Transcript Part II - Department of Electrical and Computer Engineering

MAN AND ENERGY
A case for Sustainable Living through
Renewable and Green Energy
Ali Keyhani
Professor of Electrical and Computer Engineering
The Ohio State University
Columbus, OH-43210
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1
In part I, the use of energy by man, environment and
sustainable living were presented.
Then the use energy in present time was discussed.
Based on British Petroleum (www. Bp.com), there is only ten
more years of petroleum reserve remain in US , if the current
rate of utilization continues.
British Petroleum data shows that the Middle East oil would
last only another one hundred years at the current worldwide
rate of consumption.
British Petroleum data shows that the world can continue to
use petroleum at current rate for only another forty years.
Challenge of future is to replace petroleum with renewable
energy sources.
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2
Distributed Generation System Technologies
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3
Fuel Cell Technology
Fuel Cells : Features and Types

Electrochemical energy conversion device.

Clean energy source with low emissions.

Characterized by the type of electrolyte used by them.
Fuel Cells : History

First demonstration – (in 1839 ) by Sir William Grove (English physicist)
Produced DC electric power by performing electrolysis experiment.

Demonstration of the first fully operational fuel cell – (in 1959), by Francis Thomas
Bacon, (British Engineer)

In 1960, General Electric (GE) developed PEM fuel cells for NASA which were used on
NASA’s first manned space vehicle .
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4
Important Fuel Cell Candidates for DG applications
Important Fuel Cell Candidates for DG applications
Fuel Cell
Types
Phosphoric Acid Fuel
Cells (PAFC)
Solid Oxide Fuel
Cells (SOFC)
1 kW- 10 MW
Molten
Carbonate Fuel
Cells (MCFC)
0.25 – 10 MW
Proton Exchange
Membrane Fuel Cells
(PEMFC)
0.5-250 kW
Size
100-200 kW
Operating Temperature
180 – 2000C
800 – 10000C
600 – 7000C
35 – 1000C
Installation Cost
(/kW)
Peak Power Density
(mW/cm3)
$2000-3500
$1200-4000
$800-3000
$1000-3000
~200
~200-500
~160
~700
Efficiency (Electrical)
36 - 42 %
45 - 60 %
45 - 55 %
30 – 45 %
Efficiency (with Co-generation)
Up to 80 – 85 %
Up to 80 – 85 %
Up to 80 – 85 %
Up to 80 – 85 %
Start-up Time
1-4 hrs
2-8 hrs
2-5 hrs
20 sec – 6 mins
Current Manufacturers
UTC Fuel Cells, Fuji
Electric Company Ltd,
Mitsubishi Electric
Corp.
Siemens
Westinghouse
Power Corp, Global
Thermoelectric,
ZTEK Corp.
Fuel Cell Energy,
Hitachi Ltd.
Ballard Power Systems,
Avista Labs, UTC Fuel
Cells, Nuvera Fuel
Cells, Plug Power, H
power, Ida Tech
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5
PROBLEM FORMULATION
Schematic Diagram of PEM Fuel Cell based Stand-alone DG System

Analyze the performance and the operating characteristics of stand-alone PEM fuel cell
based (5 kW) DG system feeding to the residential loads.

Develop dynamic models for PEM fuel cell and for its power conditioning unit (dc/dc
boost converter, three-phase dc/ac inverter with L-C filter and transformer ).

Develop control techniques to achieve desired performance of the system.

Determine energy capacity of the storage device needs to be connected at DC bus
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PROBLEM FORMULATION-FUEL CELLS
What are the desired performance characteristics of stand-alone PEM fuel cell based DG
system ?

Provide output voltage to residential loads at magnitude 208 V(L-L)/120 V (L-N) and
at 60 Hz frequency up to its rated value (5kW).

Provide power during peak load demand and during load transients.

Output voltage of the system must have low load regulation (< 5 %) - system must be
able to maintain steady-state output voltage independent of load conditions up to its
rated value.

Provide output voltages with low total harmonic distortion (THD) – (Reduction in 5th
and 7th harmonic)

Protect itself from overload conditions such as short circuit faults.
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PROBLEM FORMULATION
1) Operation of Power Conditioning Unit (dc/dc boost converter, three-phase dc/ac
inverter with L-C filter with transformer ) under Dynamic DC Bus Voltage

For 500-W PEM fuel cell (rated current 25 A) – output voltage varies between 40 V (noload) to 23 volts (full load).

Output voltage of PEM fuel cell is not constant.

As more power is drawn from PEM fuel cell, output voltage of 500- W PEM fuel cell
decreases from 40 volts (no-load voltage) to 23 volts (full-load voltage at rated current
25 A).


Control techniques are needed - To control the output voltage of PEM fuel cell
To control the operation of PEM fuel cell - model is required.
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PROBLEM FORMULATION-FUEL CELLS
2) Determination of Energy Capacity of Storage device to be connected at DC bus

PEM fuel cell cannot quickly respond to fast load changes during peak load demand and during load
transients.

Storage device is required to be connected at the dc bus

Energy capacity of the storage device must be determined based on peak load demand and requirement
of transient current during load switching.
3) Control of DC/DC Boost Converter

Typical output voltage of 500-W PEM fuel cell is 48-60 V. PEM is rated for up to $250Kw. It can be
connected in series or parallel to obtain the desired rating.

DC/DC converter boost converter is to boost the output voltage of PEM fuel cell to desired dc bus
voltage level (480V – 540 V, rated 10 kW).

