A MODELICA PACKAGE FOR BUILDING-TO-ELECTRICALGRID INTEGRATION

Marco Bonvini1, Michael Wetter1, and Thierry S. Nouidui11Lawrence Berkeley National Laboratory

1 Cyclotron Road, 94720 Berkeley, California

ABSTRACTThis paper presents the new Electrical package of theModelica Buildings library. The package containsmodels for different types of sources, loads, storageequipment, and transmission lines for electric power.The package contains models that can be used to rep-resent DC, AC one-phase, and AC-three phases bal-anced and unbalanced systems. The models have beensuccessfully validated against the IEEE four nodes testfeeder. An example shows how the models can be usedto study the integration and control of renewable en-ergy sources in a electric distribution grid.

INTRODUCTIONResidential and commercial buildings constitutenearly 70% of the overall electricity energy use in theUnited States. The integration of buildings and the dis-tribution grid is important to guarantee a reliable gridoperation. The need for sustainable and net zero en-ergy buildings is increasing the fraction of renewableenergy sources. Renewable sources like photovoltaics(PVs) and new types of loads such as electric vehi-cles, are intermittent. The increase of these loads andsources impacts the grid stability and reliability. In or-der to avoid problems, efficient transactions betweenbuildings and the grid need to become a reality (Xueet al., 2014).Building simulation tools have been successfullyused to design high energy-performance build-ings. Our contribution enhances the capabili-ties of simulation tools to address building-to-grid integration. We present the Electrical pack-age, a package of the Modelica Buildings library[http://simulationresearch.lbl.gov/modelica] that is afree, open-source library for modeling of building en-ergy and control systems. The Electrical package con-tains models for generation, consumption, storage, andtransmission of electric power. The models can beused to scale from the building level up to the distri-bution level. The models have been successfully val-idated against IEEE tests and can be adopted by gridoperators, planners, and researchers to design, control,and operate the grid. Those models can be integratedwith thermal building simulation models to check theimpact of advanced control strategies and demand re-

sponse on the power quality of the distribution grid.Two applications are presented. The first is the vali-dation of the models against the IEEE four nodes testfeeder. The second is the analysis of the voltage levelsin a district in which PVs are connected in an unbal-anced configuration.

CONNECTORSThe Electric package uses a new type of generalizedconnector that has been introduced by Franke andWiesmann (2014a) and is used by the Power SystemsLibrary (Franke and Wiesmann, 2014b) and the Elec-tric Power Library (Modelon, 2014).The Modelica Standard Library (MSL) version 3.2.1differs depending on the type of electric system be-ing modeled. For example, DC and AC continuoustime systems have a connector that differs from the oneused by AC models, which use the quasi-stationary as-sumption.The generalized electrical connector overcomes thislimitation. It uses a paradigm that is similar to the oneused by the Modelica.Fluid connectors.

connector Terminal"Generalized electric terminal"...replaceable package PhaseSystem =

PhaseSystems.PartialPhaseSystem"Phase system";

PhaseSystem.Voltage v[PhaseSystem.n]"Voltage vector";

flow PhaseSystem.Current i[PhaseSystem.n]"Current vector";

PhaseSystem.ReferenceAngletheta[PhaseSystem.m]"Optional vector of phase angles";

end Terminal;

The connector has a package called PhaseSystemthat contains constants, functions, and equations ofthe specific electric domain. This allows to representdifferent electrical domains using the same connector,reusing the same standardized interfaces.As the electrical connectors of the MSL, theTerminal has a vector of voltages as effort vari-ables and a vector of currents as flow variables. Theconnector has an additional vector that representsthe reference angle theta[PhaseSystem.m]. If

PhaseSystem.m>0 the connector is overdeter-mined because the number of effort variables ishigher than the number of flow variables. The over-determined connectors are defined and used in such away that a Modelica tool is able to remove the super-fluous but consistent equations, arriving at a balancedset of equations based on a graph analysis of the con-nection structure. The models in the library uses con-structs specified by the Modelica language to handlethis situation (Olsson et al., 2008).

