IEEE TRANSACTIONS ON SMART GRID 1

Distributed Predictive Control for Frequency andVoltage Regulation in Microgrids

Juan S. Gomez, Doris Saez, Senior Member, IEEE, John W. Simpson-Porco, Member, IEEE,and Roberto Cardenas, Senior Member, IEEE

Abstract—Distributed control schemes have transformed fre-quency and voltage regulation into a local task in distributedgenerators (DGs) rather than one central secondary controller.A distributed scheme is based on information shared amongneighboring units; thus, the microgrid performance is affectedby issues induced by the communication network. This paperpresents a distributed predictive control applied to the secondarylevel on microgrids. The model used for prediction purposes isbased on droop and power transfer equations, but communicationfeatures such as connectivity and latency are also included, thusmaking the controller tolerant to electrical and communicationfailures. The proposed controller considers as control objectivesfrequency and voltage regulation and consensus over the realand reactive power contributions from each power unit in themicrogrid. The experimental results show that the proposedscheme (i) responds properly to load variations, working withinoperating constraints such as generation capacity and voltagerange; (ii) preserves the control objectives when a power unit isdisconnected and reconnected without any user updating in thecontrollers; and (iii) compensates the effects of communicationissues over the microgrid dynamics.

Index Terms—Secondary Control, Distributed Predictive Con-trol, Microgrids, Constrained Optimization, Plug and Play Con-troller.

I. INTRODUCTION

M ICROGRIDS are more sensitive than large-scale powersystems to small changes in either load balance or

power capacity. Currently, the microgrid community acceptsas a fact that a distributed secondary control level is inherentlyfault tolerant to such electrical issues [1]. However, eachcontroller in a distributed scheme should be able to calcu-late its control action according to its knowledge about thecurrent state of the microgrid. The necessity of updating themicrogrid knowledge implies good communication among thecontrollers; therefore, the communication performance and themicrogrid performance are directly related.

In [2] and [3], information shared through the commu-nication network updates an electrical model used by eachsecondary controller. This model is based on the microgridadmittance matrix, and it is applied to an optimization problemto achieve a stable operation point for frequency and voltagewhen any DG is either plugged in or unplugged. In this case,the electrical model is adjusted, without any user intervention,according to Kirchhoff’s voltage law when some changeoccurs in the microgrid. This feature is called plug and play(PnP) capability.

A second approach to include the microgrid model at thesecondary control level is a graph-based representation of theinformation flow among the DGs. In this case, the DGs are

represented as the graph vertices, and the communication linksare represented as the graph edges. A weighted matrix thatrepresents the graph connectivity among DGs is called theadjacency matrix. This matrix permits exploring the propertiesof the network systems [5]. In [4], a distributed consensusproblem is applied over the microgrid. It is shown that theproblem converges if and only if the microgrid graph has apath between any two DGs (connected graph), and the finalvalue is the average of the initial conditions of the consensusvariables.

One application of consensus in microgrids is the distributedaveraging proportional-integral (DAPI) controller proposed in[6]. This scheme adds a term to the proportional-integral(PI) secondary controllers to achieve real power consensusfor the frequency loop and reactive power consensus for thevoltage loop. The DAPI controller is considered to be a PnPcontroller because the adjacency matrix can be updated online,and then the control law changes if a DG is connected to ordisconnected from the microgrid. However, this controller isnot robust against communication issues such as data dropoutsor latency because its control law only considers currentinformation.

Communication issues are not uncommon in networks be-cause communication links are susceptible to external factors,such as weather, obstructions or interference. Data latency,data losses, and network topology changes are issues thatgenerally degrade the control performance irrespective of whattechnology or topology is used in the network [8].

In [6], an updated adjacency matrix used by the DAPIcontroller permits confronting changes in the communicationnetwork topology, preserving the frequency and voltage regu-lation. In [9], latency effects in the frequency restoration loopare compensated by a PI controller with Smith predictor. Totune this, a constant delay estimation is used; however, the realdelay in communication networks is not fixed. To solve thisissue, in [10], a centralized PI controller with gain schedulingfor frequency restoration is used to change the tuned pointwhen the delay also changes.

A set of consensus-based controllers that ensure conver-gence for regulation and power sharing at a finite time haverecently been reported. These PnP controllers have showngood performance against latency and communications pathfailures. In [11], two decoupled finite-time controllers that pre-serve the relations frequency-real power and voltage-reactivepower are compared with a centralized controller using a sixDG microgrid. Conversely, in [12], four independent finite-time controllers are used by each DG to regulate frequency

2 IEEE TRANSACTIONS ON SMART GRID

and voltage and to achieve real and reactive power sharing.The stability analysis of this scheme ensures convergenceirrespective of the latency in the network.

Although predictive control is generally applied at thetertiary control level [14], its application to secondary controlin microgrids is a promising approach because it is possibleto confront data dropouts and latency. In [9], a centralizedpredictive controller is implemented to regulate the frequencyin a microgrid with two DGs, showing a better latency com-pensation than the Smith predictor. Furthermore, if predictivecontrol is combined with a distributed scheme, it is possibleto include PnP capability [16]. The challenge to implementpredictive controllers at the secondary level of microgrids isdefining an optimization problem that is able to be solved ina short sampling period.

In a distributed model-based predictive control (DMPC)scheme, a (discrete-time) system model is used by eachcontroller to predict its self-behavior over a prediction hori-zon. The used model is based on local information (i.e.,measurements) and shared information from other controllers(i.e., previously computed predictions), and it is introducedas a set of equality constraints into an optimization problem.The system solution minimizes a cost function based on thepredicted trajectory and the information exchanged with otherDGs. Although the optimal solution provides a sequence ofcontrol actions, only the first element is applied, and theoptimization problem is solved again at the next samplingperiod (rolling horizon scheme) [20].

