TITLE

Control methods for VSC active rectifier/inverters under unbalanced operating conditions

DESCRIPTION Technical Field

The present invention relates to control methods for controlling voltage source converter (VSC) active rectifier/inverters. Voltage source converters are also known as voltage source inverters (VSI). An active rectifier/inverter can be used as a machine bridge or network bridge of a power converter for interfacing an electrical machine or renewable energy device such as a fuel cell or photovoltaic cell to a supply grid or power network, for example. It can also be used as a network bridge for a static reactive compensator (STATCOM), an active filter, or a high voltage direct current (VSC-HVDC) link.

The present invention also relates to active rectifier/inverters and power converters controlled using such methods.

Background Art United States Patent 6313603 describes a method of controlling an ac induction (asynchronous) motor that receives power from an inverter. An inverter controller supplies a control voltage to the inverter. The control voltage is generated in such a manner as to servo-control the torque and the flux within the motor to reference valves that are indicative of the desired levels of torque and flux. The inverter controller receives one or more sampled signals that correspond to the stator current vector, the flux vector and the angular velocity of the rotor of the motor. Signals corresponding to the torque within the motor can be generated by an observer on the basis of continually measured stator phase currents and a signal measuring the angular velocity of the rotor as provided by appropriate sensors. At each sampling instant, the inverter controller predicts the torque and flux values for the following sampling instant and alters the control voltage accordingly so as to obtain the torque and flux values set by the reference values. The inverter controller has a first stage having a

memory in which a discrete model of the motor and the inverter system is stored. The purpose of the model is to compute how the motor and inverter system will vary between two sampling periods. A second stage of the inverter controller then computes the control voltage that is to be provided to the inverter as a function of the variation of the motor and inverter system as predicted by the first stage and the reference values for torque and flux. Such control is usually referred to as discrete- time field-oriented control (DT-FOC).

DT-FOC can also be used in situations where the inverter is providing power to an ac synchronous motor or to control an active rectifier that receives power from an ac induction or synchronous generator.

One of the limitations of DT-FOC is it can only be used in balanced operating conditions. This prevents DT-FOC from being used to control the operation of an active rectifier/inverter on the network side of a power converter, for example. In the context of a power converter for interfacing a generator providing variable voltage at variable frequency (or a motor operating at variable voltage and variable frequency) to a power network at nominally fixed voltage and frequency having a machine bridge and a network bridge, then DT-FOC cannot be used to control the network bridge because of its unbalanced operating conditions.

Summary of the Invention

The present invention provides a new control method that has certain underlying similarities with the discrete-time field-oriented control (DT-FOC) described above. However, the new control method (which will be referred to below as discrete-time voltage-oriented control (DT-VOC)) can be used in unbalanced operating conditions. More particularly, the present invention provides a method of controlling a voltage source converter (VSC) active rectifier/inverter including a plurality of semiconductor switching devices operated in accordance with a pulse width modulation (PWM) strategy and having ac terminals connected to a load system, the method comprising the steps of calculating a discrete-time model of the active rectifier/inverter and load system for both balanced and unbalanced operating conditions, using the discrete-time

model to derive modulation indexes based on an active power reference for a particular sampling period, using the modulation indexes to derive gate drive command signals, and applying the gate drive command signals to the active rectifier/inverter to control the semiconductor power switching devices of the active rectifier/inverter during a subsequent sampling period to achieve a desired level of active power at the ac terminals of the active rectifier/inverter that corresponds to the active power reference.

It is believed that the unique combination of a discrete-time approach with a model of the active rectifier/inverter and load system that represents both balanced and unbalanced operating conditions provides significant technical advantages over other known control schemes. The discrete-time model uses equations that are accurate rather than being an approximation of the operating conditions. The ability to cope with unbalanced operating conditions is particularly useful where the active rectifier/inverter uses a PWM strategy with a low switching frequency because the optimisation of control leads to the losses being minimised.

The modulation indexes derived from the discrete-time model may be further based on a reactive power reference for the particular sampling period. The gate drive command signals are then applied to the active rectifier/inverter to control the semiconductor power switching devices of the active rectifier/inverter during a subsequent sampling period to achieve desired levels of active and reactive power at the ac terminals of the active rectifier/inverter that correspond to the active and reactive power references. Active and reactive power references will normally be used if the active rectifier/inverter is a network bridge having its ac terminals connected to a power network or supply bus via an ac filter, and optionally a transformer and protective switchgear, for example.

