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Stand Alone Bio-Gas Power Plants with Induction Generator and PWM Voltage Source Inverter
STAND ALONE BIO - GAS POWER PLANTS WITH INDUCTION GENERATOR AND PWMVOLTAGESOURCEINVERTER
Jifi Klima Department of electrical engeneenng and alltomation Czech Agncldtllre Un/verslty in Praglle Praha 6, 165 21- Praha 6 - S'lIchdol ,CZECH REPUBLIC reI: 00 420 22383203 Far: : 00 420 383203 Absence: BlOga, energy conver.ion iCheme u,ing bio - ga. engine driven ielf excited induction generator a. voltage AC iiOurce and PWM Voltage Source Invener (VS I ) have been mode led and inve.tigaded In remote location, where the utility grid doe, nOl exi,t . li\and alone bioga' energy conver.ion iCheme can be uo;ed to feed local electrical load Paper preo.entl. the mathematIcal model "h,ch enable. the dueet calculatIon of the load current. from PWM VSI The method make. u"" ut Laplacei and of the Z -tran.formatlon for calculation tran,ient and ,teady li\ate component. of load current.
1.1 ntroduction Biogali can be produced by anaerobic fermentation of biological walite. The ecological alipect now plaY!i an important role.In liome i!iolated regionli a bio gali power plant may even be the ba.ic .ource of electrical and thermal energy .An induction generator ha. emerged as a suitable reiource of AC energy . However ,there is an appreciable amount of fluctuationli in the magnitude and frequency of the generated terminal voltage , due to itli dependency on rotor lipeed and parameters of the load , when induction generator is used.Hence, the variable magnitude , variable frequency voltage at the .elf - exited induction generator terminal is first rectified and DC voltage is then transferred to the local load throught Pulse Width Modulated (PWM) Voltage Source Inverter.
2.System configuration The proposed scheme consist!i of a !ielf - exiced induction generator with capacitors C , driven by gas dieiel engine, a diode bridge rectifier and PWM inverter feedeng a local load as shown in fig I.
R
E
c
Loe
Roe Tr ............-tfNV l~~----'
t
* Fig. I. System configuration
13 7
LOAD
Ga. die.el engine The 4S II OG gaii dieiel engine made by CKO Hofovice iii modified dieiel engine which mOitly u.ed ai driven unit for UPS (Uniterraptable Power Supply).
I'
Parameteri of the motor : P = 45 kW , velocity n = 1480 rpm , number of cylinderi = 4 , volume of cylinder. = 5,7 dm 3 Self - Exited Induction Generator It is eisentially an induction machine driven by a prime mover (dieiel engine) and having a iource of reactive power ( ielf - exitation capacitor bank). The dynamics of the ielf - exiced induction generator can be repreiented electromechanical equation. derived in the 'YnchronoU!~ly rotating d - g frame [2] .
by
the following
(I)
p i.t. = ( iq.IC llo. + K2 Lm Wm ) iq. - KI r\
P iq, = K2 TI iq. + LI K2 Wm
~. - (r2
i.J. + ~ Lm Wm ~r + K2 T2 i.J, - ~ Ud.
(2)
+ K2 Lm r2) L2 iq, + (LI K\ Wm- iq. IC llo.) i.t,
p ~r = -L\ K2 Wm~. + K2 T\~. - (L\ K\ Wm - ~. / C llo.) ~r + (r2 + K2 Lm T2)L 2 ~r + K 2llo.
(3) (4)
p llo. = (I / C) ( ~. - 2--J3 ht ) ioc
where
and
The above equations were derived a§§uming that initial orientation of the d - q rotating reference frame ii such that d - axis is aligned with stator terminal voltage phaior (i .e. Uq. = 0). Uncontrolled Rectifier It is a 3 - phase diode bridge rectifier which is u.ed to convert the variable magnitude , frequency voltage at the a'YnchronnoU!~ generator terminal to DC. The DC voltage UR at it. output can be expreised in term. of the peak phaiie voltage generator
Udo
= Vg
of the
DC Link and Input Filter The input filter consisti of a ieriei reactor and a shunt capacitor aii ihO\\-1l in Fig. I.The ieriei reactor reduce. the current ripple content in the rectifier output current and the .hunt capacitor reducei the ripple content in the DC link voltage providing suitable voltage source for PWM inverter. The DC link current i. governed by equation :
where Roc and Loc are the DC link reactor§ reiistance and inductance reipectively, ioc is the dc link current and UI is the DC voltage at the inverter input. 138
3.PWM Voltage Source Inverter 1 ne DC voltage available at the rectifier output i. filtered and converted to DC power u.ing PWM inverter. Space Vector Pul.e Width Modulation (SVPWM) i. u.ed for forming voltage of the load.The SVPWM ha. recently become popular, mainly due to .imple computation algorithm and ealiY digital implemantation [4) . Voltages of the phases are expressed as space vectors by means of relation :
1
Us
-
= - - (UA + e J ~'V3 UB + e-j 2~:3 uc )
where UA
3
, UB, Uc
are pha.e output voltage. reapectively.
