Accurate Power Sharing and Synthetic Inertia Control for ... Power Sharing and... · A DC building microgrid (Fig. 1) may consist of multi-ple DERs on a common bus through exclusive

Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Digital Object Identifier XX.XXXX/ACCESS.2019.DOI

Accurate Power Sharing and SyntheticInertia Control for DC BuildingMicrogrids with GuaranteedPerformanceZHEHAN YI, (Member, IEEE),XIAOYING ZHAO,(Member, IEEE),DI SHI, (Senior Member, IEEE),JIAJUN DUAN, (Member, IEEE),YINGMENG XIANG (Member, IEEE), ANDZHIWEI WANG, (Senior Member, IEEE)GEIRI North America, San Jose, CA 95134 USA (e-mail: zhehan.yi, xiaoying.zhao, di.shi, jianjun.duan, yingmeng.xiang, [email protected])

Corresponding author: Di Shi (e-mail: [email protected]).

This work is supported by the SGCC Science and Technology Program under project Distributed High-Speed Frequency Control underUHVDC Bipolar Blocking Fault Scenario (SGGR0000DLJS1800934).

ABSTRACT Direct current (DC) building microgrids allow the integrations of DC distributed energyresources (DERs) and loads with a simpler topology and eliminate alternating current (AC) system issuessuch as frequency transients and harmonics. Because of the domination of power-electronics-interfacedgenerators, islanded DC microgrids in general present very low inertia, which reveals subtle stability threatsto the systems. In addition, conventional droop-based DER power sharing mechanisms may suffer froma poor power sharing accuracy and DC bus voltage deviations that require secondary restorations. In thispaper, a novel control scheme for building-scale islanded DC microgrids is proposed based on finite controlset model predictive control (FCS-MPC). A new DER power sharing mechanism is devised in the FCS-MPC, which eliminates bus voltage deviation during load/generation fluctuation, and offers load/DERplug-and-play capabilities. Moreover, for the first time, virtual capacitance control for DC microgrids isimplemented in a model predictive manner to enhance the synthetic inertia of bus voltage. Both simulationand experimental case studies are carried out to provide verification for the promising performance of theproposed method.

INDEX TERMS DC building, DC microgrid, synthetic inertia, virtual capacitance, model predictivecontrol, distributed generation.

I. INTRODUCTION

THE worldwide Zero Net Energy (ZNE) building goalsimply a higher penetration of renewable DERs and an

increasing energy efficiency requirement in both residentialand commercial buildings [1]. The configuration of micro-grid provides a promising platform to integrate clusters ofDERs and loads, which simultaneously maximizes the valuesof renewables and improves the reliability of utility grid byenabling ancillary service and Virtual Power Plant (VPP)[2], [3]. Because the majority of DERs in building scalemicrogrids are DC based (e.g., solar PV system, energy

storage system (ESS), ultra-capacitor, etc.), and DC loadsare becoming increasingly prevalent (e.g., solid-state LEDlighting, DC ventilation, DC data center, EV charger, etc.),DC building microgrids have drawn increasing attentions dueto their promising merits that AC microgrids cannot offer [4],[5]. For instance, Robert Bosch LLC and NREL have coop-eratively installed several DC microgrid pilot demonstrationsin the US [6]. With simpler power-electronics interfaces andAC transient stability issues, DC building microgrid allowsthe ease of centralized control with a lower communicationbandwidth [7].

VOLUME X, 2019 1

Yi et al.: Accurate Power Sharing and Synthetic Inertia Control for DC Building Microgrids with Guaranteed Performance

DC/AC

DC/DC

DER1

Critical Load

DC/DC

DER2

DC/DC

DER3

DC/DC

DERn

DC

Bus

Critical Load

Critical Load

STS

PCC

Utility Grid

Other Loads

FIGURE 1. A typical configuration of DC building microgrids [8].

A DC building microgrid (Fig. 1) may consist of multi-ple DERs on a common bus through exclusive controllablepower-electronics interfaces. Critical and normal loads suchas DC data center, lighting, and ventilation can plug and playif the bus voltage is stabilized. In islanded mode, which thispaper focuses on, DC bus regulation and DER power distribu-tions become primary control objectives as the grid supportis unavailable. However, the stochastic nature of renewableDERs and loads, e.g., PV power fluctuations and electricvehicles (EV), have posed the following challenges that maylead to system instability and hinder the full potentials: 1)inaccurate power sharing among DERs, 2) DC bus voltagesteady-state deviations due to load or DER fluctuations, and3) vulnerability of the DC bus voltage due to extremely lowsystem inertia.

In the literature, droop-based methods have been widelyemployed and extensively explored for power sharing con-trol and bus voltage regulation in DC microgrids. Ref. [9]proposes a Pdc − v2

dc droop control to maintain the commonDC bus voltage and realize the power sharing among theESS, while [10] realizes the same goals by superimposinga small AC voltage with frequency droop to the DC bus.Similarly, [11] introduces an improved power-based droopcontrol for DC microgrids, which autonomously convertspower flow control to droop control and enables seamlesstransitions between islanded and grid-connected modes. Anobserver-based DC voltage droop and current feed-forwardcontrol strategy for DC microgrids is presented in [12], whichenhances the robustness compared with conventional droop.He et al. in [13] devises a method integrating close-loopcurrent regulation, droop, and coupled virtual impedance co-ordinated control techniques. There are also other advancedcontrol strategies for DC microgrids based on modified droopcontrol, i.e., the intelligent power sharing scheme based onfuzzy sliding-mode droop [14], adaptive droop with coeffi-cient shifting and circulating current reduction [15], and the

nonlinear droop method for better power sharing accuracyand voltage regulation [16]. Although these methods improvethe power sharing accuracy and voltage stability to someextent by appropriate modifications, they may suffer fromone or more of the following drawbacks: 1) unavoidable DCbus voltage deviation caused by load or generation changedue to the droop mechanism, 2) the need of additional voltagerestorations from secondary controllers, and 3) the depen-dence of extra PWM modules to implement the controllers.