The modulation indexes derived from the discrete-time model may also be further based on a flux reference or power factor reference for the particular sampling period.

The gate drive command signals are then applied to the active rectifier/inverter to control the semiconductor power switching devices of the active rectifier/inverter

during a subsequent sampling period to achieve desired levels of active power and flux or power factor at the ac terminals of the active rectifier/inverter that correspond to the active power and flux or power factor references. Active power and flux or power factor references will normally be used if the active rectifier/inverter is a machine bridge having its ac terminals connected to an electrical machine such as a generator or motor, for example.

The modulation indexes derived from the discrete-time model can be further based on one or more oscillating references for the particular sampling period. The oscillating references can be used when the active power reference (and any other applicable references) includes an oscillating component. Although the oscillating references will preferably be included in the DT-VOC scheme for completeness, they may often be set to zero.

The modulation indexes are preferably derived using a DT-VOC controller that calculates a discrete-time model of the active rectifier/inverter and load system. The gate drive command signals are preferably derived using a PWM controller. The gate drive command signals will preferably be applied to the active rectifier/inverter by the PWM controller during a subsequent sampling period.

The modulation indexes derived from the discrete-time model are preferably further based on voltage and/or current inputs for the particular sampling period. A voltage feedback signal indicative of a dc link voltage may also be used.

As described in more detail below, for "dead beat" control the gate drive command signals derived by the controller during the particular sampling period will be applied to the active rectifier/inverter during the sampling period that follows immediately afterwards.

The present invention further provides a controller for a VSC active rectifier/inverter including a plurality of semiconductor switching devices operated in accordance with a PWM strategy and having ac terminals connected to a load system, wherein the

controller is digital and calculates a discrete-time model of the active rectifier/inverter and load system for both balanced and unbalanced operating conditions, wherein the discrete-time model uses an active power reference for a particular sampling period to derive modulation indexes, and wherein the modulation indexes are used to derive gate drive command signals that are applied to the active rectifier/inverter to control the semiconductor power switching devices of the active rectifier/inverter during a subsequent sampling period to achieve a desired level of active power at the ac terminals of the active rectifier/inverter that corresponds to the active power reference.

The discrete-time model may also use a reactive power reference to derive the modulation indexes such that the gate drive command signals are applied to the active rectifier/inverter to control the semiconductor power switching devices of the active rectifier/inverter during a subsequent sampling period to achieve desired levels of active and reactive power at the ac terminals of the active rectifier/inverter that correspond to the active and reactive power references. In this case, the active rectifier/inverter may be used as a network bridge such that the load system to which the ac terminals of the active rectifier/inverter are connected preferably includes an ac filter and power network or supply bus. The dc terminals of the active rectifier/inverter may be connected to any suitable dc system depending on the particular circumstances. For example, if the network bridge is used as part of a power converter for interfacing an electrical machine (such as a permanent magnet synchronous (PMS) generator or motor) to a power network or supply bus then the dc system may include a dc link and a second VSC active rectifier/inverter operating as a machine bridge; the ac terminals of the second active rectifier/inverter being connected to the electrical machine.

The discrete-time model may also use a flux reference or power factor reference to derive the modulation indexes such that the gate drive command signals are applied to the active rectifier/inverter to control the semiconductor power switching devices of the active rectifier/inverter during a subsequent sampling period to achieve desired levels of active power and flux or power factor at the ac terminals of the active

rectifier/inverter that correspond to the active power and flux or power factor references. In this case, the active rectifier/inverter may be used as a machine bridge as part of a power converter for interfacing an electrical machine to a power network or supply bus. The load system to which the ac terminals of the active rectifier/inverter are connected is preferably an electrical machine such as permanent magnet synchronous (PMS) generator or motor, for example. The dc terminals of the active rectifier/inverter may be connected to any suitable dc system depending on the particular circumstances. For example, if the machine bridge is used as part of a power converter for interfacing an electrical machine (such as a permanent magnet synchronous (PMS) generator or motor) to a power network or supply bus then the dc system may include a dc link and a second VSC active rectifier/inverter operating as a network bridge; the ac terminals of the second active rectifier/inverter being connected to the power network or supply bus via an ac filter, and optionally a transformer and protective switchgear, for example.

