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Stochastic Model Predictive Control for Demand Response in a Home Energy Management System Preprint Kaitlyn Garifi1, Kyri Baker1, Behrouz Touri2, and Dane Christensen3 1 University of Colorado 2 University of California 3 National Renewable Energy Laboratory

Presented at the IEEE Power and Energy Society General Meeting Portland, Oregon August 5-10, 2018

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Conference Paper NREL/CP-5500-70492 November 2018

Stochastic Model Predictive Control for Demand Response in a Home Energy Management System Preprint Kaitlyn Garifi1, Kyri Baker1, Behrouz Touri2, and Dane Christensen3 1 University of Colorado 2 University of California 3 National Renewable Energy Laboratory

Suggested Citation Garifi, Kaitlyn, Kyri Baker, Behrouz Touri, and Dane Christensen. 2018. Stochastic Model Predictive Control for Demand Response in a Home Energy Management System: Preprint. Golden, CO: National Renewable Energy Laboratory. NREL/CP-5500-70492. https://www.nrel.gov/docs/fy19osti/70492.pdf.

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Stochastic Model Predictive Control for DemandResponse in a Home Energy Management System

Kaitlyn Garifi, Kyri BakerUniversity of Colorado Boulder

Boulder, CO, USAEmail: {kaitlyn.garifi;kyri.baker}@colorado.edu

Behrouz TouriUniversity of California San Diego

San Diego, CA, USAEmail: btouri@ucsd.edu

Dane ChristensenNational Renewable Energy Laboratory

Golden, CO, USAEmail: dane.christensen@nrel.gov

Abstract—This paper presents a chance constrained, modelpredictive control (MPC) algorithm for demand response (DR)in a home energy management system (HEMS). The HEMSoptimally schedules controllable appliances given user prefer-ences such as thermal comfort and energy cost sensitivity, andavailable residentially-owned power sources such as photovoltaic(PV) generation and home battery systems. The proposed controlarchitecture ensures both the DR event and indoor thermalcomfort are satisfied with a high probability given the uncertaintyin available PV generation and the outdoor temperature forecast.The uncertainties are incorporated into the MPC formulationusing probabilistic constraints instead of computationally limit-ing sampling-based approaches. Simulation results for varioususer preferences and probabilistic model parameters show theeffectiveness of the HEMS algorithm response to DR requests.

NOMENCLATUREButil DR reduction request from utility (kW)ce Cost of Pgrid ($/kWh)dhvac HVAC control signal (duty cycle)E Battery state of charge (kWh)Emax Maximum energy storage in battery (kWh)Emin Minimum energy storage in battery (kWh)η Battery charging/discharging efficiencyPc Power consumed by HVAC when cooling (kW)Pch Power injected into battery storage (kW)Pdis Power drawn from battery storage (kW)Pgrid Power consumed from the grid (kW)Pmax Maximum charging/discharging power (kW)Ppred Predicted Pgrid consumption with no DR (kW)PPV Solar power consumed (kW)Prad Solar Irradiance (W/m2)Psol Available solar power (kW)Puc Residential load from uncontrollable devices (kW)ρDR Probability that DR request is satisfiedρT Probability that Tin bounds are satisfiedtDR,f End time of DR periodtDR,n Time of DR noticetDR,s Start time of DR periodTin Indoor air temperature (◦F)Tmax Maximum indoor air temperature (◦F)Tmin Minimum indoor air temperature (◦F)Tout Outdoor air temperature (◦F)Ucurt PV curtailment (percent)

I. INTRODUCTION

Renewable energy integration into the power grid has pre-sented new challenges due to uncertainty in weather fore-casts and renewable energy generation availability. Whilegeneration-side energy management solutions have beenwidely studied to account for intermittent renewable energygeneration challenges, demand-side energy management so-lutions present another approach for integrating renewable

energy sources given the current power grid architecture. Inparticular, residential demand-side energy management canbe used to address stable renewable energy integration sincethe residential buildings account for 37.6% of total electricityconsumption in the U.S., which is more than the commercialbuilding, industrial building, or transportation sector [1]. Homeenergy management systems (HEMS) provide demand-sideenergy management by coordinating multiple residential appli-ances in real-time given user preferences and renewable energyresource forecasts [2], [3]. HEMS can increase the energyefficiency of a home by leveraging controllable residentialdevices, such as heating, ventilation, and air-conditioning(HVAC) systems, which account for over 50% of total res-idential load [1]. This work provides a stochastic modelpredictive control (MPC) algorithm for demand response (DR)in a HEMS that optimally coordinates home appliances andresidentially-owned generation and storage given user comfortpreferences, energy cost sensitivity, and uncertainty in avail-able PV generation and outdoor temperature forecast.

