Optimal Load Ensemble Control in Chance-Constrained Optimal Power Flow

Distribution locational marginal prices (DLMPs) facilitate the efficient operation of low-voltage electric power distribution systems. We propose an approach to internalize the stochasticity of renewable distributed energy resources (DERs) and risk tolerance of the distribution system operator in DLMP computations. This is achieved by means of applying conic duality to a chance-constrained AC optimal power flow. We show that the resulting DLMPs consist of the terms that allow to itemize the prices for the active and reactive power production, balancing regulation, and voltage support provided. Finally, we prove the proposed DLMPs constitute a competitive equilibrium, which can be leveraged for designing a distribution electricity market, and show that imposing chance constraints on voltage limits distorts the equilibrium.

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“…24) Inserting the optimal dispatch given by (24) into (23c) and (23d) leads to the following relationship between prices π g i and π α :…”

Section: Dlmps With Chance-constrained Limits a Dlmps With Chanmentioning

confidence: 99%

Distribution Electricity Pricing Under Uncertainty

Mieth

Dvorkin

2020

IEEE Trans. Power Syst.

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“…Therefore, given the optimization described in Eq. (6)- (14), it is reasonable to select the inside temperature (T in ) and the electric power for heating (P HP j,t or P A j,t ) because these state variables are mutually dependent (i.e. an increase in electric power should result in a temperature increase).…”

Section: From Building Data To Mpmentioning

confidence: 99%

“…The MP constructed in Section III-B can now be used to implement the control of building ensembles as described in Section II-A. Using the solution procedure described in [14], we solve the optimization problem in Eq. (1)- (5) with the values of P αβ described in Fig.…”

Section: Mdp For Ensemble Controlmentioning

confidence: 99%

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A Markov Process Approach to Ensemble Control of Smart Buildings

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Hassan²,

Bruninx

et al. 2019

2019 IEEE Milan PowerTech

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This paper describes a step-by-step procedure that converts a physical model of a building into a Markov Process that characterizes energy consumption of this and other similar buildings. Relative to existing thermo-physics-based building models, the proposed procedure reduces model complexity and depends on fewer parameters, while also maintaining accuracy and feasibility sufficient for system-level analyses. Furthermore, the proposed Markov Process approach makes it possible to leverage real-time data streams available from intelligent data acquisition systems, which are readily available in smart buildings, and merge it with physics-based and statistical models. Construction of the Markov Process naturally leads to a Markov Decision Process formulation, which describes optimal probabilistic control of a collection of similar buildings. The approach is illustrated using validated building data from Belgium.

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“…Additionally, the effect of uncertain nodal injections on voltage magnitudes and line flows must be accounted for. To avoid dealing with computationally demanding scenario-based stochastic programming, [14]- [16] use the chance constrained framework. Dall'Anese et al [14] and Hassan et al [16] formulate an AC Chance-Constrained Optimal Power Flow (CC-OPF) problem by linearizing AC power flow equations and using given assumptions on the underlying uncertainty sources.…”

Section: Introductionmentioning

confidence: 99%

Online Learning for Network Constrained Demand Response Pricing in Distribution Systems

Mieth

Dvorkin

2020

IEEE Trans. Smart Grid

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Flexible demand response (DR) resources can be leveraged to accommodate the stochasticity of some distributed energy resources. This paper develops an online learning approach that continuously estimates price sensitivities of residential DR participants and produces such price signals to the DR participants that ensure a desired level of DR capacity. The proposed learning approach incorporates the dispatch decisions on DR resources into the distributionally robust chance-constrained optimal power flow (OPF) framework. This integration is shown to adequately remunerate DR resources and co-optimize the dispatch of DR and conventional generation resources. The distributionally robust chance-constrained formulation only relies on empirical data acquired over time and makes no restrictive assumptions on the underlying distribution of the demand uncertainty. The distributional robustness also allows for robustifying the otpimal solution against systematically misestimating empirically learned parameters. The effectiveness of the proposed learning approach is shown via numerical experiments. The paper is accompanied by the code and data supplement released for public use. NOMENCLATURE Sets: N Set of nodes, indexed by i = {0, 1, . . . , n}, |N | = n + 1 =: m N + Set of nodes without the root node, i.e. N + = {N \0} L Set of edges/lines indexed by i ∈ N + G Set of controllable generators, G ⊆ N A i Set of ancestor nodes of node i C i Set of children nodes of node i T Set of time intervals, indexed by t Λ t Set of historic price signals at time t X t Set of historic demand response observations at time t Variables and Parameters: c i (·) Cost function of the generator at node ī d P i,t Active power demand forecast at node i at time t d Q i,t Reactive power demand forecast at node i at time t e Column vector of ones of appropriate dimensions f P i,t Active power flow on line i towards node i at time t f Q i,t Reactive power flow on line i towards node i at time t g P i,t Active power output at node i at time t g Q i,t Reactive power output at node i at time t g P,min i,t , g P,max i,t Minimum/Maximum active power output g Q,min i,t , g Q,max i,t Minimum/Maximum reactive power output sAuxiliary variable for distributionally robust chanceconstraints reformulation u i,t Voltage squared at node i at time t w i (x) Cost/discomfort of demand reduction x x i,t Active power demand reduction at node i at time tMapping of net-injections to line flows, R n×m C Auxiliary matrix (αe ⊤ − I) ∈ R m×m that maps ǫ into changes in nodal injections I Identity matrix of appropriate dimensions M Auxiliary matrix R m+1×m+1 of decision variablesApparent power on line i T i (α) Mapping of load error vector ǫ t to voltage change at node i as a function of vector α X i Reactance of line i X Auxiliary diagonal matrix diag[X i , ∀i ∈ N + ] ∈ R n×n α i,t Participation factor of the generator at node i at time t α t Auxiliary vector {α i,t , i ∈ N } ∈ R m×1 β iParameters of the price sensitivity model at node i,Ratio between the active and reactive powe...

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Optimal Load Ensemble Control in Chance-Constrained Optimal Power Flow

Cited by 42 publications

References 37 publications

Distribution Electricity Pricing Under Uncertainty

Distribution Electricity Pricing Under Uncertainty

A Markov Process Approach to Ensemble Control of Smart Buildings

Online Learning for Network Constrained Demand Response Pricing in Distribution Systems

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