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Distributed Control & Optimization Enabling Distributed Stability Analysis and Controller Design
With the explosion of renewable generation, millions of small-capacity, volatile, and heterogeneous renewable generation sources, such as wind-turbine generators and photovoltaics, have been encroaching on the dominion of a few large-capacity traditional generators. Unfortunately, the current top-down, central-dominant stability analysis and control architecture established for the traditional power system seems not to keep the transition's pace. However, recent years have witnessed remarkable progress in distributed control theory, convex optimization, measurement and communication technologies, and advanced power electronics engineering. The cross-fertilization among these terrific successes further creates opportunities to meet the abovementioned challenges. The two most-watched of those might be: 1) relieving the strong dependence on a central coordinator and 2) reshaping the top-down architecture by breaking the original control hierarchy. The former advocates a distributed paradigm to endow the power system with higher scalability, compatibility, and robustness. At the same time, the latter suggests emerging the slow-time-scale optimization and fast-time-scale control to achieve better adaptability and faster response. Accordingly, my research works have been focused on two aspects:
distributed stability certificates for power systems with heterogeneous nonlinear dynamical devices;
distributed algorithms enabling aggregating massive fragmented controllable resources;
merging distributed optimization and distributed control to break the traditional control hierarchy.
Distributed stability certificates enabling stable integration of massive heterogeneous dynamics
Input-output interconnection of the bus dynamics and the power network
New desynchronization mechanism: universal network coupling reversal
Distributed stability conditions
The system stability nearly monotonically increases with the output-differential passivity index
It is very challenging to find out distributed certificates for stable integration of heterogeneous nonlinear dynamics since a power system is a strongly coupled nonlinear complex dynamical system. To meet this challenge, we first established a “phasor circuit” model of symmetric AC three-phase power systems and then revealed that it obeys the fundamental KCL and KVL laws (or the Tellegen theorem in a more general sense) in the dq0-coordinate [1]. The result implies that this model inherently has a decomposable energy structure. Then we revealed that the phase and amplitude dynamics of a power system inherently twist with each other, leading to potential desynchronization by breaking the positive semi-definiteness of the coupling matrix [2]. We further introduced the concept of output-differential passivity, based on which we established the distributed stability conditions for individual bus dynamics [3]. The proposed conditions offer a new approach to assessing the system-wide stability in a distributed manner, essentially allowing a “stability protocol” to canonicalize the behaviors of a great variety of dynamic components connected to the power system such that the system-wide stability can be retained. The distributed certificate also provides a simple but effective approach to the decentralized controller design for stability enhancement [4].
[1] P. Yang, F. Liu*, Z. Wang, S. Ma, Towards Distributed Stability Analytics of Dynamic Power Systems: A Phasor-Circuit Theory Perspective, the 38th Chinese Control Conference, July 27-30, 2019, Guangzhou, China.
[2] P. Yang, F. Liu*, Z. Wang, et al., Spectral Analysis of Network Coupling on Power System Synchronization with Varying Phases and Voltages, 2020 Chinese Control And Decision Conference (CCDC), 22-24 Aug. 2020, Hefei, China (Zhang Si-Ying Outstanding Youth Paper Award).
[3] P Yang, F Liu*, Z Wang, C Shen, Distributed Stability Conditions for Power Systems with Heterogeneous Nonlinear Bus Dynamics, IEEE Transactions on Power Systems, 2020, 35 (3): 2313-2324 (Best Paper of IEEE TPWRS 2018-2020).
[4] Z. Wang, F. Liu, J. Z. F. Pang, et al., Distributed Optimal Frequency Control Considering a Nonlinear Network-Preserving Model, IEEE Transactions on Power Systems, 2019, 34(1): 76–86.
Distributed algorithms enabling aggregating massive fragmented controllable resources
Our research explored the distributed optimization algorithms to aggregate massive fragmented controllable resources to solve the original centralized optimization problem. We collaborated with Prof. Peng Yi and Yiguang Hong to develop more general algorithms based on the dual decomposition methodology[5][6]. And we extend this result to deal with non-smooth objective functions[7].
