3.2 U s -I s estimator In order to integrate this estimator model in the control system of an induction machine, the stator voltages and currents are considered here as inputs, and the
Trang 23.2 U s -I s estimator
In order to integrate this estimator model in the control system of an induction machine, the
stator voltages and currents are considered here as inputs, and the estimated outputs are the
magnitude and the angle of the rotor flux and the electromagnetic torque
This estimator is derived by direct synthesis from the machine state equations which are
written in terms of the d-q axis components of the stator and rotor flux as state variables
This choice is justified by the fact that the system matrix is simpler than the d-q axis current
state space model
The machine equations are derived from its general model where the speed of the rotational
d-q system of axes ωλ = 0, since a fixed reference frame is considered here
The equations can be written in state space form The outputs will be the stator and rotor
sq sd
T sq
sd
T rq
rd sq
sd
i i
i i
y
u u
u x
0 0
i R
u L
L dt
dψ
dt
di σL
i R
u L
L dt
dψ
sq s
sq s
sq m
r sq
sd s
sd s
sd m
r sd
(32) The Simulink model of the estimator can be observed in Fig 13
Fig 13 Us-Is estimator Simulink model
The electromagnetic torque is calculated like:
sq rd sd rq
r s
m p
L z
2
3
(33) The rotor flux magnitude and angle can be written as:
2 2
Fig 14 Estimated rotor flux magnitude in d-q rotating frame using Us-Is estimator
Trang 3Fig 15 Estimated rotor flux angle in d-q rotating frame using Us-Is estimator
Fig 16 Estimated electromagnetic torque using Us-Is estimator
3.3 Us-ω estimator
A rotor flux estimator which can operate in the range of low rotational speeds can be designed if one considers as measured inputs the stator voltages and the rotor angular velocity (Apostoaia & Scutaru, 2006) This estimator is derived by direct synthesis from the machine state equations which are written in terms of the d-q axis components of the stator and rotor flux as state variables The same assumptions were made as in the previous section for the estimator Us-Is
We will denote the parameters used in the observer, as well as the estimated variables, with the same symbols like in the machine model but having the superscript “e” in addition Thus, the system of equations of the flux observer is derived as follows:
e m e sq e s e sd e
e
L
L T
T dt
e m e sq e sd e s e s
e
L
L T
T dt
r e rd e sd e s
e m e r
e
L
L T dt
r e sq e s
e m e r
e
L
L T dt
e s e e s
e r e e r
R
L
(40) The electromagnetic torque is reconstructed in terms of the estimated state variables similarly to equation (33) The rotor flux magnitude and rotor flux angle are calculated like
in (34) and (35)
The Simulink block diagram showing the Us-ω estimator can be seen in Fig 17
Trang 4Fig 15 Estimated rotor flux angle in d-q rotating frame using Us-Is estimator
Fig 16 Estimated electromagnetic torque using Us-Is estimator
3.3 Us-ω estimator
A rotor flux estimator which can operate in the range of low rotational speeds can be designed if one considers as measured inputs the stator voltages and the rotor angular velocity (Apostoaia & Scutaru, 2006) This estimator is derived by direct synthesis from the machine state equations which are written in terms of the d-q axis components of the stator and rotor flux as state variables The same assumptions were made as in the previous section for the estimator Us-Is
We will denote the parameters used in the observer, as well as the estimated variables, with the same symbols like in the machine model but having the superscript “e” in addition Thus, the system of equations of the flux observer is derived as follows:
e m e sq e s e sd e
e
L
L T
T dt
e m e sq e sd e s e s
e
L
L T
T dt
r e rd e sd e s
e m e r
e
L
L T dt
r e sq e s
e m e r
e
L
L T dt
e s e e s
e r e e r
R
L
T
(40) The electromagnetic torque is reconstructed in terms of the estimated state variables similarly to equation (33) The rotor flux magnitude and rotor flux angle are calculated like
in (34) and (35)
The Simulink block diagram showing the Us-ω estimator can be seen in Fig 17
Trang 5Fig 17 Us-ω estimator Simulink model
In Fig 18, Fig 19, and Fig 20, simulation results are shown for the Us-ω estimator, during a
start up of the squirrel cage induction motor A rated speed command under full torque
load was used in the simulations
The magnitude and the angle of the rotor flux estimates are shown in Fig 18 and Fig 19,
