INTERFACING A PRIME MOVER DRIVEN ALTERNATOR WITH AN EXISTING

POWER SUPPLY

Technical Field of the Invention

The invention relates to a method of interfacing a prime mover driven alternator with an alternating current circuit having an existing alternating current, a controller for interfacing a prime mover driven alternator with such an alternating current circuit and an interface comprising the controller.

Background to the Invention

A number of methods and devices for connecting a prime mover driven alternator (generator) to a circuit carrying an existing alternating current have previously been disclosed. In this context, the prime mover driven alternator typically comprises a Free Piston Stirling Engine (FPSE) and the circuit carrying an existing alternating current is normally an ac mains supply. Examples of such disclosures include WO 01/69078, WO 2005/076429 and WO 2006/005956.

Figure 1 shows an example circuit for connection and disconnection (interfacing) between a FPSE with linear alternator 10 and an ac mains supply 20. When a Free Piston Stirling engine is used together with a linear alternator, the acronym FPSE/LA is used.

There is a tuning capacitance 12 in series with the linear alternator 10. Terminals 13 of the linear alternator circuit supply electrical power which may be measured by voltmeter 15 and ammeter 18. Terminals 25 provide the electrical power from the ac mains supply.

The interfacing circuit comprises: a first switch SW1; a second switch SW2 ; a relay (or third switch) SW3 ; an auxiliary switch 50; a first relay-controlled switch 60; a second relay-controlled switch 70; an initialisation

resistance R _sta rt ; and a stopping resistance R _stoP - The first switch SW1 and the auxiliary switch 50 are controlled by a first control signal SI. The second switch SW2 is

controlled by a second control signal S2.

The initialisation resistance R _s t _a rt ;- the first switch SW1 and the stopping resistance R _s t _op are provided along a first, initialisation path between the terminals 13 and the terminals 25. When the first switch SW1 is suitably

configured, the linear alternator 10 is coupled to the ac mains supply 20 through the initialisation resistance R _s t _a rt and the stopping resistance R _stop - The second relay- controlled switch 70 is configured to provide a second, bypass path between the linear alternator 10 and the ac mains supply 20, in which the two are connected to each other without the initialisation resistance R _s t _a rt and the stopping resistance R _s t _op - The second switch SW2 is

configured to control the relay SW3. When the relay SW3 is activated, it causes the first relay-controlled switch 60 and the second relay-controlled switch 70 to be configured so as to close the second, bypass path. The first switch SW1 and the second switch SW2 are also configured so that, when the initialisation path and bypass path are both open, the stopping resistance R _st0p is connected in parallel with the terminals 13 of the linear alternator 10.

The interface circuitry is controlled by means of the first control signal SI and second control signal S2. These are digital signals and are generated using a finite state machine. A brief description of the sequence to start and stop a prime mover driven alternator, such as a Stirling engine generator, is shown in Table 1 below. More details may also be found in WO 01/69078, WO 2005/076429 and WO 2006/005956.

Table 1 Summary of the Invention

Against this background, the present invention provides a method of interfacing a prime mover driven alternator with an alternating current circuit having an existing alternating current. The method comprises activating an electronic load connected in parallel with the prime mover driven alternator as part of a transition between a

disconnected state and a connected state, the disconnected state being when the prime mover driven alternator is electrically isolated from the alternating current circuit and the connected state being when the prime mover driven alternator is electrically coupled to the alternating current circuit .

In this way, an electronic load (a configurable

electronically simulated resistance or current sink) can be used during connection or disconnection of the prime mover (engine) driven alternator to or from the alternating current circuit. Soft connection, disconnection or both are possible thereby. The transient response of the current generated using existing interface technologies cannot be controlled .