Since distributed algorithms usually converge slowly when the diameter of the communication network is large, we further introduced measurement feedback to speed up the convergence [8][9][10]. Its basic idea is to utilize the physical power system like a computer to physically “calculate” the result of power flow. Hence, one can remarkably accelerate the computation by directly measuring the states of the power system such that the algorithms can meet the requirement of real-time implementations. Moreover, the feedback can effectively avoid computation errors accumulation due to inaccurate models or parameters. Our works also considere imperfect communication, leading to asynchronous algorithms robust to time delays and packet loss in practice.
To further enhance the practicality of distributed algorithms, we designed a protocol based on the cutting-plane algorithm for constrained multi-agent optimization with arbitrary local solvers[11].
[5] P. Yi, Y. Hong and F. Liu, Initialization-free Distributed Algorithms for Optimal Resource Allocation with Feasibility Constraints and its Application to Economic Dispatch of Power Systems, Automatica, 2016, 74, 259-269
[6] P. Yi, Y. Hong and F. Liu, Distributed gradient algorithm for constrained optimization with application to load sharing in power systems, Systems & Control Letters, 2015, 83, 45-52.
[7] Z. Wang, F. Liu*, Y. Su, B. Qin, Asynchronous Distributed Voltage Control in Active Distribution Networks, Automatica, 2020, 122, 109269.
[8] Z. Wang, W. Wei, C. Zhao, Z. Zheng, Y. Zhang, F. Liu*, Exponential Stability of Partial Primal-Dual Gradient Dynamics with Nonsmooth Objective Functions, Automatica 2021, 129, 109585
[9] Z. Wang, L. Chen, F. Liu*, et al., Asynchronous Distributed Power Control of Multi-Microgrid Systems, IEEE Transactions on Control of Network Systems, 2020, 7(4): 1960-1973.
[10] Y. Su, F. Liu*, Z. Wang, et al., Online distributed tracking of generalized Nash equilibrium on physical networks, Autonomous Intelligent Systems, 2021, 1 (1): 1-12.
[11] Y. Zhang, Y. Su, F. Liu*, Protocol for Constrained Multi-Agent Optimization with Arbitrary Local Solvers, 2021 11th International Conference on Information Science and Technology (ICIST), 148-157, Chengdu, China.
Merging distributed optimization and distributed control
Distributed optimal control considering physical and cyber restrictions
To merge distributed optimization and distributed control and break the traditional control hierarchy, we formalize the secondary frequency control goal as a constrained optimization problem. Then, we leverage the primal-dual algorithm to solve the optimization problem to guide the controller design, such that the dynamics of the closed-loop system (approximately) carry out the primal-dual update. Specifically, we design optimal distributed secondary frequency control that restores the frequency to its nominal value while satisfying both steady-state and transient operational constraints[12][13]. We rigorously prove that the closed-loop trajectories (start within the feasible region) globally converge to the optimal operation point. In this way, the slow-time-scale economic dispatch (tertiary frequency control) is naturally embedded into the secondary control, breaking the original control hierarchy. Moreover, it offers a central-free control architecture that enables ubiquitous control and "plug-and-play" operation.
We further extend this framework to deal with various kinds of cyber or physical restrictions arising from practical requirements, such as nonsmooth objective functions [14][15], unknown disturbances caused by volatile renewable generations [16], and partial control coverage [4]. A personal account of the related work with my collaborators is summarized in [17].
[12] Z. Wang, F. Liu*, S. H. Low, et al., Distributed Frequency Control With Operational Constraints, Part I: Per-Node Power Balance, IEEE Transactions on Smart Grid, 2019, 10(1): 40–52.
[13] Z. Wang, F. Liu*, S. H. Low, et al., Distributed Frequency Control With Operational Constraints, Part II: Network Power Balance, IEEE Transactions on Smart Grid, 2019, 10(1): 53–64.
[14] Z. Wang, F. Liu*, C. Zhao, et al., Distributed optimal load frequency control considering nonsmooth cost functions, Systems & Control Letters, 2020, 136, 104607.
[15] Z. Wang, W. Wei, C. Zhao, Z. Zheng, Y. Zhang, F. Liu*, Exponential Stability of Partial Primal-Dual Gradient Dynamics with Nonsmooth Objective Functions, Automatica 2021, 129, 109585.
