Distributed population dynamics : optimization and control applications

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well-mixed populations, which limits the applications where this theory can be implemented. In this paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controllers.Peer ReviewedPostprint (author's final draft

Distributed population dynamics: Optimization and control applications

Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well-mixed populations, which limits the applications where this theory can be implemented. In this paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controllers.This work has been supported by COLCIENCIAS–COLFUTURO, grants No: 528 and 6172; and by Project ALTERNAR, Acuerdo 005, 07/19/13 CTeI–SGR–Narino, Colombia.Peer reviewe

Distributed synthetic inertia control in power systems

© 2017 IEEE Due to the increasing use of renewables into the grid connected through power converters, the rotational inertia in power systems has been reducing. Consequently the frequency response requires the activation of the so-called synthetic inertia control. The synthetic inertia control aims to inject an extra power component when the system experiences a frequency disturbance event. In this paper, it is proposed that a distributed dynamic controllers for sharing the synthetic inertia control actions between the various active power converters in the grid for the improvement of the frequency response. It is assumed that a communication structure between the synthetic inertia controllers and the local power converters is involved in the system. The convergence of the control system is reached through a game population theory and the primary frequency control has been improved. The results are validated based on simulation of a two-area test system

CURRENT TRENDS AND CHALLENGES IN DISTRIBUTED CONTROL SYSTEMS – AN OVERVIEW

In this paper, innovations in the field of distributed control systems have been considered. Without any claim for completeness, a short summary on current trends in this area has been provided. A special attention is paid to application of blockchain technologies in distributed control systems, game theoretical approach for distributed control applications, and advantages of distributed control for power systems. Also, one of the main issues of modern distributed control systems – cybersecurity has been considered

Distributed transactive control in distribution systems with microgrids

Microgrids are considered as a cornerstone in the evolution to a smarter grid. However, this evolution brings some critical challenges for the control in a real-time implementation. We present two control algorithms to operate a power system with microgrids and other two to operate microgrids in order to reach the optimal social welfare. We consider three types of agents: photovoltaic generators, conventional generators and smart loads. These agents can be aggregated into a microgrid or interact directly in the power system depending on their power. To optimize the microgrids, we use two strategies. First one is based on projected consensus algorithm, where each agent iteratively optimizes its local utility function based on local information obtained from its neighbors and global information obtained through a distributed finite-time average algorithm. The second one is based on populations game theory; specifically we use a centralized replicator dynamics where a central agent iteratively optimizes the system status. To optimize the whole power system we use two strategies, first an asynchronous algorithm based on primal-dual optimization is proposed, where we consider that agents update the primal variables and a "virtual agent" updates the dual variables. Our last algorithm is a distributed transactive control algorithm based on populations games to dynamically manage the distributed generators and smart loads in the system to reach the optimum social welfare. Agents are considered non-cooperative, and they are individually incentive-driven. The proposed algorithm preserve stability while guarantee optimality conditions considering several constraints in the system on the real-time operation. We show numerical results of the proposed control strategies.Resumen: Las microrredes están consideradas como la piedra angular de la evolución hacia una red más inteligente. Sin embargo, esta evolución trae consigo algunos retos importantes para el control en la implementación en tiempo real. Presentamos dos algoritmos de control para operar un sistema de energía con microrredes y otros dos para operar microrredes con el fin de alcanzar el bienestar social óptimo. Consideramos dos tipos de agentes: generadores convencionales y cargas inteligentes. Estos agentes pueden ser agregados en una microred o interactuar directamente en el sistema de energía dependiendo de su potencia. Para optimizar las microrredes utilizamos dos estrategias, la primera se basa en un algoritmo de consenso proyectado, donde cada una de ellas optimiza iterativamente su función de utilidad local a partir de la información local obtenida de sus vecinos y la información global obtenida a través de un algoritmo distribuido de tiempo finito promedio. El segundo se basa en la teoría de juegos de poblaciones, específicamente usamos una dinámica de replicador centralizada donde un agente central optimiza iterativamente el estado del sistema. Para optimizar todo el sistema de potencia utilizamos dos estrategias, la primera es proponer un algoritmo asíncrono basado en la optimización prima-dual, donde consideramos que los agentes actualizan las variables primarias y un ”agente virtual” actualiza las variables duales. Nuestro último algoritmo es un algoritmo de control transaccional distribuido basado en juegos de poblaciones para gestionar dinámicamente los generadores distribuidos y las cargas inteligentes en el sistema para alcanzar el bienestar social óptimo. Se considera que los agentes no cooperan y se basan en incentivos individuales. El algoritmo propuesto preserva la estabilidad a la vez que garantiza condiciones óptimas considerando varias restricciones en el sistema sobre la operación en tiempo real. Se muestran los resultados numéricos de las estrategias de control propuestas.Maestrí

Optimized Hierarchical Control for an AC Microgrid Under Attack

Context: An inverter-based microgrid working in islanded mode can suffer cyber- attacks, these can be done against either the local controller or the communication links among the inverters. Secondary control is able to reject those attacks, however, a tertiary control action is necessary in order to stabilize the power flow among the microgrid. Method: Confidence factor technique allows to reject attacks in a microgrid acting directly over the secondary control, however, this technique omits other factor related to the power available. In this case, secondary control was complemented with a tertiary control that includes optimization criteria. Results: An inverter-based microgrid is simulated in Matlab for different scenarios and under cyberattack, this allows checking the correct response of the controller under attacks and the effective powersharing among inverters. Conclusions: The tertiary control allows stabilizing the active power of the system after the rejection of a cyber-attack by the secondary control. Each inverter supplies active power according to its máximum power rating without affecting the stability of the whole system

Non-centralized Control for Flow-based Distribution Networks: A Game-theoretical Insight

This paper solves a data-driven control problem for a flow-based distribution network with two objectives: a resource allocation and a fair distribution of costs. These objectives represent both cooperation and competition directions. It is proposed a solution that combines either a centralized or distributed cooperative game approach using the Shapley value to determine a proper partitioning of the system and a fair communication cost distribution. On the other hand, a decentralized noncooperative game approach computing the Nash equilibrium is used to achieve the control objective of the resource allocation under a non-complete information topology. Furthermore, an invariant-set property is presented and the closed-loop system stability is analyzed for the non cooperative game approach. Another contribution regarding the cooperative game approach is an alternative way to compute the Shapley value for the proposed specific characteristic function. Unlike the classical cooperative-games approach, which has a limited application due to the combinatorial explosion issues, the alternative method allows calculating the Shapley value in polynomial time and hence can be applied to large-scale problems.Generalitat de Catalunya FI 2014Ministerio de Ciencia y Educación DPI2016-76493-C3-3-RMinisterio de Ciencia y Educación DPI2008-05818Proyecto europeo FP7-ICT DYMASO