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Thyristor Controller for Induction Smelting Furnace
THYRISTOR CONTROLLER FOR INDUCTION SMELTING FURNACE A. Dmowski, K. Staiikowski, R. Zajac and P. Fabijaiiski Technical University of Warsaw, Inst. of Control and Electronics, Koszykowa 75, Gm. E, pok. 316, PlOO-662 Warszawa, Poland
ABSTRACT In the paper the principle and the way design of thyristor power controller (75 kVA - 50 Hz) for 50 Hz electric heating are presented. Described controller is a model of industral controller for 650 kW smelting furnace. This controller enables compatible work with minicomputer which controls whole technological process.
INTRODUCTION The introduction of computers for controlling industrial processes made necessary for conventional control equipment to obtain a greater compatibllity wi th the new computer technique re~irements. An example here can be the automatic control system for the induction SlDel ting furnace when a specialized minicomputer is used. SJch a solution makes possible to attain the optimal utilization, both energetical and technological, of the furnace. In the present paper the thyristor controller model of 650 kVA, 50 Hz, device designed as 75 kVA, 50 Hz, is described. The model connected with the electronic interface system Camac enables a computer control of metal smelting processes. An industrial controller (650 kVA) is being bull t at present. Before experimental work the following assumptions have been made: 1. The controller should make possible to supply the furnace with the controlled sinusoidal vol tage 50 Hz, with a high watt-hour efficiency. It enables to control the supplied power in every moment of the industrial process. 2. The power coefficient of supply system for the whole technological cycle should be close to one. 3. The system should enable the supply of single-phase surface from threephase mains by syumetrical load of all phases. 4. The control networks of the controller enables interfacing wl th the computer. In Fig. 1 the block diagram of the controller ls presented. 961
962
A. Dmowski et a"l
(20%~100%)
R-U
R-S
manual control com
UM40/0
E-S
R-R
fer con/rol
Fig. 1.
Schematic diagram of the Power
Regulator
The controller consists of the following blocks. 1. Thyristor controllers of symmetrical load of three-phase mains R-S 2. Thyristor controller of alternating voltage R-U 3. Thyristor controllers of reactive power R-R 4. Central networK for interfacing wi th the Camac module B-S. The principle of operation of the power controller is as follows. At first the furnace is supplied with the voltage of 20 ~ Un which penni ts for the action of the reactive power controller R-R and the three-phase mains symmetrical load controller R-S. When the two controllers reach the assumed compensation coefficients (cosl{' = 1 ! 0.5 ~ and phase load unbalance is less than 10 ~), the voltage controller R-U is automatically switched on. The R-U controller increases the voltage to the required value. Any rise in the load voltage Uo is possible only in the case when both the R-R and the R-S reached the assumed coefficients of compensation and symmetrisation. The negative feedback loop makes the whole controller insensitive to the changes of mains supply voltage. The addi tional current feedback loop prevents from overloading the controller and supply mains.