The controller preferably includes a DT-VOC controller and a PWM controller. The DT-VOC controller calculates the discrete-time model of the active rectifier/inverter and load system, derives the modulation indexes and supplies the modulation indexes to the PWM controller. The PWM controller preferably uses the supplied modulation indexes to derive the gate drive command signals that are applied to the active rectifier/inverter by the PWM controller during a subsequent sampling period.

The discrete-time model preferably also uses voltage and/or current inputs for a particular sampling period to derive the modulation indexes. The controller may therefore further include means (such as a function block, for example) for deriving the voltage and/or current inputs from measured values of voltage and/or current taken between the active rectifier/inverter and the load system. The function block means supplies the voltage and/or current inputs to the DT-VOC controller.

Drawings

Figure 1 is a schematic drawing showing how discrete-time voltage-oriented control (DT-VOC) can be applied to a network bridge;

Figure 2 is a schematic drawing showing more detail of a function block for determining the positive and negative sequences of voltage and current outputs; Figure 3 is a schematic drawing showing a timing sequence for DT-VOC; Figure 4 is a schematic drawing showing a current control scheme for the DT-VOC function block 14 of Figure 1;

Figure 5 is a schematic drawing showing a power control scheme for the DT-VOC function block 14 of Figure 1;

Figure 6 is a schematic drawing showing how DT-VOC can be applied to a power converter that is used to interface between a wind turbine driving a variable speed generator and a fixed frequency power network;

Figure 7 is a schematic drawing showing a current control scheme for the DT-VOC function block 42 of Figure 6 (i.e. for the generator bridge controller); and Figure 8 is a schematic drawing showing how DT-VOC can be applied to a power converter that is used to interface between a variable speed motor and a fixed frequency power network.

General description of discrete-time voltage-oriented control

Discrete-time voltage-oriented control (DT-VOC) can be applied to any voltage source converter (VSC) active rectifier/inverter. For example, the active rectifier/inverter may be a network bridge (i.e. its ac terminals may be connected via an ac filter to a power network or ac supply bus) or a machine bridge (i.e. its ac terminals may be connected to an electrical machine such as a generator or motor). The subscript / and the suffix _NET are used below to denote measurements and signals relating to the network (line) side, the network bridge and its associated controller. Similarly, the subscript m and the suffixes _GEN and MOT are used below to denote measurements and signals relating to the machine side, the machine bridge when connected to a generator or motor, respectively, and its associated controller.

The application of DT-VOC to a network bridge will be described with reference to Figure 1.

The dc terminals of the network bridge 2 are connected to a generic dc system 4 by a dc link 6. The ac terminals of the network bridge 2 are connected to a power network (labelled "NETWORK") via an ac filter 8 and a transformer 10. Protective switchgear (not shown) can be included to provide a reliable connection to the power network and to isolate the network bridge 2 and the dc system 4 from the power network for various operational and non-operational requirements.

The network bridge 2 is a voltage source converter (VSC) and has a conventional three-phase two-level topology with a series of semiconductor power switching devices fully controlled and regulated using a pulse width modulation (PWM) strategy. The derivation of the gate drive command signals that are used to control the semiconductor power switching devices is described in more detail below.

As described herein, active rectification (as the prime mode of operation of the network bridge 2 in a situation where power is provided from the power network to the dc system - such as for motoring applications where low harmonics are required at the connection to the power network) is the conversion of energy from the ac terminals of the network bridge to the dc link. Similarly, inversion (as the prime mode of operation of the network bridge in a situation where power is provided from the dc system to the power network - such as for generating applications where low harmonics at the connection to the power network and the ability to maintain control during power network voltage dip conditions are required) is the conversion of energy from the dc link of the three-phase network bridge to its ac terminals. It will be readily appreciated that there may be times when it is necessary or desirable to operate the network bridge either in a motoring mode or a generating mode. For example, if the dc system 4 is an entire machine bridge, electrical machine and coupled inertia of a flywheel energy storage system then the network bridge 2 will operate as an active rectifier to charge the flywheel energy storage system and as an inverter to discharge the flywheel energy storage system.

