Output Power Increase at Idle Speed in Alternators - Semantic Scholar
Output Power Increase at Idle Speed in Alternators by
Juan Rivas B.S., Monterrey Institute of Tech.(1999)
Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of
Master of Science at the MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
June 2003
@
Massachusetts Institute of Technology, MMIII. All rights reserved.
Author epartment of Electrical Engineering and Computer Science une 1, 2003
Certified by_ David J. Perreault Associate Professor of Electrical Engineering Thesis Supervisor Certified by_ Dr. Thomas A. Keim Principal Research Scientist 0. The local average voltage (Vag) for ia(t) > 0 as a function of the duty cycle is:
(vag) = (1 - d) Vo
(2.11)
On the other hand, for ia(t) < 0 the current forces the the bottom diode to be in the ON position, thus making the voltage Vag = 0 (minus one diode drop). So it is possible to represent the voltage at the input of the SMR vag(t) as a square voltage in phase with the current ia(t), having a high voltage equal to the local average for ia(t) > 0 of (1 - d)V and zero when ia(t)
0
Vd
:iai(t)
(2.12)
< 0
which is also represented as:
vag(t)
[(
O+ d)V +2 VD 1 sgn (iai)
-d)V 2
(2.13)
The duty ratio d can vary in range between 0 and 1. As implied by Eq. (2.11) this means, that by controlling the value of d it is possibly to obtain any value of voltage (vag(t)) less than the output voltage V. The magnitude of the fundamental component of vag(t) will now a function of the duty cycle, and given by: 4 ((1 - d)Vo+V d Vagi = 2 7r
(2.14)
Plugging this new value of Vag, in equation (2.7), and again neglecting the forward diode voltage drop, it is found that the output power for the SMR can be expressed as:
POUT-=-
3 VoVa
1
,r wL
-
(2(1 - d)V 7TrVsa
2
(215
The voltage V that maximize the output power delivery can be found to be represented by the following equation:
-
30
-
2.3
Switched Mode Rectifier
Atternator Output Power vs. speed
SMR @ 50VX
4000
3500-
0 3000-
No extra power at idle 2000-
1500
I---
Diode @14V
-
- -
1000
15Mo
2000
2500
3000
3500 Alternator
4000
4500
5000
5500
6000
Speed (RPM)
Figure 2.6: Output Power vs. speed using a Diode Rectifier and an SMR
V maxP
Vsa ir 2/2(1d)
,rVsaRMS
(2.16)
2 (1-d)
Thus for a given V greater than the originals 14V the duty cycle d required to achieve a load matched condition at any given speed is given by: d loadmatched
2r Vsa = 1-
(2.17)
By operating the originally designed 14V alternator, with a SMR in a load matched condition, it is possible to obtain up to 2.5 times more power at higher speeds thus operating in an optimal condition for all alternator speeds. To demonstrate this potential, an automotive alternator was fitted with the proposed circuit, and operated using the proposed control control law (Eq. 2.17) for a range of DC voltages. The result, shown in Fig. 2.6, shows that at about 5800rpm and 50 volts, about 2.5 times as much power is produced than with the same alternator at the same speed and at 14V DC. As indicated in Fig. 2.6, the use of a SMR does not improve the output power characteristics of the alternator at low speed, specifically at idle. A significant advantage of implementing the SMR is the fact that only minor changes have to be implemented to the conventional
-
31
-
Background
*F
=_t lb
lo
*
+ V.
sytm ecuei
aciesice
r
rdrt
praei
eurd
Thos
d
ace
oa
s
Ice
condtio
ataO
sedsjs
he
ar1gon-eeecd"wihipsta
Figure 2.7: 3-phase Full wave inverter structure. system, because in order to operate in a load matched condition at all speeds just three active switches are required. Those switches are "ground referenced" which implies that no complex drivers are needed in order to switch them between the "on" and "off" states. Also, in order to control the SMR it is necessary to use information already available in the car like output voltage and speed, so no expensive complicated sensors are required.
2.4
Conventional Strategies for Increasing Output Power
Other circuits and other control strategies have been used to increase the output power of alternator systems. Among the most effective is the use of a 3-phase full wave inverter structure (Fig. 2.7). With adequate DC-side voltage, this circuit can be used in a so-called vector control mode to force the phase current waveform to be in phase with the back EMF. For a given back EMF and phase current magnitude, such control maximizes the delivered output power. This strategy has been proposed many times and implemented by commercial companies like International Rectifier [8]. There are many drawbacks of this strategy as: " The use of six active switches " The high-side switches require isolated electronics, which tend to be expensive and complicated, in order to apply the correct gating signals " The use of expensive current sensors and rotor position sensors is needed in order to correctly implement the control pattern required by the active switches, although schemes could potentially be designed that make use of simple sensors. -
32
-
2.4
Conventional Strategies for Increasing Output Power
Another strategy proposed in order to increase the output power capabilities of a system suitable to be used in automobiles is presented in [9], in which the same 6-switch active bridge structure shown in Fig. 2.7 is used, but the number of current sensor is reduced by the use of one simple position sensor which is utilized to detect a fixed point in the rotor. With this information, the 6 switches are controlled at the same electrical frequency of the system in order to artificially move the phase of the fundamental component of the current to be closer to that of the generated EMF source. This approach results in an increase in the available output power, but does not result in a load matched condition at any operational speed but idle.
