Summary - 實現感應電動車最大加速性能與最高效率之控制設計與切換策略

In this chapter, the high performance servo control of the induction machine implemented on the electric vehicle is developed to satisfy the maximum acceleration capability and the highest operating efficiency. Present achievements are summarized as follows.

(1) Successfully identify the rotor time constant of the induction machine

Rotor time constant is employed in the calculation of the synchronous angle estimator in the indirect vector control, and the traditional no-load test and locked-rotor test is not easy to implement on the vehicle. A precise identification process that can be directly performed on the vehicle is developed to obtain the

Fig. 3-18 Speed response of the vehicle when ids*

= 0.42 pu and 0.82 pu

0 2 4 6 8 10 12 14

0 5 10 15 20 25

Time (sec) Speed (km/hr) i_ds^*= 0.82 pu

i_ds^*= 0.42 pu

rotor time constant as 0.08 s.

(2) The maximum torque per amperage operation is obtained by applying the rated flux excitation

Conventional approach of equal d-q current command is unsuitable for the vehicle application in this study, in which severe flux saturation of the machine is caused and the MTPA operation is thus lost. Alternatively, the maximum torque can be obtained when the rotor flux linkage is exited at the rated value proved by the standard experimental process, and the acceleration of the machine can be improved by 65.5% with such arrangement when the maximal stator current is supplied (is*

= 2.576 pu) as shown in the following table.

(3) The highest efficiency is obtained with proper flux current setting

The highest operating efficiency of the machine is directly found by practical driving following the standard experimental process as ids*

= 0.42 pu.

Despite of weaker acceleration ability, the efficiency coefficient at such operating point can be further increased to 48.4 rad/s.A when the maximal stator current is supplied as shown in Table 3-4.

Table 3-3 Comparison of the equal d-q current command and the rated flux excitation (is*

= 2.576 pu)

Control method Acceleration

(rad/s²)

Efficiency coefficient (rad/s.A)

Final speed (km/hr)

Equal d-q current command 23.51 13.35 10.2

Rated flux excitation (i_ds^* = 0.82 pu) 38.92 36.47 14.7

Improvement 65.5% 173.2% 44.1%

Table 3-4 Comparison of the rated flux excitation and the highest efficiency operation (i_s^* = 2.576 pu)

Control method Acceleration

(rad/s²)

Efficiency coefficient (rad/s.A)

Final speed (km/hr) Rated flux excitation

(ids*

= 0.82 pu) 38.92 36.47 14.7

The highest efficiency operation (ids*

= 0.42 pu) 17.95 48.4 21.4

Improvement 32.7% 45.6%

Chapter 4 Design of the Optimal Switching Mechanism

In this chapter, the idea of designing a switching mechanism of the operating flux of the induction machine for achieving both the maximum torque and the highest operating efficiency will be developed to meet control specifications of the electric vehicle. We first propose the slip factor adjustment, γ-adjustment, for a smooth characteristic of the vehicle application. Then, the switching strategy that automatically adjusts the operation accoring to the driving conditions to satisfy the requirement is designed based on the proposed γ-adjustment.

4.1 Slip Factor Adjustment (γ-Adjustment)

First of all, we define a slip factor, γ, in the slip frequency calculation such that

ds Note that the defined slip factor is unity in general indirect vector control as seen from (3-4). As stated in Section 3.1.1, the rotor time constant of the induction machine is much smaller than the mechanical constant of the vehicle. Hence, the equation (4-1) can be rewritten by substituting p = 0 as referred to the mechanical system as

ds By substituting (3-9) into (4-2) and substituting (3-10) into (3-2), we obtain

  indicated in (3-7), and the following equation is derived:

 

With the developed rotor time constant identification described in Section 3.1.2, the estimated rotor time constantˆ can be obtained as close to the actual value_r _r. Thus, the equation (4-5) can be simplified as

 

 1tan

tan  (4-6) Relationship between the feedback and actual d-q axis currents flowing into the induction machine can be depicted based on (4-6) as shown in Fig. 4-1.

When γ = 1, the actual current is equal to the estimated or feedback value on both axes. This is what general indirect vector control is applied. If γ > 1, β will be larger than α, and the actual q-axis current flowing into the motor is smaller than its feedback while the actual d-axis current is larger than the feedback one. On the other hand, β will be smaller than α when γ < 1. In this case, the actual q-axis current is larger than its feedback while the actual d-axis current is smaller than the feedback.