A network bridge controller 12 (represented in Figure 1 by a dashed line) receives an active power reference P* and a reactive power reference Q*. The network bridge

controller 12 also receives a voltage feedback signal Vdc indicative of the dc link voltage, a composite voltage feedback signal V_NET (comprising individual voltage measurements v _m , v _ιγ and v _lB for the red (R), yellow (Y) and blue (B) phases, respectively) that is derived from three-phase measurement on the network side of the ac filter 8 and a current feedback signal I_ NET (comprising individual current measurements i _IR , i _ιγ and i _lB for the red, yellow and blue phases, respectively) that is derived from a current transducer on each of the three phase connections between the network bridge 2 and the ac filter.

In electrical engineering, the analysis of unbalanced three-phase power systems is simplified by using the method of symmetrical components where a single frequency can be represented by sets of phasors. In a three-phase power system, one set of phasors has the same phase sequence as the power system under analysis (positive sequence) and the other set of phasors has the reverse phase sequence (negative sequence). The superscripts + and - are used below to denote measurements for the positive and negative sequence, respectively.

The voltage and current feedback signals V_NET and I_NET are supplied to a function block 16 within the network bridge controller 12 which produces voltage outputs and current outputs Function block 16 incorporates a phase locked loop (PLL) system to derive a signal θ _NET , which is a measure of the positive sequence power network voltage angle. The signal θ _NET , and its inverse signal -θ _NET , are used to convert the individual voltage and current measurements for the red, yellow and blue phases into the positive and negative sequence voltage and current outputs listed above. An example schematic for the function block 16 is shown in Figure 2.

The network bridge controller 12 also includes a DT-VOC function block 14 for achieving a desired active and reactive power. In practice, it is generally preferred that the control is "dead-beat", i.e. the desired control objectives are achieved in a single sampling period. However, it may be possible in some situations for the

control objectives to be achieved in two or more sampling periods. This may be useful for several reasons. For example, if the voltage/current limitations of the network bridge (or power converter) are such that the use of "dead-beat" control might result in an over-voltage or an over-current in the network bridge then the dynamic performance of the desired active and reactive powers can be naturally reduced by increasing the number of sampling periods. Selecting a power response based on many sampling periods can also be used to avoid placing too much stress on weak networks.

The DT-VOC function block 14 and the network bridge controller 12 are designed to manage the voltage/current limitations at the output of the network bridge 2 in such a way that the best response available is always achieved. The control method may use a geometric approach to manage the voltage and current constraints as described for discrete-time field-oriented control (DT-FOC) in "Discrete-time field oriented control for SM-PMSM including voltage and current constraints", Benchaib, S. Poullain, JX. Thomas and J.C. Alacoque, IEEE International Electrical Machines and Drives Conference, vol. 2, pages 999-1005, 2003.

Oscillating component references O1 * and O2* can be used by the DT-VOC function block 14 in situations where the active and reactive power references P* and Q* include an oscillating component. In many cases, the oscillating component references 01 * and O2* would be set to zero so that the overall objectives of the active and reactive power references are achieved in the presence of unbalanced power network voltage conditions.

The DT-VOC function block 14 uses the voltage feedback signal Vdc, the active and reactive power reference P* and Q*, the oscillating component references 01 * and 02 *, the positive and negative sequence voltage and current outputs the value of the sampling period δ and the fundamental frequency of the power network ω_NET to calculate direct and quadrature axis modulation indexes for each sampling period.

Once the four modulation indexes ave been calculated by the DT-VOC function block 14 they are supplied to a PWM controller 18 where the two direct axis modulation indexes are summed to form a total direct axis modulation index m _d and the two quadrature axis modulation indexes are summed to form a total quadrature axis modulation index m _q . These total direct and quadrature axis signals are converted from Cartesian to polar co-ordinates using a coordinate converter (not shown). The total modulation index magnitude m is calculated according to the equation:

The angle between the total modulation index magnitude m and the total quadrature modulation index m _q , is θ _o and is calculated from:

The angle θ ₀ between the total modulation index magnitude m and the total quadrature modulation index m _q is added to the positive sequence power network voltage angle θ _NET to determine the angle at which the total modulation index magnitude m is to be impressed by the network bridge 2 on the network side circuit. The PWM controller 18 can include third harmonic or equivalent enhancement to the phase voltage waveforms to achieve the maximum phase to phase voltage for a given dc link voltage.