Control technique should be designed - To control the output voltage of the boost converter such that
the dc bus voltage is regulated within 5% of its desired value.
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PROBLEM FORMULATION-FUEL CELLS
4) Control of Three-phase (VSI) DC/AC Inverter

The control technique should be designed for inverter [480 V dc/ 208 V ac (L-L), rated 10 kW] to satisfy
following performance characteristics:
1.
Low Load Regulation (less than 5%)
The ac output voltage of the DG system should be maintained at 208 V (L-L)/120 V (L-N) independent of
load conditions.
2.
Minimum THD
DG system when feeding to the nonlinear loads, such as rectifiers, switch mode power supplies (SMPS),
must generate minimum harmonics currents.
3.
Fast Transient Response
System must be able to produce output ac voltage with minimum overshoot or undershoot.
4.
Short Circuit Protection
System must be able to provide protection from excessive overload conditions
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EXPERIMENTAL
AND SIMULATION TESTBED
1) Dynamic Modeling

Develop dynamic model of PEM fuel cell , rated 500-W, rated current 25 A, 40V (no-load voltage)-23
V(full-load voltage at rated current 25 A)

Validate 500- W PEM fuel cell model with published results of SR-12 PEM fuel cell manufactured by Avista
Labs.

Scale the model to 5 kW PEM fuel cell, rated current 100 A, 48 V (no-load voltage) - 24
V (V(full-load voltage at rated current 100 A)

Simulate PEM fuel cell model to study its dynamic response - Transient response and Steady-state
response

Develop dynamic model for dc/dc boost converter, (48 V – 480 V, rated 10 kW).

Develop dynamic model for three-phase dc/ac inverter (VSI), [480 V dc/ 208 V ac (L-L), rated 10 kW].
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DISTRIBUTED GENERATION STAND-ALONE
2) Determination of Energy Capacity of storage device
Perform Load following analysis of stand-alone DG system
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SINGLE FAMILY DG SYSTEM

Following load profile of a typical residential home ( 3000-ft2 house occupied by 2adults and 4-children) will be used.

Average Power Demand (base load) - Less than 5kW - satisfied by PV array unit (rated
5 kW).

Peak Load demand = Up to 8 kW

Period of peak load demand = 100 seconds (from 10.30 a.m. to 12.10 p.m.)
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STORAGE DEVICE

Response Time of PEM fuel cell = 20 sec – 6 minutes.

Storage device should be designed to satisfy peak load demand for 100 seconds.

Energy capacity of the storage device is given by:
Estorage 

1
C Vi 2  V f2
2

Vi = initial voltage of the storage device
V f = final voltage of the storage device
C = capacitance of the storage device

Energy to be stored can be given as:
Energy to be stored kW .h  
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Total Peak Load demand (kW ) x Period of peak load demand ( s)
3600
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STORAGE DEVICE SELECTION

To perform simulation – Model of storage will be developed.

The storage device will be selected based on computed energy capacity.
It will be shown that during 100 seconds period of peak load demand:
1) The discharge current of storage device is high.
2) There exists a voltage drop across the storage device.
3) The state-of-charge (SOC) of the storage device varies.
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CONTROL PROBLEM
3) Development of Control Techniques
Control of DC/DC Boost Converter

Objective of control : Regulate dc bus voltage within 5% from its desired value (480 V).
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DC/DC CONVETER

Model of the Boost Converter is needed.
(48 V – 480 V, rated 10 kW).
Lbc  1.8 mH
Cbc  55 F

DC/DC boost converter can be modeled by state space averaging technique proposed by Middlebrook and Cuk .

Inductor current

Input
and capacitor voltage
V fc  48 V  24 V
are selected as state variables.
Vdc (desired )  480 V
is the output of PEM fuel cell.
iL ,bc
vc ,bc
ubc  V fc
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DC/DC CONVERTER MODELING

State space model of DC/DC Boost Converter :
x1bc  iL ,bc

 0
Abc  
 1  D 
 Cbc
x2bc  vc ,bc
 1  D  
Lbc 

1 
Rbc .Cbc 
 1 


Bbc   Lbc 


0


ubc  V fc
Main reasons to use sliding mode control approach:
a)
Sliding mode control has low sensitivity to system parameter variations and uncertainties (load
current) in the system.
b)
Sliding mode control is based on switching control action. All dc/dc converters use switching
devices.
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CONTROL PROBLEM

In boost converter - rate of change of current is much faster than rate of change of
output voltage .

According to theory of singular perturbations, control problem can be solved by using
cascaded control structure with two control loops – inner current control loop and
outer voltage control loop.

Inner sliding mode current controller provides fast response with minimum overshoots
or undershoots and linear control techniques can be used to design voltage controller.
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CONTROL PROBLEM
Control of PEM Fuel Cell Output Voltage

Objective of control: Regulate the output voltage of PEM fuel cell

Output voltage of PEM fuel cell can be changed by varying partial pressure of hydrogen
PH or partial pressure of oxygen PO .
2
2
VO , FC  nS .E0
Cell
0.5
nS RT  PH 2 .( PO2 ) 

ln 

2F
P


H 2O
V fc  VO, FC  n S .(Vloss
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Act
 Vloss  Vloss
O
Conc
)
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FUEL CELL CONTROL
Control of PEM Fuel Cell Output Voltage
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FUEL CELL DYNAMIC MODEL

As partial pressure of hydrogen at the anode of PEM fuel cell increases, it increases
output of PEM fuel cell.

Dynamic equations of partial pressure of hydrogen in PEM fuel cell can be given as:
dpH 2
dt


dpH 2
dt

RT
mH 2 ,net  mH 2 ,cons
Va



RT
mH 2 ,in  mH 2 ,out  mH 2 ,cons
Va
(mH 2 ) net  (mH 2 ) in  (mH 2 ) out


Amount of hydrogen consumed in the reaction is directly related to the output current
of PEM fuel cell.