Obviously, by adjusting γ while keeping the current commands as the same magnitude, the actual d-q axis current can also be altered.

(a) (b)

(c)

Fig. 4-1 Relationship between the estimated and actual d-q axis currents when (a) 1 , (b) 1, and (c) 1

Fig. 4-3 Efficiency coefficient with different γ (ids*

= 0.62 pu)

0.5 1 1.5 2 2.5 3 3.5 4

10 15 20 25 30 35 40 45 50

Slip factor

Defined efficiency coefficient ( rad/sec.A ) Stator phase current = 1.623 pu Stator phase current = 2.094 pu Stator phase current = 2.576 pu

γ = 1.625 γ = 0.625

The first merit of such adjustment is that the maximum torque per amperage and the highest efficiency operation can still be obtained by properly setting γ even if ids*

is not originally set at both optimal operating points. To verify its validity, we intentionally set ids*

as 0.62 pu, which is neither the operation of the maximum torque per amperage nor the operation of the highest efficiency, and obtain γ correpsonding to these two operations through the standard experimental process developed in Section 3.2.3 and 3.2.4. Experimantal results are shown in Fig. 4-2 and 4-3.

Fig. 4-2 Acceleration with different γ (ids*

= 0.62 pu)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0 5 10 15 20 25 30 35 40 45 50 55

Slip factor

Acceleration (rad/s.s)

Stator phase current = 1.623 pu Stator phase current = 2.094 pu Stator phase current = 2.576 pu Slip factor = 1.625

γ = 1.625

From the above experimental results, it can be identified that the system has the maximum acceleration when γ = 1.625 to achieve the maximum torque per amperage operation. Additionally, the highest efficiency operation can be obtained with γ = 0.625. Data of the acceleration and efficiency coefficient when γ = 1.625 and 0.625 are summarized in Table 4-1.

Therefore, even though the flux current is not correctly operated at the maximum torque per amperage (ids*

= 0.82 pu with γ = 1) and the highest efficiency operation (ids*

= 0.42 pu with γ = 1), both of them can still be obtained by setting γ as 1.625 and 0.625 when ids*

= 0.62 pu, respectively, as shown in Table 4-1.

The approach that sets ids*

= 0.82 pu to obtain the maximum torque per amperage operation and sets ids*

= 0.42 pu to obtain the highest efficiency operation with γ = 1 is performed by different settings of ids*

. To distinguish this approach from the proposed γ-adjustment, we specifically denominate it as ids*

-adjustment. Speed responses of the vehicle with the maximum torque per amperage (MTPA) operation obtained by the ids*

-adjustment and the γ-adjustment are compared in Fig. 4-4(a), and comparison between the highest efficiency (HE) operation obtained by the ids*

-adjustment and the γ-adjustment is shown in Fig. 4-4(b). Both two figures are obtained with the maximum supplied stator current, i.e. is*

is 2.576 pu. Their acceleration and efficiency coefficient are listed in Table 4-2.

Table 4-1 Comparison of acceleration and efficiency

Acceleration (rad/s²) Efficiency coefficient (rad/sec.A) 625

1

  0.625  1.625  0.625

pu 623 .

* 1

is 17.61 7.638 36.63 49.47

pu 094 .

* 2

is 28.71 12.08 39.66 49.7

pu 576 .

* 2

is 39.27 18.36 38.11 49.88

Consequently, we can conclude that among the following four operating points:

(1) and (3) obtains equivalent maximum torque per amperage operation, while (2) and (4) obtains the identical operation of the highet efficiency.

(a) MTPA operation (b) HE operation Fig. 4-4 Comparison of the speed response obtained by

the ids*

-adjustment and the γ-adjustment

0 2 4 6 8 10 12 14

Operation Approach Operating Condition Acceleration (rad/s²)

4.2 Comparison between the γ-Adjustment and the i

-Adjustment

It can be recognized that the decoupled control will be modified by the γ-adjustment as seen from Fig. 4-1, which indicates that the operating flux will no longer be constant while changing the q-axis current, and torque ripples may be generated due to varied flux as stated in [26]. However, the ripples can be filtered out in the vehicle application because the mechanical time contant is far larger than the rotor time constant. In order to verify it, we have launched three sets of experiments in which ramp stator current commands with different slopes are fed into the system.