There are a number of other methods for voltage regu-lations in DC microgrids. Kollimalla et al. in [17] utilizeshybrid energy storage system (HESS) to accommodate powerfluctuations in DC microgrids. This work mainly focuses onthe coordination of battery and supercapacitor in compensa-tion for current fluctuations. Ref. [18] presents the modeling,design, and analysis of DC microgrid control and energymanagement system (EMS) using fuzzy logic, while [19]presents an active control method for DC data center witheight operation modes. Although these methods achieve anoptimal operation and emergency support mode, respectively,bus voltage deviation is not addressed in either methods,which may result in nuisance disturbances to sensitive loads.

Moreover, due to the high penetration level of power-electronics-interfaced DERs, microgrids in general manifesta low inertia nature, which leads to the vulnerability of busfrequency and voltage in AC and DC networks, respectively.Virtual Synchronous Generator (VSG) technology has beenapplied to AC microgrid for virtual spinning inertia supportusing inverter-based DERs. However, due to the decouplingof AC and DC, VSG is not directly applicable for DCmicrogrids. Note that inertia in DC systems is represented bythe stability of bus voltage instead of frequency. To the bestof the authors’ knowledge, very few existing schemes haveconsidered inertia enhancement for DC microgrids. Wu et al.in [20] propose a method to increase DC microgrid inertiaby the analogy of AC VSG to DC network, where the grid-connected inverter controls the DC bus. This method doesenhance the inertia of DC microgrids, however, it is onlyapplicable in grid-connected mode and the voltage deviationis not eliminated.

As an attempt to address the aforementioned limitations,this paper proposes a unified designing approach of FCS-MPC for building-scale DC microgrids featuring accuratepower sharing and virtual inertia synthesis. The major con-tributions can be summarized as follows:

• A novel power sharing mechanism for DERs is pro-posed in a predictive manner by introducing a currentsharing vector to the FCS-MPC cost function;

• Steady-state DC voltage deviation and secondaryrestoration are eliminated during the fluctuation of loadsor generations;

• Virtual capacitance control is integrated in a FCS-MPCapproach for the first of its kind, which enables theadaptive synthetic inertia and stabilizes the DC busvoltage in case of disturbances;

2 VOLUME X, 2019


• The proposed approach follows an optimal control de-signing procedure that makes it scalable with guaran-teed steady-state and dynamic performances; and

• The proposed method eliminates the needs of externalPWM modules and reduces the parameter tuning efforts.

The remainder of this paper is organized as follows: Sec-tion II presents the designing flow of the proposed FCS-MPC-based control strategy for building-scale DC micro-grids, followed by the virtual capacitance control implemen-tation in Section III; Section IV analyzes the stability of theproposed method and presents the simulation case studies;Section V demonstrates the experimental verification; andSection VI concludes the paper.

II. THE PROPOSED CONTROL STRATEGY FORISLANDED DC BUILDING MICROGRIDA. PROBLEM FORMULATIONThe proposed strategy features optimal and predictive controlactions in a fast and reliable manner. By taking certain mea-surements, the FCS-MPC determines future control inputsby solving an optimization problem over a finite horizon. Itintegrates the references and predictions of future states ofa DC microgrid using the past and present measurements.Firstly, a DC microgrid is formulated into a discrete-timestate-space model:

x(k + 1) = Ax(k) +Bu(k) (1)y(k) = Cx(k) +Du(k) (2)

where x is the n-dimensional system states (x ∈ X ∈ Rn)and u is the m-dimensional control inputs (u ∈ U ∈ Rm), bywhich future state variables x(k+ 1) of the microgrid can bepredicted. The control process can be further formulated intoan optimization problem with the finite input set UM (x) =u(0), u(1), . . . , u(M − 1) and terminal region Xf :

minu

J (x,u)|u ∈ UM (x)

s.t. x(k) ∈ X, ∀k ∈ 0, . . . ,Mu(k) ∈ U, ∀k ∈ 0, . . . ,M − 1x(k +M) ∈ Xf

(3)

with a quadratic cost function:

J (x,u) =

M−1∑k=0

ξ(x(k), u(k)) + Jt(x(k +M)) (4)

where Jt(x(k + M)) is the terminal cost that imposes thestates’ convergence to references and ξ(x(k), u(k)) is stagecost that represents the predicted evolution of the states andcontrol inputs [21]. For the sake of a simpler presentation, theproposed method will follow a one-horizon-step prediction.Therefore, when the microgrid reaches an equilibrium point,it satisfies x(k + 1) = x(k) = x∗. In practice, there arefinite elements in the control input set UM (x), which areessentially the power electronics control signals. Therefore,Eq. (4) will be evaluated by each element of UM (x) until theoptimal input sequence is obtained. The model moves step by

DC Bus

DC Loads

DER1

DER2

DERN

DC/AC

Utility Grid

1S

2S

NS

1inV

2inV

inNV

1Li

2Li

1L

2L

NL LNi

VCDCZ

1LV+ -

+ -

+ -

2LV

LNV

Loadsi

busV +-

PCC

DC Microgrid FCS-MPC From Higher-Level

EMS

*mgx

VCi

FIGURE 2. Schematic of the studied DC building microgrid with the proposedcontroller.

step in the sample horizon as measurements, predictions, thevalue of cost function update iteratively. Detailed designingprocedures are elaborated below.