[16] Z. Wang, S. Mei, F. Liu*, et al., Distributed load-side control: Coping with variation of renewable generations, Automatica, 2019, 109, 108556.
[17] Feng Liu*, Zhaojian Wang, Changhong Zhao, Peng Yang, Merging Optimization and Control in Power Systems, Wiley, in press.
Applications
The controller design methods have been preliminarily applied to design the control systems in the “Smart and Clean-Energy Campus Demonstration” project initiated at Qinghai University, the 60MW Compressed Air Energy Storage Demonstration Project of the National Energy Administration, and the 100MW battery energy storage system of Henan Provincial Power Grid. Related applications won the second prize in Science and Technology Progress, which Henan Province awarded.
In addition, based on the proposed distributed stability certificates, we are currently developing an online stability-supporting assessment system for the 550MW battery energy storage system (BESS) in Inner Mongolia, China, which is one of the largest BESSs under construction in the world. We are trying to enable an online quantitative evaluation of the capability of BESS to support system-level stability in the presence of high-penetration volatile renewables, including frequency stability, voltage stability, and transient stability.
Online stability supporting assessment system(under construction)
Key Projects
In this area, I received two NSFC projects, “Intelligent Optimal Control in Power Systems Based on Approximate Dynamic Programming (2014-2017)” and “Generic Control Protocol Design for Integrating Massive Heterogeneous Distributed Resources”(2017-2020); both were evaluated as “Excellent.” I also joined the NSFC key project “Autonomous Control and Operation of Distributed Generation Clusters in Distribution Networks” as Co-PI (2018-2021). In addition, I am currently acting as the PI of the National Key Research and Development Plan sub-project, “Stability Supporting Capability Assessment of Energy Storage Clustering,” and the key project “Control Theory and Methodologies for Future Power Systems with High-penetration of Renewables and Power Electronics”(2022-2024) sponsored by the State Grid Corporation of China.
Ongoing Work: Equilibrium-free Stability Analytics based on Augmented Synchronization
Traditionally, the classic Lyapunov argument plays a central role in classic power system stability analysis in a centralized manner. It generally requires a given equilibrium, whether for Lyapunov function or approximate linearization, which is difficult, if not impossible, to adapt to future power systems suffering from unknown or time-varying equilibrium. On the other hand, it needs to collect the exact information of the overall system to process the stability analysis, which is not scalable. Although it literally can admit heterogeneity in dynamics, it is practically impossible to acquire the exact dynamics of millions of devices, including massive wind generators, PVs, EVs, and energy storage. Therefore, it is desired to develop a distributed equilibrium-free stability analytic tool. To this end, we alternatively study the stability of the equilibrium set, instead of a single equilibrium point, of a power system, which is defined by so-called “augmented synchronization”[S1]. We use the term "augmented" because it requires voltage convergence in addition to the conventional frequency synchronization. Obviously, augmented synchronization is a necessary condition for the stability of AC power systems in various working conditions. We then turn to study the stability of augmented synchronization, instead of a given equilibrium point. In this way, we could characterize the system stability without the knowledge of the equilibrium point of the post-fault system. Essentially, we move from "stability of a given equilibrium point" to "convergence of the equilibrium set". We expect this work could extend power system stability analytics to enable an equilibrium-free analysis. Some basic idea is presented in my recent talk.
This work is supported by the key project “Control Theory and Methodologies for Future Power Systems with High-penetration of Renewables and Power Electronics,” sponsored by the State Grid Cooperation of China, and the sub-project of the National Key Research and Development Plan “Stability Supporting Capability Assessment of Energy Storage Clustering.”
[S1] P Yang, F Liu*, T Liu, D J Hill, Augmented Synchronization: Bridging the Theory-Practice Gap in Transient Stability Analysis, submitted to IEEE Transactions on Automatic Control, arXiv preprint
Invited talk. "Towards Equilibrium-independent Stability Analytics for Future Power Systems: The Concept of Augmented Synchronization", International Top-Level Forum on Engineering Science and Technology Development Strategy & the 6th Purple Mountain Forum, Nanjing, China, 2021
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