Various HEMS architectures have been proposed for in-creasing residential energy efficiency [3]. Many of the con-trol methods studied for HEMS applications also includeDR grid service capabilities such as real-time pricing anddirect load control, which encourage consumers to shift theload of flexible devices away from peak demand periods[2], [3]. Typically, advanced HEMS algorithms use optimiza-tion techniques such as MPC [2], [4], mixed-integer linearprogramming (MILP) [5], or various artificial intelligencetechniques [3], [6], [7]. One approach to using stochasticoptimal control methods in HEMS algorithms is the use ofMonte Carlo sampling for representing uncertainties in variousparameters such as outdoor temperature and renewable energysource generation [8], which is computationally restrictive.Another approach for incorporating uncertainty in HEMSalgorithms is using the Markov chain modeling framework[9]. To include probabilistic models in a HEMS algorithm,we propose a chance constrained MPC-based optimizationformulation. Chance constrained optimization has been usedto incorporate uncertainty in renewable energy generationinto optimal energy storage sizing problems [10] and ACoptimal power flow problems [11]. Chance constrained MPChas also been used to include uncertainty in weather forecastsfor energy efficient HVAC system usage in buildings [12].

1This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Fig. 1. Overall HEMS control and data schematic.

Chance constrained optimization for a HEMS has been usedto incorporate uncertainty in dynamic pricing and system loads[13]. However, in this work we use a chance constrained MPC-based HEMS to incorporate uncertainty in the weather forecastand renewable energy generation while ensuring both the DRrequest and users’ thermal preferences are satisfied with highprobability.

In this work, we provide a chance constrained MPC al-gorithm for a HEMS capable of satisfying grid DR requestswhere usage of flexible (i.e. controllable) devices, such asHVAC systems, are shifted away from peak demand periodson the power grid. We assume the DR event is communicatedto the HEMS before the DR period begins in the form of arequest for some amount of grid power reduction Butil relativeto amount of grid power the HEMS predicts the home requiresduring the DR period. We consider a HEMS that coordinatesa residentially-owned PV array and battery storage system,an HVAC system, and uncontrollable devices to satisfy theDR event while ensuring user thermal comfort. Uncontrollableresidential devices include lighting, television, and plug loads,which we assume cannot be controlled with a HEMS. Thechance constraints in the HEMS algorithm are used to ensurethat both the DR reduction request and the users’ thermalcomfort are satisfied with high probability given uncertainty inavailable PV power and outdoor air temperature. An overviewof the considered HEMS system is shown in Fig. 1.

The rest of this paper is organized as follows: Section IIprovides the mathematical formulation of the HEMS devicemodels and chance constraints for modeling uncertainty in PVgeneration and outdoor air temperature forecast. In Section III,we provide the overall stochastic MPC HEMS optimizationproblem. The simulation results of the proposed HEMS algo-rithm are provided in Section IV. In Section V, conclusions onthe effectiveness of the proposed stochastic MPC-based HEMSalgorithm are discussed, as well as areas of future work.

II. RESIDENTIAL DR CONTROL STRUCTURE

In this section, the mathematical models for the indoor airtemperature dynamics and residential devices are provided.In this work, we assume that the HEMS must coordinatethe HVAC system, the residential PV generation, the batterystorage system, uncontrollable loads, and any additional powerneeded from the grid to satisfy the load. The chance constraint

formulations for incorporating the uncertainty in PV genera-tion PPV and outdoor air temperature Tout are also provided.The temporal index is denoted with the superscript (t).