B. ISLANDED DC MICROGRID MATHEMATICALMODELING WITH POWER SHARING MECHANISMFig. 2 illustrates the schematic of the studied DC buildingmicrogrid with N parallel DERs, which can be renewablegenerators such as PV array, diesel generator, ESS, etc. Itis noteworthy that although the following design process ismodel-based, it is a unified approach that is adaptable to othertypes of DC microgrids with proper modifications. To enablethe plug and play of loads or DERs in islanded mode, thebus voltage should always be stabilized. Mathematically, theprediction for output current of DERi can be formulated as:

iLi(k + 1) = [SiV

ini (k)− Vbus(k)][Ts/Li] + iLi

(k) (5)

where Si = 0, 1 is the converter switch status and Ts de-notes the sampling period of the discrete system. Therefore,the DC bus voltage can be formulated by:

Vbus(k + 1) =ZDC

N∑i=1

iLi(k + 1)

=ZDCTs[1

L1. . .

1

LN][S1V

in1 (k)− Vbus(k) . . .

SNVinN (k)− Vbus(k)]T + Vbus(k)

(6)given the fact that:

ZDC

N∑i=1

iLi(k) = Vbus(k) (7)

VOLUME X, 2019 3


where the instant DC load impedance, ZDC , can be deter-mined by real-time measurement of the bus current. By Eq.(6) and (7), the future value of the DC bus voltage can bepredicted in a one-step horizon, which will be utilized forbus voltage regulation later.

A current sharing mechanism is implemented in the FCS-MPC model by inserting a current sharing vector

Γ = γ1, γ2, . . . , γN−1 (8)

which imposes the load sharing among DERs in a predictivefashion. Then, the following term is defined:

iγi(k + 1) = iLi(k + 1)− γiiLi+1

(k + 1) (9)

This controls the output current ratio between the ith and(i + 1)th DERs. Therefore, from Eq.’s (5)-(9), the state-space model of the entire N -DER DC microgrid can bemathematically represented as:

xmg(k + 1) = Axmg(k) +Bumg(k) (10)

xmg =

Vbusiγ1iγ2...

iγN−2

iγN−1

umg =

S1Vin1

S2Vin2

S3Vin3

...S3V

inN−1

S3VinN

A =

1− TsZDC

L1. . .− TsZDC

LN0 0 . . . 0 0

γ1Ts

L2− Ts

L11 0 . . . 0 0

γ2Ts

L3− Ts

L20 1 . . . 0 0

......

.... . . 0 0

γN−1Ts

LN− Ts

LN−10 0 . . . 0 1

B =

ZDCTs

L1

ZDCTs

L2

ZDCTs

L3. . . ZDCTs

LN−1

ZDCTs

LNTs

L1−γ1Ts

L20 . . . 0 0

0 Ts

L2−γ2Ts

L3. . . 0 0

......

.... . . −γN−2Ts

LN−10

0 0 0 . . . Ts

LN−1−γN−1Ts

LN

C. CONTROLLER DESIGN WITH PERFORMANCEGUARANTEESFuture values of state variables of the DC microgrid, xmg(k+1), can therefore be predicted by Eq. (10) using presentstate measurements xmg(k) and tentative control actionsumg(k). Consequentially, DC bus voltage regulation andpower sharing mechanism can be achieved simultaneouslyby controlling xmg(k + 1) to track the designated referencex∗mg , via minimization of the following cost function at eachsampling step:

J (xmg, umg) = [xmg(k + 1)− x∗mg]TP [xmg(k + 1)− x∗mg]+ [(xmg(k)− x∗mg]TQ [xmg(k)− x∗mg]+ [umg(k)− u∗mg]TR [umg(k)− u∗mg]

(11)

where the semi-positive definite matrices Q and R andpositive definite matrix P are the weighting factors of thepredicted behavior and controlled states, respectively. In thepractical case presented in this paper, the reference can be setas x∗mg = [V ∗bus 0 0 . . . 0]T to impose the output currentratios during the control actions, which will yield iL1/iL2 =γ1, iL2

/iL3= γ2, . . . , iLN−1

/iLN= γN−1. For each

sampling instant, cost function (11) will be evaluated onceand predictive optimal control inputs for the DC microgrid,uoptmg , can be obtained, i.e.,uoptmg , argmin

umg

J (xmg, umg).The results of J (xmg, umg) and uoptmg are updated interac-

tively as the time-series sampling instant moves forward. Byproperly designing the P , Q, and R, the MPC control loopwill exhibit guaranteed and provable performance. It has beenproven in [22] that, finding proper weighting matrices for theMPC formulation to guarantee its initial-state practical con-trol Lyapunov stability is equivalent to solving the followingAlgebraic Riccati equation:

ATKPAK − P +Q+KTRK = 0 (12)

where

K = −(BTPB +R)−1BTPA (13)

AK , A+BK (14)

By defining the maximum input umax, the nominal controlset can be defined as:

U , u ∈ Rn : |u| ≤ |umax| (15)

Then, the maximum quantization error of the control input∆q can be obtained. The terminal region Xf can be charac-terized by:

Xf , xmg ∈ Rn : |xmg − x∗mg| ≤|umax||K|

(16)

The cost function Eq. (11) can be considered as a practi-cal control Lyapunov function, satisfying that, for all statesx ∈ XM , where XM is the domain of the cost function, thefollowing conditions hold:

J (x) > α1|x|2, ∀x ∈ XM (17)

J (x) < α2|x|2, ∀x ∈ Xf (18)

∆J (x) < −α3|x|2 + |BTPB +R|∆2q (19)

where α1 = λmin(P), α2 = λmax(P), α3 = λmin(Q). Thedecaying factor, denoted by ρ, can be calculated by:

ρ = 1− α3/α2 (20)

and the ultimately bounded set Xb for the state variables canbe found by:

Xb , xmg ∈ Rn : |xmg − x∗mg|2 ≤|BTPB +R|α1(1− ρ)

∆2q(21)

The region of attraction XMPC , which is defined as:

XMPC , Xf ∪ xmg ∈ Rn : ∆J (xmg) < 0 (22)

can be obtained by enlarging Xf while guaranteeing that∆J (xmg) ≤ 0.