There are two methods to solve the DMPC. The iterativemethod optimizes and shares the result with other DMPCsseveral times within the time step. The noniterative methodoptimizes only once per time step to reduce the traffic overthe communication network [19].

Three iterative DMPC schemes for frequency regulation inlarge-scale power systems are proposed in [21]. The modelused for these controllers is based on the frequency-activepower relationship, and these are compared with an automaticgeneration controller (AGC) and a centralized MPC (CMPC)over a communication network with the same topology asthe electrical system. Because these are iterative schemes,they require considerable computational effort and a high-performance communication network; therefore, the imple-mentation of these predictive controllers is expensive for actualmicrogrids.

In [22], an unconstrained DMPC, which include consensus,is proposed for voltage regulation in microgrids, whereas thefrequency regulation is achieved using a DAPI controller. Inthis scheme, an analytical solution is achieved for voltageregulation, reducing the computational effort.

A. Paper Contributions

As it was shown, the PnP schemes using consensus tech-niques in addition to the regulation task (frequency and/orvoltage) enable improving the microgrid secondary level per-formance in several scenarios. However, we consider that thepredictive control has not been completely exploited for theseapplications. In this paper, we propose a noniterative DMPC

that is capable of real-time operation in environments withcommunications issues, preserving the PnP capability.

The main advantage of our controller is the model used topredict the microgrid behavior. This model is based on localvoltage, frequency and power equations, and it includes a com-munication network model that also represents connectivityand latency. The local model on each controller is updatedonce per sampling period with local measurements over eachDG and with information shared from neighboring DGs. Themodel permits including explicit operational constraints, suchas voltage range and apparent power limits. Experimental re-sults over a three DG microgrid validate the good performanceof the proposed controller.

This paper is organized as follows. In Section II, the frame-work of the model used to build the optimization problem ispresented. In Section III, the optimization problem used in theDMPC is detailed. The features of and parameters used in theexperimental setup, as well as the obtained results, are shownin Section IV. The paper conclusions and final remarks arepresented in Section V.

II. MODEL USED FOR CONTROL DESIGN

Considering that variables such as frequency, voltage, andreal and reactive power are coupled in microgrids, the pro-posed model reflects this behavior based on droop, powertransfer and phase angle equations. Additionally, a commu-nication network model that considers the latency, defined bydelay terms (z−τij ), and the connectivity, defined by adjacencyterms (aij), is also proposed.

Because the model computes the power contribution of DGito the microgrid, external measurements are required. Voltage,frequency and phase angle are measured/estimated at the LCfilter output (Vi, ωi, θi) and at an adjacent measurement node(V ∗i , ω

∗i , θ

∗i ). This adjacent measurement node is defined as

the downstream node to the coupling inductance Li.The control scheme for DGi in the microgrid is shown in

Fig. 1. Note that the inner and droop controllers (primarylevel) work on a dq framework, whereas ωs,i and Vs,i sig-nals are droop inputs that compensate voltage and frequencydeviations. These signals and Xi are from the proposed DMPC(secondary level), and these are computed as a solution to anoptimization problem. Xi is composed by frequency, voltageand power predictions, and it is shared with neighboring DGsusing the communication network.

A description of each equation used to build the proposedmodel is included below, and the optimization problem andXi will be defined in Section III.

A. Droop Equations

Droop control provides statism to the microgrid, changingthe operating point from the nominal frequency/voltage toensure the real/reactive power supply when the microgrid isdisturbed. The droop control laws (1) and (2) define the linearrelations frequency-real power and voltage-reactive power,respectively, where ω0 and V0 represent the nominal frequencyand voltage, Mpω,i and Mqv,i are the droop slopes, andωs,i and Vs,i are the secondary control actions for unit i.

GOMEZ et al.: DISTRIBUTED PREDICTIVE CONTROL FOR FREQUENCY AND VOLTAGE REGULATION IN MICROGRIDS 3

Output filter node

Local measurement node

Vi*, i*, i*θ ω

Lfi

Cfi

DGiLi

InnerControllers

Vi

Droop P­ω

abc/dq

θi

∫

ωi

abc/dq

ωs,i

DMPCi

To the microgrid

i1

To neighboring DGs

From neighboring DGs

n

...

z­τin

ai1

ain

i1

in

Droop Q­v

Vidq

ΔVs,i

Vi, i, iθ ω

∫

Vs,i

∫

Δωs,i

z­τi1

Fig. 1. DMPCi Diagram.

Droop equations are included in the secondary control modelbecause they determine the joint point between the primaryand secondary control levels.

ωi(t) = ω0 +Mpω,iPi(t) + ωs,i(t) (1)

Vi(t) = V0 +Mqv,iQi(t) + Vs,i(t) (2)

B. Phase Angle Equation

The phase angle deviation (δθi) generated for unit i by thecoupling inductance Li is defined by (3). The coupling induc-tance is a common passive element used to connect the low-pass filter output to the microgrid. For our controller, the phaseangle deviation is required for estimating the real/reactivepower transferred from the DG to the microgrid. To estimateδθi(t) properly, phase-looked loops (PLLs) should be placedat the output filter and the adjacent measurement node.

δθi(t) = θi(t)− θ∗i (t) =

∫ t

0

[ωi(τ)− ω∗i (τ)] dτ (3)

C. Power Transfer Equations

To achieve power consensus in the microgrid, it is neces-sary to estimate the power contribution of each DG in themicrogrid. In this case, our controller neglects the use ofan admittance matrix-based model, as is generally used, topropose a model based on the power transferred through thecoupling inductance. The equations that determine the powertransferred from unit i to the microgrid are defined in (4) and(5), where Bi = 1/Liω0.

