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Control Engineering Practice 53 (2016) 184–193
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Control Engineering Practice
http://d0967-06
n CorrE-m
mohamKwang_
journal homepage: www.elsevier.com/locate/conengprac
Distributed generation system control strategies with PV and fuel cellin microgrid operation
Wenlei Bai n, M. Reza Abedi, Kwang Y. LeeBaylor University, Waco, TX 76706, USA
a r t i c l e i n f o
Article history:Received 11 May 2015Received in revised form4 February 2016Accepted 5 February 2016Available online 17 February 2016
Keywords:Distributed generationPVSOFCMicrogridDroop controlPQ controlArtificial bee colony (ABC)Heuristic optimization
x.doi.org/10.1016/j.conengprac.2016.02.00261/& 2016 Elsevier Ltd. All rights reserved.
esponding author.ail addresses: [email protected] (W. Bai)[email protected] (M.R. Abedi),[email protected] (K.Y. Lee).
a b s t r a c t
Control strategies of distributed generation (DG) are investigated for different combination of DG andstorage units in a microgrid. In this paper the authors proposed a microgrid structure which consists of adetailed photovoltaic (PV) array model, a solid oxide fuel cell (SOFC) and various loads. Real and reactivepower (PQ) control and droop control are developed for microgrid operation. In grid-connected mode,PQ control is developed by controlling the active and reactive power output of DGs in accordance withassigned references. Two PI controllers were used in the PQ controller, and a novel heuristic method,artificial bee colony (ABC), was adopted to tune the PI parameters. DGs can be controlled by droopcontrol both under grid-connected and islanded modes. Droop control implements power reallocationbetween DGs based on predefined droop characteristics whenever load changes or the microgrid isconnected/disconnected to the grid, while the microgrid voltage and frequency is maintained at ap-propriate levels. Through voltage, frequency, and power characteristics in the simulation under differentscenarios, the proposed control strategies have demonstrated to work properly and effectively. The si-mulation results also show the effectiveness of tuning PI parameters by the ABC.
& 2016 Elsevier Ltd. All rights reserved.
1. Introduction
A microgrid is a system that aggregates generators, consumers,energy storage devices and hybrid devices such as electric vehicleswhich are able to both produce and consume energy. In general,microgrid is considered as a localized grid where a cluster of dis-tributed generators (DGs) are connected to the main utility grid,usually through voltage source converter (VSC) based interfaces(Cho et al., 2011). The key factor of microgrid is that it can bedisconnected from the main grid, operating autonomously to en-hance the resiliency of the power grid. Distributed generation (DG)technologies, such as photovoltaics (PV), wind energy, fuel cell,storage system, etc., are the main parts in microgrid (Puttgen,MacGregor & Lambert, 2003).
DGs encompass a wide range of technologies, such as windpower, micro turbines, internal combustion engines, gas turbines,photovaltaics (PV), fuel cells, and storage systems. However thechallenges rise up at the same time in controlling a potentiallyhuge number of DGs, and operating the network safely and effi-ciently (Hatziargyriou, Asano, Iravani & Marnay, 2007). This chal-lenge can be partially addressed by the proper design and control
,
of power electronic devices. (Ebad & Song, 2012). For example, if aPV system needs to be connected to the grid, a converter whichconverts the output voltage to a certain voltage level and an in-verter which transfer the DC voltage to three-phase AC are needed.The interface between distributed generators and grid is calledpower conditioning system which places a vital role of regulatinghigh quality power that injects to the grid (Wu, Lee & Yang, 2013).Microgrid can operate in two modes: grid-connected mode andislanded mode. In normal grid-connected mode power will besupplied to loads either though the main grid or the microgrid;however when there is a failure in the main grid, microgrid willdisconnect itself from the grid and operate in an islanded mode.
Different from traditional utility grid, a microgrid contains DGsthrough VSC to interface with utility. The VSC have more con-trolled variables than the commonly used synchronous generators(Tan, So & Chu, 2010). Thus one of the key problems in microgridoperation is to determine control strategies. When load changes ordisconnection occur, controllers need to coordinate DGs to guar-antee power quality and meet the demand in the microgrid. In Caiand Mitra (2010), decentralized control using multi-agent systemsapproach is implemented by using only the local information ofDGs. The decentralized architecture of the microgrid is equippedwith power electronic devices and all the agents are working au-tonomously and equally. The agents only communicate with theirneighbors to achieve power balancing to maintain voltageand frequency. However this method requires large amount
PV(MPPT)
FC
Breakerload1
load2
R1 L1
R2 L2 380v:13.8×103 v
load3
LgRg
Lf1
Cf1 Transformer
PCC
VSI
VSI
PWM
PWM
Cf2
Lf2
Fig. 1. Schematic of a microgrid, which is powered by a PV and FC and connected to the main power grid at PCC. The circuit breaker indicates the status of grid-connectedmode and islanded mode of operation.