4 VOLUME X, 2019


( )mgx k

1

2

2

1

*

*

*

*

*

*

N

N

VC

mg

V

i

ix

i

i

Minimize Eq. (11) ( 1) ( ) ( )optmg mg mgx k Ax k Bu k

( 1)mgx k

DC Microgrid

EMS

Current Sharing Ratios

( )optmgu k

FCS-MPC

Predict

Measure

Eq. (25)

MonitoringVirtual Capacitance Control

*busV

FIGURE 3. The proposed control strategy for DC Microgrid.

III. VIRTUAL CAPACITANCE CONTROLIn addition to guarantee the initial-state practical stability,virtual capacitance control is proposed for stabilizing the DCbus voltage in transient scenarios. The proposed method iselaborated in this section. Due to high penetration of power-electronics DERs, DC building microgrids in general exhibitextremely low inertia phenomenon and the bus voltage isvulnerable to abrupt load or renewable changes. There areresearches seeking for methods to provide virtual inertiasupport for AC microgrids to maintain a stable frequency,for instance, by active power injection or VSG. Nevertheless,in DC microgrids, instead of frequency stability, the lack ofsystem inertia can lead to bus voltage instability. To the bestof authors’knowledge, DC microgrid virtual capacitance con-trol with FCS-MPC has not been considered in the literature.To address this issue, MPC-based virtual capacitance controlis proposed to enhance the synthetic inertia of DC micro-grids. This is achieved by synthesizing the effect of a virtualcapacitor across the DC bus to suppress voltage fluctuations.Instead of directly using the static voltage reference V ∗busfrom upper-level EMS, the controller hypothesizes that thereis an ultra-capacitor CV across the DC bus that is absorbinga virtual current as:

iV C = CVdVbus(t)

dt= CV

Vbus(k)− Vbus(k − 1)

Ts(23)

As is illustrated in Fig. 2, the virtual capacitor yields thecurrent fed to the DC loads to be:

iV Cload =

N∑i=1

iLi− iV C (24)

Therefore, from (23) and (24) and by taking into account thedynamic effect of virtual capacitor, the synthetic bus voltagereference is given by:

V ∗V C = ZDC · iV Cload

= V ∗bus −Vbus(k)

iload(k)· CV ·

Vbus(k)− Vbus(k − 1)

Ts(25)

1

1.645 1.65 1.655 1.660.98

1

1.02Bus Disturbance Occurs Here

Time (s)

Vpu

V ∗V C

Vbus

V ∗bus

FIGURE 4. Dynamic response of the virtual-capacitance-enabled DC busvoltage Vbus and reference V ∗

V C during an abrupt load change.

TABLE 1. Parameters of the Case Study System

Parameter Symbol Value

Voltage of DER1 V in1 2 pu



Output Filter Inductor of DER1 L1 1 mHOutput Filter Inductor of DER2 L1 1 mHOutput Filter Inductor of DER3 L1 1 mHCurrent Sharing Ratio 1 γ1 1.2Current Sharing Ratio 2 γ2 1.2Desired DC Bus Voltage Vbus 1 puSampling Period Ts 80 usInitial DC Load Impedance ZDC 1 pu

which is adaptive to the dynamics of bus voltage Vbus. Fig.3illustrates an outline of the proposed strategy. When there arevoltage perturbations, e.g., due to load or power fluctuations,the virtual capacitor will buffer the extra amount of currentand dynamically adjust the value of V ∗bus to smooth the DCbus voltage. For instance, when DC load suddenly increases,Vbus will decrease, which yields two successive voltagemeasurements Vbus(k) < Vbus(k − 1) and results in V ∗V C toincrease dynamically as per Eq. (25). The controller noticesthe change of reference and will force Vbus to track the newV ∗V C with the best effort, which reduces the dip of bus voltageVbus. As Vbus goes back on the track, V ∗V C converges to V ∗buswhen Vbus(k) = Vbus(k−1). Consequentially, the bus voltagewill be stabilized to EMS reference V ∗bus in steady state. Thisprocess is shown in Fig. 4, where the blue and red curves areV ∗V C and Vbus, respectively.

IV. SIMULATION CASE STUDIESA. SYSTEM SETUPTo validate the proposed control scheme, a building-scaleDC microgrid is modeled in the PSCAD/EMTDC softwarepackage. The microgrid under investigation shares the sameconfiguration as Fig. 2 with three parallel DC DERs on theDC bus. The microgrid operates in islanded mode withoututility power exchange. Detailed parameters of the testedsystem are presented in Table 1. For a clearer comparison,per-unit values are used, with voltage base 1 kV, current

VOLUME X, 2019 5


1

0 0.5 1 1.5 2

·10−2

0

1

2

·10−2

Time (s)

J

FIGURE 5. FCS-MPC cost function minimization iterations.

base 1 kA, impedance base 1Ω, and power base 1 MW. Itis noteworthy that the proposed method follows a unifieddesigning approach which is scalable and can be applied toother DC microgrids in different configurations via propermodifications. Multiple case studies are perform and theresults are analyzed below.