Pi(t) = BiVi(t)V∗i (t) sin (δθi(t)) (4)

Qi(t) = Bi[Vi(t)2 − Vi(t)V ∗

i (t) cos(δθi(t))] (5)

D. Discrete Time Model

Before deriving a predictive model, equations (1) to (5)are discretized using the forward Euler method, where tn =nTsec, n ∈ Z+, and Tsec is the sampling period used at thesecondary control level. To eliminate the steady-state error,integrators are added at the DMPC outputs; therefore, the

incremental operator ∆, defined by (??), is applied on (1)and (2) to compute ∆ωs,i and ∆Vs,i.

∆f(tn) = [f(tn)− f(tn−1)] (6)

Additionally Taylor expansion is applied to (4) and (5)around the measured/estimated point ωi(tn), ω∗

i (tn), Vi(tn),V ∗i (tn), δθi(tn), Pi(tn), Qi(tn), simplifying the optimization

problem. The linear and discrete time model is shown in (6).

ωi(tn+1)=ωi(tn)+Mpω,i[Pi(tn+1)−Pi(tn)]+∆ωs,i(tn) (7a)

Vi(tn+1)=Vi(tn)+Mqv,i[Qi(tn+1)−Qi(tn)]+∆Vs,i(tn) (7b)

δθi(tn+1)=δθi(tn)+Tsec[ωi(tn+1)−ω∗(tn)] (7c)

Pi(tn+1)=Pi(tn)+[Vi(tn+1)−Vi(tn)]BiV∗i (tn)sin(δθi(tn))

+[δθi(tn+1)−δθi(tn)]BiVi(tn)V ∗i (tn)cos(δθi(tn)) (7d)

Qi(tn+1)=Qi(tn)

+[Vi(tn+1)−Vi(tn)]Bi[2Vi(tn)−V ∗i (tn)cos(δθi(tn))]

+[δθi(tn+1)−δθi(tn)]BiVi(tn)V ∗i (tn)sin(δθi(tn)) (7e)

E. Communication Network Model

In this work, a full-duplex communication network is con-sidered in which the bidirectional link between units i and j isrepresented by an adjacency term aij and a delay term τij . Theadjacency term represents the connectivity between two unitsand is defined as (7). This term is updated at the beginning ofeach sampling period according to the information received inunit i.

aij(tn) =

1 Data from unit j arrives to unit i at tn0 Data from unit j does not arrive to unit i at tn0 j = i

(8)

The delay term (τij ≥ 1) is measured in sampling periods, andit represents the time required for the transmission-receptionprocess between DGi and DGj . Since the communicationis full duplex, the associated graph is undirected; then, theequalities τij = τji and aij = aji are satisfied.

III. OPTIMIZATION FOR PREDICTIVE CONTROL

Predictive control optimizes a cost function using a set ofequalities and inequalities as constraints that reflect the systembehavior. The cost function and the constraints should befunctions of the predicted variables. The optimal solution is avector X that contains the predicted values over the predictionhorizon Ny and the control sequence over the control horizonNu. For our controller, it is possible to use the set of equations(6) to predict the DG behavior. Because controlled variablesare explicit in the predictive model, it is possible to directlyinclude operational constraints. The optimization problem andhow it is solved are detailed bellow.

4 IEEE TRANSACTIONS ON SMART GRID

A. Predictive Model

The set of equations (6) can be used to determine the DGbehavior at tn+k, where k ∈ Z+. Considering the linearizationof (6d) and (6e) around the measured point at tn, theircoefficients are updated each sampling period and assumed tobe constants through the prediction horizon in the optimizationproblem.

ωi(tn+k)=ωi(tn+k−1)+Mpω,i[Pi(tn+k)−Pi(tn+k−1)]

+∆ωs,i(tn+k−1) (9a)

Vi(tn+k)=Vi(tn+k−1)+Mqv,i[Qi(tn+k)−Qi(tn+k−1)]

+∆Vs,i(tn+k−1) (9b)

δθi(tn+k)=δθi(tn+k−1)+Tsec[ωi(tn+k)−ω∗(tn)] (9c)

Pi(tn+k)=Pi(tn)+[Vi(tn+k)−Vi(tn)]BiV∗i (tn)sin(δθi(tn))

+[δθi(tn+k)−δθi(tn)]BiVi(tn)V ∗i (tn)cos(δθi(tn)) (9d)

Qi(tn+k)=Qi(tn)

+[Vi(tn+k)−Vi(tn)]Bi[2Vi(tn)−V ∗i (tn)cos(δθi(tn))]

+[δθi(tn+k)−δθi(tn)]BiVi(tn)V ∗i (tn)sin(δθi(tn)) (9e)

B. Operational Constraints

The set of operational constraints is composed of equalitiesand inequalities included to ensure the DG performance withinthe physical limits. This set of constraints is defined in (9).

ωi(tn+k)=ωi(tn+k)+

∑nj=1aij(tn)ωj(tn+k−τij )

1+∑n

j=1aij(tn)(10a)

V i(tn+k)=Vi(tn+k)+

∑nj=1aij(tn)Vj(tn+k−τij )

1+∑n

j=1aij(tn)(10b)

ωi(tn+Ny)=ω0 (10c)

V i(tn+Ny)=V0 (10d)

V min≤V i(tn+k)≤V max (10e)

|Pi(tn)|+|Qi(tn)|+sign(Pi(tn))[Pi(tn+k)−Pi(tn)]

+sign(Qi(tn))[Qi(tn+k)−Qi(tn)]≤Smax (10f)

Note that equations (9a) and (9b), which define the frequencyand voltage averages, include the parameters aij and τij .Therefore, aij forces including only the received informationto estimate and predict the averages, providing robustnessagainst communication path failures and data losses. τij rep-resents the delay estimation in the communication process forcompensating the network latency over the predicted averages.