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193 185
of communication, which increases the complexity when im-plemented for control.
In (Barsali, Ceraolo, Pelacchi & Poli, 2002) voltage and fre-quency (V/f) control was implemented to control DGs in an is-landed mode by maintaining voltage and frequency at references.However pure V/f controller for DGs in islanded mode is not ableto respond to load changes, thus in Chen, Wang and Wang (2013),a master–slave control configuration of a microgrid is built. Ingrid-connected mode all DGs are equipped with PQ controllers,and under islanded mode only the master inverter switches to V/fcontrol to maintain the microgrid voltage level and frequency. Thedrawback of master–slave method is that it also takes largeamount of communication. In practical microgrid operation, con-trollers for different types of DGs vary extensively. For example,micro turbines and fuel cell can be equipped with either PQ con-troller to follow real and reactive power references or V/f con-troller to maintain stability of microgrid's voltage and frequency;however for renewable energy DGs such as wind turbine and PV,due to their intermittency, PQ controller will have to be used tomaximize renewable energy.
The use of droop characteristics concepts is commonly used incontrolling generating units in power system (Kundur, 1993). Interms of the interfacing a microgrid to the utility grid, DGs shouldachieve proper load sharing. By retrieving the grid parameterssuch as the voltage, frequency, grid impedance, the inverters basedon droop control method are able to inject real and reactive powerto the grid (Vasquez, Guerrero, Luna, Rodriguez & Teodorescu,2009). A detailed hierarchical droop control strategy has beenproposed to manage power between distributed generation andgrid (Guerrero, Vasquez, Matas, Vicuna & Castilla, 2011). In orderto enhance dynamic performance of parallel inverters, researchershave developed a novel droop control method by utilizing thelocally measureable feedback signals (Guerrero, Vicuna, Matas,Castilla & Miret, 2004). We want to implement a load sharing withminimal communication because of the complexity of networksystem and thus droop control method is adopted in this paper.Both PV and DG were carried out with PQ control in grid-con-nection mode, while they were switched into droop control oncedisconnected from the grid.
In order to operate microgrid under both modes effectively bysatisfying the load demand and voltage/frequency stability, whileminimizing the communication between DGs in microgrid control,a PQ controller and droop controller are adopted in this paper. Thecontrol strategies presented here is to overcome the drawback ofpure V/f control which leads to the failure of responding to loadchanges while requiring less communication compared to themaster–slave control. PI controllers are the most common solutionin industry (Sun, Li & Lee, 2015), and they were used in both PQand droop controllers. However, the tuning process, in many cases,is made by extensive trial and error approaches, which is verytime-consuming (Kishnani, Pareek & Gupta, 2014). To tackle the
problem, we proposed a novel heuristic method, artificial beecolony (ABC), to find the optimal PI parameters. The main ad-vantage of heuristic method is that without the complete in-formation of system and the knowledge of tuning parameters it isable to find optimal parameters by intelligent search process.
The paper is organized as follows: Section 2 describes theproposed architecture of the microgrid, and PV model, the solidoxide fuel cell (SOFC) and controller design process was describedin Section 3. In Section 4, ABC is introduced first and the im-plementation of ABC to PI parameters tuning is presented. Theperformance of the proposed controller is tested and results areshown in simulation in Section 5. Finally the conclusion is drawnin Section 6 with recommendation for future works.
2. Microgrid architecture
In order to test the effectiveness and efficiency of controllers, amicrogrid structure is developed as shown in Fig. 1. The microgridcontains one PV array and one SOFC. The PV provides DC voltage,and MPPT was implemented to obtain the maximum power re-ference for PV.
In Fig. 1, PV and FC are connected to voltage source inverters(VSI) controlled by pulse width modulation (PWM) controller. TheVSI converts DC voltage to AC voltage and then the power gothrough a low pass LC filter to filter high frequency noise. Load1 and load 2 are connected to PV and FC after filters, respectively,and load 3 is connected at the point of common coupling (PCC).DGs are connected to the main grid through transmission line,circuit breakers and transformers. The voltage ratio of transformeris 380:13.8�103 (v). Note that both PV and SOFC implements PQcontroller under grid-connected mode and droop controller can beimplemented under either grid-connected or islanded mode. Inthis paper the PV was modeled as a current source in parallel withan ideal diode. The SOFC is a dynamic model characterizing re-lationship between the input fuel and output voltage.