CUR.RENr SYMMETRIZATlON NETWORK R-S
The supply of one-phase induction furnace requires the load balance of three-phase transfonners. This syumetrization can be reached by means of a static networK which consists of the inductance co11 and the condenser battery. One of the most popular networks is shown in Fig. 2. The condenser battery sections are switched w1 th the aid of thyristor inverse parallel switches. The whole network is composed of the following blockl!l: I. The main circui t
Thyristor controller for induction smelting furnace
s
R
963
T
PP1 PP2
Ip
eT
Fig.2
Schematic diagram of R-S regulator
1. thyristor switch L11 (T1; T2), L12 (T3; T4), LN1 (T5, T6), LN2 (17, '1'8) 2. permanent battery section C5 3. switched condensers sections C1, rn 4. coil for symmetrization DL 5. resistor for preliminary battery load R II. The control circu1 t 1. error measurement circuit PU 2. AI C converter 3. the circuit which memorize dig! ts of measurement error - AK 4. the block of timeliness measurement US 5. clock pulse generator G 6. the distribution circui t of thyristor gate pulses RI 7. the circuit for setting in which prepares switched sections for steady state conditions SA 8. gate control circu1 ts of thyristor switches KM1, ••• ,KMN. The operation principle of the device is as follows. The permanent battery section syumetrises the supply mains. The other sections are loaded via resistor R and thyristors T1, T5 by positive half waves of the line-voltage URS• The transit is about 0.2 sec. and after that time the resistor R is short circui ted by the thyristor 51 and actual action is started then. The ouiput voltage error appears as a signal which is a difference between the two phase Olrrents I R and IS. The signal is changed by the A/c converter into a dig1 tal signal in the 8421 code. The error signal sign determines whether a certain number equal to that of clock pulses synchronized at the instant by
964
A. Dmowski et aZ
the US circuit is added or subtracted in the reverse counter of the A/c converter. After the measurement action the AK cireu1 t ..emorizes dig! ts of measurement error. The ou~ut signal of AK c1rcui ts controls inputs of pulse amplifiers of thyristors KM1 ••• KMN. On switching on the thyristor sw! tch one of the sections C1 ••• CN is immediately connected in parallel to the inductance coil or to the permanent battery section c • A proper moment for the on-and -off action of the thyristor 5 swi tch prevents from overloading in the circuit. The appropriate current symmetrization in transformers coils is possible when the following conditions are satisfied:
where
I p =Y3' 11.
(~)
I p =: Y3' le
( 2)
URS
= UST = UTR
and the capac1 ty reactance is equal to the inductive reactance of the symmetrization coil. n=N
LXCn =X L
(3)
n=1
= Is or R !or :z IS. (This relation is present in the circuit). From (3) appears that the total reactive power of the condenser battery must satisfy:
If (3) is :fulfilled, the conditions (1) and (2) are fulfilled when I
n=N
LQcn==QL.
(4)
n=1
where QL is the reactive power of inductance coil. The reactive power of the smallest section of condenser battery which ensures more than 5 per cent accuracy is g!ven by:
()
- 0.1
USC1-
IT
R 0
(5)
where Po is a load active power. The smallest power of permanent section is given by:
_ Pomin --QC 5Y7j
(6)
where Po min is the minimum value of load active power. By diminishing the value of QC5 (5) one can obtain a smaller asymmetrization of phase currents but a number of condenser sections will then increase. The tests of the model 75 kVA, 50 Hz have confirmed the validity of the theoretical assumptions which were the basis for designing the current symmetrization cireu1t. In Fig. 3 an oscillograph record of the following signals in the and synchronization circuit are presented: 1. the voltage signal for comparison with the control error P2, 2. the signal of measurement time of the control error P, 3. the output signal of the comparator C, 4. the control signal of reverse counter C3, In Fig. 4, respectively
A/c converter
Thyristor controller for induction smelting furnace
965
A
sv--3.3ms
p
(UST)
C
(URSUrR)
-
5V
5V-
C3
Fig3
B
-
P1
Flg.4.
1. the signal synchronizing the circu1 t with the U - A voltage, RS 2. the signal synchronizing the circu1 t with the UST - B voltage, 3. the signal proportional to the measurement time ot the control error P1, In the presented model an asymmetry ot the phase circuit is less than 5 per cent.