Fig. 4-5 shows the patterns of the ramp stator current commands as:

(1) Slope1 = 2.576 pu/s (2) Slope2 = 1.0304 pu/s (3) Slope3 = 0.5752 pu/s

Vehicle speed response corresponding to (1) ~ (3) operated at the maximum torque per amperage by the ids*

-adjustment (ids*

= 0.82 pu with γ = 1), and the γ-adjustment (ids*

= 0.62 pu with γ = 1.625) are compared in Fig. 4-6(a) ~ (c), respectively.

Fig. 4-5 Three stator current commands applied for the verification of torque ripples

0 2 4 6 8 10 12 14

0 0.5 1 1.5 2 2.5 3 3.5 4

Time (sec)

Stator current command (pu)

(1) 1.0 s from 0 to 2.576 pu (2) 2.5 s from 0 to 2.576 pu (3) 5.0 s from 0 to 2.576 pu

(a) The ramp stator current command with slope 1

0 2 4 6 8 10 12 14

0 5 10 15 20

Speed (km/hr)

0 2 4 6 8 10 12 14

0 5 10 15 20

Time (sec)

Speed (km/hr) gamma-adjustment

ids*-adjustment

(b) The ramp stator current command with slope 2

0 2 4 6 8 10 12 14

0 5 10 15 20

Speed (km/hr)

0 2 4 6 8 10 12 14

0 5 10 15 20

Time (sec)

Speed (km/hr) gamma-adjustment

ids*-adjustment

As seen from Fig. 4-6, torque ripples are eliminated by the system with large mechanical time constant in the experiments, since no ripples are present in the practical speed response with the γ-adjustment. In fact, with the results shown in Fig.

4-6 we can also prove that the operation with ids*

= 0.82 pu and γ = 1 and the operation with ids*

= 0.62 pu with γ = 1.625 are equivalent to each other once again.

Then, to further investigate the difference between the ids*

-adjustment and the γ-adjustment, operation with the maximum toruqe per amperage and that with the highest efficiency are switched back and forth with is*

= 2.576 pu step command for testing. The patterns of the testing switching process between these two operations for the ids*

-adjustment and the γ-adjustment are shown in Fig. 4-7. Note that γ is kept as unity and ids*

is switched between 0.42 pu and 0.82 pu when the ids*

-adjustment is applied, while ids*

is kept as 0.62 pu and γ is switched between 1.625 and 0.625 when the γ-adjustment is applied in the testing process. Experimental results are shown in Fig. 4-8.

Fig. 4-6 Comparison of the vehicular speed response operated at the maximum torque per amperage by the ids*-adjustment and the γ-adjustment

0 2 4 6 8 10 12 14

0 5 10 15 20

Speed (km/hr)

0 2 4 6 8 10 12 14

0 5 10 15 20

Time (sec)

Speed (km/hr) gamma-adjustment

ids*-adjustment

(a) (b)

Fig. 4-7 Patterns of the testing switching process between the MTPA and the HE:

(a) ids*

-adjustment and (b) γ-adjustment

0 2 4 6 8 10 12 14 Fig. 4-8 Results of the testing switching process obtained by the

ids*

-adjustment and the γ-adjustment

0 2 4 6 8 10 12 14

Stator phase current magnitude response (pu)

overshoot

As seen from Fig. 4-8, the operation of the currents of the γ-adjustment is smoother than that of the ids*

-adjustment with the given switching process.

Particularly in the time interval between the 7^th second and the 10^th second, the q-axis currents of both approaches decrease significantly since the rotor flux linkage and thus the back-emf constant becomes stronger when the operation is switched from the HE to the MTPA. It can be noticed that the q-axis current response of the ids*

-adjustment instaneously drops to negative values, indicating torque with the opposite direction is developed. This phenomenon can be detected as well from its own speed response, where drastic speed drop occurs and causes more uncomfortable driving experience, as shown in Fig. 4-8(a). On the other hand, the q-axis current value of the γ-adjustment is always positive regardless of the varied operations, and the torque will always be of the forward direction. Accordingly, the γ-adjustment yields smoother operating performance that is more applicable to traction control of the electric vehicle when the switching machanism is applied. This is the second merit of the γ-adjustment approach.

4.3 Switching Strategy for Both the MTPA and the HE Operation

4.3.1 Design of the switching strategy

It has been already verified in the previous section that the γ-adjustment possesses relatively smooth driving performance with the switching machanism.

Therefore, the γ-adjustment is applied as the basis of the switching strategy designed for obtaining both the maximum acceleration and the highest efficiency.