Figure 2 .howii a diagram of voltage .pace vector. in the comlex plane
V3
V2
f:;
----~~~~--~
V4
V6
V5
Fig.2 Diagram of voltage vectorii
The concept of SVPWM i§ ba§ed on the following principle§: [2) a)
Every sixth of a period is divided into NJ sectors duration tlT
b) Two adjacent direction. of the .pace voltage vector are utilized in each .ector c) Vecton. Vo and V7 zero vector. are applied at the beginning and end of each .ector re.pectively. F or practical perpoie. the §equency of pu\iie§ and gapii , defined for 1/6 of a period , i. .tored in the microcomputer memory .ln the iiub.equent .ixth of the period the direction of the voltage iii rotated through 1[/3.
From Fig.2 relation
lii
iieen that for fir.t iiector , where 0 tlT
$
P
$
rr./3 the mean value can be calculated uiiing the
tlTJ U tlT2 ..I n·.' - - + - -C' T 3 T 3 T For the next we iihall expre§§ time in termii of the interval number n and variable .I' _AV--e 4
U
U
(5)
= -
139
E
a.
TI t
= (n + E) - - = (n + E) T
(6)
n = 0, 1,2 .. .. ... .
6
Expressing (5) in komplex plane we get times for duration of vectors VI , V2 and Vo or V7 respectively .
4.Current of tbe load
In view of the .ymmetry of the switching process the space vector of the load voltage (whose initial value is Us (0» may be expressed in terms
(7) where f(E) expresses the time dependency of the vector \vithin interval T.Dis;crete function (7) can be used to compute the pattern in Z - transformation z
!.IS< e"T) = Z _
, Z = e"T
e In 13
(8)
This relation can be used to express the Laplace trans;formation I
Us (p) = T J US< o
e"T ) e -pT( dE
(9)
By subs;tituting (8) to (9) with regard to SVPWM s;trategy mentioned we get
Us (0)
e"T (10)
p A(p)
IfG(p) = - - is; admitance of the load, we can write for load B (p) A(p) !(p) = !}s ( p ) -
(11 )
B(p) EkA, EkE are the beginning and end of K - puliOe respectively By subs;tituting (9) into (11) we arrive at the Laplace tran.formation of the space vector of the load current.By trans;forming these relation. into the modified Z transformation we arrive at (12)
where Zm {X(p)} = X(Z,E) is; the transformation from Laplace into modified Z trans;formation.But solving (12) we must use translation theorem in Z transformatin I for 0 Zm {e-P"F(p)} =Z->F(z,E-a+y) where
y=
o for
~
E< a (13 )
a ~ E< 1 Time dependency (original function) we can expresse from (12) by means of inver.e transformation 1 I(n,£)
=-
4> I (z,£)
,,-Idz
(14 )
21tj 140
5.Simulation results
A. an example of the load current computing by preiented method there ii given load current from SVPWM inverter (load ii R,L character) Fig,3 ,how, trajectol)' of the load current in komplex plane and Fig.4 ,how. time dependency of the 5teady rute current given by equation i(n,E) = Re{ I (n,E)} 0 .2
o m
-0.1
-0 . 2
. 0.3
-0 . 4 . Cl. 4
Fig.3 Load current
D.::'
- Cl. =-
In
komplex plane
6.References
[I] Klima,l: Energy balance of bio gas power plants in the Czech Republic . International conference Rational use of renewable energy. Budapest, 1996. [2] Muray,Y,Ohasi,K. : New PWM method for fully digitized inverters. IEEE Trans.Ind.Appl. (I) 1990. [3] Cade,M :Improvement of induction machine stability by modulating techniquelEE Proceedings - B (6) ,1994. [4] Klima,l: Performance of induction motors fed from VSI with Bus - Clamped SVM.Acta Technica SCAV , I 996. [5] Klima,J: Analytical solution of the current response m a space vector PWM induction motor drive. Acta Technica SCAV ,1993 .