The individual upper (U) and lower (L) gate drive command signals for the three phases red, yellow and blue resulting in individual signals RU, RL, YU, YL, BU and BL of the network bridge 2 are calculated in the PWM controller 18 using the total

modulation index magnitude m, the sum of the angles θ ₀ and θ _NET and the PWM frequency. Since the voltage feedback signal Vdc is included in the discrete-time model there is no need to factor it into the calculation of the PWM controller 18.

As shown in Figure 3, all of the above calculations take place during a single sampling period δ. The individual gate drive command signals RU, RL, YU, YL, BU and BL are therefore derived in a given sampling period and subsequently applied to the network bridge 2 by the PWM controller 18 to control the semiconductor switching devices to open and close during the next sampling period to achieve the levels of active and reactive power at the ac terminals of the network bridge that correspond to the active and reactive power references P* and Q* supplied to the DT- VOC function block 16. All inputs are sampled simultaneously by a sample and hold system at the instant k, k+l, etc. and are therefore assumed to be held constant over the relevant sampling period δk δ _k+1 etc. The sampled inputs are then processed during the subsequent sampling period δ generally as follows. Block A represents the time taken to compute the positive and negative sequence voltage and current output provided by the function block 16. Block B represents the time taken for the DT-VOC function block 14 to carry out the calculations and derive the four modulation indexes Finally, block C represents the time taken for the PWM controller 18 to combine the four modulation indexes to give the total modulation index magnitude m and to derive the gate drive command signals.

The gate drive command signals derived during the sampling period δ _k are then applied to the network bridge 2 by the PWM controller 18 during the subsequent sampling period δ _k+1 as shown by the upper block in Figure 3.

Two alternative DT-VOC schemes for the DT-VOC function block 14 will now be described in more detail with reference to Figures 4 and 5, respectively. The first scheme uses an n-samples discrete-time current controller (Block 4 of Figure 4) while the second scheme uses an n-samples discrete-time power controller (Block 6 of

Figure 5). In both cases, the DT-VOC function block 14 represents a discrete-time model of the network bridge and network system for both balanced and unbalanced operating conditions. In other words, the discrete-time model can cope fully with unbalanced operating conditions. As a balanced condition is just one specific case of the unbalanced system with zero negative sequence components, then the discrete- time equations presented below operate equally well for balanced operating conditions as well. If balanced conditions are the only conditions for which operation is necessary, then significant simplification to the equations can be considered.

Current control scheme

With reference to Figure 4, the DT-VOC function block 14 includes four separate function blocks.

Block 1 : Block 1 calculates current references for each sampling period δ from the positive and negative sequence voltage outputs the active and reactive power references P* and Q* and the oscillating component references Ol * and 02* as follows:

Block 2:

Block 2 calculates the continuous-time matrices [A ⁺ ], [A- ] and [B] as follows:

Positive sequence state matrix

Negative sequence state matrix

Input matrix

where:

R is the resistance between the network bridge 2 and the transformer 10 (i.e. the resistance of the ac filter 8);

L is the inductance between the network bridge and the transformer; and ω_NET is the fundamental frequency of the power network voltage. The frequency could be slightly variable for a power network or fully variable for the application to a permanent magnet synchronous machine (PMSM), for example.

The continuous-time state matrices [A ⁺ ] and [A- ] must be calculated every time ω_NET changes. In other words, the continuous-time matrices may need to be calculated for each sampling period δ or less frequently if the fundamental frequency is changing more slowly.

Block 3: Block 3 calculates the discrete-time matrices that are used by the n-samples discrete- time current controller described below with reference to Block 4. It is possible to adjust the time response as an expected integer number. "Dead-beat" control can be achieved for n = 1.

The space-state representation of a linear continuous-time model can be represented by:

where: x(t) is defined as the derivative of the state x(t) ; u(t) is defined as the control inp [A] is the continuous-time state matrix; and [B] is the continuous-time input matrix.

Given the sampling period δ, and under the assumption that a sample and hold is used for the sampling of the state x(f) and the control input u(t) then the discrete-time state- space representation of the previous model can be represented by:

where: x _k+1 is the state calculated for the next sample, associated with the instant t _k+1 ; u _k is the input available at the instant^ ; is the discrete-time state matrix; and is the discrete-time input matrix, with [I _d ] defined as the identity matrix.

The discrete-time model can be interpreted as a "one-sample" prediction model for unbalanced operating conditions.

