## Power Factor

3.3.2.1 The Problem

A problem common to all VRPMs is that they tend to operate at low power factors under load, values in the range of 0.35-0.55 are typical [69]. The highly effective magnetic circuit of the machine, which is key to its high shear stresses, presents this inherent disadvantage. The problem is compounded by the desire for many turns on the coil to further enhance the change in flux linkage from the slow physical velocity. The result of these factors is that current flowing within the coils produces a strong flux pattern. Any change in this current flow is hence resisted by a large change in flux flow, producing a back emf. In practice this phenomena manifests itself as a large inductance in series with the electrical machine resisting any change in current. The subsequent phase lag between emf and current results in the terminal voltage collapsing when current flows.

Consider the simple circuit and phasor diagram shown in Figure 3.6. The magnet flux, is pointing top left, with the subsequent emf induced in the coil lagging by 90°, pointing top right. Regarding the coil as a pure inductor and connecting it to a pure erinf

Figure 3.6: Phasor Diagram of VRPM

erinf

Figure 3.6: Phasor Diagram of VRPM

resistor, the emf induced, E, will be dropped across the external resistance, IR, and the internal inductance, IX. The voltage across an inductor leads the current by 90°, which causes a phase difference, between the internal emf and current. The terminal voltage is IR.

The power factor is defined as cos^, where ^ is found from inspection of Figure 3.6 to be equal to arcsin(IX/E). Thus the value of IX/E sets the power factor, where a value of unity is obtained when IX/E equals zero and a value tending towards zero when IX/E tends to one, i.e. when all the emf is dropped across the internal inductance. This ratio, described as the flux ratio, maybe qualitatively described as the stator flux linkage due to electric excitation only divided by that due to magnet excitation only, or yi/yM. A high internal power factor therefore requires either a very high flux linkage from the magnets or a very low flux linkage from the coil.

The flux due to the two sources follows the same low reluctance path, and hence gives low power factors. Furthermore, in order to exploit the effect of magnetic gearing, each of the stator magnets has oppositely polarised neighbours making a large amount of leakage and fringe flux inevitable.

Reducing the number of turns on the coils would reduce the mmf, NI, applied to the machine for a given current excitation. Less flux would cut the coil and hence the power factor would improve. This, however, would be at the expense of a lower induced emf and a lower shear stress.

The low power factor of VRPMs will hamper their useful power output. The requirements of this topology and the utilisation of magnetic gearing make it an inherent feature which must be overcome by electronic means.

### 3.3.2.2 The solution

In order to reduce the power factor and bring the current and voltage of the generator in phase, reactive power must be provided. Two alternative methods are detailed below. Tuning capacitor

The effect of a low power factor may be compensated for by the addition of a parallel capacitor across the load. Chen et al. [70] demonstrated this de-tuning effect for PM machines used in wind turbines. The choice of capacitance, C, to achieve maximum power transfer is dependant on frequency, and is given by Chen et al. as (3.6).

A fixed capacitance will only have benefits at a single resonant frequency. The electrical frequency in machines used in this application is proportional to translator velocity, which will constantly vary. Therefore, in order to benefit from assisted excitation at all frequencies, thyristor switched capacitors would have to be used. In reality there is a limit to the usefulness of this method at a large scale feeding a non constant load whilst excited at a non constant velocity.

### Active rectifier

More efficient power take off can be expected with the use of an active rectifier ensuring the power flow from the generator is unidirectional. This implies that the output current wave form has the same frequency and polarity as the internal emf, forcing them to be in phase with each other and bringing the power factor up to unity, which can be achieved by an active rectifier acting as a Unity Power Factor (UPF) controller. Although power electronics is outside the scope of this thesis, in order to obtain useful power out of VRPM machines their presence must be assumed. A very brief outline of the operation of a UPF controller is hence given.

Using a search coil or a look up table, the internal emf of the generator is always known at a given current, speed and position. The maximum theoretical current may be calculated by scaling this value. The voltage difference at the terminals of each coil can then be manipulated to achieve this current. Pulse Width Modulation (PWM) with a frequency of the order of 10 kHz is used to control the terminal voltage, the characteristics of which are calculated from the difference in actual and expected coil current [55]. Work being carried out elsewhere in the School of Engineering, University of Durham, is striving to achieve this.

## 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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