PHASE SYSTEMSThe PhaseSystem is a package that contains con-stants, equations, and functions that provide a mathe-matical representation of a given electrical domain. Byreplacing the PhaseSystem, it is possible to seam-lessy switch from one domain to an other. The packagedefines:

• PhaseSystem.n – the number of independentvoltage and currents.

• PhaseSystem.m – the number of reference an-gles,

• functions that compute the system voltage, cur-rents, phases, powers, etc.

More details about the PhaseSystem can be foundin Franke and Wiesmann (2014a).

DC PACKAGEThe Electrical.DC package contains models thatrepresent direct current systems. The mathematicsneeded to describe DC systems is contained in thepackage PhaseSystems.TwoConductor, wheren=2 and m=0. This package assumes that the volt-age vector at the connector is the voltage drop whilethe reference angle is 0, as it is not needed in the DCdomain.

Ideal voltage source

The ideal voltage source is a simple model that speci-fies the voltage increase of an ideal generator withoutany loss as

V1−V2 =V, (1)

where V1 and V2 are the two components ofthe voltage vector specified by the connec-tor. The following code snippet shows howthe model extends a generalized source modelElectrical.Interfaces.PartialSourceand then redeclares the phase system.

model ConstantVoltage"Model of a constant DC source"

extendsElectrical.Interfaces.PartialSource(redeclare package PhaseSystem =PhaseSystems.TwoConductor,

redeclare Interfaces.Terminal_p terminal,...)parameter Voltage V"Value of the constant voltage";

equationterminal.v[1] = V;terminal.v[2] = 0;sum(terminal.i) = 0;

end ConstantVoltage;

Load model

The load mode can be used to represent a system thateither produces or consumes power. The constitutiveequation of the load is

(V1−V2)i1 = PLOAD, (2)

where V1 and V2 are the two components of the volt-age vector specified by the connector, i1 is the currentleaving the component, and PLOAD is the power. Byconvention, if PLOAD > 0 the load is producing power,otherwise it is consuming power. The power PLOADcan be specified either as a parameter or an input.

Linearized load model

R

VS

LOAD

V

i

+

-

PLOAD

Figure 1: This simple DC circuit, in which the powerconsumed by the load is prescribed, leads to a nonlin-ear system of equations.

Consider the simple DC circuit shown in Figure 1,where VS is a constant voltage source and R is a lineresistance. The load has a voltage V across its electri-cal pins and a current i. If the power consumed by theload is PLOAD, the equation that describes the circuit is

VS−Ri− PLOAD

i= 0 . (3)

To compute the current i that is drawn by the load, anonlinear equation has to be solved. If the number ofloads increases, as typically happens in grid simula-tions, the size of the system of nonlinear equations tobe solved increases too, causing the numerical solverto slow the simulation. A linearized load model cansolve such a problem.The first step to linearize the load model is to defineits nominal voltage Vnom, around which it will be lin-earized. The constitutive equation of the load

i =PLOAD

V(4)

can be linearized by a Taylor series expansion around

the nominal voltage V =Vnom as

i =

[PLOAD

V

]V=Vnom

+(V −Vnom)

[∂

∂VPLOAD

V

]V=Vnom

+o((V −Vnom)2) (5)

that leads to the linearized formulation

i =(

2Vnom

− VV 2

nom

)PLOAD. (6)

The linearized error grows proportional to (V −Vnom)

2. When multiple loads are connected in a gridthrough cables that cause voltage drops, the dimensionof the system of nonlinear equations increases linearlywith the number of loads. This nonlinear system ofequations introduces challenges during the initializa-tion, as Newton solvers may diverge if initialized farfrom a solution. The initialization problem can be sim-plified using the homotopy operator. The homotopyoperator uses two different types of equations to com-pute the value of a variable: the actual one and a sim-plified one. The actual equation is the one used duringthe normal operation. During initialization, the simpli-fied equation is first solved and then slowly replacedwith the actual equation to compute the initial val-ues for the nonlinear systems of equations. The loadmodel uses the homotopy operator, with the linearizedmodel being used as the simplified equation. This nu-merical expedient has proven useful when simulatingmodels with more than ten connected loads.