3. PV model and controller design
3.1. PV model
The main component of a solar panel is a solar cell. A singlesolar cell can be modeled as a current source connected with onediode and two resistors (Fig. 2). A photovoltaic (PV) module is builtby simply connecting many solar cells in series and parallel.
The characteristic equation for a single solar cell can be foundin the paper of Villalva, Gazoli and Ruppert (2009):
Iph
IdIsh
Rs I
VRsh
Fig. 2. Single diode model of a solar cell.
START
V(k) - V(k-1) >0 V(k) - V(k-1) >0
Decrease V(ref)
Increase V(ref)
UpdateV(k-1)=V(k)P(k-1)=p(k)
Decrease V(ref)
Increase V(ref)
YN
Y N N Y
ΔP>0?
MeasureV(k) I(k)
P(k) = V(k)×I(k)ΔP = P(k) - P(k-1)
Fig. 4. The MPPT with Perturb and Observe method.
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193186
( )= −
+− −
+
( )⎪ ⎪
⎪ ⎪⎧⎨⎩
⎡⎣⎢⎢
⎤⎦⎥⎥
⎫⎬⎭
I I Iq V R I
nkTV R I
Rexp 1
1ph
s s
sh0
where V is output voltage, I is output current, I0 is cell reversesaturation current, Iph is light-generated current, q is electroncharge, 1.6�10�23 (C), T is cell temperature in Celsius, k is Bolt-zamann's constant, 1.38�10�19 (J/k), Rsh is shunt resistance and Rsis series resistance. For actual non-ideal diode, ideality factor n isintroduced in the denominator of the exponent, which rangesfrom 1 to 2, representing the defects from ideal diode.
The P–V and I–V curves are important two indicators to char-acterize properties of a solar cell. Fig. 3 shows the effect of solarirradiation variation (from 200 to 1000 (w/m2)) on P–V and I–Vcurves for the solar cell used in this paper.
3.2. Maximum power point tracking
The efficiency of a solar cell is very low; however, if the PVsource and load can be matched properly, the efficiency will beincreased. One such method is the so-called maximum powerpoint tracking (MPPT). As the P–V and I–V curves indicate in Fig. 3,when the output voltage increases, power increases first and thendrops, thus there exists a voltage corresponding to the maximumpower output. This voltage can be found and maintained by uti-lizing a boost converter whose duty cycle is controlled by theMPPT algorithm. Perturb and Observe (P&O) method (Ropp &Gonzalez, 2009) is used to implement the MPPT, and the algorithmis based on the calculation of the PV array current and voltage.
The P&O is demonstrated in a flow chart in Fig. 4. Given avoltage perturbation first, then V(k) and I(k) are sampled at time k,and then calculate power P(k)¼V(k)� I(k). Compare P(k) with P(k�1); if power increases, keep searching in the same direction,while if power decreases, search in the opposite direction to getfinal output voltage V. The P&O method leads to power oscillationabout MPP, and reducing the voltage perturbation step size can
0 5 10 15 20 25 30 35 400
1
2
3
4
5
6
7
8
9
10
voltage (V)
curre
nt(A
)
200(W/m2)500(W/m2)
800(W/m2)1000(W/m2)
Fig. 3. I–V and P–V curves for
minimize the oscillation. However, small step size slows down theMPPT. For different values of irradiance and cell temperatures, thePV array would exhibit different characteristic curves and eachcurve has its MPPT. The maximum voltage corresponding to thispoint is supplied to the converter as the reference voltage.
3.3. Solid oxide fuel cell (SOFC)
The solid oxide fuel cell (SOFC) is one of the most promisingfuel cell technologies (Padullés, Ault & McDonald, 2000). It con-verts the chemical energy to electrical energy during the electro-chemical reaction of hydrogen and oxygen. Hydrogen is suppliedinto the anode (negative post) and catalytically split into protonsand electrons. The electrons are flowing through external circuit;at cathode (positive post) side, oxygen is delivered to form reac-tion with protons and the electrons arriving through the externalcircuit to formwater molecules. The protons permeate through thepolymer electrolyte membrane.
The model in this study is based on the dynamic SOFC stackmodel developed in Padullés' work (Padullés, Ault and McDonald,
0 5 10 15 20 25 30 35 400
50
100
150
200
250
voltage (V)
pow
er(W
)
200(W/m2)
500(W/m2)
800(W/m2)
1000(W/m2)
different solar irradiation.