Equations (9c) and (9d) force the average values to con-verge at the end of the prediction horizon Ny . Additionally,inequalities (9e) and (9f) ensure that the average voltage inthe microgrid and the apparent power of DGi remain within aspecific range. Inequality (9f) is defined as a polytopic innerapproximation of (10) using the triangular inequality.

|Si(t)| = (Pi(t)2 +Qi(t)

2)1/2 < Smax (11)

C. Cost FunctionThe cost function (11) is built from six weighted terms,

where each one represents a control objective in the microgrid.The first two terms represent the average frequency andaverage voltage regulation. Although the optimization problemis local for each DG, the regulation is global over the entiremicrogrid because these terms are based on predictions sharedthrough the communication network. The third and fourthterms minimize the control action required by DGi to achievethe control objectives. The last two terms find a consensus overthe contribution of real and reactive power for neighboringDGs.

Ji(tn) =

Ny∑k=1

[λ1i(ωi(tn+k)− ω0)

2 + λ2i(V i(tn+k)− V0)2]

+

Nu∑k=1

[λ3i(∆ωs,i(tn+k−1))

2 + λ4i(∆Vs,i(tn+k−1))2]

+

n∑j=1,j 6=i

Ny∑k=1

λ5iaij(tn)

(Pi(tn+k)

|Simax|−

Pj(tn+k−τij )

|Sj max|

)2

+

n∑j=1,j 6=i

Ny∑k=1

λ6iaij(tn)

(Qi(tn+k)

|Simax|−

Qj(tn+k−τij )

|Sj max|

)2

(12)

D. Quadratic Programming FormulationIt is possible to build a quadratic programming (QP) prob-

lem for each DG in the microgrid, as is defined in (??), wherematrices/vectors Hi, Fi, Ai, Bi, Aeq,i, Beq,i are built from (8),(9) and (11). Then, the output vector Xi is defined by (??),where the set of predicted variables is represented by Xp,i andthe predicted control sequences X∆,i are defined by (??) and(??), respectively.

minimizeXi

Ji(tn) :=1

2XTi HiXi + FTi Xi

subject to AiXi ≤ Bi

Aeq,iXi = Beq,i

(13)

Xi =Xp,i,X∆,i (14)

Xp,i =ωi(tn+k), V i(tn+k), ωi(tn+k), Vi(tn+k),

δθi(tn+k), Pi(tn+k), Qi(tn+k)Nyk=1

(15)

X∆,i = ∆ωs,i(tn+k), ∆Vs,i(tn+k)Nuk=1 (16)

As mentioned in [20], a stable predictive control requiresa feasible solution to the optimization problem. Note that(9c) to (9f) are related to the QP feasibility, ensuring thatthe system operates within physical limits over the wholeprediction horizon. To ensure a feasible initial condition, theDMPC is enabled when the microgrid is operating at ω0 andV0. In a black start scenario, this state is achieved when theprimary control level operates without load.

The computational cost is also related to the QP feasibility.Range and final value constraints limit the feasible solutionspace of the QP problem; then, the computational cost to solveit is also reduced [20]. In this case, we use the QPKWIKalgorithm to solve the QP problem (??), which is an efficientand stable variation of the classic active-set method [26].

GOMEZ et al.: DISTRIBUTED PREDICTIVE CONTROL FOR FREQUENCY AND VOLTAGE REGULATION IN MICROGRIDS 5

IV. EXPERIMENTAL SETUP AND RESULTS

A. Experimental Setup

To validate the proposed DMPC strategy, an experimen-tal setup was built in the Microgrids Control Lab. of theUniversity of Chile. The setup uses PM15F120 and PM5F60Triphase R© modules to emulate a three DG microgrid. Eachmodule is controlled by a real-time target (RTT) computer,where the DMPC for each DG is downloaded. External mea-surement devices were connected to the measurement nodes,and these have direct communication with their respectiveRTTs. A diagram of the setup is shown in Fig. 2, and a photoregister is shown in Fig. 3. In Table I and Table II, electricaland droop parameters are presented.

L1

V2, 2, 2θ ω

2 = 2­ 2*δθ θ θ

V1, 1, 1θ ωV1*, 1*, 1*θ ω

1 = 1­ 1*δθ θ θ

Z1L12

V2*, 2*, 2*θ ω

L2

V3, 3, 3θ ω3 = 3­ 3*δθ θ θ

V3*, 3*, 3*θ ω

L3

L23Z2

Ethernet

Communication

Optical Communication

Direct

Communication

Fig. 2. Experimental Microgrid Diagram.

PM15F120: U1 + U2

PM5F60: U3

RTT U3

RTT U1 + U2

Z2

Z1

Measurements U3

RTT: Real Time Target

Measurements U1 + U2

L3 + L23

L1 + L12 + L2

Fig. 3. Experimental Setup.