and the electromagnetic torque estimation is seen in Fig 20
Fig 18 Estimated rotor flux magnitude in d-q rotating frame using Us -ω estimator
Fig 19 Estimated rotor flux angle in d-q rotating frame using Us ω estimator
Fig 20 Estimated electromagnetic torque using Us ω estimator
Trang 6Fig 17 Us-ω estimator Simulink model
In Fig 18, Fig 19, and Fig 20, simulation results are shown for the Us-ω estimator, during a
start up of the squirrel cage induction motor A rated speed command under full torque
load was used in the simulations
The magnitude and the angle of the rotor flux estimates are shown in Fig 18 and Fig 19,
and the electromagnetic torque estimation is seen in Fig 20
Fig 18 Estimated rotor flux magnitude in d-q rotating frame using Us -ω estimator
Fig 19 Estimated rotor flux angle in d-q rotating frame using Us ω estimator
Fig 20 Estimated electromagnetic torque using Us ω estimator
Trang 73.4 Neural network based speed estimator
The inputs to the neural networks are the stator voltages and stator currents at time step
kand k 1 ( , , , ) u u i isd sq sd sq The target is the rotor speed in revolutions per minute at
The network is a feedforward network with backpropagation algorithm The training
method is Levenberg-Marquardt (Caudill & Butler, 1999)
The neural network has 2 layers with 30 neurons on the hidden layer, and with ‘tansig’
activation function, and one neuron on the output layer, with ‘purelin’ activation function
The derivative of the speed is estimated because the feedforward, backpropagation method
is not appropriate of estimating integral components The estimation of an integral
component require some knowledge of the previous states and it would mean that the
output of the network would need to be feed back as another input to the network After the
derivative component of the speed is estimated the simple integral method is used to extract
the speed value, using ‘cumsum’ from MATLAB
The derivative component of the speed can be seen in Fig 21, while the estimated rotor
speed after the integration can be found in Fig 22
As it can be seen from the below figures very good simulation results can be obtained using
neural network for speed estimation, which can be used in combination with any other
estimator in a sensorless vector control scheme or in sensor fusion control scheme(Simon,
2006)
Fig 21 The derivative component of the rotor speed using neural network
Fig 22 The estimated rotor speed using neural network
by the incremental encoder mounted on the induction generator shaft which is coupled with the wind turbine The information from and to the computer is transferred through the dSpace board using the Digital I/O connector
The Real-Time Simulink model of the estimator and measurement channels can be seen in Fig 23 In the feedback loop of the system two stator currents are measured together with the rotor speed The currents are measured with LEM LA-NP 1752 currents transducers and the user has access to these measurements through BNC connectors These signals are fed to the dSpace board, and from the board to the computer The DS1104ADC_C5 and DS1104ADC_C6 blocks are used for the current measurements The scaling factor for these measurement blocks is 1:20 For smoother measurement and better wave visualization a first order filter is also used
The speed is measured using digital encoder and with the help of the blocks DS1104ENC_POS_C1 and DS1104ENC_SETUP can be used as an input for the observer In order to receive the radian angle the DS1104ENC_POS_C1 block needs to be multiplied by
2
encoder
In this experiment the encoder lines=1000 To obtain the desired speed the delta
position scaled has to be divided by the sampling time
in rotating reference frame the rotor flux magnitude is calculated using equation (33)
Trang 83.4 Neural network based speed estimator
The inputs to the neural networks are the stator voltages and stator currents at time step
kand k 1 ( , , , ) u u i isd sq sd sq The target is the rotor speed in revolutions per minute at
The network is a feedforward network with backpropagation algorithm The training
method is Levenberg-Marquardt (Caudill & Butler, 1999)
The neural network has 2 layers with 30 neurons on the hidden layer, and with ‘tansig’
activation function, and one neuron on the output layer, with ‘purelin’ activation function
The derivative of the speed is estimated because the feedforward, backpropagation method
is not appropriate of estimating integral components The estimation of an integral
