## 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

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 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 4.53 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.

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