The electronic load connected in parallel to a prime mover driven alternator may provide the features of soft starting and stopping the prime mover. This may result in lower vibration and noise levels during the start sequence. As a consequence, lower wear rates during the running-in period and lower noise levels may be expected. Also, the controlled slow start-up may allow extension of the

operating envelope for starting in terms of heater head and coolant temperatures. The generator may be further stopped off-grid, preferably running at its natural mechanical oscillation frequency. Moreover, the soft disconnection may provide a cost-sensitive solution for controlling engines (particularly Stirling engines) in biomass and solar

applications where the thermal inertia of the engine head is high. With a suitable control method, the maximum heat power removed by the engine can be defined depending on the head temperature when the engine is grid connected and off- grid. For a constant heat input power existing control methods and interfaces may stop the engine after a grid fault. As a consequence, the head temperature may rise as the engine is stopped because there is no conversion of heat into mechanical energy. The soft disconnection may further enable quicker restarts due to cooling during the stopping phase and may help protect components and the engine if the heat source is still enabled.

In the preferred embodiment, the prime mover is a Stirling engine. Most preferably, the prime mover is a Free Piston Stirling engine. Preferably, a linear alternator is used (and the acronym FPSE/LA is then used) .

In some embodiments, the prime mover driven alternator is initially electrically isolated from the alternating current circuit. Hence, the method is for connecting the prime mover driven alternator to the alternating current circuit. The method may further comprise receiving a signal indicating that the prime mover driven alternator is to start generating current, the step of activating the

electronic load being performed in response to receiving the signal. Thus, an initialisation signal may be used to activate the electronic load as part of the connection steps.

Optionally, the method further comprises electrically coupling the prime mover driven alternator to the

alternating current circuit via a coupling impedance, in response to receiving the signal. The coupling impedance is preferably a resistance and may comprise more than one component, for example multiple resistors. Then, the method may further comprise: identifying that power is being generated at the prime mover driven alternator; and

electrically coupling the prime mover driven alternator to the alternating current circuit bypassing the coupling impedance, in response to the identification. Thus, the prime mover driven alternator may be coupled to the

alternating current circuit through two separate paths, one path has a coupling impedance component and the other does not. This latter path may be considered a direct connection between the prime mover driven alternator and the

alternating current circuit.

Advantageously, the method may further comprise:

electrically coupling the prime mover driven alternator to the alternating current circuit directly; and setting the electronic load to perform an integrity test on the

electronic load when the prime mover driven alternator is electrically coupled directly to the alternating current circuit. As above, this direct connection means that no specific coupling impedance is placed along the path between the prime mover driven alternator and the alternating current circuit. The integrity test on the electronic load may be used to confirm that the electronic load is operating normally before it is deactivated or disconnected.

Beneficially, the prime mover driven alternator is also electrically coupled to the alternating current circuit through a coupling impedance when the step of setting the electronic load to perform an integrity test is performed. Then, the method may further comprise: identifying that electronic load passes the integrity test; and disconnecting the electrical coupling between the prime mover driven alternator and the alternating current circuit through the coupling impedance in response to the identification that the electronic load passes the integrity test. Alternatively, the method may further comprise: identifying that electronic load fails the integrity test; and

electrically isolating the prime mover driven alternator from the alternating current circuit in response to the identification that the electronic load fails the integrity test .

In the preferred embodiment, the method further

comprises deactivating the electronic load following an identification that the prime mover driven alternator is electrically coupled to the alternating current circuit.

In some embodiments, the prime mover driven alternator is initially electrically coupled to the alternating current circuit. Here, the method is for disconnecting the prime mover driven alternator from the alternating current

circuit. Then, the method may further comprise receiving a signal indicating that the prime mover driven alternator is to stop generating current, the step of activating the electronic load being performed in response to receiving the signal. Preferably, the method further comprises

electrically isolating the prime mover driven alternator from the alternating current circuit in response to

receiving the signal, in order to effect the disconnected state. Advantageously, the method further comprises

deactivating the electronic load in response to an

identification that the prime mover has stopped. Optionally, the method may further comprise connecting the prime mover driven alternator in parallel with a stop impedance in the disconnected state, which is preferably a resistance. The stop impedance may be a component of the coupling impedance specified above.

In a second aspect, there is provided a computer program configured when operated on a processor to carry out the method described herein. In a third aspect, there is provided a controller comprising a logical finite state machine implementation configured to generate at least one signal to carry out the method described herein.