-
33
-
Chapter 3
Increased Power at Idle
3.1
Introduction
This chapter introduces two novel modulation techniques that effectively increase the output power characteristics of an alternator considering the availability of a semi-bridge Switched Mode Rectifier (SMR). The proposed schemes are simple and may be implemented without the the addition of expensive sensors in a realistic implementation. Based on the discussion presented in section 2.3 it was shown that even though an alternator with a SMR and load-matching control provides almost 2.5 times more output power at cruising speeds compared to an alternator with a simple diode bridge, no extra power is obtained at idle speed. To overcome the characteristic limitations of the load-matching technique, but keeping the simplicity of the aforementioned SMR structure, a departure from the original control is proposed. Instead of controlling the three active switches with the same duty cycle d, a new degree of freedom is added to the scheme, by modulating the switches individually. As will be shown, adding a new dimension to the control of the SMR, it is possible to advantageously manipulate the state variables of the system. In particular one can modify the magnitude and phase of the different harmonic components of the phase currents that determine the average output power.
3.2
Modulation delta
One modulation technique that we use to increase output power is illustrated in Fig. 3.1. The main goal of this simple modulation technique is to store electrical energy in the machine inductance (L,) of each phase, during one part of the electrical period, to release it in another part of the period. In order to achieve this goal, a time interval 6 is introduced for each phase starting whenever the current of a phase becomes positive. During this -
35
-
Increased Power at Idle
I
V
/
Vsa
/
ag
-
/
/ /
Vx
/
/ / / Il
64\
4-
/ \
/ \
/
Figure 3.1: Waveforms of alternator connected to SMR with an interval J introduced to enhance output power at idle speed. delta interval, the switch for that phase is held on (d = 1), while the other switches are modulated normally. This action results in the application of the full back EMF source across the winding inductance, which in turn stores additional electrical energy in that inductance; this energy will be released in another part of the conduction cycle. The modulation was selected because of its simplicity of implementation: implementation only requires sensing the direction of the current. Such information is readily available from voltage measurements done directly at the SMR. Figure 3.1 shows the waveforms of one of the phases of the SMR with an interval of length 6 introduced whenever the phase current ia turns positive. vsa is shown as a dotted line, while the current i, is shown as a distorted sinusoid as a solid line. The voltage at the input of the SMR vag is also shown. The amplitude of vag named V, represents the local average of the pulse-width-modulated waveform seen at the input of the SMR. The same figure also shows the phase angle between vsa and i, denoted as a.
-
36
-
3.2
3.2.1
Modulation delta
Analytical Model
A mathematical model for the delta modulation is derived in appendix A. There, it is shown that a considerable amount of extra output power can be obtained by changing the length of the interval 8 shown in Fig. 3.1. The same derivation demonstrates that such increase in real power is followed by a significant increase in phase current ia. The increase in losses due to dissipation will ultimately set the limit for which this modulation will be able to provide extra power at idle speed. As described in the analytical derivation, we can find an expression for the magnitude and the phase angle of the fundamental component of the phase current ia, labelled ial. The fundamental component is the only frequency component of the current that contributes to real power (given sinusoidal back EMF's). In order to find a closed-form expression for the phase current, a symmetric conduction condition is assumed. Under this approximation, a positive current iai is assumed to circulate through the alternator's winding for exactly half of the current period (i. e. for 0 < wat < 7r). The positive conduction angle of the current with the 6 modulation is not exactly 180 degrees in practice. While the symmetric conduction condition is not exact, it does provide a good insight into the benefits of the proposed modulation method. By applying this conduction condition, it is found that the magnitude ial and the phase angle a that exists between the back EMF and the phase current, can be expressed as a function of the back EMF amplitude Va, the synchronous impedance Z. = R, + jw 0 L, expressed in polar form Z, = IZ, ILz (representing the series resistance and inductance of the windings), the local average at the input of the SMR V, and the control handle 6. In particular, the phase angle a between the back EMF and the phase current can be expressed as:
a = Oz - sin-
cos
sin
+ Oz)
(3.1)
Also, the magnitude of the fundamental component of the phase current
ia1 is found to be:
(§ + 0)]
(3.2)
IalI=
[[cos (a - Oz)] - 2V cos (§) [cos
Using equations 3.1 and 3.2 we can express the average output power delivered ((POUT)) to the load by calculating the real power delivered by the back EMF source and subtracting the conduction losses occurring in the windings. The contribution of the other two phases that constitute the alternator have to be taken into account in the calculation for total power delivered. The equation for (PouT) is then: -
37
-
Increased Power at Idle
Output Power vs. 5 1 2 00 .. .. .
1 1 50 - - -.
0
. . .. . . . -. -.-.-.-.-.
-
..
-. -.
.
-
-
...
5
-
-
..-..-..-..-..-...-..- -
900 - -..--...--.
0
-
-
- -
-
-..-.. --.. . . . .. -. .. .
-
- .-..-.-.-.-
--
--
---
- -
. .. - .95 0 - -- -.
-. --
.-
- - - - ---
-
-
- ---
-. .. --..
..
.. .
1 1 0 0 - - - -01050 -
-
- . . . .. . . - . ..
10
20
15
25 8 (degs)
30
35
40
45
50
IRMS vs.8 80 - . . . .
0
5
-.
- -. . ...-. -..
- ..