TABLE IMICROGRID ELECTRICAL PARAMETERS

Parameter Description ValueTprim Primary Level Sampling Period 1/16E3 sZ1 Load 1 11 ΩZ2 Load 2 22 ΩLi Coupling Inductance 2.5 mHLij Transmission Line Inductance 2.5 mHω0 Nominal Frecuency 314.159 rad/sV0 Nominal Voltage (peak) 150 Vωc Cutoff Frecuency - Droop Controller 2π rad/s

TABLE IIPOWER CAPACITIES AND DROOP SLOPES

Power Capacities and Droop Slopes DG1 DG2 DG3

Smax [KVA] Power Capacity 2.4 1.92 1.2

Mpω

[rads W

]P-ω Droop Slope -1E-4 -1.5E-4 -2.5E-4

Mqv[ V

VAR

]Q-V Droop Slope -1E-3 -1.5E-3 -1.8E-3

The weighting factors used in the cost function allowmanaging the tradeoff among the control objectives, and ifrequired, giving priority to one of the control objectives overthe other ones. In Table III and Table IV, the DMPC generalparameters and weighting factors are shown. PI inner loopsgains and other parameters that are not relevant to DMPC areomitted in this paper.

TABLE IIIDMPC GENERAL PARAMETERS

Parameter Description ValueTsec Secondary Level Sampling Period 0.05 sτij Estimated Communication Delay 0.05 sNy Prediction Horizon 10Nu Control Horizon 10Vmax Maximum Voltage 155VVmin Minimum Voltage 145V

TABLE IVDMPC WEIGHTING FACTORS

Weighting Factors DG1 DG2 DG3

λ1[ s

rad

]2 Average Frequency Error 3E4 5E4 9E4

λ2[1V

]2 Average Voltage Error 5E0 6E0 7E0

λ3[ s

rad

]2 Frequency Control Action 8E4 8E4 9E5

λ4[1V

]2 Voltage Control Action 5E3 5E3 5E3

λ5[VA

W

]2 Real Power Consensus 1.5E2 1.3E2 2E2

λ6[ VA

VAR

]2 Reactive Power Consensus 5E3 2E3 1E3

Four scenarios were implemented with the experimentalsetup using the proposed DMPC. The first (base case) scenarioshows the DMPC performance when the microgrid is disturbedwith load changes. In the second scenario, a communicationfailure between DG1 and DG2 is forced while the microgridis disturbed. The third scenario is a PnP test, where DG3 isdisconnected and reconnected to the microgrid. Finally, thefourth scenario shows the microgrid performance when thelatency changes over the communication network.

B. Test Scenario 1 (Base Case)- Load Changes

This scenario tests the microgrid behavior using the pro-posed DMPC when several load changes are applied. In thiscase, the microgrid begins without load, and at t = 38s, loadZ1 is connected to the microgrid; at t = 58s, the total load inthe microgrid is composed of Z1 and Z2; and at t = 78s andt = 98s, the load is reduced to Z1 and zero, respectively.

In Fig. 4 and Fig. 6, it is shown that the average frequencyand average voltage are regulated; however, voltage deviationsover each DG caused by the microgrid heterogeneity areobserved. Fig. 5 and Fig. 7 show that the consensus of real

6 IEEE TRANSACTIONS ON SMART GRID

and reactive power are achieved. In these figures, the powercontribution of each DG is normalized with respect to itscapacity.

40 50 60 70 80 90 100 110Time [s]

49.8

49.85

49.9

49.95

50

50.05

50.1

Freq

uenc

y [H

z]

Microgrid Frequency - DMPC Control

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

49.8

49.85

49.9

49.95

50

50.05

50.1

Freq

uenc

y [H

z]

Microgrid Frequency - Droop Control

DG 1DG 2DG 3

!"!" + !$

!$

No Load

!" !" + !$

!$ No Load

Fig. 4. Frequency Regulation Against Load Changes - DMPC Base Case.40 50 60 70 80 90 100 110

Time [s]

0

0.1

0.2

0.3

0.4

0.5

0.6

Nor

mal

ized

Rea

l P

ower

[W/V

A]

Microgrid Real Power - Droop Control

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

0

0.1

0.2

0.3

0.4

0.5

0.6

Nor

mal

ized

Rea

l P

ower

[W/V

A]

Microgrid Real Power - DMPC Control

DG 1DG 2DG 3

!"

!" + !$

!$

No Load

!" !" + !$

!$ No Load

Fig. 5. Real Power Consensus Against Load Changes - DMPC Base Case.40 50 60 70 80 90 100 110

Time [s]

149

149.5

150

150.5

151

Vd [V

]

Microgrid Direct Voltage - Droop Control

DG 1DG 2DG 3Average

40 50 60 70 80 90 100 110Time [s]

149

149.5

150

150.5

151

Vd [V

]

Microgrid Direct Voltage - DMPC Control

DG 1DG 2DG 3Average

!"

!" + !$

!$

No Load

!"

!" + !$!$

No Load

Fig. 6. Voltage Regulation Against Load Changes - DMPC Base Case.40 50 60 70 80 90 100 110

Time [s]

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Nor

mal

ized

Rea

ctiv

e P

ower

[VA

R/V

A]

Microgrid Reactive Power - Droop Control

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Nor

mal

ized

Rea

ctiv

ePo

wer

[VA

R/V

A]

Microgrid Reactive Power - DMPC Control

DG 1DG 2DG 3

!"

!" + !$

!$

No Load

!"

!" + !$ !$

No Load

Fig. 7. Reactive Power Consensus Against Load Changes - DMPC BaseCase.

Over the whole test, the microgrid is preserved as in Fig. 2,and the disturbances are limited to load changes. In this case,the adjacency matrix is constant and given by (12).

A(t) =

a11 a12 a13a21 a22 a23a31 a32 a33

=

0 1 11 0 11 1 0

(17)

This test scenario shows the basic microgrid operation, andit is considered as a base case for comparisons with the nextscenarios tested in this paper.

C. Test Scenario 2 - Communication Path Failure

This scenario adds to the base case a failure over thecommunication path between DG1 and DG2 at t = 50s. Thisfailure is kept until the end of the test. This type of failurecan be understood as a physical failure over the communi-cation path or a simple data packet loss. In this case, as theadjacency matrix is a function of the information received foreach controller, it is updated when the communication fails,preserving the average values.