component require some knowledge of the previous states and it would mean that the
output of the network would need to be feed back as another input to the network After the
derivative component of the speed is estimated the simple integral method is used to extract
the speed value, using ‘cumsum’ from MATLAB
The derivative component of the speed can be seen in Fig 21, while the estimated rotor
speed after the integration can be found in Fig 22
As it can be seen from the below figures very good simulation results can be obtained using
neural network for speed estimation, which can be used in combination with any other
estimator in a sensorless vector control scheme or in sensor fusion control scheme(Simon,
2006)
Fig 21 The derivative component of the rotor speed using neural network
Fig 22 The estimated rotor speed using neural network
by the incremental encoder mounted on the induction generator shaft which is coupled with the wind turbine The information from and to the computer is transferred through the dSpace board using the Digital I/O connector
The Real-Time Simulink model of the estimator and measurement channels can be seen in Fig 23 In the feedback loop of the system two stator currents are measured together with the rotor speed The currents are measured with LEM LA-NP 1752 currents transducers and the user has access to these measurements through BNC connectors These signals are fed to the dSpace board, and from the board to the computer The DS1104ADC_C5 and DS1104ADC_C6 blocks are used for the current measurements The scaling factor for these measurement blocks is 1:20 For smoother measurement and better wave visualization a first order filter is also used
The speed is measured using digital encoder and with the help of the blocks DS1104ENC_POS_C1 and DS1104ENC_SETUP can be used as an input for the observer In order to receive the radian angle the DS1104ENC_POS_C1 block needs to be multiplied by
2
encoder
In this experiment the encoder lines=1000 To obtain the desired speed the delta
position scaled has to be divided by the sampling time
in rotating reference frame the rotor flux magnitude is calculated using equation (33)
Trang 9Fig 23 Real-time Simulink model of the measurement channels and the estimator
The real-time estimated values can be followed on the dSpace Control Desk as seen in Fig
The Us-Is estimator has a big advantage that it can be used in variable speed applications and a big advantage is the fact that the estimator equations are not containing the rotor resistance as parameter, which eliminates the problems caused by the temperature
The estimator based on Us-ω has the advantage that is simple to implement but meanwhile
is not taking into account any real system noise Also uses open mathematical integration for the parameter estimation which is hard to implement in real applications
The block diagrams were used to simulate the system in real time using an existing dSPACE
DS 1104 control board This board is based on a floating point DSP with high speed ADC converters which makes suitable for the cross compilation of the Simulink models into the dedicated platform
Further steps of this research would involve the validation of the presented models and estimators for a real life small wind turbine All the necessary software and hardware design
is available through the use of the modern HIL dSpace cards
6 References
L Tamas & Z Szekely (2008): “Feedback Signals Estimation of an Induction Drive with
Application to a Small Wind Turbine Generator, Automation Computers and Applied Mathematics, Volume 17, Number 4, 2008, p.642-651
Szekely, Z (2008) “Extended Speed Control of an Induction Motor Drive utilizing Rotor
Flux Orientation Technique in Real-Time”, Masters Thesis, Purdue University Calumet, Hammond, Indiana, USA
Scutaru, Gh & Apostoaia, C (2004) “MATLAB-Simulink Model of a Stand- Alone Induction
Generator”, in Proc OPTIM 2004, “Transilvania” University of Brasov, Romania, May 20-21, 2004, vol II, pp.155-162
Apostoaia, C & Scutaru, Gh (2006) “A Dynamic Model of a Wind Turbine System”, in
Proceedings OPTIM 2006, “Transilvania” University of Brasov, Romania, May
18-19, 2006, vol II, pp.261-266
A Kelemen, M Imecs (1991): Vector Control of AC Drives, Volume 1; Vector Control of
Induction Machine Drives, OMIKK-Publisher, Budapest, Hungary Kalman, R.E (1960): A new approach to linear filtering and prediction problems．
Transactions of the ASME-Journal of Basic Engineering，Vol 82 Simon, D (2006): Optimal State Estimation．v l.，Willey Interscience
