Grid Pv System

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Power Electronics and Control in

Grid-Connected PV Systems

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2 ECEN2060

Grid-Connected PV System

AC utility grid i_ac + − v_ac + − V_PV I_PV PV array Power electronics converter

DC input

PV PV PV

V

I

P

=

PV PV

I

V

,

One possible grid-connected PV system architecture

AC output

( )

t V t v_ac( ) = 2 _RMS sin ω

( )

t I t i_ac( ) = 2 _RMS sin ω RMS RMS ac

V

I

P

=

Functions of the power electronics converter

• Operate PV array at the maximum power point (MPP) under all conditions

• Generate AC output current in phase with the AC utility grid voltage

• Achieve power conversion efficiency close to 100%

PV PV RMS RMS PV ac converter

I

V

I

V

P

=

η

• Provide energy storage to balance the difference between P

_PV

and p

_ac

(t)

Desirable features

• Minimum weight, size, cost

• High reliability

(

)

(

t

)

I

V

i

v

t

p

_ac

(

)

=

_ac _ac

=

_RMS _RMS

1 −

cos

2 ω

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Power Electronics for Grid-Connected PV System

One possible realization:

AC utility grid i_ac + − v_ac + − V_PV I_PV PV array Boost DC-DC converter Single-phase DC-AC inverter Energy-storage capacitor + − V_DC C

DC-DC control DC-AC control

Boost DC-DC converter

• Set the PV operating point (V_PV, I_PV) to MPP

• Efficiently step up V_PV to a higher DC voltage V_DC

DC-AC inverter

• Efficiently generate AC output current i_ac in phase with the AC grid voltage v_ac

• Balance the average power delivery from the PV array to the grid, P_ac = P_pv * η_DC-DC * η_DC-AC

Energy storage capacitor C

• Balance the difference between the instantaneous power p_ac(t) and the average power

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4 ECEN2060

DC-AC Inverter Control

One possible realization:

• The control variable for the DC-AC inverter is the RMS current reference I_RMSref

• The inverter output current i_ac(t) is controlled so that it is in phase with the grid voltage v_ac(t) and so that it’s RMS value equals the reference:

= I

_RMSref

I

_RMS

= I

_RMSref

One possible current control approach, based on a comparator with hysteresis, has been discussed in class, see Intro to Power Electronics notes

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Simulation model: pv_boost_dcac_averaged.mdl

ECEN2060

PV + Boost DC-DC + DC-AC inverter averaged model ECEN2060

6-module PV Array

Average output AC power

Average input AC power DC-AC average power

and efficiency

Set Boost Iref to operate PV array

at MPP

Set DC-AC Iref to balance the power, i,e

to keep VDC constant PV output power 60 fac_out 60 fac_in 103.2 Vpv 199.8 Vout (boost) = VDC Product 510.8 Ppv 492.6 Pout boost 472.8 Pout 493.2 Pin Ipv Insolation Vpv Ppv PV module (I) PV6 Ipv Insolation Vpv Ppv PV module (I) PV5 Ipv Insolation Vpv Ppv PV module (I) PV4 Ipv Insolation Vpv Ppv PV module (I) PV3 Ipv Insolation Vpv Ppv PV module (I) PV2 Ipv Insolation Vpv Ppv PV module (I) PV1 4.95 PV current 3.94 Iref 1 s Integrator(pout) 1 s Integrator(pin) 1000 Insolation Vdc Iref v ac iac iin D pin pout DC-AC inverter (averaged) DC-AC Inverter 0.9586 DC-AC Efficiency DC-AC scope Compute efficiency Boost scope 0.9643 Boost efficiency Vg Iout Iref Vout D ef f iciency Pout Boost DC-DC (averaged, C) current control Boost DC-DC Add v ac iac iin Duty pin pout Vout Vpv Vpv Vpv Ppv Ipv = Iref Ipv = Iref Duty ef f iciency pin, pout

I

_RMSref

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6 ECEN2060

How to achieve average power balance?

Simulation example:

• 6-module (85 W each) PV array with full sun (1,000 W/m2 _insolation)

• PV array operates at MPP: P_pv = 6*85 W = 510 W • AC grid RMS voltage: 120 V

• Run simulations for 3 different values of I_RMSref and observe boost output voltage V_out(t) = V_DC(t)

I_RMSref = 3.94 A

I_RMSref = 4.4 A

I_RMSref = 3.4 A

T_ac = AC line period (1/60 seconds)

I

_RMSref

is too low

P

_ac

< P

_pv

V

_DC

increases

I

_RMSref

is too high

P

_ac

> P

_pv

V

_DC

decreases

I

_RMSref

is just right

P

_ac

≈ P

_pv

V

_DC

starts at 200 V

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Average Power Balance by Automatic Feedback Control