The microgrid response is shown in Fig. 8. From the results,it is possible to state that the microgrid remains stable, achiev-ing the four control objectives (frequency/voltage regulationand real/reactive power consensus) even when the communi-cation path fails, it can be understood as a communication faulttolerance feature of the proposed DMPC; however, as shown inFig. 9, a difference in the transient state is observed when loadchanges are applied. This change is caused by the relationshipbetween the adjacency matrix and the cost function (11); asthe adjacency terms are updated, but not the weighting factors,the tuned parameters do not compensate the load changes aswhen the communication network is complete.

40 50 60 70 80 90 100 110Time [s]

49.8

49.9

50

50.1

Freq

uenc

y [H

z]

Microgrid Frequency - DMPC Control

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

0

0.2

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0.6

Nor

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ized

Rea

l P

ower

[W/V

A]

Microgrid Real Power - DMPC Control

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

149

150

151

Vd [V

]

Microgrid Direct Voltage - DMPC Control

DG 1DG 2DG 3Average

40 50 60 70 80 90 100 110Time [s]

-0.02

0

0.02

0.04

Nor

mal

ized

Rea

ctiv

e P

ower

[VA

R/V

A]

Microgrid Reactive Power - DMPC Control

DG 1DG 2DG 3

𝑍" 𝑍"+𝑍#

𝑍#

No load

Communication Failure

Fig. 8. Microgrid Response Against Communication Failure Between DG1

and DG2.

GOMEZ et al.: DISTRIBUTED PREDICTIVE CONTROL FOR FREQUENCY AND VOLTAGE REGULATION IN MICROGRIDS 7

60 70 80

0.2

0.3

0.4

0.5

0.6

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ower

[W/V

A]

Microgrid Real Power - Without Communication Failure

DG 1DG 2DG 3

60 70 80

0.2

0.3

0.4

0.5

0.6

Microgrid Real Power - With Communication Failure

DG 1DG 2DG 3

60 70 80Time [s]

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Nor

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ized

Rea

ctiv

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ower

[VA

R/V

A]

Microgrid Reactive Power -Without Communication Failure

DG 1DG 2DG 3

60 70 80Time [s]

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Microgrid Reactive Power - With Communication Failure

DG 1DG 2DG 3

!"+!#

!#

!"+!#

!#

!"+!#

!#

!"+!#

!#

$ % =0 1 11 0 11 1 0

$ % =0 0 10 0 11 1 0

𝐴 𝑡 =0 1 11 0 11 1 0

𝐴 𝑡 =0 0 10 0 11 1 0

Fig. 9. Consensus Detail - Microgrid Response Against CommunicationFailure Between DG1 and DG2.

D. Test Scenario 3 - Plug and Play CapabilityThis test shows the microgrid response when DG3 fails and

it is disconnected (at t ≈ 49s), and after a synchronizationsequence, it is reconnected to the microgrid (at t ≈ 75s).When DG3 is disconnected from the microgrid, its secondarycontrol is disabled, and after the reconnection, it is enabledagain. Fig. ?? shows a power distribution according to theDGs connected to the microgrid. Because the adjacency matrixA(t) depends on the information received by each DG, it isupdated when DG3 is disconnected and reconnected, adjustingthe consensus and the average values in the optimizationproblem. Between t ≈ 75s and t ≈ 78s, the real andreactive power contributions of DG3 are not in consensus eventhough it is connected to the microgrid. In this period, DG3

is synchronized (δθ3 = 0), and its secondary controller isdisabled; then, according to (4) and (5), only the reactivepower flow through L3 is feasible. When the secondarycontroller is enabled on DG3, the power consensus amongthe three units is re-established.

E. Test Scenario 4 - Communication Delay ResponseThis scenario compares the microgrid response at different

values of τij but preserving τij at one sampling period (0.05s).For each test, the same load changes from scenario 1 areapplied. The results for frequency regulation and real powerconsensus are shown in Fig. ?? and Fig. ??, respectively.From the results, it is possible to state that the microgridresponse increases its overshoot and its settling time when thecommunication delay also increases; however, the microgridachieves the control objectives even when the delay is twentytimes the sampling period (Tsec).

40 50 60 70 80 90 100Time [s]

-0.2

0

0.2

0.4

0.6

0.8

Nor

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ized

Rea

l Pow

er [W

/VA

]

Microgrid Real Power - Plug and Play Scenario

DG 1DG 2DG 3

40 50 60 70 80 90 100Time [s]

0

0.05

0.1

0.15

Nor

mal

ized

Rea

ctiv

e Po

wer

[VA

R/V

A] Microgrid Reactive Power - Plug and Play Scenario

DG 1DG 2DG 3

!"

!" +!$!$

DG 3 Disconnection

DG 3 Reconnection

DG 3 DMPC enabled

!"