Caudill, M & C Butler (1992) Understanding Neural Networks: Computer Explorations,
Vols 1 and 2, Cambridge, MA: The MIT Press
Trang 10Fig 23 Real-time Simulink model of the measurement channels and the estimator
The real-time estimated values can be followed on the dSpace Control Desk as seen in Fig
The Us-Is estimator has a big advantage that it can be used in variable speed applications and a big advantage is the fact that the estimator equations are not containing the rotor resistance as parameter, which eliminates the problems caused by the temperature
The estimator based on Us-ω has the advantage that is simple to implement but meanwhile
is not taking into account any real system noise Also uses open mathematical integration for the parameter estimation which is hard to implement in real applications
The block diagrams were used to simulate the system in real time using an existing dSPACE
DS 1104 control board This board is based on a floating point DSP with high speed ADC converters which makes suitable for the cross compilation of the Simulink models into the dedicated platform
Further steps of this research would involve the validation of the presented models and estimators for a real life small wind turbine All the necessary software and hardware design
is available through the use of the modern HIL dSpace cards
6 References
L Tamas & Z Szekely (2008): “Feedback Signals Estimation of an Induction Drive with
Application to a Small Wind Turbine Generator, Automation Computers and Applied Mathematics, Volume 17, Number 4, 2008, p.642-651
Szekely, Z (2008) “Extended Speed Control of an Induction Motor Drive utilizing Rotor
Flux Orientation Technique in Real-Time”, Masters Thesis, Purdue University Calumet, Hammond, Indiana, USA
Scutaru, Gh & Apostoaia, C (2004) “MATLAB-Simulink Model of a Stand- Alone Induction
Generator”, in Proc OPTIM 2004, “Transilvania” University of Brasov, Romania, May 20-21, 2004, vol II, pp.155-162
Apostoaia, C & Scutaru, Gh (2006) “A Dynamic Model of a Wind Turbine System”, in
Proceedings OPTIM 2006, “Transilvania” University of Brasov, Romania, May
18-19, 2006, vol II, pp.261-266
A Kelemen, M Imecs (1991): Vector Control of AC Drives, Volume 1; Vector Control of
Induction Machine Drives, OMIKK-Publisher, Budapest, Hungary Kalman, R.E (1960): A new approach to linear filtering and prediction problems．
Transactions of the ASME-Journal of Basic Engineering，Vol 82 Simon, D (2006): Optimal State Estimation．v l.，Willey Interscience
Caudill, M & C Butler (1992) Understanding Neural Networks: Computer Explorations,
Vols 1 and 2, Cambridge, MA: The MIT Press
Trang 12Mamadou Lamine Doumbia and Kodjo Agbossou
Hydrogen Research Institute Department of Electrical and Computer Engineering
Université du Québec à Trois-Rivières C.P 500, Trois-Rivières (Québec) G9A 5H7
Canada
1 Introduction
Renewable energy systems (RES) such as photovoltaic and wind generators are increasingly
used as a means to satisfy the growing need for electric energy around the world For many
years, the Hydrogen Research Institute (HRI) has developed a renewable
photovoltaic/wind energy system based on hydrogen storage The system consists of a
wind turbine generator (WTG) and a solar photovoltaic (PV) array as primary energy
sources, a battery bank, an electrolyzer, a fuel cell stack, different power electronics
interfaces for control and voltage adaptation purposes, a measurement and monitoring
system The renewable energy system can operate in stand-alone or grid-connected mode
and different control strategies can be developed
This paper presents the HRI’s grid-connected renewable energy system (RES) The system’s
main components i.e photovoltaic arrays, wind turbine, batteries, electrolyzer and fuel cell,
are described individually and their modelling and simulation methodologies are presented
The complete system model is developed by integrating individual sub-units
Matlab/Simulink and LabVIEW softwares are used for modelling, programming and
analyzing the behavior of each system sub-unit The state of charge control method was
used to validate the developed simulation models The results obtained with the two
modelling and simulation softwares were compared Stand-alone and grid-connected
operating conditions are investigated and experimental data are provided to support
theoretical and simulation analyses The power transfer study in the interconnected system
is also presented Such a global model is useful for understanding the system’s operation,
