Extracting flexibility of heterogeneous deferrable loads via polytopic projection approximation

Zhao, Lin; He, Hao; Zhang, Wei

doi:10.1109/cdc.2016.7799293

Cited by 25 publications

(25 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many energy systems are abstracted as idealized energy buffers subjected to power and energy constraints (1) and (2) only, see [6], [18], among others. Such systems are referred to as PE-systems, and their feasible sets are called PE-polytopes.…”

Section: ) State Constraintsmentioning

confidence: 99%

See 1 more Smart Citation

Aggregation and Disaggregation of Energetic Flexibility From Distributed Energy Resources

Müller

Szabó

Sundström

et al. 2019

IEEE Trans. Smart Grid

126

View full text Add to dashboard Cite

Abstract-A variety of energy resources has been identified as being flexible in their electric energy consumption or generation. This energetic flexibility can be used for various purposes such as minimizing energy procurement costs or providing ancillary services to power grids. To fully leverage the flexibility available from distributed small-scale resources, their flexibility must be quantified and aggregated. This paper introduces a generic and scalable approach for flexible energy systems to quantitatively describe and price their flexibility based on zonotopic sets. The description proposed allows aggregators to efficiently pool the flexibility of large numbers of systems and to make control and market decisions on the aggregate level. In addition, an algorithm is presented that distributes aggregate-level control decisions among the individual systems of the pool in an economically fair and computationally efficient way. Finally, it is shown how the zonotopic description of flexibility enables an efficient computation of aggregate regulation power bid-curves.

show abstract

Section: ) State Constraintsmentioning

confidence: 99%

“…In contrast, inner-approximations provide sufficient conditions for feasibility. Approaches for computing inner-approximations are based on zonotopics sets [10] or on projection to polytopic sets [6]. Both inner-and outerapproximations for battery models are provided in [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Aggregation and Disaggregation of Energetic Flexibility From Distributed Energy Resources

Müller

Szabó

Sundström

et al. 2019

IEEE Trans. Smart Grid

126

View full text Add to dashboard Cite

show abstract

“…In [8]- [10], individual flexibility of each DER is described as a polytopic feasible set, then the aggregate flexibility is calculated as the Minkowski sum of the individual polytopes. Reference [11] applies the polytopic projection to procure the aggregate flexibility and formulates an approximated optimization problem for tractable solution.…”

Section: Introductionmentioning

confidence: 99%

Aggregate Power Flexibility in Unbalanced Distribution Systems

Chen

Dall’Anese

Zhao

et al. 2020

IEEE Trans. Smart Grid

113

View full text Add to dashboard Cite

With a large-scale integration of distributed energy resources (DERs), distribution systems are expected to be capable of providing capacity support for the transmission grid. To effectively harness the collective flexibility from massive DER devices, this paper studies distribution-level power aggregation strategies for transmission-distribution interaction. In particular, this paper proposes a method to model and quantify the aggregate power flexibility, i.e., the net power injection achievable at the substation, in unbalanced distribution systems over time. Incorporating the network constraints and multi-phase unbalanced modeling, the proposed method obtains an effective approximate feasible region of the net power injection. For any aggregate power trajectory within this region, it is proved that there exists a feasible disaggregation solution. In addition, a distributed model predictive control (MPC) framework is developed for practical implementation of the transmission-distribution interaction. At last, we demonstrate the performances of the proposed method via numerical tests on a real-world distribution feeder with 126 multi-phase nodes.Index Terms-Power aggregation, distributed energy resources, unbalanced optimal power flow, power flexibility, distributed optimization. NOMENCLATUREA. Parameters N Number of buses (except the substation). N Y , N ∆ Number of buses with wye-, delta-connection. L Number of distribution lines. v, v Upper, lower limits of the three-phase nodal voltage magnitudes for all buses. i L , i L Upper, lower limits of the three-phase line current magnitudes for all distribution lines. P g,ψ i,t , P g,ψ i,t Upper, lower limits of active PV power generation in phase ψ of bus i at time t. S g,ψ i,t Apparent power capacity of PV units in phase ψ of bus i at time t. P e,ψ i,t , P e,ψ i,t Upper, lower limits of active power output of ES devices in phase ψ of bus i at time t. S e,ψ i,t Apparent power capacity of ES devices in phase ψ of bus i at time t. E i , E i Upper, lower limits for state of charge of ES devices at bus i. X. Chen and N. Li are with the School of Engineering and Applied Sciences, Harvard University, USA. d,ψ i,t , P d,ψ i,t Upper, lower limits for controllable active loads in phase ψ of bus i at time t. F out i,t Outside temperature for HVAC systems at bus i at time t. F i , F i Upper, lower limits of comfortable temperature zone for HVAC systems at bus i. ∆t Length of each time slot under discretized time horizon. B. Variables p Y , q Y ∈ R 3N Y Column vector of the three-phase active, reactive power injection via wye-connection. p ∆ , q ∆ ∈ R 3N∆ Column vector of the three-phase active, reactive power injection via delta-connection. v ∈ R 3N Column vector collecting the three-phase nodal voltage magnitudes for all buses. i L ∈ R 3L Column vector collecting the three-phase line current magnitudes for all distribution lines. p 0 ∈ R 3 Column vector of the three-phase net active power injection at the substation. P g,ψ i,t , Q g,ψ i,t Active, reactive PV power generation ...

show abstract

“…Several theoretical works have then proposed frameworks for computing the tracking capabil-ity of such systems. Several model-based methods using robust programming concepts have been proposed including [14], [15], [16], [17]. Other works have proposed analytical methods to analyze the aggregate flexibility of populations of loads in order to characterize it as an equivalent 'virtual battery' [4], [18], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of buildings providing frequency regulation services in the Swiss market

Gorecki

Fabietti

Jones

2017

Energy and Buildings

View full text Add to dashboard Cite

This paper investigates the potential of commercial buildings to offer ancillary services to the grid. We consider a tracking procurement inspired by secondary frequency control, where the resource needs to commit to a nominal consumption profile ahead of time and then receives a power consumption deviation around this profile. We propose a model-based predictive scheme which formally assesses the amount of power flexibility that can be offered by the resource and of attaining the best trade-off between comfort and financial gain during real-time operation by adjusting the nominal power consumption with a delay, in accordance to the regulations of the Swiss energy market. Extensive simulation results highlight how the possibility to perform adjustments on the scheduled energy profile is of paramount importance for both maintaining comfortable operational conditions and offering larger tracking flexibility. Finally, the effectiveness and robustness of the proposed methodology are demonstrated by means of full-day experiments in an occupied office space.

show abstract

Extracting flexibility of heterogeneous deferrable loads via polytopic projection approximation

Cited by 25 publications

References 26 publications

Aggregation and Disaggregation of Energetic Flexibility From Distributed Energy Resources

Aggregation and Disaggregation of Energetic Flexibility From Distributed Energy Resources

Aggregate Power Flexibility in Unbalanced Distribution Systems

Experimental demonstration of buildings providing frequency regulation services in the Swiss market

Contact Info

Product

Resources

About