I
I
10
15
I.
20
(POUT) = 3
.
25 5 (degs)
Figure 3.2: Calculated Output Power vs. modulation 6 (V2 14V).
[Vaiai
..
. .. .
-. .. -.-.-.
30
co~t]-
. . . .
. .
40
45
35
3 and I1RMS vs.
.-.-.
..
3
. .
50
at idle speed using the
3 [RJai](.3
- 3.3 we can plot, the output power (POUT) as a function of the control handle 65 (simulation file presented in appendix B.2). Figure 3.2 shows the average
Making use of equations 3.1
output power (PouT) and the RMS value of the fundamental component of the phase current (iai). The circuit parameters used in this simulation (representing the components
shown for the model shown in Fig. 1.3) are: VsaRMS =10.716V, RJ = 37mQ, L. 120p.H 180Hz; where VSaRMS represents the back EMF at idle speed (e. g. electrical and f8 frequency f8 180Hz) and full field current (e. g. if = 3.6A), and the control parameter S was varied from 0 to 500, V4 = 14V. Furthermore Fig. 3.3 shows the percent increase in output power and the percent increase in RMS phase current ia1, again as a function of 3. As mentioned before, the increase in output power is accompanied by a corresponding increase in phase current, which in turn increases dissipation in the machine windings. This, in turn limits the maximum power increase achievable within the thermal limits of
- 38
3.2
Modulation delta
Percent increase in output power vs. 8 20 --
15 (D Cz
- -.-
-
-. .. -. .. -.
-.
t 10
-
-. -.
-
-.-.-.--.-..... .....
.
5
00
10
5
15
25
20
30
S (degs)
Percent increase in
11RMS
40
35
45
50
vs. 8
0 40 -
- -. -~
S30
~
-
--
..-. . . -.
-
-
-
- .-. .. .-.
-
-
-
-
-
..-.. -
. - ..... -- -----.-.-.-. -......
--
-..
-..
20
--
10 U""
0
5
10
15
20
25
S (degs)
30
35
40
45
50
Figure 3.3: Calculated Output Power increase vs. 6 and IARMS increase vs. 6 at idle speed using the modulation 6 (V = 14V). the alternator. The main advantage of this modulation technique is its simplicity, because in a practical implementation the direction of the phase current ia can be easily obtained from measured voltages at the input of the SMR.
3.2.2
Pspice Verification
In order to corroborate the validity of the mathematical model described in section 3.2.1 and Appendix A, a PSPICE model was developed for the system. A detailed description of the PSPICE model can be found in Appendix C. Figure 3.4 shows a comparison between the results obtained using the Pspice model and the results presented in section 3.2.1. In particular it shows the output power (POUT) and the approximate RMS phase current vs. the control parameter 6. The alternator parameters used for the simulation are: VsaRMS = 10.716V, R, = 37mQ, L, = 120pH, f, = 180Hz and full field current (e. g. if = 3.6A). Again, Rs is the winding resistance and L, is the machine inductance. The results shown in Fig. 3.4 corresponds to a modulation such -
39
-
Increased Power at Idle
Pout
o increase vs. 5
vs.
1200
1100-
15
-:1000
-o
OWM
S10 a-0
onb
5
900 [-800
--
- -
0
10
20
30
40
-- Matlab
Fia-
I
Ppice 50
0
10
MSI RMS Mvs I IRMS
20
30
Pspice 40
50
increase vs. S
iRMS
80
(D
40
1R
30 0
S60
MRla
....... .....-.
50
F
210 -1
Mattab
0
10
2
20
30
40
--
- [-
~
-L
-=Pspice 40'
P sp....
50
0
10
20
30
40
50
Figure 3.4: Comparison between the MATLAB and PSPICE models for power and current vs. the control parameter 6.
that V = 14V. The 6 control parameter is varied from 0 to 50'. From the figure it can be appreciated that there is good agreement between the two models. The principal differences between the models are because the analytical model considered here only takes into account dissipation due to the fundamental component of the phase current, while the circuit simulation incorporates all dissipation components.
3.3
Complete Modulation
Based on the encouraging results obtained from the models presented in section 3.2, an augmented modulation is proposed in which additional control handles are added to the modulation scheme. Figure 3.5 shows the phase current and the instantaneous phaseto-ground rectifier voltage for one phase over an alternator electrical cycle for the full modulation scheme explored here. The switching function for each of the legs of the SMR structure is realized at a frequency many times higher than the line-current frequency and the duty cycle is modulated in such a way as to obtain the "local-average" phase to ground
-
40
-
3.3
Vsa
Complete Modulation
'D
\a
/ /
9
/D v
\vBASE
\
2)r /
Figure 3.5: Waveforms for new modulation technique. voltage Vag shown in Fig. 3.5. Looking at this local average voltage waveform it is possible to
define the different intervals that describe the modulation scheme. The back EMF voltage Vsa is shown with a dotted line, while the current ia is shown as a distorted sinusoid with
a solid line. The pattern is the same for the other phases, but delayed by 120 electrical degrees of the fundamental. The complete modulation technique consists then of the following subintervals:
*
5 : During this sub-interval, beginning when the phase current becomes positive, the switch is kept on, forcing the phase-to-ground voltage to be near zero. During this J portion, additional energy is stored in the winding inductance. Operation at a nominal duty ratio and local average voltage Vase. This voltage is close to that for the load matching condition, and will be a function of the alternator speed.