// How the homotopy operator is// used in the DC load modeli[1] = - homotopy(

actual =P/(v[1] - v[2]),

simplified =P*(2/V_nominal -(v[1] - v[2])/V_nominal^2)

);...

Renewable energy sources and batteries

The DC package also has models for renewable en-ergy sources such as PV panels and wind turbines thatnatively produce DC power. The renewable sourcesare modeled with loads that produce a variable amountof power that depends on either the solar irradiationor the wind speed. The package contains also a sim-ple battery model that stores electrical energy and ac-counts for different losses during the charge or dis-charge phase.

ASSUMPTIONS FOR ALL AC PACKAGESThe Electrical.AC package contains componentmodels for AC systems. The mathematics that de-scribes AC systems is contained in the package

PhaseSystems.OnePhase, in which n=2 andm=1. The AC models that are part of the library canuse two different assumptions.The first assumption is that the frequency is modeledas quasi-stationary, assuming a perfect sine wave withno higher harmonics. Voltages and currents are con-sidered as sine waves and just their amplitudes andphase shifts are taken into account during the analy-sis. With such an assumption, electric quantities canbe represented with a phasor, i.e., a vector in the com-plex plane.The second assumption is the so-called dynamic pha-sorial representation. The basic idea of the dynamicphasorial representation is to account for dynamicvariations of the amplitude and the angle of the pha-sors. With such an approach, it is possible to analyzefaster dynamics without directly representing all theelectromagnetic effects and high-order harmonics (formore details Stankovic et al. (1999); Stankovic andAydin (2000)).

AC ONE PHASEWe will now present some models of theElectrical.AC.OnePhase. The modelscontained in this package are particularly importantbecause other AC domains can be represented byreusing these models.

Ideal voltage source

The ideal voltage source is a simple model that speci-fies the voltage increase of an ideal generator withoutlosses

[V1,V2] =V [cos(θ),sin(θ)], (7)

where V1 and V2 are the two components of thevoltage vector that represent the phasor of theconnector, while θ is the phase angle of thephasor. The following code shows how thismodel extends the generalized source modelElectrical.Interfaces.PartialSourceand redeclares the phase system.

model FixedVoltage"Model of a fixed voltage AC source"

extendsElectrical.Interfaces.PartialSource(redeclare package PhaseSystem =PhaseSystems.OnePhase,

redeclare Interfaces.Terminal_p terminal,...)parameter Voltage V = 120"RMS value of the voltage";

parameter Frequency f = 60"Frequency of the source voltage";

parameter Angle phi = 0"Phase shift of the source";

Angle thetaRel"Relative angle of the source";

equationif connection.isRoot(terminal.theta) then

PhaseSystem.thetaRef(terminal.theta) =2*Modelica.Constants.pi*f*time;

end if;

thetaRel = PhaseSystem.thetaRel(terminal.theta);

terminal.v[1] = V*cos(thetaRel + phi);terminal.v[2] = V*sin(thetaRel + phi);

end FixedVoltage;

Impedances

This model represents a generalized impedance. Theimpedance can be purely resistive, purely inductive,purely capacitive, inductive, or capacitive. The valueof the resistance, inductance, and capacitance can bespecified by parameters or inputs. The model of theimpedance is

[V1,V2] = Z I = [Ri1−Xi2, Ri2 +Xi1], (8)

where I is the current phasor specified by the connec-tor, i1 and i2 are its two components, and Z = [R,X ]is the impedance, with the first component R being theresistance and the second component X being the reac-tance. When the impedance is inductive, the reactanceis X = ωL; otherwise it is X =−1/(ωC).