A. HEMS Device Models

The residential indoor temperature model, coupled with theHVAC model and thermal comfort preferences, is given by thefollowing dynamic equations:

T(t+1)in = T

(t)in + β1(T

(t)out − T

(t)in )− β2d(t)hvac + β3P

(t)rad, (1)

Tmin ≤ T (t+1)in ≤ Tmax, (2)

where d(t)hvac ∈ [0, 1] is the HVAC duty cycle, β1 representsthe building envelope, β2 is the cooling gain, and β3 is thesolar gain. The residential PV system model is given by

P(t)PV = (1− U (t)

curt)P(t)sol , (3)

where Ucurt ∈ [0, 1] is the fraction of available PV generationthat is curtailed, and P (t)

sol is a function of the solar irradiance,array size, and array efficiency.

The residential battery storage system state of charge (SOC)and power charged/discharged are modeled by the following:

E(t+1) = E(t) + ηP(t)ch ∆t− 1

ηP(t)dis∆t, (4)

Emin ≤ E(t+1) ≤ Emax, (5)

0 ≤ P (t)dis , P

(t)ch ≤ Pmax, (6)

where Emin and Emax are 15% and 85% of the rated energystorage capacity, respectively, which limits battery degradationwhen operating in this region [14]. From the structure of thisproblem, it is assumed the optimization will not find it optimalfor the battery to charge and discharge simultaneously. Thissimplification can be addressed with MILP or including theconstraint P (t)

ch P(t)dis = 0. While the constraint is not included

in this work, we have confirmed that for all simulation resultsprovided in Section IV, the battery does not simultaneouslycharge and discharge.

The overall power balance in a home is given by thefollowing equation:

0 = −P (t)grid + P

(t)load − P

(t)PV + P

(t)ch − P

(t)dis , (7)

where the total power demand for a home is given byP

(t)load = P

(t)uc + Pcd

(t)hvac. The total HVAC load is given by

P(t)hvac = Pcd

(t)hvac.

B. Inclusion of Uncertainty

Chance constraints are introduced into the problem to ensureboth the DR request is satisfied and the user thermal comfortis maintained with high probability given uncertainty in fore-casting errors in weather parameters that dictate available PVpower and the indoor air temperature. First, we will focus onthe constraint that ensures the DR reduction request is satisfiedwith probability ρDR, which is given by the following:

Pr

(tDR,f∑t=tDR,s

P(t)pred −

tDR,f∑t=tDR,s

P(t)grid ≥ Butil

)≥ ρDR, (8)

2This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

where the actual grid power consumed P (t)grid is dependent on

the power balance equation in (7). The available PV powercan be represented as P (t)

PV = P(t)f + P

(t)err , where P

(t)f and

P(t)err are the solar forecast and solar forecast error at timet, respectively. We assume the solar forecast error P (t)

err isNormally distributed P

(t)err ∼ N (µ

(t)Perr

, σ2(t)Perr

) and P(t)err are

independent. Then, we obtain the following for P (t)grid in (8):

P(t)grid = Pcd

(t)hvac + P (t)

uc + P(t)ch − P

(t)dis − P

(t)f − P (t)

err . (9)

Notice that the sum of Normally distributed forecast errorswill result in another Normally distributed random variabledenoted Perr ∼ N (µP , σP ) where µP =

∑tDR,f

t=tDR,sµ(t)Perr

and

σ2P =

∑tDR,f

t=tDR,sσ2(t)Perr

. Then we can write the constraint in (8)that ensures DR is met with probability ρDR as the following:

Pr(XP ≤ 0) ≥ ρDR. (10)

where P (t)grid is given in (9) and XP is given by:

XP =tDR,f∑t=tDR,s

P(t)grid + Butil −

tDR,f∑t=tDR,s

P(t)pred.

Since Perr is Normally distributed, XP is also Normallydistributed with the following mean µ and variance σ:

µ =tDR,f∑t=tDR,s

(Pcd(t)hvac + P

(t)uc + P

(t)ch − P

(t)dis − P

(t)f )− µP

+Butil −tDR,f∑t=tDR,s

P(t)pred,

σ = σP .