Flow rate of hydrogen consumed in the electrochemical reaction is given by
mH 2 ,cons 
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nS . I fc
2F
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FUEL CELL DYNAMIC MODEL

Hydrogen utilization factor is defined as:
UH 
mH 2 ,cons
mH 2 ,in

High utilization factors (65-85 %) are desired in PEM fuel cell operation as it minimizes
the required hydrogen flow.

The reference value of hydrogen flow rate can be computed as :
mH 2 ,ref 
nS . I fc,ref
2 FU H

Difference between the required flow rate of hydrogen and flow rate of hydrogen
consumed in the electrochemical reaction is fed to the fuel flow controller.

Hydrogen flow controller controls the valve on hydrogen line to the PEM fuel cell.
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23
DC/AC INVERTER
Control of Three-phase Inverter

Inverter model is needed
Inverter output line-to-line voltage can be represented by the vector –
Three-phase inverter output current scan be represented by -
,
,
Vi  ViAB
iiA
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iiB
ViBC
ViCA 
T
iiC
24
INVERTER MODELING
Inverter Line current vector can be defined as -
=
I i  iiAB iiBC
Transformer primary side - Delta - connected
Primary side line-to-line voltage vector –
iiCA 
T
iiA  iiB
iiB  iiC
iiC  iiA 
T
Primary side line current vector -

Transformer secondary side – Wye - connected
Secondary side phase voltage vector –
V p  V pAB V pBC V pCA

I p  I pA
Secondary side phase current vector –
I pB
I pC

T

T
Load voltage vector -
Load current vector -
Vs  Vsa Vsb Vsc 
T
I s  I sa
I sb
I sc 
T
VL  VLa VLb VLc 
T
I L  I La
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I Lb
I Lc 
T
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INVERTER MODELING

Primary side voltage V p , inverter current I i , load voltageVL , and secondary side
current
are selected as the state variables of the model.
Is

Model of three-phase dc/ac inverter (VSI) with L-C Filter and delta-wye transformer:
xi  Ai xi  Bi ui  Ei di
V pqd 
I 
iqd 
xi  
VLqd 


 I sqd 
V 
ui   iq ,
Vid 
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
 02 x 2

 1 I
 L f 2x2
Ai  
 02 x 2

 1
 Tvqd
 LT
i 
di   iq ,
iid 
1
I2x2
3C f
02 x 2
02 x 2
02 x 2
02 x 2
02 x 2
02 x 2
1
I 2x2
LT

1

Tiqd 
3C f

02 x 2 


1
I2x2 

CL

 RT
I2x2 
LT
 8 x8
Tvqd  Tvqd 0

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row1, 2

 02 x 2 
1

I

2x2 
Bi   L f

 02 x 2 


 02 x 2 8 x2
1 Ns  1  3


2 Np  3
1 
26
VOLTAGE AND CURRENT CONTROL

Voltage control technique for single inverter system based on perfect control of robust
servomechanism problem (RSP) See References.

Voltage control technique is combined with a fast current controller using discrete time
sliding mode controller for limiting the inverter currents under overload conditions.

RSP Voltage controller is used in outer loop and is cascaded with current controller in
the inner loop.
•
M.N. Marwali and A. Keyhani, “Control of distributed generation systems, part I: voltages and currents control,” IEEE Transactions on
Power Electronics, Vol. 19, No.6, pp 1541-50, Nov. 2004.
M.N. Marwali, J.W. Jung, and A. Keyhani, “Control of distributed generation systems, Part II: Load Sharing Control,” IEEE Transactions
on Power Electronics, Vol. 19, No.6, pp. 1551-61, Nov. 2004.
•
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CONTROL OF DC/AC INVERTERS

The control techniques needs to achieve:
1.
2.
3.
4.
Low Load Regulation
Minimum THD
Fast Transient Response
Short Circuit Protection
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PEM FUEL DYNAMIC PERFORMANCE
Dynamic Model of PEM Fuel Cell

The model of 500-W PEM fuel cell , rated 500-W, rated current 25 A, 40V (no-load
voltage)-23 V(full-load voltage at rated current 25 A) is developed.

Two approaches are used to develop the model.
A)
State Space Modeling of PEM Fuel Cell
i) Open-circuit Output Voltage
ii) Irreversible Voltage Losses
iii) Humidification
iv) Mass Balance
v) Thermodynamic Energy Balance
vi) Formation of charge Double Layer
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PEM FUEL DYNAMIC PERFORMANCE
The model is trained and used to obtain:
i)
V-I characteristics.
ii)
Polarization curves for different values of input
iii) Transient response over short-time period (2-5 seconds) and long-time period (5-6
minutes).
iv) Robustness of against the measurement noise is investigated .
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WORKING OF PEM FUEL CELL
Oxidation reaction
at Anode
2 H 2  4 H   4e
Reduction reaction at Cathode
O2  4e   4 H   2 H 2 O
-
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STATE SPACE MODELING OF PEM FUEL CELL
Open-Circuit Output Voltage of PEM Fuel Cell

The reversible electric potential of one cell:
E

Cell
G

2F
F
The change in Gibb’s free energy:
 PH .( PO2 )
G  G 0  RT ln  2
PH 2O

0.5
PH 2



: Partial pressure of hydrogen
E
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 E0
Cell
: Partial pressure of water
PH 2O
0.5
RT  PH 2 .( PO2 ) 

ln 

2 F 
PH 2O

: Stack temperature
: Universal gas const
R
Open-circuit output voltage of one cell:
Cell
: Partial pressure of oxygen
PO2
T

: Faraday’s const.
where,
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E0
 G 0
  
 2F
Cell



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STATE SPACE MODELING OF PEM FUEL CELL

Open-circuit output voltage of PEM fuel cell:
VO, FC  nS .E Cell
VO , FC  n S .E 0
Cell
0.5
n S RT  PH 2 .( PO2 ) 

ln 

2F
P


H 2O
E Cell : Reversible cell potential
E0
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Cell
n S : Number of PEM fuel cell stacks
: Standard reference potential at standard operating conditions
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STATE SPACE MODELING OF PEM FUEL CELL
Irreversible Voltage Losses in PEM Fuel Cell

Output voltage of PEM fuel cell at normal operating conditions is determined by
voltage losses in PEM fuel cell.