In another aspect, there is provided a controller for interfacing a prime mover driven alternator with an

alternating current circuit having an existing alternating current. The controller comprises a processor arranged to receive a signal indicating a transition between a

disconnected state when the prime mover driven alternator is electrically isolated from the alternating current circuit and a connected state when the prime mover driven alternator is electrically coupled to the alternating current circuit. The processor is further configured to generate a signal to activate an electronic load connected in parallel with the prime mover driven alternator in response to receiving the signal indicating a transition.

In some embodiments, the controller further comprises: a start signal input for receiving a start signal indicating that the prime mover driven alternator is to start

generating current, the processor being configured to generate the signal to activate the electronic load in response to the start signal. The processor is preferably further configured to generate a signal to electrically couple the prime mover driven alternator to the alternating current circuit via a coupling impedance, in response to receiving the signal. Optionally, the controller further comprises a running signal input for receiving a running signal indicating that power is being generated at the prime mover driven alternator. Then, the processor may be further configured to generate a signal to electrically couple the prime mover driven alternator to the alternating current circuit bypassing the coupling impedance, in response to the running signal.

Advantageously, the processor may be further configured to generate at least one signal to electrically couple the prime mover driven alternator to the alternating current circuit directly and set the electronic load to perform an integrity test on the electronic load at the same time.

Then, the controller may further comprise an integrity test signal input for receiving an integrity signal indicating a result of the integrity test from the electronic load.

Preferably, the processor is further configured to generate a signal to disconnect an electrical coupling between the prime mover driven alternator and the alternating current circuit through a coupling impedance in response to the integrity signal indicating that the electronic load passes the integrity test. Then, the processor is optionally further configured to generate a signal to electrically isolate the prime mover driven alternator from the

alternating current circuit through a coupling impedance in response to the integrity signal indicating that the

electronic load fails the integrity test.

Advantageously, the processor is further configured to generate a signal to deactivate the electronic load

following an identification that the prime mover driven alternator is electrically coupled to the alternating current circuit .

In some embodiments, the controller may further

comprise a stop signal input for receiving a stop signal indicating that the prime mover driven alternator is to stop exporting power to the external ac circuit, the processor being configured to generate the signal to activate the electronic load in response to the stop signal. Then, the processor is optionally further configured to generate a signal to electrically isolate the prime mover driven alternator from the alternating current circuit in response to the stop signal.

In a further aspect, the present invention may provide an interface between a prime mover driven alternator and an alternating current circuit having an existing alternating current. The interface comprises: a first pair of terminals for receiving a connection to the prime mover driven

alternator; a second pair of terminals for receiving a connection to the alternating current circuit; an electronic load, arranged across the first pair of terminals; and a controller as described herein. In the preferred embodiment, the prime mover is a Stirling engine and preferably a Linear Free Piston Stirling Engine. The alternator is preferably a linear alternator.

Optionally, the interface further comprises a switching arrangement, configured between the first pair of terminals and the second pair of terminals to electrically couple or isolate the prime mover driven alternator and the

alternating current circuit selectively. Then, the

controller may be configured to generate signals to control the switching arrangement.

Beneficially, the interface further comprises an initialisation path arranged for electrically coupling the prime mover driven alternator and the alternating current circuit through a coupling impedance. Then, the switching arrangement may comprise a first switch arranged along the initialisation path and configured to select between a connected state, in which the initialisation path is

connected and a disconnected state in which the

initialisation path is disconnected. Preferably, the first switch comprises two switches, one connected on a path between first polarity terminals of the first and second pairs of terminals and the other connected on a path between second polarity terminals of the first and second pairs of terminals, the two switches being controlled by a single signal .

