deviations away from synchronous operation [5], [6]. If the existing ED paradigm persists, significant AGC control effort would be needed in real time to maintain synchronous fre- quency and economic efficiency of the generators. Moreover, the existing AGC does not guarantee system cost minimiza- tion, especially if the real-time load deviates significantly from the forecast. To this end, we propose a combined architecture composed of: i) a continuous-time ED problem P. Chakraborty and M. Parvania are with the Department of Electrical and Computer Engineering, The University of Utah. S. V. Dhople is with the Department of Electrical and Computer Engineering, University of Minnesota. Y. C. Chen is with the Department of Electrical and Computer Engineering, The University of British Columbia. Funding support from the National Science Foundation, through grant NSF-ECCS-1453921, Office of Naval Research, through grant N000141812395, and Natural Sciences and Engineering Research Council of Canada (NSERC), through grant RGPIN- 2016-04271 is acknowledged. that acknowledges continuous load variations so that real- time control effort is reduced, and ii) an optimal AGC scheme that provides a mechanism to price AGC control effort while minimizing total cost of generation in real time. Recognizing the need to improve economic and dynamic performance of power system operations in the face of challenges such as increasing intermittency and variability, a variety of approaches have been put forward to optimize ED and AGC. Some approaches have proposed improve- ments to classical AGC [7], [8]. Model predictive control approaches have been proposed for developing economic dispatch [9]–[11]. In [12], ED and AGC are connected by reverse engineering AGC from an optimization point of view. In [13], a joint problem is decomposed to a multi-period ED and the AGC from [12]. A frequency-aware ED has been proposed in [14]. Primal-dual gradient methods have also been proposed to design decentralized feedback control laws [15]–[19]. Our central idea is to include a continuous-time dynamic model of the generators in existing methods for ED, and also conceptualize an AGC approach that ensures economic efficiency in real time. We begin with an ideal optimal control problem for the system operator where total cost of generation is minimized across timescales currently pertinent to ED and AGC while dynamically enforcing operational constraints. However, we will find that this optimal control problem cannot be solved simultaneously for ED and AGC actions since the real-time load is not known when ED is solved. Recognizing this limitation, and the fact that the objectives and constraints are required to be satisfied at two different timescales, we define a combination of two problems that can be solved and the solutions of which are close to those of the ideal problem. We refer to these prob- lems as: continuous-time economic dispatch (CTED) and optimal automatic generation control (OAGC). The CTED problem considers the dynamic constraints of generators and minimizes cost of generation over a scheduling horizon on the order of that considered for ED. We have developed a function space-based method to reformulate the infinite- dimensional CTED problem into a linear program [20]. (See also [21], [22] for related work.) With our previous effort in [20] covering the dispatch timescale, for real-time operation, the formulated OAGC problem minimizes the sum of well-defined cost functions for generators while ensuring frequency is restored to synchronous value. We develop an optimization-based control algorithm to solve OAGC. Importantly, the proposed approach embeds two different 2020 American Control Conference Denver, CO, USA, July 1-3, 2020 978-1-5386-8266-1/$31.00 ©2020 AACC 1292 Authorized licensed use limited to: Birla Institute of Technology & Science. Downloaded on August 03,2020 at 15:50:59 UTC from IEEE Xplore. Restrictions apply.