THE R-U VOLTAGE CONTROLLER
The main task ot R-U controller is to control voltage supply U ot the load. o This voltage should be controlled within 20 96 - 100 96 ot Un. The block diagram of the controller is presented in Fig. 5. This controller consists of 1. Autotransfonner AT with five taps A, B, C, D, E (in which UA == UB == UC == UD == UE == 20 96 Un) 2. Booster transfonner Td 3. Eleven double thyristor switches T1, T2, ••• T21, T22 4. Electronical circu1 t of regulator control. The control block consists of: a) A circui t which controls the difference between the set point vol tage (Ust) and the controller ou1;put voltage (U ) o b) two electronical reverse counters which control the sw! tch ot apprioprlate thyristor pairs (Ll - thyristor pairs T1, T2, ••• '19, T10 and L2 - thyristor pairs T11, T12, ••• T21, T22) c) L1 and ~ counters switching generator d) a circuit for synchronization and distribution of thyristor control pulses. The principle of controller: The supply voltage Un switches on the pairs of thyristors T1, T2 and T21, T22. This stage refers to the zero state of both counters L , L • In the case when the voltage control value U increases 2 st 1 and coefficients of syometrization and compensation have appropriate values
966
A. Dmowski et al-
Fig. 5
Voltage Regulator R-U
the generator G is unblocked. At each end of positive half - wave of supply voltage U on the generator G n ou1put a pulse for counter sw1 tch appears. Each state of these two counters causes the conduction of an appriopriate thyristor pair. These thyristors conduct unless the ou1put voltage U reaches the value of the control voltage. o In the case when U = U st the pulse train is subtracted up to the moment o when Uo = Ust.U~s each change of counter state causes the change of Uo vol tage of z 2 value. The principle of the regulator is illustrated in Fig. 6 in which the oscillograph of U ~ E voltage versus time when o 2 step UD1t signal of magnitude (20 % U - 120 % U ) was applied. (The load st st current = 50 A and cos tp = 0.9 ind.).
-rJl
Each moment of thyristor switch causes a high hannonic dystribution in Uo vol tage. The magni tude of these hannonics can be evaluated on the base of the eqUivalent circuit given in Fig. 7. In this diagram 1T and 2T are on the state of conduction and 3T, 4T will be
swi tched in the next instant. On the basis of Fig.
7 the following set of equations can be written
Thyristor controller for induction smelting furnace
967
Flg.6.
M=o VL n LT; for 0= 1
~
n =..!!..z,
L-
Trz - r;r-
"
z
IT
2T
Fig.7 Equivalent circuit
U=
\
L
R l + di2 \ L - d11 M dt L
2 2.
U = L R1 l1
2
+ di 1 ~L dt L -'I
dt
dl2
dt
M
(7 )
(8)
this set of equations can be rewri tten in a matrix fonD.
X=A x+BHt) The solution of (9)
(9)
for non-sin inputs takes fonD. (whAn
(10)
968
A. Dmowski 6t al
when:
of her
Fm =
~
wise
(ak - jb K )
(11 )
01:=0
JL { sin(1-rk)lp + sin[( 1+k)Tf] + (1-k) If
b = K
TT
2(1-k)
+
Sin (1-k)lp+ Sin[(1 -k)1T J+(1-k)!P}
+
2(1-k) Fig. 8 and Fig. 9 give the values of hannonic contains in output voltage caused by the switches of thyristors. These results permit for evaluation of the number of autotransfonner AT taps (A,B,C,D,E) and thyristor pairs for given harmonic contain in controller output vol tage (for assumed cOlllIll.l.tation angle).
--
E,(K=1}
E,(K=I)
0,8
~
0,6 0,4 0,2 0
" K=3
--
0
./
"
~"""
"i<=S
O,B L=Q
I'..
.........
~
R=O 'K=1
0,4 0,2
.........
..........