141
1 , (I
1
o
s
-] ,0 (i
s
2
----U!t
FigA Time dependency of the load current
142
f,
Jifi Klima Department of electrical engeneenng and alltomation Czech Agncldtllre Un/verslty in Praglle Praha 6, 165 21- Praha 6 - S'lIchdol ,CZECH REPUBLIC reI: 00 420 22383203 Far: : 00 420 383203 Absence: BlOga, energy conver.ion iCheme u,ing bio - ga. engine driven ielf excited induction generator a. voltage AC iiOurce and PWM Voltage Source Invener (VS I ) have been mode led and inve.tigaded In remote location, where the utility grid doe, nOl exi,t . li\and alone bioga' energy conver.ion iCheme can be uo;ed to feed local electrical load Paper preo.entl. the mathematIcal model "h,ch enable. the dueet calculatIon of the load current. from PWM VSI The method make. u"" ut Laplacei and of the Z -tran.formatlon for calculation tran,ient and ,teady li\ate component. of load current.
1.1 ntroduction Biogali can be produced by anaerobic fermentation of biological walite. The ecological alipect now plaY!i an important role.In liome i!iolated regionli a bio gali power plant may even be the ba.ic .ource of electrical and thermal energy .An induction generator ha. emerged as a suitable reiource of AC energy . However ,there is an appreciable amount of fluctuationli in the magnitude and frequency of the generated terminal voltage , due to itli dependency on rotor lipeed and parameters of the load , when induction generator is used.Hence, the variable magnitude , variable frequency voltage at the .elf - exited induction generator terminal is first rectified and DC voltage is then transferred to the local load throught Pulse Width Modulated (PWM) Voltage Source Inverter.
2.System configuration The proposed scheme consist!i of a !ielf - exiced induction generator with capacitors C , driven by gas dieiel engine, a diode bridge rectifier and PWM inverter feedeng a local load as shown in fig I.
R
E
c
Loe
Roe Tr ............-tfNV l~~----'
t
* Fig. I. System configuration
13 7
LOAD
Ga. die.el engine The 4S II OG gaii dieiel engine made by CKO Hofovice iii modified dieiel engine which mOitly u.ed ai driven unit for UPS (Uniterraptable Power Supply).
I'
Parameteri of the motor : P = 45 kW , velocity n = 1480 rpm , number of cylinderi = 4 , volume of cylinder. = 5,7 dm 3 Self - Exited Induction Generator It is eisentially an induction machine driven by a prime mover (dieiel engine) and having a iource of reactive power ( ielf - exitation capacitor bank). The dynamics of the ielf - exiced induction generator can be repreiented electromechanical equation. derived in the 'YnchronoU!~ly rotating d - g frame [2] .
by
the following
(I)
p i.t. = ( iq.IC llo. + K2 Lm Wm ) iq. - KI r\
P iq, = K2 TI iq. + LI K2 Wm
~. - (r2
i.J. + ~ Lm Wm ~r + K2 T2 i.J, - ~ Ud.
(2)
+ K2 Lm r2) L2 iq, + (LI K\ Wm- iq. IC llo.) i.t,
p ~r = -L\ K2 Wm~. + K2 T\~. - (L\ K\ Wm - ~. / C llo.) ~r + (r2 + K2 Lm T2)L 2 ~r + K 2llo.
(3) (4)
p llo. = (I / C) ( ~. - 2--J3 ht ) ioc
where
and
The above equations were derived a§§uming that initial orientation of the d - q rotating reference frame ii such that d - axis is aligned with stator terminal voltage phaior (i .e. Uq. = 0). Uncontrolled Rectifier It is a 3 - phase diode bridge rectifier which is u.ed to convert the variable magnitude , frequency voltage at the a'YnchronnoU!~ generator terminal to DC. The DC voltage UR at it. output can be expreised in term. of the peak phaiie voltage generator
Udo
= Vg
of the
DC Link and Input Filter The input filter consisti of a ieriei reactor and a shunt capacitor aii ihO\\-1l in Fig. I.The ieriei reactor reduce. the current ripple content in the rectifier output current and the .hunt capacitor reducei the ripple content in the DC link voltage providing suitable voltage source for PWM inverter. The DC link current i. governed by equation :
where Roc and Loc are the DC link reactor§ reiistance and inductance reipectively, ioc is the dc link current and UI is the DC voltage at the inverter input. 138
3.PWM Voltage Source Inverter 1 ne DC voltage available at the rectifier output i. filtered and converted to DC power u.ing PWM inverter. Space Vector Pul.e Width Modulation (SVPWM) i. u.ed for forming voltage of the load.The SVPWM ha. recently become popular, mainly due to .imple computation algorithm and ealiY digital implemantation [4) . Voltages of the phases are expressed as space vectors by means of relation :
1
Us
-
= - - (UA + e J ~'V3 UB + e-j 2~:3 uc )
where UA
3
, UB, Uc
are pha.e output voltage. reapectively.