Fig. 5. SOFC stack dynamic model.
Grid
VdcLf
RgLg
+-
P,Q_ref
iL ig
ug,abc
iL,abc
Three Phase Inverter
LCL FilterT1
T2
T3
T4
T5
T6RfCf
PLL
dqabc
Power Control
uduq
PI Current Control
id_ref
iq_ref
ω
ud_ref
uq_ref
id
iq
PWMuref abc
dq
Fig. 6. Schematic of the PQ control for VSI.
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193 187
2000). Based on the hydrogen, water and oxygen partial pressureequations the block diagram of the SOFC stack dynamic model isshown in Fig. 5.
By Nernst equation and Kirchhoff’s voltage law (KVL), the stackoutput voltage can be described by the following expression:
= + −( )
⎡
⎣⎢⎢
⎛⎝⎜⎜
⎞⎠⎟⎟⎤
⎦⎥⎥V N E
RTF
p p
prI
2ln
2
H O
H OFC0 0
2 2
2
where H2, H2O and O2 represent hydrogen, water and oxygenmolar species. For i¼H2, H2O or O2, Ki is the valve molar constant[(kmol kg)0.5(atm s)�1], Mi is the molar mass [kg kmol�1], pi ispartial pressure, qi is molar flow [kmol s�1], qi
in is input molar flow
[kmol s�1], qiout is output molar flow [kmol s�1], qi
r is flow thatreact [kmol s�1], and τi is time constant [s]. IFC is FC stack current[A], Kr is modeling constant [kmol (s A)�1], N0 is number of seriesfuel cells in the stack, R is universal gas constant [(J) (kmol K)�1], Tis absolute temperature [K], F is the Faraday's constant[C (k mol)�1], r is the ohmic losses of the stack, E0 is standard noload voltage [V], and V is the stack output voltage [V]. It should benoted that the partial pressure pi is defined as the ratio of con-centrations (actual concentration divided by the reference con-centration); hence, it does not contain units.
SOFC is operating in parallel with PV, and when PV is notgenerating power during night or cloudy day, the FC can be con-sidered as constant source to supply power.
3.4. Power flow control and PQ controller design
In the grid-connected operation mode, the main function of aDG is to generate the real and reactive power, where the realpower reference can be taken from the grid energy managementcontroller. The real and reactive power can be controlled throughcurrent regulation or voltage regulation (Peng, Yun & Tolbert,2009; Peng, Luo, Lv, Wu & Yu, 2011); here, the current regulationscheme is adopted in this paper.
In PQ control, the variables controlled by the inverter are thereal and reactive power injected to the grid, and it is desired tomeet the power and reactive power references. The three-phaseoutput voltage and current x in the abc frame of inverter can berepresented as
ω
ω π
ω π=
( )
−
+( )
⎜ ⎟
⎜ ⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥
⎡
⎣
⎢⎢⎢⎢⎢⎢
⎛⎝
⎞⎠
⎛⎝
⎞⎠
⎤
⎦
⎥⎥⎥⎥⎥⎥
xxx
X t
X t
X t
cos
cos23
cos23 3
a
b
c
m
m
m
where Xm is the maximum magnitude of voltage or current, ω isthe angular frequency. The three-phase stationary coordinatesystem can be transformed to the d–q rotating coordinate systemby Park’s transformation (Wu, Liang, Zargari & Kouro, 2011), and itis described as
( )
( )
ω ω π ω π
ω ω π ω π=
− +
− +( )
→
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎡
⎣
⎢⎢⎢⎢
⎛⎝
⎞⎠
⎛⎝
⎞⎠
⎛⎝
⎞⎠
⎛⎝
⎞⎠
⎤
⎦
⎥⎥⎥⎥
Tt t t
t t t
23
cos cos23
cos23
sin sin23
sin23 4
abc dq
After applying the Park's transformation, the real power andreactive power can be expressed as:
( )
( )
= ⋅ +
= ⋅ − ( )
P v i v i
Q v i v i
32
32 5
q q d d
q d d q
Thus the output current from inverter after Park's transfor-mation can be calculated. In the current regulation scheme, thereal power control loop generates the synchronous frame d-axisreference current (id_ref) and the reactive power control loopgenerates the q-axis reference current (iq_ref) as follows (Figueres,Garcerá, Sandia, González & Rubio, 2009):
_ = ⋅+
+
_ = ⋅−
+ ( )
iPv Qv
v v
iPv Qv
v v
23
23 6
d refd q
d q
q refq d
d q
2 2
2 2
The PQ control is demonstrated in Fig. 6. Reference real powerand reactive power are decoupled into reference current in d- andq-axis in ‘Power Control’ block, and then reference current arecontrolled by ‘PI Current Controller’ in order to make steady stateerror equal to zero. Phase Lock Loop (PLL) is used to synchronizefrequency and phase of DG with the main grid.