~
200 400 600 800 1000 1200 Il,()O 16()O 18/Y' 90
"
Fig. 8
REACTIVE POWER CONTROLLER
\
0,6
~
-
\
0
~
~5
~
1100
Fig. 9
~R
The main task of reactive power controller is to keep the value of power factor (cos tp ) dose to 1. Uncompenated furnace has this coefficient within the range 0.15-0.22 depending on the teclmologica1 process. The reactive power is compensated by an additional condenser ba.ttery the capac1 ty of which should be adjustable in the ca.se when the value of cos If close to 1 1s desired. A diagram of reactive power controller is presented in Fig. 10. This controller consists of a) the condensor battery divided into n sections w1 th capaci ties C1 "" Cn weighted binary i.e. C1 ' C2 = 2C ' ••• 'C = 2n - 1C n 1 1 b) semicondUctor swi thes (dioda - thyr1stor) for bettery sw1 tching c) voltage meassurent block with adjustable on 50 Hz fl1 ter and phose-shift
Thyristor controller for induction smelting furnace
969
UI
} Le
Fig ,10
Schematic
diagram of R-R regulator
c1rcu1 t FU and R1 d) current measurement block wi th 50 Hz f11 ter and phase - shift circui t FI and PI e) the phase - shift angle FK measurement block (the angle is measured between vol tage and current supplying the furnace) f) the reverse counter block L g) the clock pulse generator G h) the block of synch...ronization ignition pulses with mains vol tage UST i) the block of synchronization block L output pulses with UST-US j) the amplifiers of thyristors KM ignition pulses The principle of the controller is as follows: Signals proportional to the first hannonics of the load voltage and current are lead from the output of PU and PI blocks to the input of FK block. The block FK output rectangular pulses have a width proportional to the phose shift between supply voltage and load current. In the case when the load is indu c ti ve the ou tpu t si gnal app ears on the IQ L output, otherwise in the !Pc output. The block FK output signals If L and Lp C cause addition or sub-traction of counter digits, respectively. The block L consists of two counters first of which controls the switch the battery wi th capaci ty from C to c., the second from C. -I< -1<+1 to Cn· 1 Thest. counters for large values cos If are connected in series otherwise the paraller connection is used (in the case of cos If small values). This
A. Dmowski et al
970
counter control enlarges the dynamics of whole controller R-R. The set-point vol tage 4' m controls the tolerancy of cos Lf (cos \.Pea = 1 : Lp m 96), the second set - point vol tage ~ z Hmi ts the boundary value of phase - shift which causes the switch from series to paraller counter connection. The task of US, UST, KM blocks is appropriate control of thyristors ign1 tion. The compensation accuracy depends on the capacity of the smalest battery section (C ••• Cn). 1 For g1 ven reactive power of the smallest battery section QCi the minimal accuracy of compensation can be evaluated via the following expressions
~~:n
=arctg
fcamtn
Qcmax ==
(12)
(13 )
tg l!Jt.. mOX
Pmln
Qcmln
= Prnin *9 tpt.. mln
- constant (unregulated) term
(14 )
Qc reg
= Qcmax
- controlled term
(15)
- Qcmln
the number of battery section is given by
n=
~~~ +1] --=--,....---:------=:.-.
( 16)
19 [
Lg 2
fea
{DE,(;J
(lfL)
9
0L.l
° ... ° ° ° °
8
M-.. r-,....
i\..:
7
L
L
60
5
3
L ~
h
-r::
Id f=2I
20
o 0
~
h
....
W=~KHlJ
L
r
0,01,
,...,
q: 6 Io,i Uo.16
1.. 0.20 0,21, 078. 0,32 q,16
Ft: I 0f.lJ OF- {5j
L..
Fig. 11 In Fig. 11 the computed transients of the regulation excited by unit step are presented (time t ) for the following set of parameters: 1 p= 4KW) lpL= 84 °el) QC1 =225 Var ) (=21 4,10 KHz) Qcmtn =0 In Fig. 12 to 15 the osclllographs of the mains current for the parameters
listed above are presented. (The controller action start at the moment t = 0).
Thvristor controller for induction smelting furnace
125A
125.4
f25A
tf (f=2KHz)
971
i.""" l' I
I
.. :
l.tf(f="K.Hz) .1
Fig.12
Fig .14.
Fig.13
~'~\~\t~G~~.n fi ~WW~jW~/Vv~ ~ V~
1.3A
I
V
I I
14
I
tf (1::4KHz)
I
., I
Fig 15. CONCLUSIONS
The results of modelling and experimental works prove the possibllity of thyristor circuit application for 50 Hz electric heating devices. The digital inputs of thyristor controller are compatible with the minicomputer outputs which m~e possible to control the whole group of thyristor controller by one minicomputer, simultaneously in teclmological process. Different parts of power controller (R-U, R-S) can be utilize in other application, for example) mains compensation, their voltage stabilization
etc. REFERmCES
(1) H. Frank and B. Landstrom, Electronics D1vision ASEA, Power-factor correction with thyristor - controlled capacitors ASEA Journal 6 (1971) (2) A. K. Sz1blowski, Simmetrirowan1e riezima mnogofaznej sistemy pri p1taniu adnofazowych nagruzok, &terda (1974 (3) S. Lloyd, P. Marshall, Dinamical performance of a s1ngle-pha8e thyriator a.c. regulator, Proc. !nam. Electr. &tgrs. 122, 12 (1975)
ABSTRACT In the paper the principle and the way design of thyristor power controller (75 kVA - 50 Hz) for 50 Hz electric heating are presented. Described controller is a model of industral controller for 650 kW smelting furnace. This controller enables compatible work with minicomputer which controls whole technological process.