The chance constraint in (10) can be written as:

Pr(XP ≤ 0) = Φ(0−µσ

)≥ ρDR, (11)

where Φ(·) is the CDF of the Normal distribution N (0, 1).The chance constraint that ensures the DR request is satisfiedwith a high probability is obtained by taking the inverse CDFof both sides of (11), which is given by:

tDR,f∑t=tDR,s

P(t)pred−

tDR,f∑t=tDR,s

(Pcd(t)hvac +P (t)

uc +P(t)ch −P

(t)dis −P

(t)f )

+ µP −Butil ≥ Φ−1(ρDR)σP . (12)

Next, we provide the mathematical formulation for thechance constraints that ensure the users’ thermal comfortpreferences are satisfied with a high probability during the DRperiod given uncertainty in the outdoor temperature. Giventhe thermal comfort bounds in (2), the constraints requiringthat the thermal comfort bounds are satisfied with at leastprobability ρT during the DR period are as follows:

Pr(Tmin ≤ T (t+1)in ) ≥ ρT , (13)

Pr(T(t+1)in ≤ Tmax) ≥ ρT . (14)

For the probabilistic equation in (13), let the outdoor tem-perature be written in terms of the forecasting error: T (t)

out =

T(t)f +T

(t)err , where T (t)

f is the forecast outdoor temperature andT

(t)err is the outdoor temperature forecast error. The outdoor

temperature forecast error is assumed to be Normally dis-tributed T (t)

err ∼ N (µ(t)T , σ

2(t)T ) [15]. With similar analysis, we

obtain the following constraint that ensures the users’ thermalcomfort lower bound in (13) is satisfied with probability εT :

(1− β1)T(t)in + β1(T

(t)f + µ

(t)T )− β2d(t)hvac + β3P

(t)rad − Tmin

≥ −Φ−1(ρT )β1σ(t)T . (15)

Similarly, the chance constraint for the thermal comfort upperbound in (14) is obtained

Tmax − (1− β1)T(t)in − β1(T

(t)f + µ

(t)T ) + β2d

(t)hvac − β3P

(t)rad

≥ Φ−1(ρT )β1σ(t)T . (16)

III. STOCHASTIC MPC FORMULATION FOR HEMSIn this section, we provide the overall chance constrained

MPC optimization problem for the HEMS. The following ob-jective function is minimized at each step of the optimization:

fcost(t, {x(t),u(t)}Nht=1) =

Nh∑t=1

(ceP(t)grid + P

(t)solU

(t)curt),

where Nh denotes the prediction horizon, the optimization de-cision variables at each time t are collected in the vector u(t) =[P

(t)grid, U

(t)curt, d

(t)hvac, P

(t)ch , P

(t)dis ], and the state variables at each

time t are collected in the vector x(t) = [T(t)in , E

(t), P(t)PV]. The

overall chance constrained convex optimization problem is thefollowing:

min{x(t),u(t)}Nh

t=1

fcost(t, {x(t),u(t)}Nht=1) (17)

subject to

0 ≤ P (t)grid ∀t, (18)

0 ≤ U (t)curt ≤ 1 ∀t, (19)

P(t)PV = (1− U (t)

curt)P(t)sol ∀t, (20)

0 ≤ d(t)hvac ≤ 1 ∀t, (21)

T(t+1)in = T

(t)in + β1(T

(t)out − T

(t)in )− β2d(t)hvac + β3P

(t)rad

∀t ∈ [1, . . . , Nh − 1], (22)

Tmin ≤ T (t+1)in ≤ Tmax ∀t /∈ [tDR,s, tDR,f ], (23)

Tmax − (1− β1)T(t)in − β1(T

(t)f + µ

(t)T ) + β2d

(t)hvac

− β3P (t)rad ≥ Φ−1(ρT )β1σ

(t)T ∀t ∈ [tDR,s, tDR,f ], (24)

(1− β1)T(t)in + β1(T

(t)f + µ

(t)T )− β2d(t)hvac + β3P

(t)rad

− Tmin ≥ −Φ−1(ρT )β1σ(t)T ∀t ∈ [tDR,s, tDR,f ], (25)

P(t)grid + P

(t)PV + P

(t)dis = P (t)

uc + Pcd(t)hvac + P

(t)ch ∀t, (26)

E(t+1) = E(t) + ηP(t)ch ∆t− 1

η∆tP

(t)dis ∀t ∈ [1, . . . , Nh − 1], (27)

Emin ≤ E(t+1) ≤ Emax ∀t ∈ [1, . . . , Nh − 1], (28)

0 ≤ P (t)dis ≤ Pmax ∀t, (29)