It is shown from (6) that the objective of controlling real andreactive power P and Q is equivalent to controlling the current; inother words, as long as the PQ controller implements tracking thecurrent reference iref, both P and Q can be controlled. Currentcontrol is accomplished by the PI current controller.
Eq. (7) gives the voltage equation of inverter in the rotating d–qreference frame (Choi & Sul, 1998):
PI
PI
ωL
ωL
id
id_ref
iq
iq_ref
id
iq
ud_ref
uq_ref
ud
uq
Fig. 7. PI Controller with feedforward compensation.
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193188
ωω
=−
+( )
⎡⎣⎢
⎤⎦⎥
⎡⎣⎢
⎤⎦⎥⎡⎣⎢⎢
⎤⎦⎥⎥
⎡⎣⎢
⎤⎦⎥
uu
Ls LL Ls
i
i
vv 7
d
q
d
q
d
q
where ud and uq are the grid voltage, id and iq are the invertercurrent, L is the filter inductance, and vd and vq are the controlsignals of the voltage.
It is shown from (7) that the inverter current is coupled interms of the d and q axes, and id and iq are not only affected by vdand vq but also the coupled voltage ωLi. Thus in order to control idand iq independently, the coupled value needs to be canceled, andcurrent feed forward compensation is usually used to decouple thecurrent in the d–q frame. By introducing �ωLiq and ωLid thecurrent controller with PI control is written as:
ωω
= − +_
_+ −
( )
⎡⎣⎢
⎤⎦⎥
⎡⎣⎢
⎤⎦⎥
⎛⎝⎜
⎞⎠⎟⎡⎣⎢⎢
⎤⎦⎥⎥
⎡⎣⎢
⎤⎦⎥⎡⎣⎢⎢
⎤⎦⎥⎥
vv
uu k
ks
i
iL
L
i
i0
0 8
d
q
d
qp
i d ref
q ref
q
d
Note here the vd and vq are actually the control signals ud_ref,and uq_ref coming out from the “PI current control” block. Inserting(8) into (7), the relationship between reference control currentand inverter current can be derived as:
_
_=
++
( )
⎡⎣⎢⎢
⎤⎦⎥⎥
⎛
⎝⎜⎜
⎞
⎠⎟⎟⎡⎣⎢⎢
⎤⎦⎥⎥
i
iLs
k
i
i1
9
d ref
q ref pks
d
qi
From (9) we find that by introducing feed forward compensa-tion reference current is decoupled into d and q axes, and thusthey can be controlled independently. Fig. 7 demonstrates the PIcontroller with feedforward compensation.
3.5. Droop controller design
In power systems, by approximation the active power flowbetween two buses has linear relationship with the phase angledifference (δ) between the two buses, while the reactive power
Fig. 8. Droop characteristics f
flow has the linear relationship with the voltage magnitude dif-ference between the two buses (Hu, Zhu & Platt, 2011; Katiraei &Iravani, 2006). It is analogical to the power system that in micro-grid when the load demand increases a generator which is con-nected to the utility drops its frequency. Therefore the voltage andfrequency droop control method in microgrid can be defined as(Brabandere et al., 2004):
( )( )
ω ω= * − − *
= * − − * ( )
m P P
V V n Q Q 10
where P* and Q* are the nominal real and reactive power, ω* and V*
are the grid rated angular frequency and voltage, ω and V are thereferences, and m and n are the slopes of the droop characteristics.The strategy of droop control is that each DG shares the powerdemand according to its own droop characteristic functions. Thedroop characteristic is shown in Fig. 8.
Fig. 8 shows that DGs allocate power according to the newstable working point at ω and V and it is also shown that the DGwith steeper slope will share less power. The schematic of droopcontrol is demonstrated in Fig. 9 and the details of ‘Voltage For-mation’ block is given in Fig.10.
As shown in Fig. 9, the measured P and Q, nominal P* and Q*,nominal f* and V* are considered as the input to calculate thefrequency and voltage magnitude, f_ref and V_ref, at the stableworking point in ‘droop control’ block after load changes. ud_ref anduq_ref are voltage at the stable working point in d and q axes, re-spectively, after ‘voltage formation’ block.