INTRODUCTION The introduction of computers for controlling industrial processes made necessary for conventional control equipment to obtain a greater compatibllity wi th the new computer technique re~irements. An example here can be the automatic control system for the induction SlDel ting furnace when a specialized minicomputer is used. SJch a solution makes possible to attain the optimal utilization, both energetical and technological, of the furnace. In the present paper the thyristor controller model of 650 kVA, 50 Hz, device designed as 75 kVA, 50 Hz, is described. The model connected with the electronic interface system Camac enables a computer control of metal smelting processes. An industrial controller (650 kVA) is being bull t at present. Before experimental work the following assumptions have been made: 1. The controller should make possible to supply the furnace with the controlled sinusoidal vol tage 50 Hz, with a high watt-hour efficiency. It enables to control the supplied power in every moment of the industrial process. 2. The power coefficient of supply system for the whole technological cycle should be close to one. 3. The system should enable the supply of single-phase surface from threephase mains by syumetrical load of all phases. 4. The control networks of the controller enables interfacing wl th the computer. In Fig. 1 the block diagram of the controller ls presented. 961
962
A. Dmowski et a"l
(20%~100%)
R-U
R-S
manual control com
UM40/0
E-S
R-R
fer con/rol
Fig. 1.
Schematic diagram of the Power
Regulator
The controller consists of the following blocks. 1. Thyristor controllers of symmetrical load of three-phase mains R-S 2. Thyristor controller of alternating voltage R-U 3. Thyristor controllers of reactive power R-R 4. Central networK for interfacing wi th the Camac module B-S. The principle of operation of the power controller is as follows. At first the furnace is supplied with the voltage of 20 ~ Un which penni ts for the action of the reactive power controller R-R and the three-phase mains symmetrical load controller R-S. When the two controllers reach the assumed compensation coefficients (cosl{' = 1 ! 0.5 ~ and phase load unbalance is less than 10 ~), the voltage controller R-U is automatically switched on. The R-U controller increases the voltage to the required value. Any rise in the load voltage Uo is possible only in the case when both the R-R and the R-S reached the assumed coefficients of compensation and symmetrisation. The negative feedback loop makes the whole controller insensitive to the changes of mains supply voltage. The addi tional current feedback loop prevents from overloading the controller and supply mains.
CUR.RENr SYMMETRIZATlON NETWORK R-S
The supply of one-phase induction furnace requires the load balance of three-phase transfonners. This syumetrization can be reached by means of a static networK which consists of the inductance co11 and the condenser battery. One of the most popular networks is shown in Fig. 2. The condenser battery sections are switched w1 th the aid of thyristor inverse parallel switches. The whole network is composed of the following blockl!l: I. The main circui t
Thyristor controller for induction smelting furnace
s
R
963
T
PP1 PP2
Ip
eT
Fig.2
Schematic diagram of R-S regulator
1. thyristor switch L11 (T1; T2), L12 (T3; T4), LN1 (T5, T6), LN2 (17, '1'8) 2. permanent battery section C5 3. switched condensers sections C1, rn 4. coil for symmetrization DL 5. resistor for preliminary battery load R II. The control circu1 t 1. error measurement circuit PU 2. AI C converter 3. the circuit which memorize dig! ts of measurement error - AK 4. the block of timeliness measurement US 5. clock pulse generator G 6. the distribution circui t of thyristor gate pulses RI 7. the circuit for setting in which prepares switched sections for steady state conditions SA 8. gate control circu1 ts of thyristor switches KM1, ••• ,KMN. The operation principle of the device is as follows. The permanent battery section syumetrises the supply mains. The other sections are loaded via resistor R and thyristors T1, T5 by positive half waves of the line-voltage URS• The transit is about 0.2 sec. and after that time the resistor R is short circui ted by the thyristor 51 and actual action is started then. The ouiput voltage error appears as a signal which is a difference between the two phase Olrrents I R and IS. The signal is changed by the A/c converter into a dig1 tal signal in the 8421 code. The error signal sign determines whether a certain number equal to that of clock pulses synchronized at the instant by
964
A. Dmowski et aZ
the US circuit is added or subtracted in the reverse counter of the A/c converter. After the measurement action the AK cireu1 t ..emorizes dig! ts of measurement error. The ou~ut signal of AK c1rcui ts controls inputs of pulse amplifiers of thyristors KM1 ••• KMN. On switching on the thyristor sw! tch one of the sections C1 ••• CN is immediately connected in parallel to the inductance coil or to the permanent battery section c • A proper moment for the on-and -off action of the thyristor 5 swi tch prevents from overloading in the circuit. The appropriate current symmetrization in transformers coils is possible when the following conditions are satisfied:
where
I p =Y3' 11.
