A Mean Field control approach for demand side management of large populations of Thermostatically Controlled Loads

Abstract

This paper presents a Mean Field (MF) control approach for demand side management of large populations of flexible electric loads, such as electrical cooling/heating appliances, called Thermostatically Controlled Loads (TCLs). We model the switching dynamics of each individual TCL as the solution of a local optimization problem, characterized by individual cost function, comfort constraints, cooling/heating rates and external temperature. We consider that a central utility company broadcasts macroscopic incentives to steer the overall TCL population towards a convenient equilibrium, to avoid power demand peaks due to possible synchronization of the TCL duty cycles. To find such pricing schemes we propose an iterative algorithm where, at every step, a simple model-free feedback law is used to update the incentives, given the current aggregate demand of the TCL population only. The convergence of such algorithm is ensured for any population size, even in the presence of heterogeneous convex constraints. We illustrate our MF control approach via numerical analysis

Optimal power consumption for demand response of thermostatically controlled loads

“…The optimal controls u * i (t) (top left) with constraints C1-C3 are same as those shown in Figure 5. However, the optimal indoor temperatures * (i) 123 (t) (right bottom) are different from * (i) 12 (t) (left bottom, same as in Figure 5), for i = 1, 2 TCLs. The subscript 123 in * (i) 123 (t) denotes that constraints C1-C3 are active [Colour figure can be viewed at wileyonlinelibrary.com] Combining the aforementioned two steps, we conclude that, for̂(t) strictly decreasing, the optimal indoor temperature trajectory found in Step 1 is the optimal among all feasible indoor temperature trajectories.…”

Mean field game based control of dispersed energy storage devices with constrained inputs

“…However, the cited literature does not consider constraints on control inputs when deriving optimal control laws. In contrast, [Bagagiolo et Bauso, 2013] and [Grammatico et al, 2015] study controls of the power demands of a large number of home appliances under an MFG framework, in the presence of saturated controls. A chattering switching control is implemented in [Bagagiolo et Bauso, 2013], and at equilibrium the mean temperature and the main frequency are regulated at the desired values.…”

“…In contrast, we shall be dealing here with piecewise smooth controls. In [Grammatico et al, 2015], a pricing incentives scheme is implemented for the entire population based on the current aggregated power demand where individual control is bang-bang-like switching. In [Paccagnan et al, 2015], the set of feasible aggregated power trajectories are characterized such that a population of TCLs can follow them, where each TCL has a hybrid dynamics and the mode switching rate is constrained.…”

Multi-Agent Coordination of Thermostatically Controlled Loads by Smart Power Sockets for Electric Demand Side Management

“…This data varies greatly depending on the country, city and cost and availability of electricity with respect to natural gas or other fossil fuels. These appliances are controlled by a thermostat and therefore are characterized by a simple ON/OFF power consumption dynamics which can be modulated to act as energy storage devices to provide ancillary services to the smart grid, see [5], [6], [7], [8], [9]. Thus, large populations of actively controlled TCLs can effectively add some flexibility to modulate the urban electric power demand.…”

“…Some promising methods for electric Demand Side Management (DSM) that focus on controlling TCLs can be found in [10], [11], [7]. There, centralized strategies and distributed decision making methods supported by a centralized information aggregator are exploited to address the problem.…”