A tractable formulation for multi-period linearized optimal power flow in presence of thermostatically controlled loads

Benenati, Emilio; Colombino, Marcello; Dall’Anese, Emiliano

doi:10.48550/arxiv.1908.09167

Cited by 2 publications

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“…This model is of the form ν k+1 = ν k P k where P k is a Markov transition matrix and ν k is a marginal distribution. The works [13], [14], [15] take this route, and ν k represents the "fraction of flexible loads with state value in a certain bin." Alternative to discretization, one can define this fractional state vector in an ad-hoc fashion and develop population models by analytically computing transition probabilities [11].…”

Section: A Literature Reviewmentioning

confidence: 99%

Control oriented modeling of TCLs

Coffman¹,

Bušíć²,

Barooah³

2020

Preprint

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Thermostatically controlled loads (TCLs) have the potential to be a valuable resource for the Balancing Authority (BA) of the future. Examples of TCLs include household appliances such as air conditioners, water heaters, and refrigerators. Since the rated power of each TCL is on the order of kilowatts, to provide meaningful service for the BA, it is necessary to control large collections of TCLs. To perform design of a distributed coordination/control algorithm, the BA requires a control oriented model that describes the relevant dynamics of an ensemble. Works focusing on solely modeling the ensemble date back to the 1980's, while works focusing on control oriented modeling are more recent. In this work, we contribute to the control oriented modeling literature. We leverage techniques from computational fluid dynamics (CFD) to discretize a pair of Fokker-Planck equations derived in earlier work [1]. The discretized equations are shown to admit a certain factorization, which makes the developed model useful for control design. In particular, the effects of weather and control are shown to independently effect the system dynamics.

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Section: A Literature Reviewmentioning

confidence: 99%

Control oriented modeling of TCLs

Coffman¹,

Bušíć²,

Barooah³

2020

Preprint

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show abstract

“…The goal in much of this prior work is to modify the behavior of loads so that their aggregate power consumption tracks the reference signal r that is broadcast by a Balancing authority (BA), based on distributed control, with local randomized decision rules. Randomized control techniques for Demand Dispatch have been proposed in [25,28,1,3] based on entirely different control architectures.…”

Section: Introductionmentioning

confidence: 99%

Kullback-Leibler-Quadratic Optimal Control of Flexible Power Demand

Cammardella

Bušíć

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper presents advances in Kullback-Leibler-Quadratic (KLQ) optimal control: a stochastic control framework for Markovian models. The motivation is distributed control of large networks. As in prior work, the objective function is composed of a state cost in the form of Kullback-Leibler divergence plus a quadratic control cost. With this choice of objective function, the optimal probability distribution of a population of agents over a finite time horizon is shown to be an exponential tilting of the nominal probability distribution. The same is true for the controlled transition matrices that induce the optimal probability distribution. However, one limitation of the previous work is that randomness can only be introduced via the control policy; all uncontrolled (natural) processes must be modeled as deterministic to render them immutable under an exponential tilting. In this work, only the controlled dynamics are subject to tilting, allowing for more general probabilistic models.Another advancement is a reduction in complexity based on lossy compression using transform techniques. This is motivated by the need to consider time horizons that are much longer than the inter-sampling times required for reliable control. Numerical experiments are performed in a power network setting. The results show that the KLQ method enables the aggregate power consumption of a collection of flexible loads to track a time-varying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints.

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A tractable formulation for multi-period linearized optimal power flow in presence of thermostatically controlled loads

Cited by 2 publications

References 0 publications

Control oriented modeling of TCLs

Control oriented modeling of TCLs

Kullback-Leibler-Quadratic Optimal Control of Flexible Power Demand

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