!" +!$!$

DG 3 Disconnection

DG 3 ReconnectionDG 3 DMPC enabled

%&'()=2.4KVA%&'(*=1.92KVA%&'(+=1.2KVA

DG1: 908 WDG2: 725 WDG3: 450 W

DG1: 1174 WDG2: 940 WDG3: 0 W

DG1: 1733 WDG2: 1388 WDG3: 0 W

DG1: 1341 WDG2: 1075WDG3: 676 W

, - =0 1 11 0 11 1 0

, - =0 1 01 0 00 0 0

, - =0 1 11 0 11 1 0

DG1: 40.5 VARDG2: 26.7 VARDG3: 16.9 VAR

DG1: 49.58 VARDG2: 39.19 VARDG3: 0 VAR

DG1: 80.9 VARDG2: 64.8 VARDG3: 0 VAR

DG1: 13.4 VARDG2: 16.3 VARDG3: 124 VAR

DG1: 54.1 VARDG2: 44.2 VARDG3: 27.9 VAR

DG 3 DMPC disabled

DG 3 DMPC disabled

Fig. 10. Real Power (top) and Reactive Power (bottom) Behavior - Plug andPlay Test

40 50 60 70 80 90 100 110Time [s]

49.8

49.9

50

50.1

50.2

Freq

uenc

y [H

z]

Microgrid Frequency - Delay 0.25 s

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

49.8

49.9

50

50.1

50.2

Freq

uenc

y [H

z]

Microgrid Frequency - Delay 0.50 s

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

49.8

49.9

50

50.1

50.2

Freq

uenc

y [H

z]

Microgrid Frequency - Delay 1 s

DG 1DG 2DG 3

𝑍" 𝑍"+𝑍#

𝑍#

No load

𝑍" 𝑍"+𝑍#

𝑍#

No load

𝑍" 𝑍"+𝑍#

𝑍#

No load

Fig. 11. Microgrid Behavior with Communication Delays- Frequencyresponse- top:τij = 0.25s middle:τij = 0.5s bottom:τij = 1s

The DMPC latency compensation is related to the rollingprediction/control horizons, the sampling period and the delayestimation τij ; however, either longer horizons or a shortersampling period increase the computational effort. Even whenthe optimization problem is solved based on delayed infor-mation from neighboring DGs, the rolling horizon schemeupdates the control sequence each sampling period, compen-

8 IEEE TRANSACTIONS ON SMART GRID

40 50 60 70 80 90 100 110Time [s]

0

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ower

[W/V

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Microgrid Real Power - Delay 1 s

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

0

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ower

[W/V

A]

Microgrid Real Power - Delay 0.25s

DG 1DG 2DG 3

40 50 60 70 80 90 100 110Time [s]

0

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0.6

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ized

Rea

l P

ower

[W/V

A]

Microgrid Real Power - Delay 0.50s

DG 1DG 2DG 3

𝑍" 𝑍"+𝑍#𝑍# No load

𝑍" 𝑍"+𝑍#𝑍# No load

𝑍" 𝑍"+𝑍#𝑍# No load

Fig. 12. Microgrid Behavior with Communication Delays- Real Powerresponse- top:τij = 0.25s middle:τij = 0.5s bottom:τij = 1s

sating latency effects even beyond the prediction horizon.

V. CONCLUSIONS AND FINAL REMARKS

In this paper, a distributed predictive controller was pre-sented to regulate the frequency and average voltage and toachieve real and reactive power consensus in the microgrid.The main contribution of this paper is the proposed modelused to solve the DMPC, which is based on droop, powertransfer and phase angle equations. The proposed formulationincludes explicit operational constraints to ensure operationof the microgrid within feasible ranges, and it is able tomodify its adjacency matrix according to either electrical orcommunications disturbances.

The experimental results showed that the proposed con-troller has good performance against electrical disturbancessuch as load changes or disconnection/reconnection of DGs.Additionally, a good microgrid performance was achievedagainst communication issues such as latency and data packetlosses.

Finally, as future work, the application of this type of DMPCto hybrid AC/DC microgrids with energy storage systems issuggested.

ACKNOWLEDGMENT

Juan S. Gomez has been supported by a Ph.D. schol-arship from the CONICYT-PCHA/Doctorado Nacional paraextranjeros/2015- 21150555. This study was partially sup-ported by the FONDECYT 1170683 grant, Complex Engi-neering Systems Institute (CONICYT – PIA – FB0816), SolarEnergy Research Center SERC-Chile (CONICYT/FONDAP/Project under Grant 15110019) and the NSERC DiscoveryGrant RGPIN- 2017-04008.

REFERENCES

[1] R. Patton, C. Kambhampati, A. Casavola, P. Zhang, S. Ding, andD. Sauter, “A Generic Strategy for Fault-Tolerance in Control SystemsDistributed Over a Network,” European Journal of Control, vol. 13, no.2-3, pp. 280–296, jan 2007.

[2] M. Tucci and G. Ferrari-Trecate, “A scalable line-independent designalgorithm for voltage and frequency control in AC islanded microgrids,”CoRR, vol. abs/1703.02336, 2017.

[3] S. Riverso, F. Sarzo, and G. Ferrari-Trecate, “Plug-and-Play Voltageand Frequency Control of Islanded Microgrids With Meshed Topology,”IEEE Transactions on Smart Grid, vol. 6, no. 3, pp. 1176–1184, may2015.

[4] R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and Coop-eration in Networked Multi-Agent Systems,” Proceedings of the IEEE,vol. 95, no. 1, pp. 215–233, jan 2007.

[5] F. Bullo, “Lectures on Network Systems,” in Lectures on NetworkSystems, 2018, ch. 4, pp. 47–61, with contributions by J. Cortes, F.Dorfler, and S. Martinez.

[6] J. W. Simpson-Porco, Q. Shafiee, F. Dorfler, J. C. Vasquez, J. M.Guerrero, and F. Bullo, “Secondary Frequency and Voltage Control ofIslanded Microgrids via Distributed Averaging,” IEEE Transactions onIndustrial Electronics, vol. 62, no. 11, pp. 7025–7038, nov 2015.

[7] L. Zhang, H. Gao, and O. Kaynak, “Network-Induced Constraintsin Networked Control Systems—A Survey,” IEEE Transactions onIndustrial Informatics, vol. 9, no. 1, pp. 403–416, feb 2013.