Loads

As for the DC case, the load model is able to representa system that produces or consumes power. In the ACdomain, the power is the apparent power S computedas

S = [P, Q] =V I∗ = [V1i1 +V2i2,V1i2−V2i1], (9)

where P is the active power measured in watts, andQ is the reactive power in VAR. The overall unit ofthe apparent power S is VA. The load model has twoinputs: one to represent the active power consump-tion P and one to represent the power factor cos(φ) =atan2(Q,P) that is the angle of the complex powervector S.The load model contains nonlinear equations that re-late the current to the voltage. The nonlinearity is eas-ier to see when equation (9) is written

i1 =PV1 +QV2

V 21 +V 2

2, (10a)

i2 =PV2−QV1

V 21 +V 2

2. (10b)

This voltage dependency leads to a nonlinear systemof equations when modeling electrical networks thathave AC loads. Unfortunately, in the AC case, the non-linearity is more complex because it involves the twocomponents of the vector. In addition the solution ofthe nonlinear equation has to satisfy an algebraic con-straint that is represented by the ratio of the active andreactive power of the load. Figure 2 shows the shapeof the nonlinear function that determines i1 of a loadgiven the two voltage components, when the AC loadis purely resistive.

Figure 2: The nonlinear relationship between the cur-rent and the voltage for a purely resistive AC load.

Figure 3: The linearized relationship between the cur-rent and the voltage for a purely resistive AC load.

Given the constraints and the two-dimensional natureof the problem, it is difficult to find a linearized versionof the load model. A solution could be to divide thevoltage domain into sectors, and for each sector com-pute the best linear approximation. However the se-lection of the proper approximation depending on thevalue of the voltage can generate events that increasethe simulation time. For these reasons, the linearizedmodel assumes a voltage that is equal to the nominalvalue,

i1 =PV1 +QV2

V 2RMS

, (11a)

i2 =PV2−QV1

V 2RMS

, (11b)

where V 2RMS is the root mean square (RMS) nominal

voltage of the load. Even though this linearized ver-sion of the load model introduces an approximationerror in the current, it satisfies the contraints related tothe ratio of the active and reactive powers. The lin-earized load model is shown in Figure 3. As for theDC case, the linearized model is used during the ini-tialization phase with the homotopy operator.

Dynamic load model

Even if the load model has inputs that can vary withrespect to time, the model does not contain any dy-

namic effects. Dynamic effects are caused by induc-tive and capacitive elements that are able to store en-ergy within electromagnetic fields. Models that canaccount for such dynamics are typically described inthe time domain using an ordinary differential equa-tion (ODE). For example the differential equation thatdescribes the dynamics of a capacitor is

CdVc(t)

dt= i(t), (12)

where C is the capacity, Vc(·) is the voltage of the ca-pacitor, and i(·) is the current flowing through it. Themodel represented by equation (12) requires a time do-main simulation where sinusoidal functions are repre-sented as time-varying signals. This requires signifi-cant computing. The dynamic phasorial representation(Stankovic et al., 1999; Stankovic and Aydin, 2000) al-lows a model represented by ODEs to be transformedinto an approximated dynamic model, where the dy-namics are described using phasors. The dynamicphasorial representation describes how the voltage andcurrent phasors vary according to the differential equa-tions derived from first principle models such as (12).The underlying assumption of dynamic phasors is tolimit the analysis to the first of the harmonics. Thislimitation does not describe faster dynamics; howeverit represents slower ones with a simple model. Thefollowing code shows how the two representations cancoexist in the same model.

...equation

omega = der(PhaseSystem.thetaRef(terminal.theta));

// Electric chargeq = C*{v[1], v[2]};if mode == Assumption.FixedZ_dynamic then

// Use the dynamic phasorial// representationder(q) + omega*j(q) + R*v = i;

else// Use quasi stationary// phasorial representationomega*j(q) + R*v = i;

end if;

Generators

Generator models represent a source of power that issupplied to the grid. The generator is modeled as aload that generates a variable power that can have aphase shift with respect to the main reference angle.

Renewable sources

Renewable sources such as PV panels and wind tur-bines can be represented with a simplified AC model.In addition to the DC models, the AC models havea variable power factor that describes the phase shiftbetween the voltage and current phasors. The mod-els also have an efficiency factor that accounts for thepower loss in the transformation between DC and AC.

More detailed models can be created by coupling DCmodels and AC through an AC/DC converter.

Transformers

Transformers are devices that transfer energy betweentwo circuits through electromagnetic induction. Thepackage Electrical.AC.Conversion containsfour different transformers:

• An idealized symmetric model that describesconversion losses using an efficiency factor.

• An idealized model that describes conversion be-tween AC/DC using an efficiency factor.