As far as the traction control of electric vehicle is concerned, it is desirable to meet the following two characteritics:

(1) High torque for starting and at low speeds (2) High efficiency for high-speed cruising

Based on the fact, we can first determine speed thresholds for the operations. Fig. 4-9 shows the speed response obtained by the γ-adjustment with the maximum supplied stator current when the induction machine is operated at the MTPA and the HE. The designed switching strategy that can automatically adjust γ according to driving conditions is also illustrated in the figure. The definitions of three operations specified based on two speed threshold values, 10 and 15 km/hr, in the strategy are shown in Table 4-3.

In practical driving, the supplied stator current magnitude is determined by the accelerator in the system, and thus the q-axis current command may intensely vary.

Nonetheless, the mechanical time constant of the system is very large so that the variation of the vehicle speed acts much slower than that of the current. As a result, it is quite sufficient to check driving conditions just every second for the switching strategy as shown in Fig. 4-10.

Fig. 4-9 Illustration of the designed switching strategy for γ

0 2 4 6 8 10 12 14

0 2 4 6 8 10 12 14 16 18 20 22

Time (sec)

Speed (km/hr) 15 km/hr

10 km/hr

γ = 1.625 to provide MTPA γ = 0.625 to provide HE

γ switching interval











γ = 1.625 (MTPA) γ = 0.625 (HE)

Table 4-3 Definition of three operations in the switching strategy Specified operation Definition Description Setting Operation 1 High speed Speed > 15 km/hr γ = 0.625 Operation 2 Medium speed Speed = 10~15 km/hr γ = 0.625~1.625 Operation 3 Low speed Speed < 10 km/hr γ = 1.625

Fig. 4-10 Illustration of driving-condition checking of the switching strategy

．．．

Time (s)

0 1 2 3 4 5 6

．．．

Check driving conditions for the switching strategy

When γ = 1.625, it is obvious that the increasing rate of the speed response becomes smaller and smaller if the speed continues to increase after reaching 10 km/hr, and the speed will gradually converge to a final cruising speed value. Thus, the first speed threshold is set at 10 km/hr. When the speed is smaller than this value, it is defined as the low-speed operation (operation 3). During this operation, γ is always kept as 1.625 for providing the maximum torque.

Furthermore, 15 km/hr is determined as the second speed threshold such that operation with speed larger than 15 km/hr is defined as the high-speed operation (operation 1) while operation with speed lying between 10 and 15 km/hr is specified as the medium speed operation (operation 2). In operation 1, γ will be kept as 0.625 to obtain the highest efficiency.

Finally, there are four possibilities for the behavior of γ in the defined γ-switching interval, i.e. operation 2:

(1) γ is switched from 1.625 to 0.625 within 1 s (2) γ is switched from 0.625 to 1.625 within 1 s (3) γ is 0.625

(4) γ is 1.625

The notion of the strategy design for this operation is descriped as follows: In general, the driver will keep stepping on the accelerator pedal deeply in an attempt for acceleration if one senses that the vehicle is currently slow. Contrarily, if the driver considers that the present vehicle speed is too high, the accelerator will be shallowly stepped on so that the speed is going to slow down. The vehicle tends to operate at a high speed in the former case while it tends to be operated at a low speed in the latter case. Hence, the driving commands set by the accelerator, i.e. the commands of the supplied stator current magnitude, is*

, can be employed for a criterion to determine which action among (1) ~ (4) will be applied as shown in Fig. 4-11.

In the present implementation, we specify 1.5 pu as the theshold value of is*

. After operation 2 is confirmed, the system will check if is*

is larger than the threshold.

If it is true, γ will be switched from 1.625 to 0.625 within 1 s when γ is currently not 0.625; otherwise γ will be maintained as 0.625. If is*

is smaller than the threshold, γ will be switched from 0.625 to 1.625 within 1s when γ is not 1.625 at present, or γ will be maintained as 1.625. The flow chart and the block diagram of overall control program of the system including the switching strategy implemented on the DSP controller are shown in Fig. 4-12 and 4-13, respectively.

Fig. 4-11 Classification of actions applied in operation 2

Operation 2

is* ≥ 1.5 pu (tend to operate at high speed)

γ = 0.625 ?

γ = 0.625 (3) γ is switched from 1.625 to

0.625 within 1 s (1)

is* < 1.5 pu (tend to operate at low speed)

γ = 1.625 ?