0 ≤ P (t)ch ≤ Pmax ∀t, (30)

tDR,f∑t=tDR,s

P(t)pred −Butil −

tDR,f∑t=tDR,s

P(t)grid + µP

≥ Φ−1(ρDR)σP ∀t ∈ [tDR,n, tDR,f ]. (31)

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IV. SIMULATIONS: LOAD SHEDDING IN SUMMER

To demonstrate the effectiveness of the proposed HEMSalgorithm in (17)-(31), we provide simulation results for DRduring a summer afternoon for two different houses. TheMATLAB-based modeling system for solving disciplined con-vex programs, CVX, is used in this work. For all simulations,we assume the DR notice is received by the HEMS 2 hoursbefore the start of the summer load reduction DR event from4pm to 6pm, and the DR reduction request needs to be satisfiedwith probability ρDR = 95% while maintaining the thermalcomfort bounds with probability ρT = 95%. The preferredindoor thermal comfort band is 68◦F ≤ T

(t)in ≤ 72◦F from

9am to 5pm and restricted to 69◦F ≤ T(t)in ≤ 71◦F otherwise

when the residence is assumed to be occupied. The simulationhas a 24 hour prediction horizon with 1 hour time intervals.

The device models for both houses are assumed to have thesame parameters. The residential PV array size is 20m2 witha tilt of 30◦ and an efficiency of 16%. The 5-kWh residentialbattery system is restricted to 15% to 85% of the maximumSOC to preserve the battery lifetime [14]. The battery inverterpower limit is 3 kW with an inverter efficiency of 95%. Thebattery charging/discharging efficiency η is 95%. The powerconsumption of the HVAC when cooling Pc is 3 kW. Thecost of energy from the grid is assumed to be a flat rate of$0.11/kWh. The outdoor air temperature and solar irradianceforecasts were obtained from NOAA USCRN data [16].

A. Simulation Results

The proposed HEMS algorithm is simulated for two homes,denoted House 1 and House 2, which have different housemodel parameters and are given in Table I. The model pa-rameters are designed such that House 2 is a less-insulatedversion of House 1 and has a less efficient HVAC coolingsystem. The initial battery SOC is 1.5 kWh and initial indoortemperature is 73◦F for both homes. The simulation resultsfor House 1 are shown in Figs. 2 and 3 for a DR reduc-tion request Butil = 0.75 kW with uncertainty in availablePV σP = 0.5 kW and uncertainty in the outdoor forecastσT = 6◦F. From Fig. 2, we can see that the battery onlycharges when the available PV power exceeds the base load ofthe home, and is discharging (supplying power to the home)otherwise. During the DR notice period, the Pgrid usage isgreater than the predicted grid usage without DR Ppred toaccount for pre-cooling before the DR event. During the DRperiod, the HEMS reduces grid power usage of House 1 byleveraging the stored energy in the battery system. The indoorair temperature T (t)

in stays within the preferred thermal comfortband throughout the simulation, as shown in Fig. 3 (top). Thebattery SOC is shown in Fig. 3 (middle), which highlights theusage of energy stored in the battery during the DR period.The battery behavior is included in Fig. 3 (bottom) to showthere is no simultaneous battery charging and discharging.

Additional simulation results for both houses with varyingDR requests Butil and uncertainties σP and σT are given inTable II. Let BH1 and BH2 denote the actual reduction in grid

TABLE IHOUSE MODEL PARAMETER VALUES FOR HOUSE 1 AND HOUSE 2.

Parameter House 1 House 2β1 0.03 0.035β2 4 3β3 0.000163 0.000326

Fig. 2. Power profiles for House 1 with proposed HEMS algorithm respondingto a summer load reduction DR event of Butil = 0.75 kW with uncertaintyσP in available PV forecast and σT in outdoor air temperature forecast. Thebattery is discharging when Pbatt < 0 and charging when Pbatt > 0. TheHEMS predicted grid power usage is given by Ppred. The actual grid powerusage in the case of a DR event is denoted Pgrid.