In the preferred embodiment, the interface further comprises a direct path, in parallel with the initialisation path, arranged for electrically coupling the prime mover driven alternator and the alternating current circuit without a coupling impedance. Preferably, the switching arrangement further comprises a second switch arranged along the direct path and configured to select between a connected state, in which the direct path is connected and a

disconnected state in which the direct path is disconnected. In embodiments, the second switch comprises two switches, one connected on a path between first polarity terminals of the first and second pairs of terminals and the other connected on a path between second polarity terminals of the first and second pairs of terminals, the two switches being controlled by a single signal. Optionally, the single signal is generated by a relay and wherein the switching

arrangement further comprises a third switch, configured to select between a connected state, in which the relay is coupled to the alternating current circuit and a

disconnected state in which the relay is unpowered.

The interface preferably further comprises a fourth switch located on the initialisation path in series with the first switch path and configured to select between a

connected state, in which the initialisation path is

connected and a disconnected state in which the

initialisation path is disconnected. Then, the coupling impedance may comprise: a first resistor located on the initialisation path between the alternating current circuit and the first switch; and a second resistor located on the initialisation path between the fourth switch and the prime mover driven alternator. In such cases, the first switch, third switch and fourth switch may be configured such that the second resistor is connected in parallel with the prime mover driven alternator when the first switch, third switch and fourth switch are all configured to select their

disconnected state. Advantageously, the first switch, third switch and fourth switch are two-way switches.

It will be appreciated that the controller, interface or both may be further configured to comprise apparatus features to implement any of the method steps described above. Similarly, the method described above may be

implemented using any of the apparatus features described in connection with the controller, interface or both. Also, any combination of the individual apparatus features or method features described may be implemented, even though not explicitly disclosed.

Brief Description of the Drawings

The invention may be put into practice in various ways, one of which will now be described by way of example only and with reference to the accompanying drawings in which:

Figure 1 shows a known interface for connecting and disconnecting a generator from the ac mains supply;

Figure 2 shows an interface for connection and

disconnection of a generator to an ac mains supply according to an embodiment of the present invention;

Figure 3 shows an equivalent circuit for the interface circuit of Figure 2; Figure 4 shows an example electronic load for use in the interface of Figure 2 ;

Figure 5 shows an exemplary variation of duty cycle over time for operation of the electronic load of Figure 4;

Figure 6 shows experimental waveforms for a normal start procedure for the main interface of Figure 1 ;

Figure 7 shows example waveforms for a start procedure in accordance with the embodiment of Figure 2 ;

Figure 8 shows example properties of a generator when used with an embodiment of the present invention;

Figure 9 illustrates a generalised electronic load for use in the interface of Figure 2; and

Figure 10 shows an alternative design of electronic load to that shown in Figure 4.

Detailed Description of Preferred Embodiments

Referring now to Figure 2, there is shown an interface for connection and disconnection of a generator to an AC mains supply according to an embodiment of the present invention. Where the same features are shown as in Figure

1, the same reference numerals have been used.

Two additional features are shown in Figure 2, that are not shown in Figure 1. The first feature is an electronic load 80. This is located across the terminals 13 of the linear alternator 10. The second feature is a fourth switch

SW4. This is placed in series with the stopping resistance

R _st0p and the first switch SW1.

The fourth switch SW4 is controlled by a third control signal S3. The defaults state for the fourth switch SW4 is to couple the stopping resistance R _st0p to the first switch

SW1. When actuated, the fourth switch SW4 disconnects the stopping resistance R _s t _op from the first switch SW1. The electronic load 80 is controlled by a fourth control signal S4. This signal has more than two states. In practice, the fourth control signal S4 has four states. The electronic load 80 is a configurable electronically simulated

resistance. It can also be considered as a configurable current sink.

The first control signal SI, second control signal S2, third control signal S3 and fourth control signal S4 are generated using a finite state machine (FSM) . The FSM is controlled using two request signals. These are referred to as: ENGINE START REQ (indicating that the engine is to be started) ; and ENGINE RUNDOWN REQ (indicating that the engine is to be stopped) . A practical implementation can be achieved using one digital input signal. In this case, a rising edge transition can indicate ENGINE START REQ and a falling edge transition can indicate ENGINE RUNDOWN REQ. Table 2 and Table 3 show a fuller description of the FSM.

