Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system

Malhamé, Roland P.; Chong, Chee-Yee

doi:10.1109/tac.1985.1104071

Cited by 284 publications

(239 citation statements)

References 8 publications

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“…We present the results of a computational study for a multi-room heating benchmark introduced in [18], based on a model proposed by [28]. The objective is to assess the performance of approximate model checking for the verification of probabilistic invariance of DTSHSs.…”

Section: Case Study: the Multi-room Heating Problemmentioning

confidence: 99%

“…, q h ) ∈ Q : q i = ON}. Equation (20) is the discrete time version of the stochastic differential equation in [28] with sample time interval ∆t. The quantities b i , a ij , and c i are non-negative constants representing the average heat transfer rate from room i to the ambient (b i ) and to room j = i (a ij ), and the heat rate supplied to room i by the heater in room i (c i ), all rescaled by ∆t and normalized with respect to the thermal capacity of room i.…”

Section: Description Of the Multi-room Heating Systemmentioning

confidence: 99%

See 1 more Smart Citation

Approximate Model Checking of Stochastic Hybrid Systems

Abate

Katoen

Lygeros

et al. 2010

European Journal of Control

170

233

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Section: Case Study: the Multi-room Heating Problemmentioning

confidence: 99%

Section: Description Of the Multi-room Heating Systemmentioning

confidence: 99%

Approximate Model Checking of Stochastic Hybrid Systems

Abate

Katoen

Lygeros

et al. 2010

European Journal of Control

170

233

View full text Add to dashboard Cite

“…This section presents a case study of the multi-room heating benchmark introduced in [22], based on a model proposed by [35] and already discussed in Section 2. The objective is to evaluate the usefulness of probabilistic model checking for the (approximate) verification (and optimisation) of an LMP.…”

Section: Case Studymentioning

confidence: 99%

Probabilistic Model Checking of Labelled Markov Processes via Finite Approximate Bisimulations

Abate

Kwiatkowska

Norman

et al. 2014

Lecture Notes in Computer Science

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Abstract. This paper concerns labelled Markov processes (LMPs), probabilistic models over uncountable state spaces originally introduced by Prakash Panangaden and colleagues. Motivated by the practical application of the LMP framework, we study its formal semantics and the relationship to similar models formulated in control theory. We consider notions of (exact and approximate) probabilistic bisimulation over LMPs and, drawing on methods from both formal verification and control theory, propose a simple technique to compute an approximate probabilistic bisimulation of a given LMP, where the resulting abstraction is characterised as a finite-state labelled Markov chain (LMC). This construction enables the application of automated quantitative verification and policy synthesis techniques over the obtained abstract model, which can be used to perform approximate analysis of the concrete LMP. We illustrate this process through a case study of a multi-room heating system that employs the probabilistic model checker PRISM.

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“…Bashash and Fathy [22] utilized thermostat offset signals to control ACLs and used a novel partial differential equation framework to model ACLs. Additionally, Malhamé and Chong [23] used the statistical approach to model the dynamic behavior of aggregated air conditioners. Nonetheless, most of these works were based on statistical approaches, which require a large amount of data to be collected.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Unit Commitment of Wind-Integrated Power System Considering Air-Conditioning Loads for Demand Response

Han

Zhou

et al. 2017

Applied Sciences

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Abstract:As a result of extensive penetration of wind farms into electricity grids, power systems face enormous challenges in daily operation because of the intermittent characteristics of wind energy. In particular, the load peak-valley gap has been dramatically widened in wind energy-integrated power systems. How to quickly and efficiently meet the peak-load demand has become an issue to practitioners. Previous literature has illustrated that the demand response (DR) is an important mechanism to direct customer usage behaviors and reduce the peak load at critical times. This paper introduces air-conditioning loads (ACLs) as a load shedding measure in the DR project. On the basis of the equivalent thermal parameter model for ACLs and the state-queue control method, a compensation cost calculation method for the ACL to shift peak load is proposed. As a result of the fluctuation and uncertainty of wind energy, a two-stage stochastic unit commitment (UC) model is developed to analyze the ACL users' response in the wind-integrated power system. A simulation study on residential and commercial ACLs has been performed on a 10-generator test system. The results illustrate the feasibility of the proposed stochastic programming strategy and that the system peak load can be effectively reduced through the participation of ACL users in DR projects.

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Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system

Cited by 284 publications

References 8 publications

Approximate Model Checking of Stochastic Hybrid Systems

Approximate Model Checking of Stochastic Hybrid Systems

Probabilistic Model Checking of Labelled Markov Processes via Finite Approximate Bisimulations

Stochastic Unit Commitment of Wind-Integrated Power System Considering Air-Conditioning Loads for Demand Response

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