* Mid-cycle:
*
b : From the beginning of this interval to the end of the positive portion of the line current, the duty ratio is adjusted so as to obtain an average phase to ground voltage that exceeds the nominal Vase by V,, volts.
- 41 -
Increased Power at Idle
The modulation strategy embodied in Fig. 3.5 enables additional output power to be obtained from an alternator as compared to that achievable with diode rectification or switched-mode-rectification with load matching control. At the same time, this modulation is also simple enough to be implemented with inexpensive control hardware and without the use of expensive current or position sensors. As already mentioned, the zero crossing of the phase current waveform can be effectively detected by observing the phase-to-ground voltage during the FET off state. By means of adding these new degrees of freedom in the control of the SMR, it is possible to manipulate the state variables of the system beneficially. In particular we adjust the magnitude and phase of the different harmonic components that constitute the phase currents to enhance the average power delivered to the output.
3.3.1
Analytical Model
As mentioned, this modulation introduces two new subintervals to the normal operation of the SMR. The conduction angle interval 6 is introduced beginning when the phase current becomes positive, during which the bottom switch of the SMR is kept ON, the effect of which was already discussed in section 3.2.1. In the second new subinterval, a conduction angle interval 41 is introduced during which the duty cycle of the corresponding bottom switch is adjusted such that the local average of the voltage at the input of the SMR vag is set to a voltage V0v volts higher than in the main interval. The net result of these two subintervals will produce a phase shift that reduces the total phase angle a between the back EMF voltage va and the fundamental component of the phase current ia1 thus increasing the amount of real power obtained at idle speed (1800 rpm). Furthermore, these intervals can be used to increase the fundamental phase current, thereby increasing output power. The modulation strategy embodied by Fig. 3.5 achieves this within the modulation constraints of the semibridge SMR, and without requiring detailed position or current information. A detailed derivation that analytically solves for the magnitude and the phase of the fundamental component of the phase current ia relative to the back EMF can be found in the appendix A.3. There it is shown that the angle that exists between the back EMF v.a and the fundamental component of the phase current ia1, a depends in the values of the different control parameters, namely: Vov, 8, 4, and V.se. The expression obtained through the derivation is reproduced here:
a = 0Z + sin-[ cl sin (x - 6 - Oz)
1Va
-
42
-
(3.4)
3.3
Complete Modulation
In this expression, ci = al + b2 and x = tan. Where al and b, are the fundamental sine and cosine coefficients in the Fourier series that describes the local average of the phase to ground voltage Va. The series inductance L, and resistance R, that model the phase impedance can be represented by a total series impedance described by its magnitude IZLI and its corresponding phase 0,. The magnitude of the fundamental component of the phase current under the same modulation scheme is is also repeated here:
-l-Cos ci (X - 5 - OZ) |ZL|
|Iail = [ VaCos (a - OZ) IZLI
(3.5)
Using (3.5) and taking into account the contribution of the other two phases it is possible to obtain the same simple expression for the average output power (POUT) as in Eq. 3.3:
-3
(POUT) = 3 Vsalai c
[R,-
(3.6)
The influence of 5 in the output power and the phase current was already presented in Section 3.2, so now we will focus attention on the influence that the new control variable 4 has on those two quantities. Figure 3.6 shows the output power obtained when just the control variable 4 is applied. Again the conditions of the simulations are: VaRMS = 10.716V, R, = 37mQ, L, = 120piH and f, = 180Hz and if = 3.6A. The modulation parameters for the simulation shown in Fig. 3.4 corresponds to V , = 14V, and VOV = 20V. The value of 5 is set to zero and the parameter D is varied from 0 to 700. From Fig. 3.7, it can be seen that for small values of - a small increase in phase current ia is accompanied by significant increase in output power. With bigger values of the control parameter 4, it is possible to obtain a moderate increase in the output power but with an actual decrease in the magnitude of the phase current. This implies that is possible to obtain an increase in output power with lower conduction loss.
3.3.2
Pspice Verification
Fig. 3.8 shows the increase in output power (POUT) and the corresponding increase in RMS phase current versus the parameter D using both the PSPICE averaged model the analytical results presented in section 3.3.1. The results are qualitatively similar, though differences are significant for larger values of 4. The difference that exists between the simulation and the numerical predictions arise because interval 1b is not small, thus the symmetric
-
43
-
Increased Power at Idle
Output Power vs. 0 1400
130 0 120 0 - 0.a 1
1 00 -
0 100 0
- .
90 0 -
---..--.
-.--
.. -.. --
- - -.-- -- . ..
-. . -..
---.-
10
- -.-
30
-.-.
.-.--.-- --.-.
-
40
- -
----
--
- - --
-
-- -
20
. - -.-. - -.-.-
-.-
. - -.-- - -.-- -. .. .- -. . . . . . ..-..
--
0
--
-
- - -
-
- --
- ----
50
-60
70
4D (degs)
11RMS vs. 0 65 - -
55
J 45 - -
0
-
-.-.-
.. .-..
10
20
30
40
-
-.. .
-.. . -..
-.-.-.
-.-.-.-.
-.-
-.-... .
..
-..-
..
.. . .
w0 --
- -.-
-. -.
.
50
.
- .-..-
-.-.
---.-.