and optimal dimensioning and effective control of the renewable energy system with
hydrogen storage (RESHS) (Kim S-K et al., 2008)
14
Trang 132 System components modelling
Figure 1 shows the block diagram of the HRI renewable energy system (Doumbia et al.,
2007) The system consists of a 10 kW permanent magnet wind turbine generator and a 1
kW solar photovoltaic (PV) array as primary energy sources, a battery bank with 48V
voltage, a 5 kW electrolyzer, a 1.2 kW proton exchange membrane fuel cell (PEMFC) stack
A 5 kW reversible inverter is used to convert 48V DC bus voltage into alternating current
(AC) with 115V The inverter output can be connected to the utility grid or to power a local
AC load A buck converter is used to control the electrolyzer and a boost converter is used
to convert the 24V PEMFC output voltage into 48V DC bus voltage
Fig 1 Block diagram of the HRI’s renewable energy system with hydrogen storage
2.1 Photovoltaic Array
The solar array is a group of several modules electrically connected in series-parallel
combinations to generate the required current and voltage The photovoltaic (PV) module
current flow, and depends on the p-n junction depth, the impurities and the contact
The equations which describe the I-V characteristics of the cell are:
)1(
) (
S
e I I
where :
I 0 = diode saturation current (A)
V = solar cell terminal voltage (V)
n = diode quality factor
T = ambient temperature (K)
))(1
) 1
I G
)( 2 1
) 1 (
) 1 ( ) 2 (
I I
K
T SC
T SC T SC
I SC(T1) = short circuit current at temperature T1 (A)
I SC(T2) = short circuit current at temperature T2 (A)
Trang 14Photovoltaic/Wind Energy System with Hydrogen Storage 251
2 System components modelling
Figure 1 shows the block diagram of the HRI renewable energy system (Doumbia et al.,
2007) The system consists of a 10 kW permanent magnet wind turbine generator and a 1
kW solar photovoltaic (PV) array as primary energy sources, a battery bank with 48V
voltage, a 5 kW electrolyzer, a 1.2 kW proton exchange membrane fuel cell (PEMFC) stack
A 5 kW reversible inverter is used to convert 48V DC bus voltage into alternating current
(AC) with 115V The inverter output can be connected to the utility grid or to power a local
AC load A buck converter is used to control the electrolyzer and a boost converter is used
to convert the 24V PEMFC output voltage into 48V DC bus voltage
Fig 1 Block diagram of the HRI’s renewable energy system with hydrogen storage
2.1 Photovoltaic Array
The solar array is a group of several modules electrically connected in series-parallel
combinations to generate the required current and voltage The photovoltaic (PV) module
current flow, and depends on the p-n junction depth, the impurities and the contact
The equations which describe the I-V characteristics of the cell are:
)1(
) (
S
e I I
where :
I 0 = diode saturation current (A)
V = solar cell terminal voltage (V)
n = diode quality factor
T = ambient temperature (K)
))(1
) 1
I G
)( 2 1
) 1 (
) 1 ( ) 2 (
I I
K
T SC
T SC T SC
I SC(T1) = short circuit current at temperature T1 (A)
I SC(T2) = short circuit current at temperature T2 (A)
Trang 15The diode saturation current I0 can be determined by the equation (6) :
1 ) ( 0
qVg n
T
T I
1
1 1 1
1
) ( )
( 0
T SC T
e
I
where:
V OC(T1) = Open circuit voltage at the temperature T1 (V)
V Voc
1 dI
dV
1 1 1
) ( 1 ) (
T qVoc T
nkT
q I
Voc
dI
Fig 2 Circuit diagram of PV model
Solar panels installed at IRH are composed of 16 modules, i.e four rows of four serial
connected modules The electrical performance and the characteristic curves of the PV
modules are dependent on temperature and illumination From the preview equations, the
I-V characteristics of the PV modules are plotted for different temperature (Figure 3) and
illumination (Figure 4) conditions
Fig 3 PV module I-V characteristics for
2.2 Wind turbine
Some of the available power in the wind is converted by the rotor blades to mechanical power acting on the rotor shaft of the WT The wind turbine rotor that extracts the energy from the wind and converts it into mechanical power is a complex aerodynamic system For state-of-the-art modelling of the rotor, blade element theory must be used Modelling the rotor using blade element theory has, however, a number of drawbacks (Slootweg et al., 2003)
• Instead of only one wind speed signal, an array of wind speed signals has to be applied
• Detailed information about the rotor geometry should be available
• Computations become complicated and lengthy