In the case where: is the time constant of the network side circuit then the discrete-time state matrix [F ^± ] and the discrete-time input matrix [G ^± ] can be calculated from:

Negative sequence discrete-time state matrix

which could be written as:

Positive sequence discrete-time state matrix

which could be written as:

and Positive sequence discrete-time control matrix

which could be written as:

and Negative sequence discrete-time control matrix which could be written as:

Thus, the discrete-time state matrix [F ^± ] used in Block 4 is defined by:

and the associated discrete-time input matrix [G ^± ] used in Block 4 is defined by:

which could be simplified as follows:

Block 4:

Block 4 uses the current outputs and the discrete-time state and input matrices [F ^± ] and [G ^± ], respectively, and the current references and derived in Block 1 to calculate the four modulation indexe that are used by the PWM controller 18 to derive the gate drive command signals for the semiconductor power switching devices of the network bridge 2. The modulation indexes are represented by the following modulation vector:

Given the adjustment gain matrix [J] where:

where j = gain and "dead-beat" control is obtained for the case where / = 0 and the identity matrix [l _d ] defined by:

then the calculation of the four modulation indexe are defined by the main discrete-time equation:

It will be noted that the discrete-time input matrix [G ^± ] must be inverted for each sampling period δ. Any suitable method for inverting the discrete-time input matrix can be used. Examples would include the Gauss-Jordan elimination, Gaussian elimination and LU decomposition methods.

In general terms it is possible to use a pole placement tracking error method to set value of j. For "dead-beat" control where n = 1 then the poles of the DT-VOC function block 14 must be placed at the centre of the unit circle in the z-plane (discrete-time plane). For other values of n (i.e. two or more sampling periods) then j is calculated using the desired time-response in closed-loop of the active rectifier/inverter and network system setting poles of the DT-VOC function block 14 inside the unit circle.

For the particular case with "dead-beat" control (i.e. where j = 0) then the main discrete-time equation can be simplified to:

Power control scheme

With reference to Figure 5, the DT-VOC function block 14 includes four separate function blocks. Blocks 2 and 3 are as described above with reference to the current control scheme.

A voltage matrix [v* ] _k defined at the sample instant k can be represented as follows:

For the sampling period δ _k , the discrete-time representation of the evolution of the positive and negative sequence current outputs can be represented by:

where the matrix:

is the prediction of the current outputs for the next sampling period is the discrete-time state matrix and [G ^± ] is the discrete-time input matrix as described above.

The discrete-time "free evolution" of the current outputs is defined as follows:

The "free evolution" of the current components can be interpreted as a natural variation of these components when the modulation indexes are set to zero. Then, the voltage outputs considered in this case as disturbances, will move the currents outputs The prediction of the current outputs can then be expressed as:

Using the voltage matri , and assuming tha , the prediction of the current outputs for the next sampling period δ _/ ^i can be written as:

Block 5:

Block 5 calculates the free evolution of the power components P, Q, O1 and 02 as follows:

These power components are then used in Block 6.

Block 6:

Block 6 calculates the four modulation indexes using the following main discrete-time equation:

where [l _d ] is the identity matrix and [J] is the adjustment gain matrix as described above.

For the particular case with "dead-beat" control (i.e. where j = 0) then the previous equation can be simplified as:

It will be noted that the discrete-time matrices [G ^± ] and [v ^± ] must be inverted for each sampling period δ . Any suitable method for inverting the discrete-time matrices can

be used. Examples would include the Gauss- Jordan elimination, Gaussian elimination and LU decomposition methods.

In both the current and power control schemes, the sampling period δ may be fixed

5 and optionally set to be the same as the PWM switching period of the network bridge

2. However, the sampling period δ may also be variable, either independently or with changes in the PWM switching period. By varying the sampling period δ it is possible to apply the principles described in British Patent Application 0617371.0 where the PWM switching period of the network bridge is varied in accordance with

10 the time-varying frequency of the power network to preferably achieve only integer _r harmonics (and preferably only integer odd harmonics) of the time-varying frequency.

In other words, an integer number of PWM periods can be achieved in one period of the fundamental waveform of the power network voltage.