60
70
4) (degs)
Figure 3.6: Calculated Output Power vs. D and IIRMS vs.
Juan Rivas B.S., Monterrey Institute of Tech.(1999)
Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of
Master of Science at the MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
June 2003
@
Massachusetts Institute of Technology, MMIII. All rights reserved.
Author epartment of Electrical Engineering and Computer Science une 1, 2003
Certified by_ David J. Perreault Associate Professor of Electrical Engineering Thesis Supervisor Certified by_ Dr. Thomas A. Keim Principal Research Scientist 0. The local average voltage (Vag) for ia(t) > 0 as a function of the duty cycle is:
(vag) = (1 - d) Vo
(2.11)
On the other hand, for ia(t) < 0 the current forces the the bottom diode to be in the ON position, thus making the voltage Vag = 0 (minus one diode drop). So it is possible to represent the voltage at the input of the SMR vag(t) as a square voltage in phase with the current ia(t), having a high voltage equal to the local average for ia(t) > 0 of (1 - d)V and zero when ia(t)
0
Vd
:iai(t)
(2.12)
< 0
which is also represented as:
vag(t)
[(
O+ d)V +2 VD 1 sgn (iai)
-d)V 2
(2.13)
The duty ratio d can vary in range between 0 and 1. As implied by Eq. (2.11) this means, that by controlling the value of d it is possibly to obtain any value of voltage (vag(t)) less than the output voltage V. The magnitude of the fundamental component of vag(t) will now a function of the duty cycle, and given by: 4 ((1 - d)Vo+V d Vagi = 2 7r
(2.14)
Plugging this new value of Vag, in equation (2.7), and again neglecting the forward diode voltage drop, it is found that the output power for the SMR can be expressed as:
POUT-=-
3 VoVa
1
,r wL
-
(2(1 - d)V 7TrVsa
2
(215
The voltage V that maximize the output power delivery can be found to be represented by the following equation:
-
30
-
2.3
Switched Mode Rectifier
Atternator Output Power vs. speed
SMR @ 50VX
4000
3500-
0 3000-
No extra power at idle 2000-
1500
I---
Diode @14V
-
- -
1000
15Mo
2000
2500
3000
3500 Alternator
4000
4500
5000
5500
6000
Speed (RPM)
Figure 2.6: Output Power vs. speed using a Diode Rectifier and an SMR
V maxP
Vsa ir 2/2(1d)
,rVsaRMS
(2.16)
2 (1-d)
Thus for a given V greater than the originals 14V the duty cycle d required to achieve a load matched condition at any given speed is given by: d loadmatched
2r Vsa = 1-
(2.17)
By operating the originally designed 14V alternator, with a SMR in a load matched condition, it is possible to obtain up to 2.5 times more power at higher speeds thus operating in an optimal condition for all alternator speeds. To demonstrate this potential, an automotive alternator was fitted with the proposed circuit, and operated using the proposed control control law (Eq. 2.17) for a range of DC voltages. The result, shown in Fig. 2.6, shows that at about 5800rpm and 50 volts, about 2.5 times as much power is produced than with the same alternator at the same speed and at 14V DC. As indicated in Fig. 2.6, the use of a SMR does not improve the output power characteristics of the alternator at low speed, specifically at idle. A significant advantage of implementing the SMR is the fact that only minor changes have to be implemented to the conventional
-
31
-
Background
*F
=_t lb
lo
*
+ V.
sytm ecuei
aciesice
r
rdrt
praei
eurd
Thos
d
ace
oa
s
Ice
condtio
ataO
sedsjs
he
ar1gon-eeecd"wihipsta
Figure 2.7: 3-phase Full wave inverter structure. system, because in order to operate in a load matched condition at all speeds just three active switches are required. Those switches are "ground referenced" which implies that no complex drivers are needed in order to switch them between the "on" and "off" states. Also, in order to control the SMR it is necessary to use information already available in the car like output voltage and speed, so no expensive complicated sensors are required.
2.4
Conventional Strategies for Increasing Output Power
Other circuits and other control strategies have been used to increase the output power of alternator systems. Among the most effective is the use of a 3-phase full wave inverter structure (Fig. 2.7). With adequate DC-side voltage, this circuit can be used in a so-called vector control mode to force the phase current waveform to be in phase with the back EMF. For a given back EMF and phase current magnitude, such control maximizes the delivered output power. This strategy has been proposed many times and implemented by commercial companies like International Rectifier [8]. There are many drawbacks of this strategy as: " The use of six active switches " The high-side switches require isolated electronics, which tend to be expensive and complicated, in order to apply the correct gating signals " The use of expensive current sensors and rotor position sensors is needed in order to correctly implement the control pattern required by the active switches, although schemes could potentially be designed that make use of simple sensors. -
32
-
2.4
Conventional Strategies for Increasing Output Power
Another strategy proposed in order to increase the output power capabilities of a system suitable to be used in automobiles is presented in [9], in which the same 6-switch active bridge structure shown in Fig. 2.7 is used, but the number of current sensor is reduced by the use of one simple position sensor which is utilized to detect a fixed point in the rotor. With this information, the 6 switches are controlled at the same electrical frequency of the system in order to artificially move the phase of the fundamental component of the current to be closer to that of the generated EMF source. This approach results in an increase in the available output power, but does not result in a load matched condition at any operational speed but idle.