To overcome these difficulties, a simplified way of modelling the wind turbine rotor is normally used when the electrical behaviour of the system is the main point of interest For
β)-curve can be used An algebraic relation between wind speed and mechanical power extracted is assumed, which is described by the well-known expression (Slootweg et al., 2003), (Cardenas & Pena, 2004):
3 p
v = wind speed (m/s)
leads directly to the large size of a wind turbine The power coefficient describes that
Trang 163 1
) (
0
qVg n
T
T I
1
1 1
1
1
) (
) (
nkT T
qVoc
T SC
V OC(T1) = Open circuit voltage at the temperature T1 (V)
V Voc
1 dI
dV
1 1
1
) (
1 )
(
T qVoc
T
nkT
q I
Voc
dI
Fig 2 Circuit diagram of PV model
Solar panels installed at IRH are composed of 16 modules, i.e four rows of four serial
connected modules The electrical performance and the characteristic curves of the PV
modules are dependent on temperature and illumination From the preview equations, the
I-V characteristics of the PV modules are plotted for different temperature (Figure 3) and
illumination (Figure 4) conditions
Fig 3 PV module I-V characteristics for
2.2 Wind turbine
Some of the available power in the wind is converted by the rotor blades to mechanical power acting on the rotor shaft of the WT The wind turbine rotor that extracts the energy from the wind and converts it into mechanical power is a complex aerodynamic system For state-of-the-art modelling of the rotor, blade element theory must be used Modelling the rotor using blade element theory has, however, a number of drawbacks (Slootweg et al., 2003)
• Instead of only one wind speed signal, an array of wind speed signals has to be applied
• Detailed information about the rotor geometry should be available
• Computations become complicated and lengthy
To overcome these difficulties, a simplified way of modelling the wind turbine rotor is normally used when the electrical behaviour of the system is the main point of interest For
β)-curve can be used An algebraic relation between wind speed and mechanical power extracted is assumed, which is described by the well-known expression (Slootweg et al., 2003), (Cardenas & Pena, 2004):
3 p
v = wind speed (m/s)
leads directly to the large size of a wind turbine The power coefficient describes that
Trang 17fraction of the power in the wind that may be converted by the turbine into mechanical
and is only a maximum for a unique tip speed ratio Improvements are continually being
sought in the power coefficient by detailed design changes of the rotor and, by operating at
variable speed; it is possible to maintain the maximum power coefficient over a range of
wind speeds However, these measures will give only a modest increase in the power
output Major increases in the output power can only be achieved by increasing the swept
area of the rotor or by locating the wind turbines on sites with higher wind speeds (Burton
et al., 2001)
(Slootweg et al., 2003), (Lei et al., 2006) For the Bergey BWC Excel 10 kVA wind turbine
))
* 0762 1 exp(
292 44 1 (
* ) 2934 1 26584 0 023649 0 0007391
The battery plays the role of an energy buffer for short-term energy storage Different
models for batteries are available, in particular those suitable for electrical vehicle
applications (Kélouwani et al., 2005) For stationary applications such as the renewable
sources, the models described in (Vosen & Keller, 1999) use many experimental parameters
that cannot be estimated easily, such as the overcharge effect (though in a
properly-controlled RESHS, this effect does not happen, and hence is not included in the present
model) The main parameters which determine the battery’s performance are its internal resistance, the polarization effect, and the long-term self-discharge rate The self-discharge rate is difficult to estimate, and is itself subject to a number of factors such as the operating temperature, the number of operation cycles, and the materials and technology used in its manufacture The battery model used in this paper presents the relation between voltage, current and the battery state of charge Q as follows (Chérif et al., 2002):
In discharge mode (I<0):
It M 1
I R C
It g V ) t ( V
d
d d
It M 1 I R C
It 1 g V ) t ( V
c
c c
In (12), (13), (15) and (16) the subscripts d and c indicate the discharging and charging
modes
The state of charge Q of the battery can be calculated through the current integral
0
Q Idt
d d d
d d d
Q M I
R C
Q g V Q V
) 1 ( 1 )
c c c
c c c
Q M I
R C
Q g V Q
where :