• Voltage V_DC is sensed and compared to a reference value V_DCref (e.g. V_DCref = 200 V) • The difference V_DC – V_DCref is the error signal for the feedback controller

• If the error is positive, i.e. if V_DC is greater than V_DCref, the compensator increses I_RMSref • If the error is negative, i.e. if V_DC is less than V_DCref, the compensator decreases I_RMSref • In steady-state, I_RMSref adjusted by the automatic feedback controller is just right so that

V_DC = V_DCref, error signal is zero, and the average power P_ac delivered to the AC grid matches the power generated by the PV array

• Stability, dynamic responses and realizations of feedback controllers are topics beyond the scope of this class. These topics are addressed in Circuits, and more advanced Control and Power Electronics courses

AC utility grid i_ac + − v_ac + − V_PV I_PV PV array Boost DC-DC converter Single-phase DC-AC inverter + − V_DC DC-DC control V_DCref I_RMSref + − compensator

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8 ECEN2060

Energy storage

• Capacitor C provides energy storage necessary to balance instantaneous power delivered to the grid • Magnitude of the resulting voltage ripple ∆V_DC at twice the line frequency (2 x 60 = 120 Hz) depends

on the average power P_ac and capacitance C

P

_ac

p

_ac

(t)

t

P

t

P

t

p

P

_ac

−

_ac

(

)

=

_ac

−

_ac

(

1 −

cos

2 ω

)

=

_ac

cos

2 ω

P_ac > p_ac(t), capacitor C is charged up P_ac < p_ac(t), capacitor C is discarged

∆v

_DC

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Energy storage capacitor C

t

P

t

P

t

p

P

_ac

−

_ac

(

)

=

_ac

−

_ac

(

1 −

cos

2 ω

)

=

_ac

cos

2 ω

• Energy supplied to the capacitor during the time when P_ac > p_ac(t), i.e. when the capacitor is charged from V_DCmin to V_DCmax

P_ac > p_ac(t), capacitor C is charged up P_ac < p_ac(t), capacitor C is discarged

∆v

_DC

ω

θ

ω

π π ac ac T T ac C

P

d

P

dt

t

P

E

ac ac

∫

− −

=

∆

2 / 2 / 8 / 8 /

cos

2

2 cos

• This energy must match the change in energy stored on the capacitor:

(

)

DC DC DC DC DC DC DC DC C

CV

V

C

CV

E

=

−

=

−

+

≈

∆

2

1

2

1

_max _min min max 2 min 2 max

• Solve for the ripple voltage:

ω

ac DC DC

P

V

CV

∆

=

ω

DC ac DC

CV

P

V

=

∆

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10 ECEN2060

Energy storage analysis example

• DC-AC inverter input voltage: V_DC = 200 V

• Average power delivered to the grid: P_ac = 600 W

• Find C so that ∆V_DC = 40 V (i.e. +/-10% of the DC voltage at the input of the DC-AC inverter) • Solution:

J

6 .

1

60

2

600 =

=

∆

π

ω

ac C

P

E

ω

ac DC DC

P

V

CV

∆

=

F

200 Hz

60

2 *

V

200 *

V

40 W

600 µ

π

ω

=

∆

=

DC DC ac

V

P

C

• Note that the energy supplied (or absorbed) by the capacitor is relatively small:

• The total energy stored on the capacitor is also small

J

4

2

1

₂

=

_DC C

CV

E

• This example illustrates the need for only relatively small energy storage in a

grid-connected system, easily accomplished by a capacitor, in sharp contrast to stand-alone PV systems that require very significant energy storage (e.g. batteries)

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Maximum Power Point (MPP) Tracking

Choices for the Boost DC-DC control variable: • Duty cycle D

• Input current reference I_ref • Input voltage reference V_ref

• The objective of the MPP tracking algorithm is to adjust the DC-DC control

variable so that the PV array operates at the maximum power point

• In the example discussed here:

• It is assumed that the Boost output voltage V_out = V_DC is constant • I_ref is used as the control variable for the Boost DC-DC converter

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12 ECEN2060

Reminder: PV array characteristic

• Example: six 85 W modules in series, full sun

0 20 40 60 80 100 120 0 1 2 3 4 5 6

V

_pv

[V]

I

_pv

[A]

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0 20 40 60 80 100 120 0 50 100 150 200 250 300 350 400 450 500

P

_pv

as a function of V

_pv

• Example: six 85 W modules in series, full sun

V

_pv

[V]

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14 ECEN2060 0 1 2 3 4 5 6 0 50 100 150 200 250 300 350 400 450 500

P

_pv

as a function of I

_pv

= I

_ref

• Example: six 85 W modules in series, full sun

I

_pv

= I

_ref

[A]

P

_pv

[W]

Objective: adjust I

_pv

= I

_ref

to operate at MPP

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0 1 2 3 4 5 6 0 50 100 150 200 250 300 350 400 450 500

Simple “perturb and observe” MPP tracking algorithm

I

_pv

= I

_ref

P

_pv

MPP

Initialize I

_ref

,

∆

I

_ref

, P

_old

Measure P

_pv

P

_pv

> P

_old

?