Following the proposed procedures in Section II, state-space model of the DC microgrid with three DERs can bederived using Eq. (10) with the parameters given in Table1. For the sake of simplicity, weighting matrices in the costfunction (11) are selected as Q = I3×3 and R = 1e−3I3×3.By solving the Algebraic Riccati equation (12), matrix P canbe calculated as:

P =

1.0296 0.0074 0.00740.0074 1.0783 0.03710.0074 0.0371 1.0783

(26)

while matrix K can be obtained as:

K =

−3.6851 −6.8520 −3.5539−2.9711 3.9622 −3.2936−2.3761 2.9698 6.9275

(27)

Iterations of cost function J are depicted in Fig. 5, whichshows the minimization process of Eq. (11). When the systemstarts, J begins to decay from a relatively large number.Within 2 ms, the cost of controller converges to a value nearzero, which indicates that the state variables are tracking theirreferences and the microgrid is stable.

B. CASE STUDY 1 - VIRTUAL CAPACITANCE CONTROLThe first case aims at verifying the performance of the pro-posed FCS-MPC virtual capacitance control. Fig. 6 presentsthe transient behaviors of the DC bus voltages in responseto sudden load changes with a desired voltage of 1 pu. Com-parisons are carried out with the virtual capacitance varyingfrom 0 to 150 mF with an increment of 50 mF. At t = 2 s,the load impedance at DC bus decreases from 1 pu to 0.8 pu,which results in a nuisance voltage disturbance. WithoutCV , the voltage decreases by more than 3% (black curve).However, with the synthetic capacitance, the dip of voltageresulted from load change can be mitigated to a value withinthe ± 1% zone in 200 ms (zoomed area in Fig. 6). As thevalue of CV increases, the synthetic capacitor current (iV Cin Eq. (23)) increases and so does the inertia control effectto the DC bus. At t = 3 s, the load impedance increases from

1

1.5 2 2.5 3 3.50.85

0.9

0.95

1

1.05

±1% Zone

Time (s)

v(k

V)

Cv = 0mF

Cv = 50mF

Cv = 100mF

Cv = 150mF

1.5 2 2.5 3 3.50.85

0.9

0.95

1

1.05

±1% Zone

Time (s)

v(k

V)

Cv = 0mF

Cv = 50mF

Cv = 100mF

Cv = 150mF

FIGURE 6. Case 1: Bus voltage dynamics with various virtual capacitances.

1

2 4 6 8 100.8

0.9

1

1.1

1.2

Time (s)

Ppu

Load Demand Power

0.95

1

1.05

1.1

Vpu

Vbus - Method in Ref. [20]

Vbus - Proposed Method

FIGURE 7. Case 2: Comparison of bus voltage transient response using theproposed method and controller from Ref. [20].

0.8 pu to 1 pu and the response of bus voltage verifies howthe perturbation is reduced by the virtual capacitance again.This is advantageous in practice. When there is a severedisturbance that leads to voltage violations of the DC bus, theproposed virtual capacitance control technique can increasethe system inertia and allow more time for the EMS to restorethe bus voltage and avoid interruptions to critical loads.

C. CASE STUDY 2 - LOAD FLUCTUATION RESPONSESince loads in a DC building can vary arbitrarily during dailyoperations, the DC bus voltage may suffer from frequentfluctuations. To further highlight the promising performanceof the proposed scheme, a benchmarking study is carried outby result comparison between the proposed method and theone introduced in a recent publication, Ref. [20], in which avirtual inertia control strategy for DC microgrid is proposedto restrain the DC bus voltage fluctuation. The comparedmethod utilizes a AC/DC interlinking converter (IC) anddevises a control strategy to analogize the behavior of aVSG in AC systems. Thereby, the DC bus voltage can bemaintained by the IC. A current feed-forward control loopis employed to enhance its dynamic performance. Althoughthis method restrains the voltage fluctuations, steady-statecontrol error cannot be eliminated due to its mechanism. Thiscan be seen in both the reference and the following casestudy. For comparative studies, the control method in [20] isimplemented in a DC microgrid with the same configuration

6 VOLUME X, 2019


1

2 3 4 5 60

0.2

0.4

0.6

0.8

1

Ppu

PDER1PDER2PDER3

2 3 4 5 6

0.8

0.9

1

1.1

1.2

Bus Voltage Deviation

Time (s)

Vpu

Droop Control

Method in Ref. [20]

Proposed Method

FIGURE 8. Case 3: Verification of the power sharing mechanism andcomparison of DC bus voltage behaviors by different methods.

1

0

0.5

1

Vpu

Vbus

2 4 6 80

0.5

1

Γ = 2, 2 Γ = 1, 1 Γ = 12, 12 Γ = 2, 2

Time (s)

Ppu

PDER1PDER2PDER3

FIGURE 9. Case 3: Change of the power sharing vector Γ.

and DER parameters. Fig. 7 shows the bus voltage behaviorwhen load fluctuates intensively during a short period. Asis depicted, when loads fluctuate irregularly (black curve),the bus voltage controlled by [20] can be smoothed to a cer-tain extent. However, it unavoidably suffers from continuousvoltage deviation (red dotted curve). Moreover, the situationworsens when the change of load becomes more significant.This degrades the power quality and may cause sensitiveloads to trip when the bus voltage exceed the safety margin.On the contrary, the DC microgrid regulated by the proposedmethod exhibits satisfactory bus transient dynamics, whicheliminates the voltage deviations while alleviating the fluctu-ations (red solid curve).