[8] Y.-B. Zhao, X.-M. Sun, J. Zhang, and P. Shi, “Networked ControlSystems: The Communication Basics and Control Methodologies,”Mathematical Problems in Engineering, vol. 2015, pp. 1–9, 2015.

[9] C. Ahumada, R. Cardenas, D. Saez, and J. M. Guerrero, “SecondaryControl Strategies for Frequency Restoration in Islanded MicrogridsWith Consideration of Communication Delays,” IEEE Transactions onSmart Grid, vol. 7, no. 3, pp. 1430–1441, may 2016.

[10] S. Liu, X. Wang, and P. X. Liu, “Impact of Communication Delayson Secondary Frequency Control in an Islanded Microgrid,” IEEETransactions on Industrial Electronics, vol. 62, no. 4, pp. 2021–2031,apr 2015.

[11] Y. Xu, H. Sun, W. Gu, Y. Xu, and Z. Li, “Optimal Distributed Control forSecondary Frequency and Voltage Regulation in an Islanded Microgrid,”IEEE Transactions on Industrial Informatics, vol. 3203, no. c, pp. 1–1,2018.

[12] G. Chen and Z. Guo, “Distributed Secondary and Optimal Active PowerSharing Control for Islanded Microgrids with Communication Delays,”IEEE Transactions on Smart Grid, vol. 3053, no. c, pp. 1–1, 2017.

[13] L. Liang, Y. Hou, and D. J. Hill, “Design guidelines for MPC-basedfrequency regulation for islanded microgrids with storage, voltage, andramping constraints,” IET Renewable Power Generation, vol. 11, no. 8,pp. 1200–1210, jun 2017.

[14] Y. Zhang, L. Fu, W. Zhu, X. Bao, and C. Liu, “Robust model predictivecontrol for optimal energy management of island microgrids withuncertainties,” Energy, vol. 164, pp. 1229–1241, dec 2018.

[15] L. G. Marın, N. Cruz, D. Saez, M. Sumner, and A. Nunez, “Predictioninterval methodology based on fuzzy numbers and its extension to fuzzysystems and neural networks,” Expert Systems with Applications, vol.119, pp. 128–141, apr 2019.

[16] M. H. Andishgar, E. Gholipour, and R. allah Hooshmand, “An overviewof control approaches of inverter-based microgrids in islanding mode ofoperation,” pp. 1043–1060, dec 2017.

[17] D. E. Olivares, A. Mehrizi-Sani, A. H. Etemadi, C. A. Canizares,R. Iravani, M. Kazerani, A. H. Hajimiragha, O. Gomis-Bellmunt,M. Saeedifard, R. Palma-Behnke, G. A. Jimenez-Estevez, and N. D.Hatziargyriou, “Trends in Microgrid Control,” IEEE Transactions onSmart Grid, vol. 5, no. 4, pp. 1905–1919, jul 2014.

[18] P. Sina, “State of the art in research on Microgrids.” IEEE Access, vol. 3,no. 1, pp. 890–925, 2015.

[19] P. D. Christofides, R. Scattolini, D. Munoz de la Pena,and J. Liu, “Distributed model predictive control: A tutorialreview and future research directions,” Computers & ChemicalEngineering, vol. 51, pp. 21–41, apr 2013. [Online]. Available:https://linkinghub.elsevier.com/retrieve/pii/S0098135412001573

[20] E. F. Camacho and C. Bordons, “Constrained Model Predictive Control,”in Model Predictive control, 2nd ed., ser. Advanced Textbooks in Controland Signal Processing. London: Springer London, 2007, no. december,ch. 7, pp. 177–216.

[21] R. M. Hermans, A. Jokic, M. Lazar, A. Alessio, P. P. van den Bosch,I. A. Hiskens, and A. Bemporad, “Assessment of non-centralised model

GOMEZ et al.: DISTRIBUTED PREDICTIVE CONTROL FOR FREQUENCY AND VOLTAGE REGULATION IN MICROGRIDS 9

predictive control techniques for electrical power networks,” Interna-tional Journal of Control, vol. 85, no. 8, pp. 1162–1177, aug 2012.

[22] G. Lou, W. Gu, W. Sheng, X. Song, and F. Gao, “Distributed ModelPredictive Secondary Voltage Control of Islanded Microgrids WithFeedback Linearization,” IEEE Access, vol. 6, pp. 50 169–50 178, 2018.

[23] A. J. Babqi and A. H. Etemadi, “MPC-based microgrid control with sup-plementary fault current limitation and smooth transition mechanisms,”IET Generation, Transmission & Distribution, vol. 11, no. 9, pp. 2164–2172, jun 2017.

[24] D. Clarke and R. Scattolini, “Constrained receding-horizon predictivecontrol,” IEE Proceedings D Control Theory and Applications, vol. 138,no. 4, p. 347, 1991.

[25] B. Kouvaritakis and M. Cannon, “MPC with No Model Uncertainty,”in Model Predictive Control, ser. Advanced Textbooks in Control andSignal Processing. Cham: Springer International Publishing, 2016,ch. 2, pp. 13–64.

[26] C. Schmid and L. Biegler, “Quadratic programming methods for reducedhessian SQP,” Computers & Chemical Engineering, vol. 18, no. 9, pp.817–832, sep 1994.

[27] F. Bullo, “Lectures on Network Systems,” in Lectures on NetworkSystems, 2018, ch. 2, pp. 15–28, with contributions by J. Cortes, F.Dorfler, and S. Martinez.

[28] ——, “Lectures on Network Systems,” in Lectures on Network Systems,2018, ch. 10, pp. 167–179, with contributions by J. Cortes, F. Dorfler,and S. Martinez.