In Fig.10, f* and V* are grid rated frequency and voltage mag-nitude, respectively. fref and Vref are frequency and voltage mag-nitude after load changes at the stable point, and they are obtainedby droop control characteristics. Three-phase uref is obtained bythe voltage formation device and then converted into ud_ref anduq_ref by Park's transformation.
The transition between PQ control and droop control can bemade by microgrid superisory control system. The superiosrysystem consistently check the current flowing into grid, if there isno current, meaning islanded mode, the microgrid will implementdroop control. If there is current flowing, it is under grid-con-nected mode; thus microgrid will implement PQ control and thereal power reference of PV is calculated by MPPT.
4. Tuning of pi parameters with ABC
In this section the original ABC method is introduced first, thena performance evaluation criterion (objective function) is de-scribed, and finally the implementation of ABC to tuning processcontrol parameters is described.
or voltage and frequency.
Fig. 9. Schematic of the droop control for VSI.
Fig. 10. Details of droop control and voltage formation.
Table 1Model parameters.
Load 1 P¼75 kW, Q¼20 kvarLoad 2 P¼50 kW, Q¼ 10kvarLoad 3 P¼15 kW, Q¼10 kvarFC Prated¼50 kW, Vdc¼365 VPV Prated¼80 kW, Vm¼680 V, Im¼280 ARLC filter (PV) Rf¼0.02 Ω, Lf¼0.4 mH, Cf¼2500 μFRLC filter (FC) Rf¼0.05 Ω, Lf¼0.6 mH, Cf¼2000 μFLine Z RL¼0.04 (Ω/km), XL¼0.13 (Ω/km)Transformer Y–Y: 380:13.8�103 V, R¼1%, X¼4%Droop control 1/m1¼0.8�10�5, 1/n1¼0.3�10�5,
1/m2¼0.8�10�5, 1/n2¼0.3�10�5
0 0.05 0.1 0.150
20
40
60
80
100
Time(s)
P(k
w)
ABCManual
Fig. 11. PQ control of PV with/w
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193 189
4.1. Artificial bee colony (ABC)
The original ABC algorithm was first proposed by Karaboga(2005). In the ABC, in order to find global optimum, artificial beesare searching in a multidimensional solution space. There arethree groups of bees in the ABC system: employed bees, onlookers,and scouts. Their job is to search food source (Tasgetiren, Pan,Suganthan & Chen, 2011) Karaboga & Akay, 2009). Food sourceshere are considered as feasible solutions and the quality of a foodsource means the fitness associated with the solution. Each initialsolution Xi¼{Xi,1,Xi,2,…,Xi,D} is generated randomly within therange of the parameters as follows:
= + ( )( − ) ( )X X rand X X0, 1 11i j min j max j min j, , , ,
where i¼1,2,…,SN, j¼1,2,…,D, SN is the size of employed bees or
0 0.05 0.1 0.150
4
8
12
16
20
24
Time(s)
Q(k
var)
ABCManual
ithout parameter tuning.
0 0.05 0.1 0.15 0.20
5
10
15
20
25
30
35
40
45
Time (s)
P(k
w)
ABCManual
0 0.05 0.1 0.15 0.20
2
4
6
8
10
12
Time (s)
Q (K
var)
ABCManual
Fig. 12. PQ control of FC with/without parameter tuning.
0 10 20 30 40 50 601e6
1.5e6
2e6
2.5e6
3e6
3.5e6
4e6
4.5e6
5e6
Fig. 13. Convergence characteristic of tuning PI parameters for PQ controller.
Table 2PI parameters for PQ control.
Manually tuned ABC (first stage) ABC (second stage)
kp_1¼0.263 kp_1¼0.051 kp_1¼0.05ki_1¼7.42 ki_1¼0 ki_1¼14.2kp_2¼0.014 kp_2¼0.96 kp_2¼0.98ki_2¼8.92 ki_2¼0 ki_2¼2.46kp_3¼0.139 kp_3¼0.034 kp_3¼0.031ki_3¼7.95 ki_3¼0 ki_3¼11.8kp_4¼0.134 kp_4¼0.65 kp_4¼0.62ki_4¼8.86 ki_4¼0 ki_4¼9.26
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193190
onlooker bees, D is the number of optimization variables, Xmin,j andXmax,j are the lower and upper limits for dimension j, respectively,and rand(0,1) denotes a uniformly distributed random number in(0,1). After initialization, in order to explore solutions in the searchspace, a search equation is used to generate a candidate solutionvector Vi,j
Φ= + ( − ) ( )V X X X 12i j i j i j i j k j, , , , ,
where indices i and k are distinct integers uniformly chosen from[1,SN] and j is chosen from [1, D], Φi,j is a random number in therange [�1,1]. It is worth to mention that there is only one search
equation used in ABC, which makes the algorithm easier to im-plement than other heuristic methods.