D. CASE STUDY 3 - POWER SHARING CONTROL ANDBUS VOLTAGE STABILIZATIONThis case focuses on validating the proposed method forits accurate and flexible power sharing control mechanismamong the DERs as well as the voltage dynamics during thesetransitions. Initially, the current sharing vector Γ = γ1, γ2is set as γ1 = γ2 = 1.2, which yields the power provided by

the DERs to be PDER1 = 1.2×PDER2 = 1.44×PDER3. As Fig.8 shows, before t = 3 s, the entire DC load power is 1.1 pu,which is accurately shared by three DERs with 0.436 pu,0.362 pu, and 0.302 pu, respectively. At t = 3 s, the DC loadincreases to 2.1 pu by a step change of 1 pu. The contributionof each DER increases accordingly by 0.395 pu, 0.330 pu,and 0.275 pu, respectively, resulting in a steady-state powersharing of 0.831 pu, 0.692 pu, and 0.577 pu. Finally, the loaddeclines to 1.35 pu at t = 5 s, resulting in a power sharingof 0.534 pu, 0.445 pu, and 0.371 pu. From the testing resultsshowed in Fig. 8, the proposed method is capable of con-trolling the power sharing ratio of the DERs accurately. Thesecond plot of Fig. 8 illustrates the comparison of bus voltagedynamic responses controlled by the proposed method withvirtual capacitance, controller proposed in [20], and con-ventional PI-based droop control. During these transitions,the proposed method imposes the bus voltage to track thereference smoothly with acceptable disturbances (red solidcurve in the voltage plot), while the other two methods sufferfrom bus voltage deviations (blue and green solid curves).

Moreover, the power sharing ratio vector Γ = γ1, γ2can be adapted flexibly during real-time operation accordingto the commands from EMS. This is an important featurefor islanded building-scale microgrids as the EMS should becapable of managing the outputs of each DER as per theirreal-time capacity and availability. In practice, the buildingEMS can utilize the proposed method to adjust the outputpowers of multiple energy storages according to their real-time SOCs during operation. To validate this, additional casestudies are performed and the results are depicted in Fig. 9.Initially, the power sharing ratio is set as γ1 = γ2 = 2. Poweroutputs of the three DERs follow the ratio accurately as canbe observed from the plot. At t = 2 s, the ratio is suddenlychanged to γ1 = γ2 = 1, which yields an identical outputpower from each DER. Afterwards, Γ is set as γ1 = γ2 = 1

2and γ1 = γ2 = 2 at t = 4 s and t = 6 s, respectively. As isshown in Fig. 9, the outputs of DERs are able to follow thecommand in an accurate and timely manner. During thesetransitions, the DC bus is maintained at a stable voltage(black solid curve).

E. CASE STUDY 4 - DER PLUG AND PLAYPlug-and-play capability of an islanded DC microgrid isessentially important due to the absence of utility grid. Thiscase aims at verifying the performance of proposed controlstrategy in terms of DER plug and play. During operation, amicrogrid may lose one or more of its DERs due to converteror communication failures. After cleaning the faults, the lostDER will be reconnected to the system. The controller mustbe able to handle this contingency by maintaining the busvoltage and redistribute the power among healthy DERs. Inthis case study, DER3 was disconnected by a breaker at t = 5 s.As Fig. 10 depicts, the outputs of DER1 and DER2 increasesimultaneously following the sharing ratio (γ1 = 4). At t =9 s, the fault is cleared and DER3 is reconnected to the bus.The controller successfully redistributed the power sharing

VOLUME X, 2019 7


1

0

0.5

1

Vpu

Vbus

4 6 8 10 12

0

0.2

0.4

0.6

DER3 Out DER3 In

Time (s)

Ppu

PDER1PDER2PDER3

FIGURE 10. Case 4: Verification of the DER plug-and-play capability withΓ = 4, 1.

1

1.5 2 2.5 3 3.5

1

1.2

1.4

Time (s)

vbus

(kV

)

DC Bus Reference

PI Controller

Small Virtual Capacitance

Large Virtual Capacitance

1.5 2 2.5 3 3.5

1

1.2

1.4

Time (s)

vbus

(kV

)

DC Bus Reference

PI Controller

Small Virtual Capacitance

Large Virtual Capacitance

FIGURE 11. Case 5: DC bus voltage dynamic response to reference stepchanges.

with (Γ = γ1 = 4, γ2 = 1). During the transitions, theDC bus voltage is well-maintained with slight disturbancesobserved.

F. CASE STUDY 5 - BUS VOLTAGE CHANGEThis case provides verification of the proposed FCS-MPCapproach in controlling the DC bus voltage in response tostep changes of reference, compared with conventional PI-based controllers. The bus voltage reference changes from1 pu to 0.95 pu at t = 2 s and back to 1 pu at t = 3 s. Fig.11 shows the dynamic response of the measured bus voltagecontrolled by the proposed method with small (20 mF) andlarge (150 mF) virtual capacitance (red and orange curve,respectively) and conventional PI controller (blue curve).The proposed optimal-control-based approach guarantees theconvergence of dynamic tracking error and provides a su-perior steady-state accuracy. With a proper value of virtualcapacitance, the bus voltage follows the reference within asatisfactory dynamic response. Note that PI-based controllersgenerally require extensive parameter tuning, while the pro-posed method significantly reduces this effort thanks to itsmechanism. The case study also demonstrates the influenceof a large virtual capacitor. As shown in Fig. 11, increasingthe value of virtual capacitance will increase the inertia ofDC bus, resulting in a slower response to the step change.Therefore, in practice, the proposed method will allow the

DC

Bu

s

1S

2S

1inV

2inV

1Li

2Li

DC/DC

DC/DC

DC Loads

Loadsi

Host Communication Co-Processor

Real-Time ProcessorRAMand

Flash

Local Bus

Ethernet Switch

I/O FPGA

MicroLabBox

Ethernet

Matlab/Simulink & dSPACE ControlDesk

DER2

DER1

FIGURE 12. Overall structure of the experimental system.