Figure 2 .howii a diagram of voltage .pace vector. in the comlex plane
V3
V2
f:;
----~~~~--~
V4
V6
V5
Fig.2 Diagram of voltage vectorii
The concept of SVPWM i§ ba§ed on the following principle§: [2) a)
Every sixth of a period is divided into NJ sectors duration tlT
b) Two adjacent direction. of the .pace voltage vector are utilized in each .ector c) Vecton. Vo and V7 zero vector. are applied at the beginning and end of each .ector re.pectively. F or practical perpoie. the §equency of pu\iie§ and gapii , defined for 1/6 of a period , i. .tored in the microcomputer memory .ln the iiub.equent .ixth of the period the direction of the voltage iii rotated through 1[/3.
From Fig.2 relation
lii
iieen that for fir.t iiector , where 0 tlT
$
P
$
rr./3 the mean value can be calculated uiiing the
tlTJ U tlT2 ..I n·.' - - + - -C' T 3 T 3 T For the next we iihall expre§§ time in termii of the interval number n and variable .I' _AV--e 4
U
U
(5)
= -
139
E
a.
TI t
= (n + E) - - = (n + E) T
(6)
n = 0, 1,2 .. .. ... .
6
Expressing (5) in komplex plane we get times for duration of vectors VI , V2 and Vo or V7 respectively .
4.Current of tbe load
In view of the .ymmetry of the switching process the space vector of the load voltage (whose initial value is Us (0» may be expressed in terms
(7) where f(E) expresses the time dependency of the vector \vithin interval T.Dis;crete function (7) can be used to compute the pattern in Z - transformation z
!.IS< e"T) = Z _
, Z = e"T
e In 13
(8)
This relation can be used to express the Laplace trans;formation I
Us (p) = T J US< o
e"T ) e -pT( dE
(9)
By subs;tituting (8) to (9) with regard to SVPWM s;trategy mentioned we get
Us (0)
e"T (10)
p A(p)
IfG(p) = - - is; admitance of the load, we can write for load B (p) A(p) !(p) = !}s ( p ) -
(11 )
B(p) EkA, EkE are the beginning and end of K - puliOe respectively By subs;tituting (9) into (11) we arrive at the Laplace tran.formation of the space vector of the load current.By trans;forming these relation. into the modified Z transformation we arrive at (12)
where Zm {X(p)} = X(Z,E) is; the transformation from Laplace into modified Z trans;formation.But solving (12) we must use translation theorem in Z transformatin I for 0 Zm {e-P"F(p)} =Z->F(z,E-a+y) where
y=
o for
~
E< a (13 )
a ~ E< 1 Time dependency (original function) we can expresse from (12) by means of inver.e transformation 1 I(n,£)
=-
4> I (z,£)
,,-Idz
(14 )
21tj 140
5.Simulation results
A. an example of the load current computing by preiented method there ii given load current from SVPWM inverter (load ii R,L character) Fig,3 ,how, trajectol)' of the load current in komplex plane and Fig.4 ,how. time dependency of the 5teady rute current given by equation i(n,E) = Re{ I (n,E)} 0 .2
o m
-0.1
-0 . 2
. 0.3
-0 . 4 . Cl. 4
Fig.3 Load current
D.::'
- Cl. =-
In
komplex plane
6.References
[I] Klima,l: Energy balance of bio gas power plants in the Czech Republic . International conference Rational use of renewable energy. Budapest, 1996. [2] Muray,Y,Ohasi,K. : New PWM method for fully digitized inverters. IEEE Trans.Ind.Appl. (I) 1990. [3] Cade,M :Improvement of induction machine stability by modulating techniquelEE Proceedings - B (6) ,1994. [4] Klima,l: Performance of induction motors fed from VSI with Bus - Clamped SVM.Acta Technica SCAV , I 996. [5] Klima,J: Analytical solution of the current response m a space vector PWM induction motor drive. Acta Technica SCAV ,1993 .
141
1 , (I
1
o
s
-] ,0 (i
s
2
----U!t
FigA Time dependency of the load current
142
f,