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Electrical microgrids designSession 4
Microgrid modeling
Luis Ismael Minchala Avila
Universidad de CuencaDepartamento de Elctrica, Electrnica y Telecomunicaciones
ismael.minchala@ucuenca.edu.ec
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 1 / 43
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Agenda
1 Introduction
2 Power electronic converters
3 Diesel engine generator
4 Wind-driven generation system
5 Photovoltaic generation system
6 Battery system modelation
7 Microgrid benchmark model
8 Summary and questions
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 2 / 43
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Introduction
Introduction
Control engineering most of the times is model dependent.Understanding the process, system or plant to be controlled isfundamental for proposing proper control strategies.
Current strategies on load-sharing will not work to integrate RES dueto its peak-power and intermittent operation.
New control strategies for voltage/reactive-power andload-sharing/frequency need to be developed; microgrid modeling isthe first steep prior advanced controllers design.
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 3 / 43
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Introduction
DG units modeling
A DG unit is conformed mainly of three components:
Microgeneration unit. Typical choices are: batteries, PV, WTG,flywheels, fuel cells, etc.
Power conditioning system (PCS). PCS is related with powerconversion, ac/dc or dc/ac and its control techniques.
Coupling circuit. Interface elements, most of the times a filter, forcoupling the DG unit with the network.
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 4 / 43
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Introduction
DG units modeling
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 5 / 43
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Power electronic converters
Power electronic converters
There is a trend to adopt power electronics based interfaces whichconvert the power from a DG unit, firstly to dc and then use aninverter to deliver the power to the 60 Hz ac grid.
There are mainly three power electronic circuits that need to beimplemented in order to control voltage, power and frequency outputof a DG unit: ac/dc converter, dc/dc converter and voltage sourceinverter (VSI).
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 6 / 43
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Power electronic converters
Three phase rectifiers
A three-phase, full-wave and phase-controlled rectifier will be studied.
SCRs are used in the rectifier instead of diodes. Each SCR must beturned on by a gate signal in each cycle of the supply voltage.
Under the continuous conductance condition, the average outputvoltage, Vo , of a controlled rectifier is given by:
Vo =3piVll(peak) cos (f ) (1)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 7 / 43
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Power electronic converters
Three phase rectifiers
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 8 / 43
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Power electronic converters
Three phase rectifiers
0 0.2 0.4 0.6 0.8 10
50
100
150
200
250
Time ( s )
Output volt age of t he r ect ifier
= 0 = 30 = 60 = 85
0 20 40 60 800
50
100
150
200
250
(deg re e s )
Output volt age vs (V)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 9 / 43
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Power electronic converters
dc/dc power converters
There are mainly three types of dc/dc converters: buck, boost andbuck-boost.
Buck mode converters are used in applications where a reduced dcvoltage than the one fed into the input is needed.
Boost mode converters are able to increase the output voltage.
Buck-boost mode converters are able to increase or decrease theoutput voltage with the particularity of presenting opposite polarity ofthe main source.
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 10 / 43
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Power electronic converters
dc/dc power converters
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 11 / 43
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Power electronic converters
Buck converter model
iR = iL iC (2)vC (t) =
1C
iCdt; L
diL(t)dt
= uVin vC (t)dvC (t)dt
= 1RC
vC (t) + iL(t) (3)
diL(t)dt
= 1LvC (t) +
1LuVin (4)[
dvC (t)dt
diL(t)dt
]=
[ 1RC 1 1L 0
] [vC (t)iL(t)
]+
[01Lu
]Vin (5)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 12 / 43
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Power electronic converters
Boost converter model
iR = iL iC (6)vC (t)R
= (1 u) iL(t) C dvC (t)dtdvC (t)dt
= 1RC
vC (t) +1C(1 u) iL(t) (7)
diL(t)dt
= 1 uL
vC (t) +1LVin (8)[
dvC (t)dt
diL(t)dt
]=
[ 1RC 1C (1 u) 1L (1 u) 0
] [vC (t)iL(t)
]+
[01L
]Vin (9)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 13 / 43
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Power electronic converters
Buck-boost converter model
dvC (t)dt
= 1RC
vC (t) +1C(1 u) iL(t) (10)
diL(t)dt
= 1 uL
vC (t) +1LuVin (11)[
dvC (t)dt
diL(t)dt
]=
[ 1RC 1C (1 u) 1L (1 u) 0
] [vC (t)iL(t)
]+
[01Lu
]Vin(12)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 14 / 43
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Power electronic converters
Voltage source inverter
Integrating RES, e.g. PV arrays or WTG, to the main grid or into amicrogrid is mainly done through a combination of rectifiers andinverters.
The microgeneration unit are then able to operate at unity-powerfactor or any other leading/lagging power factor.
Two modes of operation can be distinguished in the VSI of the figure:the square-wave mode, loosely related to the phase-control inrectifiers, and the PWM mode.
