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Electrical microgrids design Session 4 Microgrid modeling Luis Ismael Minchala Avila Universidad de Cuenca Departamento de Eléctrica, Electrónica y Telecomunicaciones [email protected] Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 1 / 43

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  • Electrical microgrids designSession 4

    Microgrid modeling

    Luis Ismael Minchala Avila

    Universidad de CuencaDepartamento de Elctrica, Electrnica y Telecomunicaciones

    [email protected]

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 1 / 43

  • 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

  • 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

  • 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

  • Introduction

    DG units modeling

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 5 / 43

  • 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

  • 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

  • Power electronic converters

    Three phase rectifiers

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 8 / 43

  • 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

  • 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

  • Power electronic converters

    dc/dc power converters

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 11 / 43

  • 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

  • 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

  • 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

  • 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

  • Power electronic converters

    Voltage source inverter

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 16 / 43

  • 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

  • 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

  • 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

  • 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

  • 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

  • Diesel engine generator

    Synchronous machine model

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 21 / 43

  • 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

  • Diesel engine generator

    Diesel engine model

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 23 / 43

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • Photovoltaic generation system

    PV model

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 31 / 43

  • 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

  • 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

  • Photovoltaic generation system

    PV model

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 34 / 43

  • Battery system modelation

    Battery system modeling

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 35 / 43

  • 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

  • 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

  • Microgrid benchmark model

    Benchmark model

    Ismael Minchala A. (UCuenca) uGrid modeling May, 2015 38 / 43

  • 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

  • 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

  • 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

  • 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

  • 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