Three types of voltage losses exist: a) Activation losses b) Ohmic losses and c)
Concentration losses.
A) Activation Losses

Governance of sluggish electrode kinetics by the rate of electrochemical reaction at an
electrode surface gives rise to activation losses

Dominant at low current density (i.e. at the beginning of V-I characteristic curve).

The activation losses for a single cell stack can be modeled by Tafel equation:
Vloss
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Act

RT  I 
ln    T .[a  b ln( I )]
2 F  I d 
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STATE SPACE MODELING OF PEM FUEL CELL
B)
Ohmic losses

Ohmic resistance of PEM fuel cell that includes the resistance of anode and cathode
due to imperfections in electrode manufacturing and the resistance of polymer
electrolyte membrane to movement of ions.

Ohmic voltage loss for a single PEM fuel cell stack can be given as:
Vloss  I .R O  VA  VC  VM
O
O
O
O
C)
Concentration losses

Formation of concentration gradients of reactants at the surface of the electrodes give
rise to concentration losses

The concentration losses for a single cell stack can be given as:
Vloss

Conc

RT 
I
ln 1 
eF  I L



Significant at higher currents ( at the end of V-I characteristics of the PEM fuel cell).
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STATE SPACE MODELING OF PEM FUEL CELL

Hence, actual output voltage of PEM fuel cell at normal operating conditions :
V fc  VO, FC  n S .(Vloss
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Act
 Vloss  Vloss
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O
Conc
)
36
STATE SPACE MODELING OF PEM FUEL CELL
Humidification in PEM Fuel Cell

In PEM fuel cell, conduction of hydrogen ions through the polymer membrane
depends on the membrane humidity.

The ohmic resistance of the membrane increases as membrane dries out. Hence, it
is essential that membrane remains humidified for efficient operation of PEM fuel
cell.

Therefore, hydrogen gas and air are passed through the humidifier before reaching
the electrodes.

The total vapor transfer through the polymer membrane can be given as :

The relative humidity
at anode and at cathode can be given as:
a
n I
  a
(mv ) M  M v . AS .n S  d d  c
tm
 F
a 
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PH 2O
PH 2O
Sat
c 
PH 2O
PH 2O



c
Sat
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STATE SPACE MODELING OF PEM FUEL CELL
Mass Balance in PEM Fuel Cell

Material conservation of oxygen at cathode can be given as:
mO2  (mO2 ) in  (mO2 ) out  (mO2 ) cons

Net mole flow rate of oxygen at cathode is:
(mO2 ) net  (mO2 ) in  (mO2 ) out

Rate at which oxygen is consumed at cathode in the reaction can be given as:
m 
O2 cons

 mO2  (mO2 ) net  (mO2 ) cons

nS .I
4F
Net mole flow rate of oxygen at cathode can be given as:
M O2 , net
 I
(mO2 ) net  

C
 4F
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



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STATE SPACE MODELING OF PEM FUEL CELL
Mass Balance in PEM Fuel Cell

Material conservation of hydrogen at anode can be given as:
mH 2  (mH 2 ) in  (mH 2 ) out  (mH 2 ) cons

Net mole flow rate of hydrogen at anode is:
(mH 2 ) net  (mH 2 ) in  (mH 2 ) out

Rate at which hydrogen is consumed at anode in the reaction can be given as:
m 
H 2 cons

 mH 2  (mH 2 ) net  (mH 2 ) cons

nS .I
2F
Net mole flow rate of hydrogen at anode can be given as:
M H 2 , net
 I
(m H 2 ) net  

A
 2F
3/28/2016




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39
STATE SPACE MODELING OF PEM FUEL CELL
Mass Balance in PEM Fuel Cell
x1  M O2 , x 2  M O2 , net
x3  M H 2 , x 4  M H 2 , net
 1 
n


 x1  0
C   x1   1 4 F  S 4 F 
I
 x     1   x   
1

2
 2  0

C 
4F




 1 
n


 x 3  0
 A   x3   1 2 F  S 2 F 
I
 x     1   x   
1

0
 4 
 A   4  
2F


Material conservation of water can be given by subtracting rate of flow water going
outside the cell from rate of generation of water in the cell:
x 5  M H 2O
3/28/2016
 x5  

nS
.I
2F 
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40
STATE SPACE MODELING OF PEM FUEL CELL
PEM Fuel Cell Stack Temperature

Temperature of PEM fuel cell assembly increases as electrochemical reaction proceeds
in PEM fuel cell

The net increase in temperature of PEM fuel cell assembly can be given by as:
dT
1  dQC dQE dQL 





dt M fcC fc  dt
dt
dt 
Let
x6  T , x10  QC , x11  QE , x12  QL
 x 6 
3/28/2016
1
x10  x11  x12 
M fc C fc
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41
STATE SPACE MODELING OF PEM FUEL CELL