(~)
I p =: Y3' le
( 2)
URS
= UST = UTR
and the capac1 ty reactance is equal to the inductive reactance of the symmetrization coil. n=N
LXCn =X L
(3)
n=1
= Is or R !or :z IS. (This relation is present in the circuit). From (3) appears that the total reactive power of the condenser battery must satisfy:
If (3) is :fulfilled, the conditions (1) and (2) are fulfilled when I
n=N
LQcn==QL.
(4)
n=1
where QL is the reactive power of inductance coil. The reactive power of the smallest section of condenser battery which ensures more than 5 per cent accuracy is g!ven by:
()
- 0.1
USC1-
IT
R 0
(5)
where Po is a load active power. The smallest power of permanent section is given by:
_ Pomin --QC 5Y7j
(6)
where Po min is the minimum value of load active power. By diminishing the value of QC5 (5) one can obtain a smaller asymmetrization of phase currents but a number of condenser sections will then increase. The tests of the model 75 kVA, 50 Hz have confirmed the validity of the theoretical assumptions which were the basis for designing the current symmetrization cireu1t. In Fig. 3 an oscillograph record of the following signals in the and synchronization circuit are presented: 1. the voltage signal for comparison with the control error P2, 2. the signal of measurement time of the control error P, 3. the output signal of the comparator C, 4. the control signal of reverse counter C3, In Fig. 4, respectively
A/c converter
Thyristor controller for induction smelting furnace
965
A
sv--3.3ms
p
(UST)
C
(URSUrR)
-
5V
5V-
C3
Fig3
B
-
P1
Flg.4.
1. the signal synchronizing the circu1 t with the U - A voltage, RS 2. the signal synchronizing the circu1 t with the UST - B voltage, 3. the signal proportional to the measurement time ot the control error P1, In the presented model an asymmetry ot the phase circuit is less than 5 per cent.
THE R-U VOLTAGE CONTROLLER
The main task ot R-U controller is to control voltage supply U ot the load. o This voltage should be controlled within 20 96 - 100 96 ot Un. The block diagram of the controller is presented in Fig. 5. This controller consists of 1. Autotransfonner AT with five taps A, B, C, D, E (in which UA == UB == UC == UD == UE == 20 96 Un) 2. Booster transfonner Td 3. Eleven double thyristor switches T1, T2, ••• T21, T22 4. Electronical circu1 t of regulator control. The control block consists of: a) A circui t which controls the difference between the set point vol tage (Ust) and the controller ou1;put voltage (U ) o b) two electronical reverse counters which control the sw! tch ot apprioprlate thyristor pairs (Ll - thyristor pairs T1, T2, ••• '19, T10 and L2 - thyristor pairs T11, T12, ••• T21, T22) c) L1 and ~ counters switching generator d) a circuit for synchronization and distribution of thyristor control pulses. The principle of controller: The supply voltage Un switches on the pairs of thyristors T1, T2 and T21, T22. This stage refers to the zero state of both counters L , L • In the case when the voltage control value U increases 2 st 1 and coefficients of syometrization and compensation have appropriate values
966
A. Dmowski et al-
Fig. 5
Voltage Regulator R-U
the generator G is unblocked. At each end of positive half - wave of supply voltage U on the generator G n ou1put a pulse for counter sw1 tch appears. Each state of these two counters causes the conduction of an appriopriate thyristor pair. These thyristors conduct unless the ou1put voltage U reaches the value of the control voltage. o In the case when U = U st the pulse train is subtracted up to the moment o when Uo = Ust.U~s each change of counter state causes the change of Uo vol tage of z 2 value. The principle of the regulator is illustrated in Fig. 6 in which the oscillograph of U ~ E voltage versus time when o 2 step UD1t signal of magnitude (20 % U - 120 % U ) was applied. (The load st st current = 50 A and cos tp = 0.9 ind.).