4.2. Performance evaluation of PI controller
In general, the integrated absolute error (IAE) is commonlychosen as the PI controller tuning evaluation:
∫= ( ) ( )∞
IAE e t dt 130
In our case, the objective function of PQ control can be writtenas:
∫ ∫( ) = ( ) + ( ) ( )∞ ∞
f K e t dt e t dtmin 14p q0 0
where K is the vector of PI parameters, ep, and eq are the errors ofactual real and reactive powers from references. Note that thedomain of K needs to ensure the stability of the system. By trialand error approach, the solution domain of kp is from (0, 1), andthe solution domain of ki is chosen from (0, 20).
The algorithm repeats the search processes a predefinediteration times. The framework of the ABC algorithm is summar-ized as follows:
Step (1) Initialization:(1.1) Randomly generate SN points in the search space as fea-
sible solution xi by (11).(1.2) Run PQ control, detect the output response and evaluate
the fitness function.Step (2) For all employed bees (i¼1,…,SN):(2.1) Generate a candidate solution Vi by (12).(2.2) Run PQ control, detect the output response and evaluate
the fitness function by (14), and calculate the probability p asso-ciated with its fitness.
(2.3) Choose a solution (from xi and Vi) with better fitnessfunction.
Step (3) For all onlooker bees (will only be executed undercertain probability p):
(3.1) Generate a new candidate solution by Vi (12).(3.2) Run PQ control, detect the output response and evaluate
the fitness function by (14).(3.3) Choose a solution (from xi and Vi) with better fitness
function.(3.4) Best solution so far is memorized.Step (4) For all scout bees (they will be executed only after the
maximum trial m). Note that the maximum trial m is a predefinednumber that if a certain food cannot be improved by an employedbee after m times, the employed bee will become a scout bee.
3.5 4 4.5 5 5.5 6 6.5 7 7.5
-400
-300
-200
-100
0
100
200
300
400
Time (s)
Vol
tage
(V)
Fig. 14. Frequency profile and voltage profile at PCC.
4 5 6 70
20
40
60
80
Time (s)
pow
er (k
w/k
var)
real powerreactive power
4 5 6 70
10
20
30
40
50
60
70
Time(s)
pow
er(k
w/v
ar) real power
reactive power
Fig. 15. PV/FC combined real and reactive power output.
3.5 4 4.5 5 5.5 6 6.5 7 7.559.8
59.9
60
60.160.1
Time(s)
Freq
uenc
y(H
z)
Measured fnominal f
3.5 4 4.5 5 5.5 6 6.5 7 7.5
-400
-300
-200
-100
0
100
200
300
400
Time (s)
Vol
tage
(V)
Fig. 16. Frequency profile and voltage profile at PCC.
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193 191
(4.1) Replace xi with a new random solution xi by (11).Note that the PI parameter optimization was only im-
plemented in the PQ controller, and there were four parameters,kp_d, ki_d for controlling id, and kp_q, ki_q for controlling iq. Indroop control, the output real and reactive powers were basedon defined droop characteristics, in other words, the objective ofthe controller is to achieve a new stable working point based onthe droop characteristics. Thus no output references can be ob-tained, and the optimal tuning objective function cannot beformed.
5. Case study
Test of controllers are carried out on Matlab/Simulink. Differentscenarios have been studied in order to test the effectiveness ofthe proposed control strategies.
5.1. Model parameters
As shown in Fig. 1, under grid connection mode PV and fuelcell were operating with PQ control, meaning that they were told
4 5 6 710
20
30
40
50
60
70
80
Time (s)
Pow
er(k
w/k
var)
Real powerReactive power
4 5 6 70
10
20
30
40
50
60
70
Time(s)
Pow
er(k
w/k
var) Real power
Reactive power
Fig. 17. PV/FC combined real and reactive power output.
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193192
to generate exact real and reactive power according to respectivereferences. In order to verify the droop controller, the system is firstconnected with grid and at 4 second the grid is disconnected andreconnected at 7 s. The procedure will cause the frequency variancewhich leads to the response of droop control; then under the is-landed mode, PV and fuel cell were operating with droop control aswell, meaning that when load changes, both DGs will automaticallyallocate power according to predefined droop characteristics.Parameters such as line impedance, rated power, voltage level,transformer setting, load, and control parameters are listed in Ta-ble 1. Note that loads are modeled as constant power loads.