Dynamic equations of partial pressures of hydrogen can be given as:
   m   m  
 R.T 
. mH 2
 
dt
V
 a 
dPH 2
Let
H 2 out
in
H 2 cons
x7  PH 2
 R.T  M H 2 ,net  R.T 
.
.I
 x 7  
 
V

2
.
V
F
A
 a 
 a 
1
 x 7   .u PA  1 ( x6 ).I
A 
where,
3/28/2016
 R.x 6 

 2.Va F 
1 ( x6 )  
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42
STATE SPACE MODELING OF PEM FUEL CELL

Dynamic equations of partial pressures of oxygen can be given as:
x8  PO2 , x9  PH 2O
1
x 8   .u PC   2 ( x6 ).I
 c 
Let
 R.x 6 

 4.Vc F 
 2 ( x6 )  
where,

Dynamic equations of partial pressures of water can be given as:
x9  3 ( x5 ).x6   4 ( x6 ).I
where,
3/28/2016
 R.x 6 

 2.Va F 
1 ( x6 )  
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43
STATE SPACE MODELING OF PEM FUEL CELL
Thermodynamic Energy Balance in PEM Fuel Cell

Heat generation during electrochemical reaction QC  :
Function of change in Gibbs’s free energy and rate of consumption of molar mass of
hydrogen during the reaction
nI

x10  G. S
2 F 

 x10   5 ( x6 , x7 , x8 , x9 ).I
where,
3/28/2016
 n S G 0 n S R.x 6  x 7 .x8 0.5
 5 ( x 6 , x 7 , x8 , x 9 )  

ln 
 x
2
F
2
F

9

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



44
STATE SPACE MODELING OF PEM FUEL CELL
Thermodynamic Energy Balance in PEM Fuel Cell

Heat generation due to electrical output power : depends on the open-circuit voltage
and the stack current of PEM fuel cell
 x11  [VO , FC ].I
 x11   6 ( x6 , x7 , x8 , x9 ).I
where,
3/28/2016
0.5

n S R.x 6  x 7 .x 8
Cell
 6 ( x 6 , x 7 , x 8 , x 9 )  n S E 0 
ln 
 x
2F

9

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



45
STATE SPACE MODELING OF PEM FUEL CELL
Thermodynamic Energy Balance in PEM Fuel Cell

Heat loss due to air convection
dQL
 (T  uTR ).h S .n S . AS
dt
 x12  [hS n S AS ]. x6  [hS n S AS ].uTR

The net increase in temperature of PEM fuel cell assembly can be given by:
 x 6 
1
x10  x11  x12 
M fc C fc
 h n A
x 6   S S S
 M fc C fc
where,
3/28/2016

 h S n S AS
x


(
x
,
x
,
x
,
x
).
I

 6

7
6
7
8
9

 M fc C fc

 u TR

Cell
 x 7 .x8 0.5
nS E0
n S R.x 6
 7 ( x 6 , x 7 , x8 , x 9 ) 

ln 
M fc C fc FM fc C fc  x 9
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



46
STATE SPACE MODELING OF PEM FUEL CELL
Formation of Charge Double Layer in PEM Fuel Cell

In PEM fuel cell, electrons from anode flow towards cathode via external circuit and
positive hydrogen ions reach cathode through the polymer membrane.

Two charged layers of opposite polarities are formed at cathode.

Charge double layer can store electrical charge and behaves like a capacitor.
3/28/2016
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47
STATE SPACE MODELING OF PEM FUEL CELL
FORMATION OF CHARGE DOUBLE LAYER IN PEM FUEL CELL
The electric charge formed at the cathode can be modeled by capacitor as
The voltage across the capacitor is given as
dV 

VC   I  C C  R Act  R Conc
dt 



The value of the capacitance is given as :
C  e AS dl 
3/28/2016
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48
STATE SPACE MODELING OF PEM FUEL CELL
OVERALL STATE SPACE MODEL OF PEM FUEL CELL
x (t )  A( ).x(t )  B( ).u (t )  G ( ).w(t )
y (t )  C ( ).x(t )  v(t )
x(t ) = system states
y (t ) = system output
u (t ) = control input
w(t ) = disturbance
v (t ) = measurement noise
 = state-dependent parameter vector
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49
STATE SPACE MODELING OF PEM FUEL CELL

 0

 0


 0


 0
A
 0
 0

0 2 x1
 0

0 2 x1

 0
 0
1
C
0
0
0
0
01x 6
C
0
0
0
0
01x 6
0
0
A
0
0
01x 6
1
1
1
0
0
A
0
0
01x 6
0
0
0
0
0
01x 6
0
0
0
0
A6 x 6
01x 6
0 2 x1
0
0 2 x1
0
0 2 x1
0
0 2 x1
0
0 2 x1
 3  x5 
02 x6
01x 6
0 2 x1
0 2 x1
0 2 x1
0 2 x1
0 2 x1
0
0
0
0
hS .nS . AS 
02 x6
0
0
0
0
0
  h .n . A
A6 x 6   S S S
 M fc .C fc
01x 6
01x 6
0 5 x1

 0

 1

B   A

 0

0 3 x1
 0

 0
0 5 x1
0
0
1
C
0 3 x1
0
0







0


0


0 3 x1

 hS .nS . AS  
0

0 5 x1
  hS .n S . AS

 M .C
fc
fc




1
, A13x13  
Act
Conc 

C R  R

C  01x5  8 ( x7 , x8 , x9 ) 01x 6
3/28/2016

0 

0 


0 


0 

0 
0 

0 2 x1 
0 

0 2 x1 

0 
A13x13 


nS 
 8 ( x7 , x8 , x9 ) 
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nS R  x7 .x80.5 
ln 