-rJl
Each moment of thyristor switch causes a high hannonic dystribution in Uo vol tage. The magni tude of these hannonics can be evaluated on the base of the eqUivalent circuit given in Fig. 7. In this diagram 1T and 2T are on the state of conduction and 3T, 4T will be
swi tched in the next instant. On the basis of Fig.
7 the following set of equations can be written
Thyristor controller for induction smelting furnace
967
Flg.6.
M=o VL n LT; for 0= 1
~
n =..!!..z,
L-
Trz - r;r-
"
z
IT
2T
Fig.7 Equivalent circuit
U=
\
L
R l + di2 \ L - d11 M dt L
2 2.
U = L R1 l1
2
+ di 1 ~L dt L -'I
dt
dl2
dt
M
(7 )
(8)
this set of equations can be rewri tten in a matrix fonD.
X=A x+BHt) The solution of (9)
(9)
for non-sin inputs takes fonD. (whAn
(10)
968
A. Dmowski 6t al
when:
of her
Fm =
~
wise
(ak - jb K )
(11 )
01:=0
JL { sin(1-rk)lp + sin[( 1+k)Tf] + (1-k) If
b = K
TT
2(1-k)
+
Sin (1-k)lp+ Sin[(1 -k)1T J+(1-k)!P}
+
2(1-k) Fig. 8 and Fig. 9 give the values of hannonic contains in output voltage caused by the switches of thyristors. These results permit for evaluation of the number of autotransfonner AT taps (A,B,C,D,E) and thyristor pairs for given harmonic contain in controller output vol tage (for assumed cOlllIll.l.tation angle).
--
E,(K=1}
E,(K=I)
0,8
~
0,6 0,4 0,2 0
" K=3
--
0
./
"
~"""
"i<=S
O,B L=Q
I'..
.........
~
R=O 'K=1
0,4 0,2
.........
..........
~
200 400 600 800 1000 1200 Il,()O 16()O 18/Y' 90
"
Fig. 8
REACTIVE POWER CONTROLLER
\
0,6
~
-
\
0
~
~5
~
1100
Fig. 9
~R
The main task of reactive power controller is to keep the value of power factor (cos tp ) dose to 1. Uncompenated furnace has this coefficient within the range 0.15-0.22 depending on the teclmologica1 process. The reactive power is compensated by an additional condenser ba.ttery the capac1 ty of which should be adjustable in the ca.se when the value of cos If close to 1 1s desired. A diagram of reactive power controller is presented in Fig. 10. This controller consists of a) the condensor battery divided into n sections w1 th capaci ties C1 "" Cn weighted binary i.e. C1 ' C2 = 2C ' ••• 'C = 2n - 1C n 1 1 b) semicondUctor swi thes (dioda - thyr1stor) for bettery sw1 tching c) voltage meassurent block with adjustable on 50 Hz fl1 ter and phose-shift
Thyristor controller for induction smelting furnace
969
UI
} Le
Fig ,10
Schematic
diagram of R-R regulator
c1rcu1 t FU and R1 d) current measurement block wi th 50 Hz f11 ter and phase - shift circui t FI and PI e) the phase - shift angle FK measurement block (the angle is measured between vol tage and current supplying the furnace) f) the reverse counter block L g) the clock pulse generator G h) the block of synch...ronization ignition pulses with mains vol tage UST i) the block of synchronization block L output pulses with UST-US j) the amplifiers of thyristors KM ignition pulses The principle of the controller is as follows: Signals proportional to the first hannonics of the load voltage and current are lead from the output of PU and PI blocks to the input of FK block. The block FK output rectangular pulses have a width proportional to the phose shift between supply voltage and