5.2. Simulation results
To verify the effectiveness of the PQ and droop controls, grid-connected and islanded modes were simulated for controllertesting. Note that the use of PQ or droop control can be decided bysupervisory control system of microgrid. In grid-connected mode,microgrid was operating with the PQ control. The P and Q refer-ences for PV were 80 kW and 20 kvar, respectively. Since SOFC hasslower dynamics at beginning, in order to verify the controller stepreferences are applied: P reference steps from 20 to 40 kW at 0.1 sand Q reference steps from 5 to 10 kvar respectively. The PI con-troller parameters of proportional gain kp and integral gain ki weretuned by ABC. The control results are demonstrated in Figs. 11 and12. Note that the P reference for PV is the actually the maximumpower of PV calculated by MPPT.
As shown in Figs. 11 and 12, both controllers for PV and FC havequick responses and track the references effectively. It is alsoshown that the PI parameters found by ABC gives less overshoot,less steady-state errors and faster rising time. Fig. 13 gives theconvergence characteristics. The size of the bee colony is 80(employed bees and onlooker bees). It is worth mentioning thatsince there are 8 parameters total: kp_1, kp_2, ki_1 and ki_2 are theparameters for PQ controller of PV; kp_3, kp_3, ki_4 and ki_4 arethe parameters for PQ controller of FC. In the first tuning stage allfour ki parameters were set to zero and tuned kp only. After fouroptimal kp parameters were found, they were used as initialcondition to be tuned along with the four ki parameters in thesecond stage. Table 2 demonstrates the tuning process and optimalkp and ki parameters.
Senario 1: For droop controller verification we first apply itunder such scenario: microgrid is connected with grid in the be-ginning but disconnected from the grid at 4 s, and reconnected tothe grid at 7 s Fig. 14 illustrates the frequency and voltage profileof PPC. Fig. 15 shows real and reactive power responses.
Frequency at PCC decreases when the microgrid is dis-connected from the grid at 4 s, because the real power generationof PV and FC increase in order to match the load demand, and bythe droop characteristics frequency will decrease. The voltage atPCC increases as microgrid is disconnected from the grid, becausethe reactive power of both DGs decrease, meaning that the gridwas absorbing reactive power from micrigrid while connected. At7 s when microgrid is reconnected to the grid, frequency increasesas real power decreases and voltage decreases as reactive powerincreases.
Senario 2: Then another scenario was implemented to verifydroop controller: microgrid was operating at the islanded mode bydroop control in the beginning and load 3 disconnected at 4 s, andyet reconnected to the grid at 7 s are shown in Figs. 16 and 17.
Frequency at PCC is not at rated value when microgrid is op-erating in the islanded mode. At 4 s load 3 is disconnected frommicrogrid, and the frequency increases because the total powergeneration decreases to match the load demand. The voltage atPCC increases because the reactive power decreases as well. At7 second, when load 3 is reconnected to the microgrid, the realand reactive power generation of both DGs increase in order tomeet the load demand, therefore the frequency and voltage de-crease. Both cases have shown that the droop controller workseffectively in terms of reallocating power sharing between twoDGs and fast responding to load changes while maintaining thefrequency and voltage at acceptable level.
6. Conclusions and future work
In this paper a detailed PV model with MPPT, SOFC and PQ anddroop controllers are developed for inverter interfaced DGs. Theuse of PQ control ensures that DGs can generate certain power inaccordance with real and reactive power references. Droop con-troller is developed to ensure the quick dynamic frequency re-sponse and proper power sharing between DGs when a forcedislanding occurs or load changes. Tuning PI controller parameterscan be tedious and time-consuming, and in order to avoid suchproblem here we used a heuristic method, ABC, to search for theoptimal parameters. In comparison with manually tuned para-meters, ABC tuned parameters have better performance in termsof percentage of overshoot and steady state error. Compared topure V/f control and master–slave control, the proposed controlstrategies which have the ability to operate without any onlinesignal communication between DGs make the system operationcost-effective and fast responding to load changes. The
W. Bai et al. / Control Engineering Practice 53 (2016) 184–193 193
simulation results obtained shows that the proposed controller iseffective in performing real and reactive power tracking, voltagecontrol and power sharing during both grid-connected mode andislanded mode.
To fully represent the complexity of the microgrid, futurework will include the development of hierarchical controllersfor a microgrid consisting of several DGs and energy storagesystem. The function of primary controller is to assign optimalpower reference to each DG to match load balances and thesecondary controllers are designed to control local voltage andfrequency.
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