• An asymmetric model that describes losses on theprimary side.

• An asymmetric model that describes losses onprimary and secondary sides as well as core andmagnetization losses.

AC THREE PHASES BALANCEDUnder the assumption that the electrical system andthe loads are symmetric, it is possible to reduce athree-phase circuit to an equivalent circuit with asingle-phase representation. This representation re-duces the number of variables and keep the com-putational effort low. The price to pay is a lessdetailed description of the system that cannot ac-count for unbalanced conditions that typically hap-pen in real systems. The model in this packagerepresents a simplification that can be used to per-form faster simulation of large systems. The pack-age Electrical.AC.ThreePhasesBalancedcontains models that have been extended from thepackage Electrical.AC.OnePhase. The inter-faces and nominal values of the voltages have beenupdated to represent three-phases systems. However,the mathematics remains the same.

AC THREE PHASES UNBALANCEDThe AC three-phases unbalanced models accountfor a more detailed representation of electric net-works. Diverse types of loads and different patternsof consumption cause voltages and currents to dif-fer among the three phases. The unbalanced systemsare modeled using components that are part of theElectrical.AC.OnePhase package. The mod-els are connected together to represent sources, lines,and loads. The models can be used to represent three-phase systems with and without the neutral cable.

Connector

The connector for three-phase unbalancedsystems is a vector that contains threeElectrical.AC.OnePhase connectors. Thenumber of connectors becomes four when the neutralcable is represented.

connector Terminal

Electrical.AC.OnePhase.Interfaces.Terminal phase[3]

"Vector of AC connectors, one foreach phase";

end Terminal;

Ideal voltage source

The ideal voltage source consists of three differ-ent AC.OnePhase voltage sources, one for eachphase. Given the phase-to-phase VRMS voltage, themodel parametrizes the RMS voltage of each phaseas VRMS/

√3. The correspondent voltage phasors are

shifted by 120◦. By convention the first phase has anangle equal to zero, the second phase −120◦, and thethird phase +120◦.

model FixedVoltage"Model of a fixed AC voltage 3 phasesunbalanced source"parameter Voltage V = 480

"RMS value line to line";parameter Frequency f = 60

"Frequency of the source voltage";parameter Angle phi = 0

"Phase shift of the source";Electrical.OnePhase.Sources.FixedVoltage

Vphase[3](each f = f,each V = V/sqrt(3),phi = {phi,

phi - angle120,phi + angle120})

protectedconstant Angle angle120 =

2*Modelica.Constants.pi/3"Shift angle between the sources";

equation...

end FixedVoltage;

Impedances and loads

The impedance and load models are the same as in thepackage AC.OnePhase.Loads. The main differ-ence is that it is possible to select in which way theyare connected. There are two configurations: star (alsoknown as Y) and triangle (also known as D). Whenconnected in the Y configuration, each load is con-nected to a single phase. When connected in the Dconfiguration, the loads are connected between twophases.

Transformers

The transformer models reuse the models of theAC.OnePhase.Conversion package in differentconfigurations. The various configurations depend onthe possibility to connect the primary and the sec-ondary sides of the transformer either with a Y or Dconfiguration.

TRANSMISSION LINESThe package Electrical.Transmission lever-ages the abstraction level provided by the gener-

1 2 3 4SourceLoad

Transformer

Figure 4: IEEE four-nodes test feeder.

alized connectors and contains models that can beused to represent transmission lines in the DC or ACsingle/multi-phases domains. The models ranges fromsimple resistance versions to more detailed modelsthat account for the inductive and capacitive effects ofthe cables. The cables can be automatically sized, orthe user can select between a collection of commercialcables.

VALIDATIONThe models of the Buildings.Electricalpackage have been successfully validated to ensuretheir correctness and acccuracy. The package fol-lows the same development guidelines as the ModelicaBuildings library. Every component of the package isverified in a simulation example. The aim of the exam-ples is to compare the model results to the analyticalresults if possible. Each simulation model has beenincluded in the regression tests of the Modelica Build-ings library. The regression tests enable users to checkthe correctness of the models during further develop-ment of the library. The next section reports the resultsof the validation of the AC three-phases unbalancedmodels against the IEEE four-nodes test feeder.