Control signals

S4

STATE

SI S2 S3 NO START RUN INTEGRITY

LOAD UP DOWN TEST

INITIAL

0 OFF OFF OFF ON OFF OFF OFF STATE

START

1 ON OFF OFF OFF ON OFF OFF FPSE/LA

FPSE/LA

2 GRID ON ON OFF OFF ON OFF OFF CONNECTED

ELECTRONIC

3 LOAD ON ON OFF OFF OFF OFF ON INTEGRITY

ENGINE

4 OFF ON ON ON OFF OFF OFF RUNNING

ENGINE

5 OFF OFF ON OFF OFF ON OFF RUNDOWN

FAULT

6 OFF OFF OFF ON OFF OFF OFF DETECTION Table 2

STATE ACTION TRANSITION

SW1 in Normally Closed

position (C-l connected to

NC-1 and C-2 to NC-2) After an ENGINE SW2 in Normally Closed START REQ the position. Relay SW3 is state is updated

INITIAL

not activated. to START FPSE/LA STATE SW4 in Normally Closed Stay in INITIAL position . STATE after an Engine is stopped and ENGINE RUNDOWN REQ isolated from the ac power

source .

SW1 in Normally Open

position (C-l connected to

NO-1 and C-2 to NO-2)

If Engine power is SW2 in Normally Closed

within a position. Relay SW3 is

predetermined not activated.

range then jump to SW4 in Normally Closed

FPSE/LA GRID

START position .

CONNECTED state FPSE/LA Engine is connected to

otherwise jump to mains by Rstart and Rstop

INITIAL STATE

resistors .

Jump to INITIAL The electronic load will

STATE after an control the transient

ENGINE RUNDOWN REQ

current generated by the

linear alternator driven

by a LFPSE.

FPSE/LA is directly After some time connected to the grid (for example Is) bypassing Rstart and jump to ELECTRONIC

FPSE/LA

Rstop . LOAD INTEGRITY GRID SW2 is in the normally state

CONNECTED

open position. Current is Jump to INITIAL flowing through the relay STATE after an activating SW3. ENGINE RUNDOWN REQ

If the electronic load integrity

FPSE/LA is directly

test fails then

ELECTRONIC connected to the grid. A

jump to FAULT LOAD test is performed to check

DETECTION STATE. INTEGRITY if the electronic load is

Otherwise jump to connected .

ENGINE RUNNING STATE Jump to INITIAL

STATE after an ENGINE RUNDOWN REQ

Jump to ENGINE

Engine is running as a RUNDOWN state

ENGINE

4 grid connected generator after an ENGINE RUNNING

or a motor RUNDOWN REQ

Wait until the engine stops to jump to INITIAL STATE or when a

ENGINE Engine is running off-

5 fault condition RUNDOWN grid .

arises such as an overvoltage trip jump to FAULT DETECTION STATE

Engine is stopped

Jump to INITIAL

FAULT connecting the stop

6 STATE after an DETECTION resistor in parallel with

START REQUEST

the generator.

Table 3

This implementation, especially the use of electronic load 80, is intended to address a drawback of existing interfaces, particularly as shown in Figure 1. Control of the transient response of the generated current is difficult in existing interfaces between FPSE/LA 10 and mains power supply 20. By controlling the current transient response, a reduction in vibration and noise levels can result. This may lead to a longer engine life expectancy.

The soft disconnection may comprise running the engine off-grid. During the rundown and stop condition, the engine is isolated from the AC power supply. It is, in fact, isolated both at the live and neutral terminals due to the first relay-controlled switch 60 and the second relay- controlled switch 70. The electronic load 80 is used to run the engine off-grid. Fault conditions can occur, which can be dealt with in a different way from existing interfaces. After starting the engine, a dump load integrity test is performed, which checks that a dump load (such as an immersion heater) is operative. In case that this test fails the engine is stopped using the stopping resistor R _st0 p (the fourth switch SW4 is turned off) . In case there is a fault condition such as an overvoltage trip, for instance due to the dump load being broken during the rundown state, the fourth switch SW4 (which may also be termed a soft stop relay) is turned off and the engine is stopped using the stopping resistor R _s t _op - A more detailed description is shown in Tables 2 and 3 above .

