04_ugmodel

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


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.


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.


Introduction

DG units modeling


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).



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)




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)



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.



dc/dc power 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)



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)



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)



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.




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)




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



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


A diesel generator is the combination of a DE with an electricalgenerator to produce electrical energy.



Synchronous machine model



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



Diesel engine model



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)



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)


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.



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)



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



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)



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)


Photovoltaic generation system

PV model



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)



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)



PV model


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)




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


Microgrid benchmark model

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



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



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)


Summary and questions

Summary

In this session we have studied:

Microgrids component models;Simulations in MATLAB


Appendix Questions

Preguntas


IntroductionPower electronic convertersDiesel engine generatorWind-driven generation systemPhotovoltaic generation systemBattery system modelationMicrogrid benchmark modelSummary and questionsAppendix

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