APPLICATIONSThis section contains two examples. The first de-scribes the validation of the models contained in theBuildings.Electrical package against a stan-dard test provided by IEEE. The second example fo-cuses on the impact that the connection of PVs canhave on the voltage of a residential district network.

IEEE four-nodes test feeder validation

This example shows a validation of theBuildings.Electrical models against theIEEE four-nodes test feeder validation procedure(Kersting, 2001). The tests that are part of the vali-dation certify the capability to represent transformersof various configurations, full three-phase lines, andunbalanced loads. Figure 4 shows the structure of thefour-nodes network. The voltage source is connectedto the load through two lines and a transformer.The validation procedure consists of mutliple testsin which the type of the load and the type of thetransformer vary. The test cases that have beensuccessfully implemented using the models of theBuildings.Electrical package are listed inTable 1. Each row describes one validation tests.For example Gr Y - D Step Up indicates that thetransformer has a grounded Y connection at the pri-mary side, and a D connection at the secondary side.

Figure 5: Residential distribution network inspired bythe IEEE 34 nodes test feeder. The nodes in the gridare residential units. Red dots are residential units withPVs installed.

Step up indicates that the voltage at the secondaryside is higher than the primary side. Each test listedin the table produces results that differ from thereference IEEE values by less than 0.05%, which isthe threshold defined by IEEE to determine whetherresults should be accepted or not.

Table 1: IEEE four-nodes test feeder that has beensuccessfully reproduced using the models of theBuildings.Electrical package

TRANSFORMER LOADGr Y - Gr Y Step Up Balanced

Gr Y - D Step Up BalancedD - D Step Up Balanced

Gr Y - Gr Y Step Down BalancedGr Y - D Step Down Balanced

D - D Step Down BalancedGr Y - Gr Y Step Up Unbalanced

Gr Y - D Step Up UnbalancedD - D Step Up Unbalanced

Gr Y - Gr Y Step Down UnbalancedGr Y - D Step Down Unbalanced

D - D Step Down Unbalanced

Impact of PVs on district voltage

This example investigates how the installation of PVpanels in a district with residential homes can impactthe voltages of the electric network. The district net-work considered in this example is shown in Figure5. The network has the same topology as the IEEE34-nodes test feeder (Kersting, 2001) but has beenadapted in order to represent a residenatial district net-work. There are 34 nodes. The first node representsthe voltage source, while the remaining 33 nodes areresidential units. The nodes colored in red are residen-tial units that have PVs. The residential district grid ismodeled using a three-phase unbalanced system, andeach residential unit is connected to a single phase.The residential units are connected to the single phasesin a way that keeps the loads on each phase approxi-mately the same. The PVs are connected to a singlephase; the phase to which they are connected can be

Figure 7: Probability distribution of the energy pro-duced per day and house. The distribution is obtainedassuming that the PVs are randomly connected to oneof the three phases in the grid.

modified in order to analyze the impact they have onthe voltage of the grid. Each PV has a local controllerthat disconnects the PV if the RMS voltage is outsideof ±10% of 230 V. The controller disconnects the PVto protect the grid. However, when disconnected thePV produces no power. Both the residential units andthe PV have been modeled using AC loads with a pre-scribed variable power consumption and production.The data series used for this example was taken fromLabeeuw and Deconinck (2013). The model has beenused to simulate a week during the month of June. Fig-ure 6 shows the RMS voltage of each phase for everynode in the grid. The RMS nominal voltage is 230V, and the black lines in Figure 6 show the upper andlower limits within which the voltage of every nodemust remain. Figure 6 (left) shows the voltages ofthe grid nodes when the PVs have been connected uni-formly in order to keep the network balanced. Figure6 (center) shows the voltages of the grid nodes whenall PVs have been connected to phase 1 without acti-vating the voltage controller. The blue lines (voltageson phase 1 at every node) fall outside the limit andare generally higher than the nominal value. Figure6 (right) shows the voltages of the grid nodes whenall PVs have been connected to phase 1 and the localvoltage controller is active. The blue lines (voltageson phase 1 at every node) remain within the limitsbut are still generally higher than the nominal value.Figure 6 compares the ideal case, in which the PVsare connected to keep the network balanced, and theworst case, in which all the PVs have been connectedto phase 1. In a more realistic case, the PVs are in-stalled without knowing how the other PVs have beenconnected. To represent such a case, the PVs havebeen connected randomly to one of the phases. Figure7 show the probability that a house will produce a cer-tain amount of energy per day given the random dis-tribution of PV. In the current grid configuration, thereis a high probability (45%) that even with a randomconnection of the PVs, the energy produced by eachhouse is close to its maximum. The results depend onthe type of cables used in the grid and the amount ofpower generated by the PVs. The higher the resistanceof the cables, the higher will be the voltage overshootand undershoot. The same applies for the power. The