2 F  x9 
50
STATE SPACE MODELING OF PEM FUEL CELL
x  [M O2 M O2 ,net
M H2

u  u PA
u PC
M H 2 ,net
uTR
M H 2O T
PH 2
PO2
PH 2O
QC
QE
QL VC

T

T
  1 ( x6 )  2 ( x6 )  3 ( x5 )  4 ( x6 )  5 ( x6 , x7 , x8 , x9 )  6 ( x6 , x7 , x8 , x9 )  7 ( x6 , x7 , x8 , x9 )8 ( x7 , x8 , x9 )T
 1
n  1 
G  
 S 

 4 F 4 F   4 F 
  4 ( x6 )
 1   nS 
   7 ( x6 , x7 , x8 , x9 )


 2F   2F 
 5 ( x6 , x7 , x8 , x9 )  6 ( x6 , x7 , x8 , x9 )
w  I 
3/28/2016
n 
 1
 S 

 2F 2F 

v   nS .RO
0
1
C 
 1 ( x6 )
  2 ( x6 )
T

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51
STATE SPACE MODELING OF PEM FUEL CELL
Parameters of 500-W PEM Fuel Cell (Avista Labs SR- 12 PEM Fuel Cell)
3/28/2016
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52
IMPLEMENTATION OF MODEL IN MATLAB/SIMULINK
3/28/2016
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53
SIMULATION RESULTS
V-I Characteristics of PEM Fuel
Cell Model
- Model is simulated for 2720 seconds
with of input variables:
u P = 2 pa, u P = 1 pa, uT = 308 K
A
C
R
Validation of PEM Fuel
Cell Model
-Simulation results are validated with published
results of Avista Labs SR-12 PEM Fuel Cell by
Caisheng Wang, Nehrir, M.H., Shaw S.R**
- The current is varied from 1 A to 25 A over
a period of 2720 seconds in steps of 0.4A
** - Caisheng Wang, Nehrir, M.H., Shaw S.R., “Dynamic Models and Model Validation for PEM Fuel Cells Using Electrical Circuits”, IEEE
Transactions on Energy Conversion, Vol. 20, Issue 2, pp. 442-451, June 2005.
3/28/2016
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54
SIMULATION RESULTS
Temperature Response of PEM Fuel Cell Model

Stack temperature of PEM fuel cell increases to 316 K from 308 K as electrochemical
reaction proceeds in PEM fuel cell

u P A = 2 pa,
3/28/2016
u P=
C 1 pa,
uT =
R 308 K
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55
SIMULATION RESULTS
Power vs. Current characteristics of PEM Fuel Cell Model

Maximum output power is obtained close to the fuel cell rated current (25A) but not
exactly at the rated current.

PEM fuel cell goes in the concentration region near rated current (25 A)