Host Server - Controller

Oscilloscope

dSPACE MicroLabBox

DERs

LC Filters

DC/DC

Converters

Loads

dSPACE ControlDesk

FIGURE 13. Experimental verification system laboratory setup.

change of CV value during operation. For example, furtheralgorithms can be developed on top of the proposed mecha-nism to make CV adaptive, so the desired dynamics of busvoltage will become flexible.

V. EXPERIMENTAL CASE STUDIESTo further validate the proposed method, a laboratory DC mi-crogrid prototype is set up and multiple real-time experimen-tal tests are performed. Fig. 12 and 13 present the system con-figuration and the prototype test-bench, respectively. The DCmicrogrid consists of two DERs and multiple DC loads on acommon bus. Two DC/DC buck converters are used to inter-face the DERs. dSPACE MicroLabBox (DS1202) hardware-in-the-loop (HIL) platform is employed to integrate the test-bench and the proposed controller that is implemented in thehost server using Matlab/Simulink and dSPACE ControlDesksoftware packages. Both DER voltages (V in1 and V in2 ) are setas 24 V and the DC bus voltage (Vbus) is regulated at 10 V.

8 VOLUME X, 2019


𝑖

𝑖

𝑖

(a)

(b)

FIGURE 14. (a) dSPACE ControlDesk capture of load, DER1, and DER2currents during a load disturbance; (b) DC bus voltage during the loaddisturbance.

The current sharing ratio is set as γ1 = 2.2, and dSPACEsampling period is Ts = 100 us. The weighting matrices arechosen as Q = I2×2 and R = 02×2. By Eq.’s (14) and (15),one can calculate P = I2×2 and

K =

[−0.6 201.8 −20

](28)

A. CASE STUDY 1 - POWER SHARING MECHANISMFirstly, performance of the power sharing mechanism andbus voltage regulation is verified. As Fig. 14 depicts, loadson the DC bus draw a total current (iLoads) of 0.8 A at thebeginning of testing, which is distributed by the two DERswith approximately iL1 = 0.25 A and iL2 = 0.55 A, whichcomplies with γ1 = 2.2. At around 9.6 s, a sudden loadchange increases iLoads to 0.84 A. As a result, the contribu-tions of DERs, iL1 and iL2, increase to 0.58 A and 0.26 Aat a ratio of around 2.2. At 15.4 s, loads decrease and thecontributing currents of both DERs decline accordingly. Fig.14(a) illustrates the real-time current measurements capturedby the dSPACE ControlDesk. During these processes, the DCbus voltage (Vbus) is regulated at 10 V stably, with slightdisturbances during the transitions (oscilloscope screenshotin Fig. 14(b)).

B. CASE STUDY 2 - VIRTUAL CAPACITANCE CONTROLThe second case evaluates the virtual capacitance control ofthe DC bus. Comparisons are carried out by measuring thedynamics of Vbus during the transition of load step change

9.225V

(a)

9.635V

(b)

FIGURE 15. DC bus voltage: (a) without virtual capacitor control; (b) withvirtual capacitance control (CV = 10 mF).

from 10 to 8.5 Ω. Fig. 15 shows the oscilloscope screenshots,where (a) is the voltage disturbance without virtual capaci-tance control and (b) is with virtual capacitanceCV = 10 mF.As is measured by the cursors, the undershoot of Vbus reaches9.225 V without virtual capacitance control. However, withCV = 10 mF, the undershoot of Vbus is improved to 9.635 V,which further validates the effectiveness of the proposedmethod.

VI. CONCLUSIONThis paper presents a novel control strategy for islandedbuilding-scale DC microgrids, which eliminates the DC busvoltage deviations under system disturbances. A new DERpower sharing mechanism is proposed in a predictive fashionby introducing a current sharing vector in the MPC modelof DC microgrid. Moreover, virtual capacitance control isimplemented in the MPC to provide adaptive synthetic inertiasupport. The state-space modeling procedures of DC micro-grids are presented, based on which the control scheme isdevised in a optimal control basis with Lyapunov stabilityperformance guarantees. The controller predicts future be-haviors of state valuables, and, by minimizing a cost functionwith certain practical constraints, offers optimal actions forthe DERs to track EMS references. Both simulation andexperimental case studies with benchmarking comparisonsand in-depth analyses are carried out. Results verify the

VOLUME X, 2019 9


promising performance of the proposed strategy.

REFERENCES[1] K. Peterson, P. Torcellini, R. Grant, and et al., “A common definition

forzero energy buildings,” Department of Energy (DOE), Tech. Rep., 2015.[2] D. Shi, X. Chen, Z. Wang, X. Zhang, Z. Yu, X. Wang, and D. Bian, “A

distributed cooperative control framework for synchronized reconnectionof a multi-bus microgrid,” IEEE Trans. Smart Grid, vol. PP, no. 99, pp.1–1, 2017.

[3] Z. Yi and A. H. Etemadi, “Line-to-line fault detection for photovoltaic ar-rays based on multiresolution signal decomposition and two-stage supportvector machine,” IEEE Trans. Ind. Electron., vol. 64, no. 11, pp. 8546–8556, Nov 2017.