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 15 / 43
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Power electronic converters
Voltage source inverter
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 16 / 43
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Power electronic converters
Voltage source inverter
In the carrier-based sinusoidal PWM method (SWPM), three phasesinusoidal waves are used for the modulating signals, and they arecompared with a high frequency triangular wave. Considering:
vA = Vm sin (t)
vB = Vm sin(t 2
3pi
)(13)
vC = Vm sin(t +
23pi
)the ratio between the amplitudes of the carrier signal and the control signalis called modulation index,
m =VmVc
(14)
V1 =mVdc22
(15)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 17 / 43
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Power electronic converters
Voltage source inverter
In the carrier-based sinusoidal PWM method (SWPM), three phasesinusoidal waves are used for the modulating signals, and they arecompared with a high frequency triangular wave. Considering:
vA = Vm sin (t)
vB = Vm sin(t 2
3pi
)(13)
vC = Vm sin(t +
23pi
)the ratio between the amplitudes of the carrier signal and the control signalis called modulation index,
m =VmVc
(14)
V1 =mVdc22
(15)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 17 / 43
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Power electronic converters
Voltage source inverter
0.2 0.21 0.22 0.23 0.24 0.25250
200
150
100
50
0
50
100
150
200
250
Time (s) (a)
V, A
Voltage & current m = 12
Phase voltagePhase current
0.2 0.21 0.22 0.23 0.24 0.25250
200
150
100
50
0
50
100
150
200
250
Time (s) (b)
V, A
Voltage & current m = 2
Phase voltagePhase current
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 18 / 43
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Power electronic converters
Voltage source inverter (control
A more efficient PWM approach could also be used, e.g. voltage spacevector PWM (SVPWM). Parks transformation is used to represent thethree-phase voltages in a vectorized way:
v = vd + jvq (16)[vdvq
]=
[1 12 120
32
32
] vAvBvC
(17) vABvBC
vCA
= Vdc 1 1 00 1 11 0 1
abc
(18) vANvBN
vCN
= Vdc3
2 1 11 2 11 1 2
abc
(19)Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 19 / 43
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Diesel engine generator
Diesel engine generator
A diesel generator is the combination of a DE with an electricalgenerator to produce electrical energy.
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 20 / 43
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Diesel engine generator
Synchronous machine model
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 21 / 43
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Diesel engine generator
Synchronous machine model
Ldxdt
= Ax+ BvF (20)
x =
idiqiF
A =
(Rs + RL) Ls 0Ls (Rs + RL) Lm0 0 RF
L =
Ls 0 Lm0 Ls 0Lm 0 LF
B =
001
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 22 / 43
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Diesel engine generator
Diesel engine model
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 23 / 43
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Diesel engine generator
Diesel engine model
Kau(t) = Tasx1(t) + x1(t)
x1(t) = 1Ta x1(t) +KaTa
u(t) (21)
sx2(t) = x2(t) + Kbx1 (t )x2(t) = Kbx1 (t ) x2(t)_x(t) =
[ 1Ta 00
]x(t) +
[0 0Kb 0
]x(t ) +
[ KaTa0
]u(t)(22)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 24 / 43
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Diesel engine generator
Diesel engine model
0 0.002 0.004 0.006 0.008 0.010
0.2
0.4
0.6
0.8
1
Time ( s )
Volt age amplit ude (pu)
0 1 2 3 40.98
0.985
0.99
0.995
1
1.005
1.01
1.015
1.02
Time ( s )
Fr equency r esp ons e (pu)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 25 / 43
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Wind-driven generation system
Wind-driven generation system
A horizontal axis WT has been chosen as prime mover and aninduction generator for energy conversion.
This combination of WT and asynchronous machine is the mostcommonly WTG found in commercial versions for generating powersranging from a few kilowatts to 3 MW.
Combinations of several WTG form the so-called wind farms, withgeneration capacities up to 200 MW.
Wind energy has some limiting characteristics such as:non-schedulability, uncontrollable, etc. To obtain relatively constantpower, variable blade pitch angle controls are installed.