A soft disconnection of a FPSE/LA therefore enables a known and controlled source of heat removal in most fault or shutdown conditions. In contrast, existing interfaces may stop the engine when a grid fault occurs. With the proposed system, in case a grid fault occurs the engine continues to run off-grid.

Known generators can show a transient response that is dependent on the excitation voltage before the tuning capacitor 12. Low excitation voltages may be related to low peak current and low vibration levels. It is known that vibration and current through the FPSE/LA 10 are directly related. As a consequence, the transient current response may be controlled using the electronic load 80 in parallel with the FPSE/LA 10. If the impedance connected in parallel to the FPSE/LA 10 is relatively low compared with the impedance of the generator 10, then the voltage and current flowing through the engine may be indirectly controlled.

There is shown in Figure 3 an equivalent circuit for the interface circuit of Figure 2. This can help to explain this transient response effect, by analysing the voltage and current across the engine when an impedance is connected in parallel with it.

The equivalent circuit comprises: generator equivalent impedance Z _eng ; parallel equivalent impedance Z _p ; and

limiting resistance equivalent impedance R _L . The generator equivalent impedance Z _eng is considered the resulting impedance of the FPSE/LA and linear alternator 10 plus the tuning capacitor 12. This is in parallel with the parallel equivalent resistance Z _p , which is the impedance connected in parallel with the engine (electronic load 80 or variable resistor) . In series with the generator equivalent

impedance Z _eng and parallel equivalent impedance Z _p is the limiting resistance R _L , which is equal to the initialisation resistance R _st art plus the stopping resistance R _st op-

The voltage across the generator equivalent impedance

^J eng and parallel equivalent impedance Z _p in parallel, V2 and the current through the generator i _eng may be determined on the basis of the voltage across the whole equivalent Vi .

This is shown in Equation 1 below.

It may be considered that the parallel equivalent impedance Z _p is much lower than the generator equivalent impedance Z _eng . Then, it may be assumed that the limiting resistance R _L is also greater than the generator equivalent impedance Z _eng . In this case, the voltage across the generator V ₂ and the current through the generator i _eng may be directly related to the parallel equivalent impedance Z _p , as shown in Equation 2 below. This concept may be exploited to limit the current through the engine i _eng and to perform a soft start with low vibration levels.

Referring now to Figure 4, there is shown an example of the electronic load 80 for use in the interface of Figure 2. The example illustrates a simple implementation of an AC electronic load, which is based on a floating load buck regulator. The electronic load may be implemented using different types of power electronic topologies to meet specific design requirements, such as load isolation that requires the use of an isolated power electronic topology. This will be discussed further below.

The electronic load 80 comprises a DC chopper 85. The

DC chopper comprises a series resistance R and inductance L in parallel with a diode D. These components are connected in series with a high speed switch HF with a duty cycle d. A capacitance C is connected in parallel with the DC chopper 85. Rectifying diodes 81, 82, 83 and 84 are connected with respect to AC input 86 in order to full-wave rectify the AC input 86 and provide this rectified DC across the

capacitance C and DC chopper 85.

As shown in Figure 4, this electronic load 80 is equivalent to a variable resistor. The variable resistor would have the equivalent resistance of R/d . Thus, the resistance can be set by changing the duty cycle d.

Referring to Figure 5, there is shown an exemplary variation of duty cycle over time for operation of the electronic load of Figure 4. It has been found

experimentally that a soft start can be achieved by varying the duty cycle of the electronic load 80. The equivalent resistance Req is increased (ramped) over time after some initialisation period by reducing the duty cycle. The skilled person will appreciate that a soft start can be achieved by applying other types of ramps using the concept described in relation to Figure 3 and equations 1 and 2.

Referring to Figure 6, there is shown experimental wave forms for a normal start procedure for the known interface of Figure 1. It will be noted that the FPSE/LA voltage increases over time and reaches a steady state at the same level as the grid voltage. However, the FPSE/LA current can be quite high at the start and takes some time to settle.