I

_ref

= I

_ref

+

∆

I

_ref

∆

I

_ref

= −

∆

I

_ref

Always step I

_ref

in the

direction of increasing P

_pv

P

_old

= P

_pv Continue in the same direction Change direction

YES

_NO

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16 ECEN2060

MATLAB code: MPP tracking algorithm initialization

Initialize I

_ref

,

∆

I

_ref

, P

_old

Measure P

_pv

P

_pv

> P

_old

?

I

_ref

= I

_ref

+

∆

I

_ref

∆

I

_ref

= −

∆

I

_ref

P

_old

= P

Initialize I

_ref

,

∆

I

_ref

, P

_old

Measure P

_pv

P

_pv

> P

_old

?

I

_ref

= I

_ref

+

∆

I

_ref

∆

I

_ref

= −

∆

I

_ref

P

_old

= P

_pv Continue in the same direction Change direction YES NO

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MATLAB code: MPP tracking algorithm

Initialize I

_ref

,

∆

I

_ref

, P

_old

Measure P

_pv

P

_pv

> P

_old

?

I

_ref

= I

_ref

+

∆

I

_ref

∆

I

_ref

= −

∆

I

_ref

P

_old

= P

Initialize I

_ref

,

∆

I

_ref

, P

_old

Measure P

_pv

P

_pv

> P

_old

?

I

_ref

= I

_ref

+

∆

I

_ref

∆

I

_ref

= −

∆

I

_ref

P

_old

= P

_pv Continue in the same direction Change direction YES NO

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18 ECEN2060

Simulation model: pv_boost_mpp_Iref.mdl

ECEN2060 6-module PV Array 85 x 6 = 510 W DC system Insolation 1-5 Insolation 6 PV power PV energy [kWh] Ideal PV energy [kWh]

ECEN 2060 PV array with MPP tracking Boost DC-DC converter 1 time unit = 1 minute PV voltage Output energy [kWh] -K-kWh (pv) -K-kWh (out) 103.4 Vpv 200 Vout Select insolation for modules 1-5 Select insolation for module 6 Select controller 1000 S6 (constant) S6 (time varying) 1000 S1-5 (constant) S1 (time varying) 510.8 Ppv Ipv Insolation Vpv Ppv PV module (I) PV6 Ipv Insolation Vpv Ppv PV module (I) PV5 Ipv Insolation Vpv Ppv PV module (I) PV4 Ipv Insolation Vpv Ppv PV module (I) PV3 Ipv Insolation Vpv Ppv PV module (I) PV2 Ipv Insolation Vpv Ppv PV module (I) PV1 PV MPP scope P MPPT Iref MPP tracking controller MPPtrackIref.m 4 Iref (constant) 1 Ipv = Iref 4.94 Ipv 1 s Integrate Ppv 1 s Integrate Pout 1 s Integrate Pideal 4.081 Epv 3.936 Eout 4.087 Eideal -K-Convert to kWh Compute Ppv 0.9644 Boost efficiency Vout Vg Iref Iout Pout ef f iciency D Boost DC-DC (averaged) Iref control Boost DC-DC Add -K-85/1000 5 5 modules 1 1 module Ipv Vpv Vpv Vpv Vpv Ppv Ppv Iref 1 Iref Iref Iref Pout Ppv ideal Ppv ideal Pout, Ppv , Pideal Pout, Ppv , Pideal Pout, Ppv , Pideal Duty ef f iciency ef f iciency

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MPP tracking operation

Boost DC-DC converter duty cycle D

PV array voltage V_pv

Boost DC-DC converter input current reference, I_ref = I_pv

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20 ECEN2060

The Future of

Grid-Connected PV Systems

I_pv, V_pv Converter PV Controller I_pv, V_pv I_pv, V_pv Converter PV Controller I_pv, V_pv I_pv, V_pv Converter PV Controller I_pv, V_pv I_pv, V_pv Converter PV Controller I_pv, V_pv I_pv, V_pv Converter PV Controller I_pv, V_pv I_pv, V_pv Converter PV Controller I_pv, V_pv Inverter _{60 Hz AC} Utility

• Scalable modular power electronics: distributed DC-DC conversion

• Much improved performance in the presence of module mismatches or partial shading • Ongoing projects in the Colorado Power Electronics Lab (CoPEC) at CU ECE Dept led

by Prof. Erickson

Innovations in system architecture, control, and power electronics circuit design

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Module-Integrated DC-DC Converter (MIC)

for the Smart PV Roofs