Output power decreases with increasing load current due to decrease in PEM fuel cell’s
output voltage
3/28/2016
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56
SIMULATION RESULTS
Polarization Curves of PEM Fuel Cell Model for Different values of Input Variables
V-I Characteristics of PEM Fuel Cell
V-I Characteristics of PEM Fuel Cell
Model for increasing values of
Model for increasing values of
uPA
uPC
= 2 pa, 10 pa, 30 pa, 50 pa
uPA
= 1 pa ,
uPC
3/28/2016
= 1 pa, 10 pa, 30 pa, 50 pa
uPC
= 308 K
= 2 pa,
uT R
uPA
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= 308 K
uT R
57
SIMULATION RESULTS
Transient Response of PEM Fuel Cell Model
Transient Response of PEM Fuel Cell
Model over Short-Time Period
Transient Response of PEM Fuel Cell
Model over Long-Time Period
u P A = 5 pa, u P C = 5 pa,
3/28/2016
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uT R = 308 K
58
SIMULATION RESULTS
Behavior of PEM Fuel Cell Model under Resistive (R) Load
uPA
= 5 pa,
= 5 pa,
uPC
= 308 K
uT
R
- Response at : No load, 1/4th (quarter)
resistive
load, 1/2 (half) resistive load,
3/4th resistive load and full resistive load
- As the load is increased from no-load to fullload condition, output voltage is reduced
- Stack temperature of PEM Fuel Cell with
corresponding increase in resistive load
3/28/2016
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ncreases
59
SIMULATION RESULTS
Transient Response of PEM Fuel Cell Model
Transient Response of PEM Fuel Cell
Model over Short-Time Period
u P A= 2.5 pa ,
3/28/2016
Transient Response of PEM Fuel Cell
Model over Long-Time Period
u P C= 1 pa,
uT R= 308 K
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60
Distributed Generation Systems
3/28/2016
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61
•
•
•
•
•
•
Distributed Energy Sources:
Photo voltaic Energy
Wind Energy
Fuel Cells
Micro Turbines
Storage Devices
3/28/2016
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62
contains a 100W solar panel, a 12V battery and a charge controller, and a 12VDC/220VAC power inverter.
100 W Solar Photo Voltaic Energy Source
12VDC/220VAC
Power Inverter
12V/100W
Solar Panel
Charge
Controller
3/28/2016
12V Battery
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63
APET018 - 2MVA UPS
Loss budget Large UPS NXL750kVA – Raptor (With Transformer)
Q3
Main & Bypass
Input – 12P
Raptor 750kVA LNA 12P Loss budget
Static Switch & Output
Bypass Input
380V/400V/415V/50Hz,
3ph/4w
Q2
SCR 7-9
V_Byp_A
V_Byp_B
1.60%
V_Byp_C
V_Byp_N
V_PE
SCR 1-3
3
Tin
Input Transformer
DCFA
LR0
DCFB
DCCT
DCFC
Tout
Output Transformer & Inductor
SCR 10-12
F1-3
CT 7-9
F 16-18
1.40%
LR0
DCCC
DCCB
DCCA
Bypass & Main
input connect as
default
configuration
1.20%
CT 3-4
HPA-C
Q4
Lin
Q1
IGBT 1-4
IGBT 5-8
1.00%
IGBT 9-12
V_Inp_A
SCR 4-6
V_Inp_B
Inverter
CT 1-2
F4-6
LR0
V_Inp_C
Main Input
380V/400V/415V/50Hz,
3ph/3w
0.80%
C 13-15
CT 5-6
Battery Cabinet
M1
BCB
CT10
2
HP1
Batt_POS
Battery
Output Transformer
& Filter
0.60%
Batt_NEG
LTx
Rectifier – 12P
1
C 10-12
Internal Optional passive filter
Input Filter and REC
Front End – 12P
0.40%
M1 is an option for Internal optional passive filter
2
Tin is WYE/Delta connection for Raptor B
3
The position of LR0 may change to downstream of F1 to F3
0.20%
0.00%
Lin
AC tot
Ca
p
• Total losses – 44.8kW
Re
DC ctifi
e T
Ca r S in
p CR
&
Bl s
ee
d
T
o
IN
V ut
IG
BT
Ou
L
t A ou
C t
C
S n ap
ub
be
Fu r
se
s
Fa
A
B u ux ns
s S PS
tru U
ct
ur
e
1
In
p
ut
• Efficiency – 93.8%
• Switching frequency – 2.5kHz
• Low frequency 12 pulse isolated input
and PWM inverter isolated output
3/28/2016
Transformer and IGBT switches are the most
significant, … followed by the fans.
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64
APET018 - 2MVA UPS
Loss Budget Medium UPS NXA200kVA (Without transformer)
NX 200kVA ENPC PWM Loss Budget
1.60%
1.40%
1.20%
1.00%
0.80%
0.60%
0.40%
0.20%
• Efficiency – 92.8%
• Switching frequency – 5kHz
0.00%
In Lin
pu
t A (L3
C )
L1 Cap
RE ( Re
C c)
IG
D C BT
Ba Cap
lI
IN GB
V T
IG
B
Ou L1 T
t A ou
ou C C t
tp
ut ap
SC
Fu R
se
s
Fa
A
n
B u ux s
P
sS S
tru U
cu
re
• Total losses - 12.4kW
• PWM rectifier and inverter
• Input and output not isolated
Inductors and IGBT switches are the
most significant
3/28/2016
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65
1400A/1200V IGBT Infineon
APET018 - 2MVA UPS
• Cooligy cold plate with
Infineon
Liquid
cooling of semiconductors
modules for UPS Refrigerant
R134a
• Wind power project ENPC Water
cooling
Semikron Skiip copper base plate less
1800A/1200V Semikron Skiip
module - Water cooled
3/28/2016
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66
APET018 - 2MVA UPS
Liquid cooling of semiconductors (Liebert XD - extreme density)
Pre-piping assembly
Retrofit
Any floor
Any space
Any time
Refrigerant pipes directly
connected to the cold plate
under the semiconductors
3/28/2016
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67
APET018 - 2MVA UPS
Example of size difference PFC power components
Option 12 PFC cabinet
Option 8 PFC cabinet
Topology affects directly size and performance for
same switching frequency
3/28/2016
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68
• Distributed Generation
– Distributed sources close to end users
– Island mode
• Standby backup power
– Grid-connected mode
• Grid support – peak shaving
– Solid-state power conversion in DG
• Technical Areas
–
–
–
–
3/28/2016
Power electronics
Controls
DSP and embedded systems
Electromechanical systems
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69
Three-Phase Four-Wire
Inverter Control
3/28/2016
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70
Three-Phase Four-Wire Inverter Control (1)
• The 3-ph 3-wire topology, for comparison
3/28/2016
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71
Three-Phase Four-Wire Inverter Control (2)
• The 3-ph 4-wire transformerless split dc bus
topology
3/28/2016
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72
Three-Phase Four-Wire Inverter Control (3)
• Specifications
– Input: 3-ph utility 240 V line-to-line, 60 Hz
– Dc link: ± 270 V
– Output: 3-ph 120 V line-to-neutral, 60 Hz
3/28/2016
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73
Three-Phase Four-Wire Inverter Control (4)
• About the topologies: 4-wire vs. 3-wire
– Without output isolation transformer
• Less weight, volume, and cost
• Lower order in the model
• Both the rectifier and the inverter requires 3
dimensional control – the 0 sequence
• More challenge for THD control – the triplets
– Center grounded dc link
• Lower dc voltage utilization in PWM
3/28/2016
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74
Three-Phase Four-Wire Inverter Control (5)
• Control goals – voltage control
–
–
–
–
Low steady state error
Low THD
Robust to load disturbances
Fast transient response
• Challenges
–
–
–
–
3/28/2016
Nonlinear load
Unbalanced load
Transient load disturbances
Model uncertainties
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75
Three-Phase Four-Wire Inverter Control (6)
• Output L-C filter design – differential filtering
– Cut-off frequency
1
fC 
2 L f C f
– Limit Lf and Cf values to lower weight, volume, and cost
– Small enough C to limit fundamental filter current
– Choose Lf = 10.2 mH and Lf = 55 μF.
• Therefore, fC=212 Hz
• Common mode choke issue for the 0-axis component
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76
Three-Phase Four-Wire Inverter Control (7)
• The control strategy
– Discrete-time sliding mode controller (DSMC)
• Used for current control
• Fast response without overshoot
– Robust servomechanism controller (RSC)
•
•
•
•
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Used for voltage control and THD elimination
Zero tracking error
Elimination of harmonics of specified frequencies
Overall stability and robustness
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77
Three-Phase Four-Wire Inverter Control (8)
• Control system structure:
–The inner loop: current control
–The outer loop: voltage control
–Current limiter: limit the inductor current
Vref, 0 + ev,0
-
VL, 0
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RSC
Icmd, 0*
Current
Limiter
IL
Vi,cmd,0
Icmd, 0
ei,0
+
DSMC
SVPWM
Vi
Plant
X
-
Ii, 0
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X
78
Three-Phase Four-Wire Inverter Control
• Inner loop design (4-wire): DSMC
– The plant
  AX  Bu  Ed
X