Fig. 3. Simulation of House 1 with proposed HEMS algorithm responding toa summer load reduction DR event of Butil = 0.75 kW with uncertainty σPin available PV forecast and σT in outdoor air temperature forecast. Indoorair temperature Tin (top). The outdoor air temperature forecast Tf is shownfor reference. Residential battery system SOC (middle). Battery charging anddischarging behavior (bottom).

power usage that House 1 and House 2 were able to achieve,respectively. From Table II, we can see that the BH1 and BH2

increase as the uncertainty in the solar forecast increases. ForHouse 1 with constant σP , as the uncertainty in the outdoorair temperature forecast increases, BH1 decreases since moreenergy is required to maintain the indoor house temperature.For the simulation of House 2 with constant σP , in some casesthe HEMS does not need to compensate further as σT variessince the uncertainty in the available PV is more restrictive.House 1 is able to achieve grid power usage reduction greaterthan or equal to the reduction achieved by House 2 due tothe increased cooling efficiency and lower building envelopecoefficient of House 1 relative to House 2.

B. Chance Constraint Validation

Monte Carlo simulations were conducted to validate thatthe chance-constrained optimization solutions actually satisfy

4This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

TABLE IIADDITIONAL HEMS ALGORITHM SIMULATION RESULTS.

σP (kW) σT (◦F) Butil (kW) BH1 (kW) BH2 (kW)0.25 3 0.5 0.9443 0.91720.25 6 0.5 0.9392 0.91390.5 3 0.5 1.3379 1.32240.5 6 0.5 1.3348 1.3224

0.25 3 0.75 1.1836 1.16260.25 6 0.75 1.1787 1.16120.5 3 0.75 1.5802 1.57240.5 6 0.75 1.5771 1.5724

TABLE IIIMONTE CARLO SIMULATIONS FOR CHANCE CONSTRAINT VALIDATION.

Constraint House 1 House 2BH ≥ Butil 95.28% 95.16%

Tmin ≤ T(17)in ≤ Tmax 95.16% 95.2%

Tmin ≤ T(18)in ≤ Tmax 95.24% 95.4%

the DR request with probability ρDR = 95% and the thermalcomfort bounds are satisfied with probability ρT = 95%.Monte Carlo simulations use the chance-constrained optimalsolution and solar forecast error and outdoor temperature fore-cast error sampled randomly from their respective distributionsto check that constraints in (2) and (8) are satisfied. Using 5000Monte Carlo simulations for validating the HEMS solutionsfor both House 1 (shown in Figs. 2 and 3) and House 2with the same simulation parameters, it is confirmed that thechance constrained optimal solution satisfies the constraintsin (2) and (8), which is shown in Table III. The percent-ages in Table III represent the empirical distributions of theMonte Carlo simulations that satisfy the DR request in (8)and temperature bounds in (2) during the DR period. Thus,in view of Table III, the Monte Carlo simulations validatethat the solution obtained with the chance constrained MPCoptimization problem ensures the DR request and temperaturebounds are satisfied with probability ρDR and ρT , respectively.

V. CONCLUSION

A chance-constrained MPC-based algorithm is proposed fora HEMS capable of responding to grid DR events. Chanceconstraints were incorporated into the optimization problemto ensure the DR request and home temperature preferencesare satisfied with a high probability given uncertainty in boththe solar and outdoor temperature forecasts. The chance con-strained optimization solution was validated with Monte Carlosimulations. Simulation results show the proposed HEMSalgorithm responded to the DR request by coordinating flexibledevices during the DR notice period prior to DR event.

Future work includes validating the proposed HEMS onhardware in the loop testbeds such as Foresee [2]. Additionally,incorporating other flexible loads such as a dishwasher, waterheater, and electric vehicles (EVs) into the proposed HEMSframework may allow for further load flexibility during theDR notice and DR event period to ensure both the DR requestand users’ thermal comfort are satisfied with a high probability

given uncertainties in PV availability and outdoor temperature.Further work on a stochastic HEMS algorithm also includesincorporating uncertainty in home occupancy schedules, whichis not effectively modeled by a Gaussian distribution in thechance constraint formulation. While we assume the randomvariables in this work are Normally distributed, the use ofchance constraints can be extended to non-Gaussian distribu-tions using existing techniques in the literature [11].

ACKNOWLEDGMENT

This work was supported in parts by the ESIF SummerGraduate Internship Program at NREL, US Department ofEnergy Building Technologies Office, Bonneville Power Ad-ministration, and the Air Force Office of Scientific Researchunder the AFOSR-YIP award FA9550-16-1-0400.

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5This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.