Figure 6: RMS voltages of the residential grid nodes. The blue lines are voltages at the nodes of phase 1, the redlines are voltages at the nodes of phase 2, and the green lines are voltages at the nodes of phase 3. The plot on theleft shows the voltages when the PVs are connected in a balanced and uniform way (best case scenario). The plotin the middle shows the voltages when the voltage controller of the PVs is not active and all the PVs are connectedto phase 1. The plot on the right shows the voltages when the voltage controller of the PVs is active and all thePVs are connected to phase 1.

higher the power generated by the PVs, the higher willbe the voltage overshoot and undershoot. In this ex-ample, just 11 out of 33 residential units have PVs in-stalled. If the number of PVs installed increases, therewill be a higher probability that PVs are disconnected,and hence, less power will be produced.

CONCLUSIONThe interaction between buildings and electrical sys-tems is becoming more important if the fraction of re-newable energy sources on the grid increases. Thispaper presents a package that extends the ModelicaBuildings library by introducing models that repre-sent the interaction between buildings and the elec-trical grid. The models were developed using a flex-ible approach that allows users to seamlessly switchbetween different electrical domains by leveraging ab-stract and standardized interfaces. The models havebeen implemented in a way that leads to more robustinitialization. For some components, linearized ver-sions are available to reduce the simulation time.

ACKNOWLEDGEMENTThis research was supported by the Assistant Secretaryfor Energy Efficiency and Renewable Energy, Officeof Building Technologies of the U.S. Department ofEnergy, under Contract No. DE-AC02-05CH11231.The authors thank Juan Van Roy for providing thedata as well as useful feedbacks during the develop-ment of the models. The authors also thank SpyrosChatzivasileiadis, Ciaran Roberts, and Emma Stewartfor their suggestions and feedback.

REFERENCESFranke, R. and Wiesmann, H. 2014a. Flexible model-

ing of electrical power systems - the modelica pow-ersystems library. In Proceedings of the 10th Inter-national Modelica Conference, volume 1.

Franke, R. and Wiesmann, H. 2014b. Modelica powersystems library.

Kersting, W. H. 2001. Radial distribution test feed-ers. In Power Engineering Society Winter Meeting,2001. IEEE, volume 2, pages 908–912. IEEE.

Labeeuw, W. and Deconinck, G. 2013. Residentialelectrical load model based on mixture model clus-tering and markov models. Industrial Informatics,IEEE Transactions on, 9(3):1561–1569.

Modelon 2014. Electric power library.

Olsson, H., Otter, M., Mattsson, S. E., and Elmqvist,H. 2008. Balanced models in modelica 3.0 for in-creased model quality. In Proceedings of the 6thInternational Modelica Conference, volume 1.

Stankovic, A. M. and Aydin, T. 2000. Analysis ofasymmetrical faults in power systems using dy-namic phasors. Power Systems, IEEE Transactionson, 15(3):1062–1068.

Stankovic, A. M., Lesieutre, B. C., and Aydin, T.1999. Modeling and analysis of single-phase induc-tion machines with dynamic phasors. Power Sys-tems, IEEE Transactions on, 14(1):9–14.

Xue, X., Wang, S., Sun, Y., and Xiao, F. 2014. An in-teractive building power demand management strat-egy for facilitating smart grid optimization. AppliedEnergy, 116(0):297 – 310.