Capacitor loading

The model results are compared with the experimental values with a 630Q resistor in parallel with a 150^F capacitor. The experimental results are summarised in Table 4-6 Table 4-6: Experimental results for a 630Q resistor and 150^ F capactor

Max:

504 Volts

Min:

-472 Volts

RMS:

211 Volts

Figure 4.48 to Figure 4.55 give examples of results from 'model A' to 'model E' simulating this situation.

Model A Integration method i

time Cs)

Figure 4.48: Capacitive loaded results for model A I

time Cs)

Figure 4.48: Capacitive loaded results for model A I

Figure 4.48 shows a comparison of the experimental results and the simplest of the model predictions. The agreement of the two in terms of shape is good, with the predicted waveform having a credible profile.

time Cs)

Figure 4.49: Differential of voltage used in model A i time Cs)

Figure 4.49: Differential of voltage used in model A i

The results of Figure 4.49 show that the derivative of voltage, which appears to be a noise signal, bears no relation to the curve expected if, for example, the flux pattern was simplified to a sine function. It is included here to demonstrate that, although the predicted voltage is acceptable, this model is not functioning properly.

N. J. Baker Chapter 4: The Linear Vernier Hybrid Machine Model A Integration method ii

Figure 4.50: Capacitive load results for model A ii

The graph of Figure 4.50 is almost identical to that of Figure 4.48 and thus demonstrates the limited effect of integration method on overall model behaviour. Model C Integration method i

Figure 4.51: Capacitive load results for model C i

Figure 4.51 shows the results as predicted by model C i compared with the experimental. The model appears to act in a similar manner to model A. Figure 4.52 is included to further highlight the problems experienced when specifying a model that contains numerical differentiation. In this model, there is a term involving the double time differential of inductance, Table 4-3. Inspection of Figure 4.52 show how the oscillating value of inductance is distorted through two numerical differentiation processes.

Figure 4.52: Calculated values of inductance and its differentials in model C i
Figure 4.53: Capacitive load results for model C i, settle period

Figure 4.53 demonstrates that models require some time to settle before accurate results are obtained. For the first 0.2 seconds large amplitude voltages are predicted, until the effect of the initial conditions is replaced with the true transient response.

Model E Integration method i

time Cs)

Figure 4.54: Capacitive load results for model E i

time Cs)

Figure 4.54: Capacitive load results for model E i

Model E Integration method ii

time Cs)

time Cs)

Figure 4.55: Capacitive load results for E ii

Table 4-7: Summary of VHM model results

Figure 4.55: Capacitive load results for E ii

Table 4-7: Summary of VHM model results

A.i

A.ii

B.i

B.ii

C.i

C.ii

Value

%

Value

%

Value

%

Value

%

Value

%

Value

%

Max

552

10

552

10

549

9

551

9

491

3

551

9

Min

-560

19

-560

19

-559

18

-560

19

-502

6

-557

18

RMS

217

3

217

3

216

2

217

3

201

5

216

2

D.i

D.ii

E.i

E.ii

Value

%

Value

%

Value

%

Value

%

Max

776

54

550

9

550

9

550

9

Min

-760

61

-558

18

-558

18

-558

18

RMS

332

57

216

2

216

2

216

2

Table 4-7 compares the results of all 5 models and the two alternative methodologies for differentiation, giving an indication of the small differences between them. Figure 4.49 and Figure 4.52, however, show why some of the models cannot be functioning properly. Even though the results do little to differentiate, it is likely the model which best represents the results predicted by the FEA is model E.

The non-constant velocity prevented the capacitor and machine inductance from reaching the resonance required to drive large currents through the VHM. The relatively low resulting currents were not enough to demonstrate appreciable differences in modelling methods.

Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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