y1  C1X

VL 0 
X

I
i

0



 033
A
 1 I
 L f 33

Vi 
u  Vi 
Vi 0 
iL 
d  iL 
 iL 0 
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1

I 33 
Cf

033 


 033 
B 1 I 

33 
 L f

C1  033
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 1


I
3

3

E   Cf


 033  63
I3 
79
Three-Phase Four-Wire Inverter Control
• Reference frame transformation
– αβ0 vs. abc
β
b
α
a

1
 f 

2
 f   0
  3
 f 0 
1
2

1

2
3
2
1
2
1 
 
2 f 
 a
3  

fb 

2 
1   f c 
2 
c
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80
Three-Phase Four-Wire Inverter Control
• Convert into per-unit values
– Per-unit equivalent circuit
1
Sb  S rated
3
Ib  2
R
C
Vb  2Vrated
Sb
Vrated
Rf
Zb
Zb 
L
1 L f
Zb
Vb
Ib

1
1

Lf
Zb
1
1
  C f Zb
1
1
1C f
Zb
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81
Three-Phase Four-Wire Inverter Control
–Plant model in discrete time
X(k  1)  A* X(k )  B*u(k )  E*d (k )

y1 (k )  C1X(k )

A e
*
ATs
Ts
B  e
*
0
A (Ts  )
Bd
Ts
E   e A (Ts  ) Ed
*
0
–Discrete-time sliding mode control:
• For an arbitrary finite-dimensional discrete-time
system, a continuous equivalent control law yields
system modes on manifold s=0 within one sampling
period. If control force is bounded, sliding mode s=0
can take place in finite number of steps.
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82
Three-Phase Four-Wire Inverter Control
–The equivalent control

ueq (k )  C1B*
 I
1
cmd , 0
(k )  C1A* X(k )  C1E*d(k )

–The final control, u0 is determined by SVPWM
inverter
u eq (k )
for u eq (k )  u 0

u( k )   u 0
u (k ) for u eq (k )  u 0
 u (k ) eq
 eq
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83
Three-Phase Four-Wire Inverter Control (14)
• RSC
–Internal model principle
• Asymptotic tracking of controlled variables toward the
corresponding references in the presence of
disturbances (zero steady state tracking error) can be
achieved if the modes that generate these references
and disturbances are included in the stable closed loop
systems.
–Optimal control
• Overall stability guaranteed
• Arbitrary good transient response
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84
Three-Phase Four-Wire Inverter Control (15)
–The original discrete-time model
X(k  1)  A * X(k )  B*u(k )  E*d(k )
–Include the dynamics of the DSMC
X(k  1)  A d X(k )  B d u1 (k )  E*d(k )

y (k )  C d X(k )

where

A d  A*  B* C1B*

B d  B* C1B*

1
C1A*

1
Cd  1 0
u1 (k )  I cmd , 0 (k )
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85
Three-Phase Four-Wire Inverter Control (16)
–Design of the servocompensator
• Specifying the tracking/disturbance poles:
– j1,  j3,  j5, and  j7,
• The servocompensator
 0
  2
 1


Ac  






1
0
0
1
 32
0
• In discrete time
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0
1
 52
0
0
 72









1

0
η  A c η  B cev 0
0 
1 
 
0 
 
1
Bc   
0 
 
1 
0 
 
1
η(k  1)  A*c η(k )  B*cev 0 (k )
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86
Three-Phase Four-Wire Inverter Control
– Design of the servocompensator
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87
Three-Phase Four-Wire Inverter Control
–Design of the control gain K
• The augmented system:
ˆX
ˆ (k  1)  A
ˆ (k )  B
ˆ u (k )  E
ˆ d(k )  E
ˆ y (k )
X
1
1
2 ref
ˆ ( k )   X( k ) 
X
 η(k ) 


ˆ   Ad
A
 B * C
 c d
u1 (k )  I cmd , 0 (k )
0  ˆ B d 
B 
A *c 
0
d(k )  I L 0 (k )
*

E
ˆ   
E
1
0
ˆE   0 
2
B * 
 c
y ref (k )  Vref , 0 (k )
• Linear quadratic performance index

ˆ T (k )QX
ˆ (k )  u T (k )u(k )
J   X
k 0
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88
Three-Phase Four-Wire Inverter Control
• The Algebraic Riccati
Equation
• The control gain
ˆ T P  PA
ˆ  Q  1 PBˆ Bˆ T P  0
A

1 ˆT
K B P

ˆ (k )
u1 (k )  I cmd , 0 (k )  KX
• The control
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 K 0
 X( k ) 
K1 
 K 0 X(k )  K1η(k )

 η(k ) 
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89