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 26 / 43
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Wind-driven generation system
Wind turbine model
Cp (, ) = 0.5716 [116 0.4 5] e21 + 0.0068 (23) =
(1
+ 0.08 0.0353 + 1
)The dynamic output mechanical torque of the WT, Tm is expressed as:
Tm =ARCpV 2w
2(24)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 27 / 43
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Wind-driven generation system
Wind turbine model
0 2 4 6 8 10 12
0.4
0.2
0
0.2
0.4
0.6
(a)
pu
Power coeffic ient
= 0 = 10 = 15 = 20
0 0.5 1 1.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Turbine speed (pu)(b)
Mechanical torque = 0
Vw = 6Vw = 8Vw = 12Vw = 14
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 28 / 43
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Wind-driven generation system
Induction generator model
vqs = rs iqs +
bds +
pbqs (25)
vds = rs ids bqs +
pbds (26)
v qr = rr iqr +
( rb
)dr +
pbqr (27)
v dr = rr idr +
( rb
)qr +
pbdr (28)
pbr =
12H
(Te T0) (29)Te = qr i
dr dr i qr (30)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 29 / 43
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Wind-driven generation system
Induction generator model
0 1 210
8
6
4
2
0
2
4
6
8
10Stat or cur r ent (pu)
Time ( s )0 1 2
10
8
6
4
2
0
2
4
6
8
10Rotor cur r ent (pu)
Time ( s )0 1 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time ( s )
Rotor sp eed (pu)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 30 / 43
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Photovoltaic generation system
PV model
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 31 / 43
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Photovoltaic generation system
PV model
Applying Kirchhoffs first law and a non-linear current relation of the diodeshown in Figure, iD , it is possible to find the mathematical relationship ofthe PV current,
i(t) = iph iD V + iRsRsh = iph Is(eq
V+iRsAkT 1
) V + iRs
Rsh(31)
where iph, Is , q, k , T , A, Rs and Rsh are the photocurrent, diodesaturation current, Coulomb constant
(1.602e19 C
), Boltzmanns
constant(1.38 1023 JK
), cell temperature (oK ), P-N junction ideality
factor, series and parallel resistances, respectively.Photocurrent depends on the solar radiation and cell temperature,
iph =SSref
(iph,ref + CT (T Tref )
)(32)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 32 / 43
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Photovoltaic generation system
PV model
where S is the solar radiation(Wm2); Sref , Tref , iph,ref are the solar
radiation, cell absolute temperature and photocurrent in standard testconditions; CT is a temperature coefficient
( AoK
).
Diode saturation current varies with cell temperature as follows:
Is = Is,refT 3
TrefeqEgAk
(1
Tref 1T
)(33)
where Is,ref , is the diode saturation current in standard test conditions andEg represents the band-gap energy of the cell semiconductor (eV ).
i(t) = Np iph NpIs(e
qAkT
(VNs
+ iRsNp
) 1) Np
Rsh
(VNs
+iRsNp
)(34)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 33 / 43
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Photovoltaic generation system
PV model
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 34 / 43
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Battery system modelation
Battery system modeling
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 35 / 43
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Battery system modelation
Battery system modeling
V0 = Rd i(t) +1C
[i(t) + iB(t)] dt
Vp(t) =1C
[i(t) + iB(t)] dt
V0 = RdCdVp(t)dt
+1CiB(t) +
1RdC
V0
dVp(t)dt
= 1RdC
Vp(t) 1C iB(t) +1
RdCV0 (35)
VB(t) = Vp(t) RB iB(t) (36)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 36 / 43
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Battery system modelation
Battery system modeling
0.1 0.2 0.3 0.4 0.51.6
1.7
1.8
1.9
2
2.1
2.2
iB(t) (A) (a)
V
Battery voltage (discharge)
Battery VoltageCapacitor Voltage
0.1 0.2 0.3 0.4 0.585
90
95
100
iB(t) (A) (b)
%
State of charge
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 37 / 43
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Microgrid benchmark model
Benchmark model
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 38 / 43
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Microgrid benchmark model
Benchmark model
0 10 200
0.05
0.1
0.15pu
0 10 200
0.01
0.02
0.03
0.04
0 10 200
0.5
1
1.5x 10
3
0 10 200
0.5
1
1.5x 10
3
0 10 200
0.5
1
1.5
2
2.5
3x 10
3
0 10 200
1
2
3
4x 10
3
0 10 200
0.5
1
1.5
2
2.5
3x 10
3
pu
0 10 200
1
2
3
4
5
x 104
0 10 200
0.5
1
1.5
2
2.5
3x 10
3
0 10 200
1
2
3
4x 10
3
0 10 200
1
2
3
4x 10
4
0 10 200
0.5
1
1.5
2x 10
3
0 10 200
0.5
1
1.5
2
2.5
3x 10
3
pu
Time (h)0 10 20
0
0.05
0.1
0.15
Time (h)0 10 20
0
0.005
0.01
0.015
0.02
0.025
0.03
Time (h)0 10 20
0
0.5
1
1.5x 10
4
Time (h)0 10 20
0
0.5
1
1.5
2x 10
3
Time (h)0 10 20
0
0.5
1
1.5x 10
3
Time (h)
RealReactive
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 39 / 43
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Microgrid benchmark model
Benchmark model
0 5 10 15 20
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
Time (h)
Volt age amplit ude at Node-1 (pu)
0 5 10 15 20
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
Time (h )
Volt age amplit ude at Node-9
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 40 / 43
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Microgrid benchmark model
Benchmark model
0 4 8 12 16 20 240
0.05
0.1
0.15
0.2
0.25
0.3
0.35DEG generated power (pu)
Time (h)0 4 8 12 16 20 24
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2WTG power (pu)
Time (h)0 4 8 12 16 20 24
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02PV1 power (pu)
Time (h)
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 41 / 43
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Summary and questions
Summary
In this session we have studied:
Microgrids component models;Simulations in MATLAB
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 42 / 43
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Appendix Questions
Preguntas
Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 43 / 43
IntroductionPower electronic convertersDiesel engine generatorWind-driven generation systemPhotovoltaic generation systemBattery system modelationMicrogrid benchmark modelSummary and questionsAppendix
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