load current. In the case when the load is indu c ti ve the ou tpu t si gnal app ears on the IQ L output, otherwise in the !Pc output. The block FK output signals If L and Lp C cause addition or sub-traction of counter digits, respectively. The block L consists of two counters first of which controls the switch the battery wi th capaci ty from C to c., the second from C. -I< -1<+1 to Cn· 1 Thest. counters for large values cos If are connected in series otherwise the paraller connection is used (in the case of cos If small values). This
A. Dmowski et al
970
counter control enlarges the dynamics of whole controller R-R. The set-point vol tage 4' m controls the tolerancy of cos Lf (cos \.Pea = 1 : Lp m 96), the second set - point vol tage ~ z Hmi ts the boundary value of phase - shift which causes the switch from series to paraller counter connection. The task of US, UST, KM blocks is appropriate control of thyristors ign1 tion. The compensation accuracy depends on the capacity of the smalest battery section (C ••• Cn). 1 For g1 ven reactive power of the smallest battery section QCi the minimal accuracy of compensation can be evaluated via the following expressions
~~:n
=arctg
fcamtn
Qcmax ==
(12)
(13 )
tg l!Jt.. mOX
Pmln
Qcmln
= Prnin *9 tpt.. mln
- constant (unregulated) term
(14 )
Qc reg
= Qcmax
- controlled term
(15)
- Qcmln
the number of battery section is given by
n=
~~~ +1] --=--,....---:------=:.-.
( 16)
19 [
Lg 2
fea
{DE,(;J
(lfL)
9
0L.l
° ... ° ° ° °
8
M-.. r-,....
i\..:
7
L
L
60
5
3
L ~
h
-r::
Id f=2I
20
o 0
~
h
....
W=~KHlJ
L
r
0,01,
,...,
q: 6 Io,i Uo.16
1.. 0.20 0,21, 078. 0,32 q,16
Ft: I 0f.lJ OF- {5j
L..
Fig. 11 In Fig. 11 the computed transients of the regulation excited by unit step are presented (time t ) for the following set of parameters: 1 p= 4KW) lpL= 84 °el) QC1 =225 Var ) (=21 4,10 KHz) Qcmtn =0 In Fig. 12 to 15 the osclllographs of the mains current for the parameters
listed above are presented. (The controller action start at the moment t = 0).
Thvristor controller for induction smelting furnace
125A
125.4
f25A
tf (f=2KHz)
971
i.""" l' I
I
.. :
l.tf(f="K.Hz) .1
Fig.12
Fig .14.
Fig.13
~'~\~\t~G~~.n fi ~WW~jW~/Vv~ ~ V~
1.3A
I
V
I I
14
I
tf (1::4KHz)
I
., I
Fig 15. CONCLUSIONS
The results of modelling and experimental works prove the possibllity of thyristor circuit application for 50 Hz electric heating devices. The digital inputs of thyristor controller are compatible with the minicomputer outputs which m~e possible to control the whole group of thyristor controller by one minicomputer, simultaneously in teclmological process. Different parts of power controller (R-U, R-S) can be utilize in other application, for example) mains compensation, their voltage stabilization
etc. REFERmCES
(1) H. Frank and B. Landstrom, Electronics D1vision ASEA, Power-factor correction with thyristor - controlled capacitors ASEA Journal 6 (1971) (2) A. K. Sz1blowski, Simmetrirowan1e riezima mnogofaznej sistemy pri p1taniu adnofazowych nagruzok, &terda (1974 (3) S. Lloyd, P. Marshall, Dinamical performance of a s1ngle-pha8e thyriator a.c. regulator, Proc. !nam. Electr. &tgrs. 122, 12 (1975)