-
33
-
Chapter 3
Increased Power at Idle
3.1
Introduction
This chapter introduces two novel modulation techniques that effectively increase the output power characteristics of an alternator considering the availability of a semi-bridge Switched Mode Rectifier (SMR). The proposed schemes are simple and may be implemented without the the addition of expensive sensors in a realistic implementation. Based on the discussion presented in section 2.3 it was shown that even though an alternator with a SMR and load-matching control provides almost 2.5 times more output power at cruising speeds compared to an alternator with a simple diode bridge, no extra power is obtained at idle speed. To overcome the characteristic limitations of the load-matching technique, but keeping the simplicity of the aforementioned SMR structure, a departure from the original control is proposed. Instead of controlling the three active switches with the same duty cycle d, a new degree of freedom is added to the scheme, by modulating the switches individually. As will be shown, adding a new dimension to the control of the SMR, it is possible to advantageously manipulate the state variables of the system. In particular one can modify the magnitude and phase of the different harmonic components of the phase currents that determine the average output power.
3.2
Modulation delta
One modulation technique that we use to increase output power is illustrated in Fig. 3.1. The main goal of this simple modulation technique is to store electrical energy in the machine inductance (L,) of each phase, during one part of the electrical period, to release it in another part of the period. In order to achieve this goal, a time interval 6 is introduced for each phase starting whenever the current of a phase becomes positive. During this -
35
-
Increased Power at Idle
I
V
/
Vsa
/
ag
-
/
/ /
Vx
/
/ / / Il
64\
4-
/ \
/ \
/
Figure 3.1: Waveforms of alternator connected to SMR with an interval J introduced to enhance output power at idle speed. delta interval, the switch for that phase is held on (d = 1), while the other switches are modulated normally. This action results in the application of the full back EMF source across the winding inductance, which in turn stores additional electrical energy in that inductance; this energy will be released in another part of the conduction cycle. The modulation was selected because of its simplicity of implementation: implementation only requires sensing the direction of the current. Such information is readily available from voltage measurements done directly at the SMR. Figure 3.1 shows the waveforms of one of the phases of the SMR with an interval of length 6 introduced whenever the phase current ia turns positive. vsa is shown as a dotted line, while the current i, is shown as a distorted sinusoid as a solid line. The voltage at the input of the SMR vag is also shown. The amplitude of vag named V, represents the local average of the pulse-width-modulated waveform seen at the input of the SMR. The same figure also shows the phase angle between vsa and i, denoted as a.
-
36
-
3.2
3.2.1
Modulation delta
Analytical Model
A mathematical model for the delta modulation is derived in appendix A. There, it is shown that a considerable amount of extra output power can be obtained by changing the length of the interval 8 shown in Fig. 3.1. The same derivation demonstrates that such increase in real power is followed by a significant increase in phase current ia. The increase in losses due to dissipation will ultimately set the limit for which this modulation will be able to provide extra power at idle speed. As described in the analytical derivation, we can find an expression for the magnitude and the phase angle of the fundamental component of the phase current ia, labelled ial. The fundamental component is the only frequency component of the current that contributes to real power (given sinusoidal back EMF's). In order to find a closed-form expression for the phase current, a symmetric conduction condition is assumed. Under this approximation, a positive current iai is assumed to circulate through the alternator's winding for exactly half of the current period (i. e. for 0 < wat < 7r). The positive conduction angle of the current with the 6 modulation is not exactly 180 degrees in practice. While the symmetric conduction condition is not exact, it does provide a good insight into the benefits of the proposed modulation method. By applying this conduction condition, it is found that the magnitude ial and the phase angle a that exists between the back EMF and the phase current, can be expressed as a function of the back EMF amplitude Va, the synchronous impedance Z. = R, + jw 0 L, expressed in polar form Z, = IZ, ILz (representing the series resistance and inductance of the windings), the local average at the input of the SMR V, and the control handle 6. In particular, the phase angle a between the back EMF and the phase current can be expressed as:
a = Oz - sin-
cos
sin
+ Oz)
(3.1)
Also, the magnitude of the fundamental component of the phase current
ia1 is found to be:
(§ + 0)]
(3.2)
IalI=
[[cos (a - Oz)] - 2V cos (§) [cos
Using equations 3.1 and 3.2 we can express the average output power delivered ((POUT)) to the load by calculating the real power delivered by the back EMF source and subtracting the conduction losses occurring in the windings. The contribution of the other two phases that constitute the alternator have to be taken into account in the calculation for total power delivered. The equation for (PouT) is then: -
37
-
Increased Power at Idle
Output Power vs. 5 1 2 00 .. .. .
1 1 50 - - -.
0
. . .. . . . -. -.-.-.-.-.
-
..
-. -.
.
-
-
...
5
-
-
..-..-..-..-..-...-..- -
900 - -..--...--.
0
-
-
- -
-
-..-.. --.. . . . .. -. .. .
-
- .-..-.-.-.-
--
--
---
- -
. .. - .95 0 - -- -.
-. --
.-
- - - - ---
-
-
- ---
-. .. --..
..
.. .
1 1 0 0 - - - -01050 -
-
- . . . .. . . - . ..
10
20
15
25 8 (degs)
30
35
40
45
50
IRMS vs.8 80 - . . . .
0
5
-.
- -. . ...-. -..
- ..
I
I
10
15
I.
20
(POUT) = 3
.