[4] Z. Yi, W. Dong, and A. H. Etemadi, “A unified control and power man-agement scheme for PV-battery-based hybrid microgrids for both grid-connected and islanded modes,” IEEE Trans. Smart Grid, vol. PP, no. 99,pp. 1–1, 2017.

[5] A. Babqi, Z. Yi, and A. H. Etemadi, “Centralized finite control setmodel predictive control for a multiple distributed generators small-scalemicrogrid,” in 2017 North American Power Symposium (NAPS), Sept2017, pp. 1–5.

[6] D. Fregosi, S. Ravula, D. Brhlik, J. Saussele, S. Frank, E. Bonnema,J. Scheib, and E. Wilson, “A comparative study of dc and ac microgridsin commercial buildings across different climates and operating profiles,”in 2015 IEEE First International Conference on DC Microgrids (ICDCM),June 2015, pp. 159–164.

[7] D. E. Olivares, A. Mehrizi-Sani, A. H. Etemadi, C. A. CaÃsizares, R. Ira-vani, M. Kazerani, A. H. Hajimiragha, O. Gomis-Bellmunt, M. Saeedifard,R. Palma-Behnke, G. A. JimÃl’nez-EstÃl’vez, and N. D. Hatziargyriou,“Trends in microgrid control,” IEEE Trans. Smart Grid, vol. 5, no. 4, pp.1905–1919, July 2014.

[8] X. Lu, J. M. Guerrero, K. Sun, and J. C. Vasquez, “An improved droopcontrol method for dc microgrids based on low bandwidth communicationwith dc bus voltage restoration and enhanced current sharing accuracy,”IEEE Trans. Power Electron., vol. 29, no. 4, pp. 1800–1812, April 2014.

[9] Y. Xia, W. Wei, M. Yu, X. Wang, and Y. Peng, “Power managementfor a hybrid ac/dc microgrid with multiple subgrids,” IEEE Trans. PowerElectron., vol. 33, no. 4, pp. 3520–3533, April 2018.

[10] S. Peyghami, P. Davari, H. Mokhtari, P. C. Loh, and F. Blaabjerg,“Synchronverter-enabled dc power sharing approach for lvdc microgrids,”IEEE Trans. Power Electron., vol. 32, no. 10, pp. 8089–8099, Oct 2017.

[11] G. Liu, T. Caldognetto, P. Mattavelli, and P. Magnone, “Power-based droopcontrol in dc microgrids enabling seamless disconnection from upstreamgrids,” IEEE Trans. Power Electron., pp. 1–1, 2018.

[12] X. Li, L. Guo, S. Zhang, C. Wang, Y. W. Li, A. Chen, and Y. Feng,“Observer-based dc voltage droop and current feed-forward control of adc microgrid,” IEEE Trans. Smart Grid, pp. 1–1, 2017.

[13] J. He, L. Du, B. Liang, Y. Li, and C. Wang, “Coupled-virtual-impedancecontrol for ac/dc hybrid microgrid power electronic interlinking unit withdual converters,” IEEE Trans. Smart Grid, pp. 1–1, 2018.

[14] Y. Mi, H. Zhang, Y. Fu, C. Wang, P. C. Loh, and P. Wang, “Intelligentpower sharing of dc isolated microgrid based on fuzzy sliding mode droopcontrol,” IEEE Trans. on Smart Grid, pp. 1–1, 2018.

[15] S. Augustine, M. K. Mishra, and N. Lakshminarasamma, “Adaptive droopcontrol strategy for load sharing and circulating current minimization inlow-voltage standalone dc microgrid,” IEEE Trans. Sustain. Energy, vol. 6,no. 1, pp. 132–141, Jan 2015.

[16] P. Kou, D. Liang, J. Wang, and L. Gao, “Stable and optimal load sharingof multiple pmsgs in an islanded dc microgrid,” IEEE Trans. EnergyConvers., vol. 33, no. 1, pp. 260–271, March 2018.

[17] S. K. Kollimalla, M. K. Mishra, A. Ukil, and H. B. Gooi, “Dc grid voltageregulation using new hess control strategy,” IEEE Trans. Sustain. Energy,vol. 8, no. 2, pp. 772–781, April 2017.

[18] Y. K. Chen, Y. C. Wu, C. C. Song, and Y. S. Chen, “Design and implemen-tation of energy management system with fuzzy control for dc microgridsystems,” IEEE Trans. Power Electron., vol. 28, no. 4, pp. 1563–1570,April 2013.

[19] D. Salomonsson, L. Soder, and A. Sannino, “An adaptive control systemfor a dc microgrid for data centers,” IEEE Trans. Ind. Appl., vol. 44, no. 6,pp. 1910–1917, Nov 2008.

[20] W. Wu, Y. Chen, A. Luo, L. Zhou, X. Zhou, L. Yang, Y. Dong, and J. M.Guerrero, “A virtual inertia control strategy for dc microgrids analogized

with virtual synchronous machines,” IEEE Trans. Ind. Electron., vol. 64,no. 7, pp. 6005–6016, July 2017.

[21] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, “Con-strained model predictive control: Stability and optimality,” AUTOMAT-ICA, vol. 36, pp. 789–814, 2000.

[22] R. P. Aguilera and D. E. Quevedo, “Predictive control of power convert-ers: Designs with guaranteed performance,” IEEE Trans. Ind. Informat.,vol. 11, no. 1, pp. 53–63, Feb 2015.

10 VOLUME X, 2019

Documents

Accurate Power Sharing and Synthetic Inertia Control for ... Power Sharing and... · A DC building microgrid (Fig. 1) may consist of multi-ple DERs on a common bus through exclusive