development stimulated by power systems problems [Simpson-Porco et al., 2013], [Bolognani et al, 2015], [Dall’Anese & Simmonetto, 2016], [Hauswirth et al., 2016], [Gan & Low, 2016], [Tang & Low, 2017], ... 1 A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems Daniel K. Molzahn,⇤ Member, IEEE, Florian D¨ orfler,† Member, IEEE, Henrik Sandberg,‡ Member, IEEE, Steven H. Low,§ Fellow, IEEE, Sambuddha Chakrabarti,¶ Student Member, IEEE, Ross Baldick,¶ Fellow, IEEE, and Javad Lavaei,⇤⇤ Member, IEEE Abstract—Historically, centrally computed algorithms have been the primary means of power system optimization and con- trol. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. This paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems. Index Terms—Distributed optimization, online optimization, electric power systems I. INTRODUCTION CENTRALIZED computation has been the primary way that optimization and control algorithms have been ap- plied to electric power systems. Notably, independent system operators (ISOs) seek a minimum cost generation dispatch for large-scale transmission systems by solving an optimal power flow (OPF) problem. (See [1]–[8] for related litera- ture reviews.) Other control objectives, such as maintaining scheduled power interchanges, are achieved via an Automatic Generation Control (AGC) signal that is sent to the generators that provide regulation services. These optimization and control problems are formulated using network parameters, such as line impedances, system topology, and flow limits; generator parameters, such as cost functions and output limits; and load parameters, such as an estimate of the expected load demands. The ISO collects all the necessary parameters and performs a central computation to solve the corresponding optimization and control problems. With increasing penetrations of distributed energy resources (e.g., rooftop PV generation, battery energy storage, plug-in vehicles with vehicle-to-grid capabilities, controllable loads ⇤: Argonne National Laboratory, Energy Systems Division, Lemont, IL, USA,
[email protected]. Support from the U.S. Department of En- ergy, Office of Electricity Delivery and Energy Reliability under contract DE-AC02-06CH11357. †: Swiss Federal Institute of Technology (ETH), Automatic Control Labora- tory, Z¨ urich, Switzerland,
[email protected] ‡: KTH Royal Institute of Technology, Department of Automatic Control, providing demand response resources, etc.), the centralized paradigm most prevalent in current power systems will poten- tially be augmented with distributed optimization algorithms. Rather than collecting all problem parameters and performing a central calculation, distributed algorithms are computed by many agents that obtain certain problem parameters via communication with a limited set of neighbors. Depending on the specifics of the distributed algorithm and the application of interest, these agents may represent individual buses or large portions of a power system. Distributed algorithms have several potential advantages over centralized approaches. The computing agents only have to share limited amounts of information with a subset of the other agents. This can improve cybersecurity and reduce the expense of the necessary communication infrastructure. Distributed algorithms also have advantages in robustness with respect to failure of individual agents. Further, with the ability to perform parallel computations, distributed algorithms have the potential to be computationally superior to centralized algorithms, both in terms of solution speed and the maxi- mum problem size that can be addressed. Finally, distributed algorithms also have the potential to respect privacy of data, measurements, cost functions, and constraints, which becomes increasingly important in a distributed generation scenario. This paper surveys the literature of distributed algorithms with applications to power system optimization and control. This paper first considers distributed optimization algorithms for solving OPF problems in offline applications. Many dis- tributed optimization techniques have been developed con- currently with new representations of the physical models describing power flow physics (i.e., the relationship between the complex voltage phasors and the power injections). The characteristics of a power flow model can have a large impact on the theoretical and practical aspects of an optimization formulation. Accordingly, the offline OPF section of this survey is segmented into sections based on the power flow model considered by each distributed optimization algorithm. This paper then focuses on online algorithms applied to OPF, optimal voltage control, and optimal frequency control problems for real-time purposes. Note that algorithms related to those reviewed here have Steven Low Enrique Mallada John Simpson-Porco Changhong Zhao Claudio De Persis Nima Monshizadeh Arjan Van der Schaft Marcello Colombino Emiliano Dall’Anese Sairaj Dhople Andrey Bernstein Krishnamurthy Dvijotham Andrea Simonetto Na Li Sergio Grammatico Yue Chen Florian Dörfler Saverio Bolognani Sandro Zampieri Jorge Cortez Henrik Sandberg Karl Johansson Ioannis Lestas Andre Jokic early adoption: KKT control [Jokic et al, 2009] literature kick-started ∼ 2013 by groups from Caltech, UCSB, UMN, Padova, KTH, & Groningen changing focus: distributed & simple → centralized & complex models/methods implemented in microgrids (NREL, DTU, EPFL, ...) & conceptually also in transactive control pilots (PNNL) 11 / 46