25 5 (degs)
Figure 3.2: Calculated Output Power vs. modulation 6 (V2 14V).
[Vaiai
..
. .. .
-. .. -.-.-.
30
co~t]-
. . . .
. .
40
45
35
3 and I1RMS vs.
.-.-.
..
3
. .
50
at idle speed using the
3 [RJai](.3
- 3.3 we can plot, the output power (POUT) as a function of the control handle 65 (simulation file presented in appendix B.2). Figure 3.2 shows the average
Making use of equations 3.1
output power (PouT) and the RMS value of the fundamental component of the phase current (iai). The circuit parameters used in this simulation (representing the components
shown for the model shown in Fig. 1.3) are: VsaRMS =10.716V, RJ = 37mQ, L. 120p.H 180Hz; where VSaRMS represents the back EMF at idle speed (e. g. electrical and f8 frequency f8 180Hz) and full field current (e. g. if = 3.6A), and the control parameter S was varied from 0 to 500, V4 = 14V. Furthermore Fig. 3.3 shows the percent increase in output power and the percent increase in RMS phase current ia1, again as a function of 3. As mentioned before, the increase in output power is accompanied by a corresponding increase in phase current, which in turn increases dissipation in the machine windings. This, in turn limits the maximum power increase achievable within the thermal limits of
- 38
3.2
Modulation delta
Percent increase in output power vs. 8 20 --
15 (D Cz
- -.-
-
-. .. -. .. -.
-.
t 10
-
-. -.
-
-.-.-.--.-..... .....
.
5
00
10
5
15
25
20
30
S (degs)
Percent increase in
11RMS
40
35
45
50
vs. 8
0 40 -
- -. -~
S30
~
-
--
..-. . . -.
-
-
-
- .-. .. .-.
-
-
-
-
-
..-.. -
. - ..... -- -----.-.-.-. -......
--
-..
-..
20
--
10 U""
0
5
10
15
20
25
S (degs)
30
35
40
45
50
Figure 3.3: Calculated Output Power increase vs. 6 and IARMS increase vs. 6 at idle speed using the modulation 6 (V = 14V). the alternator. The main advantage of this modulation technique is its simplicity, because in a practical implementation the direction of the phase current ia can be easily obtained from measured voltages at the input of the SMR.
3.2.2
Pspice Verification
In order to corroborate the validity of the mathematical model described in section 3.2.1 and Appendix A, a PSPICE model was developed for the system. A detailed description of the PSPICE model can be found in Appendix C. Figure 3.4 shows a comparison between the results obtained using the Pspice model and the results presented in section 3.2.1. In particular it shows the output power (POUT) and the approximate RMS phase current vs. the control parameter 6. The alternator parameters used for the simulation are: VsaRMS = 10.716V, R, = 37mQ, L, = 120pH, f, = 180Hz and full field current (e. g. if = 3.6A). Again, Rs is the winding resistance and L, is the machine inductance. The results shown in Fig. 3.4 corresponds to a modulation such -
39
-
Increased Power at Idle
Pout
o increase vs. 5
vs.
1200
1100-
15
-:1000
-o
OWM
S10 a-0
onb
5
900 [-800
--
- -
0
10
20
30
40
-- Matlab
Fia-
I
Ppice 50
0
10
MSI RMS Mvs I IRMS
20
30
Pspice 40
50
increase vs. S
iRMS
80
(D
40
1R
30 0
S60
MRla
....... .....-.
50
F
210 -1
Mattab
0
10
2
20
30
40
--
- [-
~
-L
-=Pspice 40'
P sp....
50
0
10
20
30
40
50
Figure 3.4: Comparison between the MATLAB and PSPICE models for power and current vs. the control parameter 6.
that V = 14V. The 6 control parameter is varied from 0 to 50'. From the figure it can be appreciated that there is good agreement between the two models. The principal differences between the models are because the analytical model considered here only takes into account dissipation due to the fundamental component of the phase current, while the circuit simulation incorporates all dissipation components.
3.3
Complete Modulation
Based on the encouraging results obtained from the models presented in section 3.2, an augmented modulation is proposed in which additional control handles are added to the modulation scheme. Figure 3.5 shows the phase current and the instantaneous phaseto-ground rectifier voltage for one phase over an alternator electrical cycle for the full modulation scheme explored here. The switching function for each of the legs of the SMR structure is realized at a frequency many times higher than the line-current frequency and the duty cycle is modulated in such a way as to obtain the "local-average" phase to ground
-
40
-
3.3
Vsa
Complete Modulation
'D
\a
/ /
9
/D v
\vBASE
\
2)r /
Figure 3.5: Waveforms for new modulation technique. voltage Vag shown in Fig. 3.5. Looking at this local average voltage waveform it is possible to
define the different intervals that describe the modulation scheme. The back EMF voltage Vsa is shown with a dotted line, while the current ia is shown as a distorted sinusoid with
a solid line. The pattern is the same for the other phases, but delayed by 120 electrical degrees of the fundamental. The complete modulation technique consists then of the following subintervals:
*
5 : During this sub-interval, beginning when the phase current becomes positive, the switch is kept on, forcing the phase-to-ground voltage to be near zero. During this J portion, additional energy is stored in the winding inductance. Operation at a nominal duty ratio and local average voltage Vase. This voltage is close to that for the load matching condition, and will be a function of the alternator speed.