γ = 1.625 (4)

γ is switched from 0.625 to 1.625 within 1 s

(2)

No Yes Yes No

(a) Main program

Program starts

System initialization

Interrupt request received?

Current control branch No

Yes

(b) Current control branch

Current control branch starts

Signal calculation

(1) Three-phase feedback current (2) DC-bus voltage

(3) Accelerator voltage (4) Backward driving voltage

Current command assignment (1) Transfer accelerator voltage into is*

(2) Divide is*

into ids*

and iqs*

Backward driving voltage > 2V?

iqs*

= - iqs*

Yes No

Coordinate transformation

Current PI control

Inverse coordinate transformation

Update SVPWM control signals

Motor speed calculation

Synchronous angle estimator with γ

End of the branch Designed switching strategy

(Obtaining γ)

cnt++;

If cnt >14999, then reset cnt

Fig. 4-12 Flow chart of overall control program including the switching strategy (c) Designed switching strategy for obtaining γ

cnt = 0 ?

γ=1.625 Downflag=0

Upflag=0

γ=0.625 Downflag=0

Upflag=0

Downflag=0 Upflag=1

γ − = 1 / 15000 Yes

Check vehicle speed

≤ 10 km/hr 10 ~ 15 km/hr ≥ 15 km/hr

Check i_s^*

γ = 1.625 ?

< 1.5 pu ≥1.5 pu

γ = 0.625 ?

Yes Yes

Downflag=1 Upflag=0

No No

Downflag = 1 ?

Upflag = 1 ? γ + = 1 / 15000 No

Yes

End of the strategy Strategy starts

As shown in Fig. 4-12(b), a counter, cnt, is plus one every time when the current control branch is executed, and it will be reset to zero as long as its value is larger than 14999. Since the interrupt frequency of the system is 15 kHz, the conditional statement evaluating whether cnt is equal to zero, as illustrated in Fig. 4-12(c), is used to implement condition checking every second of the switching strategy. Besides, the actions where γ −= 1/15000 and γ += 1/15000 indicate that γ is switched from 1.625 to 0.625 within 1 s and γ is switched from 0.625 to 1.625 within 1 s, respectively.

4.3.2 Experimental verification of the designed strategy

To verify that the designed switching strategy is effective, we have performed various experiments with practical driving conditions. The first one was carried out with step 2.576 pu of is*

, and operation with MTPA only, HE only, and the designed switching strategy are compared in Fig. 4-14 and Table 4-4.

As seen from Fig. 4-14 and Table 4-4, operation with the switching strategy possesses both charateristics of MTPA (γ = 1.625) and HE (γ = 0.625) as: At start-up of the vehicle, the system is operated at the MTPA so that the maximum acceleration can be obtained. Then, the system is switched to the HE operation for higher efficiency and final speed as the speed increases until it exceeds 10 km/hr.

Fig. 4-13 Block diagram of overall control program implemented on the DSP controller

The second experiment for the verification was launched such that the driver can step on the pedal as one wants to control the vehicle. Results of control schemes with and without the switching strategy are shown in Fig. 4-16 and 4-15, respectively.

When the vehicle is driven without the switching strategy, the maximum acceleration can be obtained since γ is set as 1.625 to provide the MTPA. However, Fig. 4-15 (c), (d), (i), and (j) exhibit that the vehicle speed is limited to approximately 14.7 km/hr no matter how large the command is*

is fed. The reason is that strong rotor flux linkage is excited when the system is operated at the MTPA and it causes large back-emf. From the results shown in Fig. 4-3 we also know that the efficiency at such an operation is not desirable.

(a) Speed response (b) γ

Fig. 4-14 Experimental results of operation with the MTPA, the HE, and the switching strategy

0 2 4 6 8 10 12 14

0 5 10 15 20 25

Time (sec)

Speed (km/hr)

MTPA HE

Switching strategy

0 2 4 6 8 10 12 14

0.5 1 1.5 2

Time (sec)

Slip factor

Switching strategy MTPA HE

Table 4-4 Comparison of with the MTPA, the HE, and the switching strategy

Operation Operating Condition Acceleration (rad/s²)

Efficiency coefficient (rad/s.A)

Final speed (km/hr)

MTPA only γ = 1.625 39.27 38.11 14.7

HE only γ = 0.625 18.36 49.88 21.6

Switching strategy γ is automatically adjusted 39.27 49.88 21.6