Referring next to Figure 7, there is shown example wave forms for a start procedure in accordance with the

embodiment of the present invention shown in Figure 2. It will be noted that the FPSE/LA voltage takes longer to reach a steady state that equates with the grid voltage. However, the FPSE/LA current now generally increases gradually over time and does not result in high problematic currents that were symptomatic of existing interfaces.

Referring now to Figure 8, there is shown example properties of a generator when used in an embodiment of the present invention. This is an example of an FPSE/LA in a solar application. The temperature, power and efficiency outputs are shown over time in the drawing. The heat output power is the electrical power divided by the efficiency of the FPSE/LA. The heat removed from the engine head is known over time, allowing a known cooling rate of the engine head temperature .

Some further discussion regarding electronic loads is now provided. An electronic load is a variable load that exploits the electrical characteristics of a power

electronic topology. Referring to Figure 9, there is illustrated a generalised electronic load, comprising a power electronics converter coupled to a fixed load.

Depending on the type of power electronic topology and mode of operation of the electronic load, the Gain function (G) may be different and the resultant impedance relationship will vary accordingly. For example, a buck converter operating in CCM (Continuous Conduction Mode) will receive a PWM signal with a duty cycle defined as d, which is a variable within the range [0,1] . Then, its Gain will be defined as

V

^ in

For a boost converter in CCM, the Gain will be defined as

G V,

v _in i- d

For an isolated converter such as a flyback in CCM, the gain is a function of the duty cycle and the transformer windin s ratio, n.

For other converters, the Gain functions can also be determined . In general, it can therefore be seen that the output voltage of the electronic load is a function of the duty cycle, as given by the following relationship:

^V «.=V ^G =V/( ^d )

The following relationships are well known.

V ² V ²

P in =V in I in =—„— ¹ P out = V out■ I out = _D ^out

^K in ^K out

Using these and assuming a lossless power

transformation (P _ou t = Pin or equivalently, n = P _ou t / Pin ^¾ 1), the relationship between the input and output impedance can also be determined. Usually, the converter shows a performance less than 1 but we can assume it is one.

R R out

R R ^out

Then, specific relationships can be identified for a specific electronic load with a specific f (d) . For a buck converter in CCM: f(d) = d

and

R out R out

f ² (d) d ² _

For a boost converter in CCM: / (<* ) = ¹

1-d and

For a fl back in CCM:

As can be seen, the input impedance for a flyback converter (with galvanic isolation) is a function of the transformer winding ratio and the duty cycle.

An electronic load can therefore be implemented with any type of power electronic topology. However, the buck converter has advantages in terms of simplicity and cost. If any reason (such as safety regulations) dictates that galvanic isolation is required for the dump load (such as an immersion heater) , then another type of converter such as a half-bridge or push-pull could be used instead of the buck converter.

Another form of electronic load may use a variable autotransformer , with its wiper being moved to step up or down the voltage connected to the fixed load.

Referring next to Figure 10, there is shown an

alternative type of electronic load to a DC chopper and variable autotransformer . A discrete number of resistors (Ri, R ₂ , R _n ) are provided in parallel, with each resistor being coupled to a respective switch (SWi, SW ₂ , SW _n ) that controls whether current passes through the resistor. These may be relays or solid state switches. A control block provides a control signal (or signals) to operate or

deactivate the switches accordingly. However, this approach is bulky, costly and generally cannot achieve fine voltage regulation (as only discrete steps are possible) .

Whilst specific embodiments have been described herein, the skilled person may contemplate various modifications and substitutions. For instance, the various switching

configurations and operation of the FSM may be modified. The initialisation and stopping resistances may be generalised as impedances and implemented in different configurations and different components.

Additionally or alternatively, control signals can be provided differently to suit a different switching

configuration. Moreover, the control signals could be provided by software and not a FSM. The skilled person will understand that the electronic load could be implemented in different ways.

In the embodiment described above, especially with reference to Table 3, engine power is used as a parameter. However, it is additionally or alternatively possible to use just the current and/or voltage range.