* Mid-cycle:
*
b : From the beginning of this interval to the end of the positive portion of the line current, the duty ratio is adjusted so as to obtain an average phase to ground voltage that exceeds the nominal Vase by V,, volts.
- 41 -
Increased Power at Idle
The modulation strategy embodied in Fig. 3.5 enables additional output power to be obtained from an alternator as compared to that achievable with diode rectification or switched-mode-rectification with load matching control. At the same time, this modulation is also simple enough to be implemented with inexpensive control hardware and without the use of expensive current or position sensors. As already mentioned, the zero crossing of the phase current waveform can be effectively detected by observing the phase-to-ground voltage during the FET off state. By means of adding these new degrees of freedom in the control of the SMR, it is possible to manipulate the state variables of the system beneficially. In particular we adjust the magnitude and phase of the different harmonic components that constitute the phase currents to enhance the average power delivered to the output.
3.3.1
Analytical Model
As mentioned, this modulation introduces two new subintervals to the normal operation of the SMR. The conduction angle interval 6 is introduced beginning when the phase current becomes positive, during which the bottom switch of the SMR is kept ON, the effect of which was already discussed in section 3.2.1. In the second new subinterval, a conduction angle interval 41 is introduced during which the duty cycle of the corresponding bottom switch is adjusted such that the local average of the voltage at the input of the SMR vag is set to a voltage V0v volts higher than in the main interval. The net result of these two subintervals will produce a phase shift that reduces the total phase angle a between the back EMF voltage va and the fundamental component of the phase current ia1 thus increasing the amount of real power obtained at idle speed (1800 rpm). Furthermore, these intervals can be used to increase the fundamental phase current, thereby increasing output power. The modulation strategy embodied by Fig. 3.5 achieves this within the modulation constraints of the semibridge SMR, and without requiring detailed position or current information. A detailed derivation that analytically solves for the magnitude and the phase of the fundamental component of the phase current ia relative to the back EMF can be found in the appendix A.3. There it is shown that the angle that exists between the back EMF v.a and the fundamental component of the phase current ia1, a depends in the values of the different control parameters, namely: Vov, 8, 4, and V.se. The expression obtained through the derivation is reproduced here:
a = 0Z + sin-[ cl sin (x - 6 - Oz)
1Va
-
42
-
(3.4)
3.3
Complete Modulation
In this expression, ci = al + b2 and x = tan. Where al and b, are the fundamental sine and cosine coefficients in the Fourier series that describes the local average of the phase to ground voltage Va. The series inductance L, and resistance R, that model the phase impedance can be represented by a total series impedance described by its magnitude IZLI and its corresponding phase 0,. The magnitude of the fundamental component of the phase current under the same modulation scheme is is also repeated here:
-l-Cos ci (X - 5 - OZ) |ZL|
|Iail = [ VaCos (a - OZ) IZLI
(3.5)
Using (3.5) and taking into account the contribution of the other two phases it is possible to obtain the same simple expression for the average output power (POUT) as in Eq. 3.3:
-3
(POUT) = 3 Vsalai c
[R,-
(3.6)
The influence of 5 in the output power and the phase current was already presented in Section 3.2, so now we will focus attention on the influence that the new control variable 4 has on those two quantities. Figure 3.6 shows the output power obtained when just the control variable 4 is applied. Again the conditions of the simulations are: VaRMS = 10.716V, R, = 37mQ, L, = 120piH and f, = 180Hz and if = 3.6A. The modulation parameters for the simulation shown in Fig. 3.4 corresponds to V , = 14V, and VOV = 20V. The value of 5 is set to zero and the parameter D is varied from 0 to 700. From Fig. 3.7, it can be seen that for small values of - a small increase in phase current ia is accompanied by significant increase in output power. With bigger values of the control parameter 4, it is possible to obtain a moderate increase in the output power but with an actual decrease in the magnitude of the phase current. This implies that is possible to obtain an increase in output power with lower conduction loss.
3.3.2
Pspice Verification
Fig. 3.8 shows the increase in output power (POUT) and the corresponding increase in RMS phase current versus the parameter D using both the PSPICE averaged model the analytical results presented in section 3.3.1. The results are qualitatively similar, though differences are significant for larger values of 4. The difference that exists between the simulation and the numerical predictions arise because interval 1b is not small, thus the symmetric
-
43
-
Increased Power at Idle
Output Power vs. 0 1400
130 0 120 0 - 0.a 1
1 00 -
0 100 0
- .
90 0 -
---..--.
-.--
.. -.. --
- - -.-- -- . ..
-. . -..
---.-
10
- -.-
30
-.-.
.-.--.-- --.-.
-
40
- -
----
--
- - --
-
-- -
20
. - -.-. - -.-.-
-.-
. - -.-- - -.-- -. .. .- -. . . . . . ..-..
--
0
--
-
- - -
-
- --
- ----
50
-60
70
4D (degs)
11RMS vs. 0 65 - -
55
J 45 - -
0
-
-.-.-
.. .-..
10
20
30
40
-
-.. .
-.. . -..
-.-.-.
-.-.-.-.
-.-
-.-... .
..
-..-
..
.. . .
w0 --
- -.-
-. -.
.
50
.
- .-..-
-.-.
---.-.
60
70
4) (degs)
Figure 3.6: Calculated Output Power vs. D and IIRMS vs.