15 In a steady-state where the active and reactive power references P* and Q* remain fixed, the individual voltage measurements (and hence the voltage outputs change as a result of a change in the power network voltage conditions. For example, during a power network voltage dip event then the current references derived in Block 1 (or the power components 20 P, Q, O1 and O2 derived in Block 5) change accordingly. Block 4 and the subsequent summing blocks (or Block 6) then calculate the new modulation indexes and hence the gate drive command signals to be applied to the networ bridge 2 by the PWM controller 18 during the next sampling period to maintain the active and reactive power at the levels specified by the references P* and Q*. In the 25 presence of a power network voltage network disturbance, the DT-VOC function block 14 accommodates the disturbance and returns the active and reactive power to the reference levels in one sample period, or more as per the setting of the gain j in the adjustment gain matrix [J] defined above.

When the active and reactive power references P* and Q* change, in conjunction with a change in the power network voltage or not, then Block 1 will calculate new current output which are applied to Block 4 and the subsequent summing blocks (or used directly by Blocks 5 and 6) to calculate the new modulation indexes and hence the gate drive command signals to be applied to the network bridge 2 by the PWM controller 18 during the next sampling period to achieve the levels of active and reactive power specified by the new active and reactive power references P* and Q*, respectively.

Other disturbances or changes, for example a change in power network frequency, are accommodated by the DT-VOC function block 14 by a change to the continuous-time state matrices [A ⁺ ] and [A-] and corresponding changes to the discrete-time state matrix [F ^± J and the discrete-time input matrix [G ^± ]. These changes are then acted on by Block 4 and the subsequent summing blocks (or Blocks 5 and 6) to calculate the new modulation indexes and hence the gate drive command signals to be applied to the network bridge 2 by the PWM controller 18 during the next sampling period to achieve the levels of power and reactive power specified in the active and reactive power references P* and Q* in the presence of a frequency change.

Power converter for wind turbine applications

The basic topology of a power converter 20 that can be used to interface the generator

22 of a wind turbine to a power network will be outlined with reference to Figure 6.

The power converter 20 is used to interface between a wind turbine 24 driving a variable speed permanent magnet synchronous (PMS) generator 22 and a nominally fixed frequency power network (labelled "NETWORK"). The wind turbine typically includes three turbine blades mounted on a rotating shaft and whose pitch can be controlled by means of a pitch actuator in order to optimise and/or limit the capture of wind energy into the generator 22. A gearbox (not shown) can be used to connect the rotating shaft to the rotor of the variable speed generator. In some cases, the rotating

shafit can be connected directly to the rotor of the variable speed generator. This means that the speed of rotation of the rotor varies as a function of the wind speed and that the frequency of the voltage developed at the stator of the generator (the "stator frequency") may therefore vary over wide ranges. A number of wind turbines as represented by the entirety of Figure 6 can be connected together to define a wind farm.

The terminals of the generator 22 are connected to the ac terminals of a three-phase generator bridge 26 which in normal operation operates as an active rectifier to supply power to a dc link 28. The generator bridge 26 has a conventional three-phase two- level topology with a series of semiconductor power switching devices fully controlled and regulated using a pulse width modulation strategy. The derivation of the gate drive command signals that are used to control the semiconductor power switching devices is described in more detail below.

The dc output voltage of the generator bridge 26 is fed to the dc terminals of a network bridge 30 which in normal operation operates as an inverter. The network bridge 30 has a similar three-phase two-level topology to the generator bridge 26 with a series of semiconductor power switching devices fully controlled and regulated using a pulse width modulation strategy. The network bridge 30 is controlled to meet two principal objectives, namely active power and network voltage. A detailed description of how this control is achieved is provided below. The derivation of the gate drive command signals that are used to control the semiconductor power switching devices is also described in more detail below.

As described herein, active rectification (as the prime mode of operation of the generator bridge 26) is the conversion of energy from the ac terminals of the three- phase generator bridge to the dc link 28. Similarly, inversion (as the prime mode of operation of the network bridge 30) is the conversion of energy from the dc link 28 of the three-phase network bridge to its ac terminals. However, it will be readily appreciated that there may be times when it might be necessary or desirable to operate the generator bridge 26 as an inverter and operate the network bridge 30 as an active

rectifϊer. For example, during start-up the network bridge 30 may operate as an active rectifier to supply power from the power network to the dc link 28. In situations where a network voltage dip occurs, the generator bridge 26 may operate in either an active rectifier mode or in an inverter mode as required in order to control the voltage of the dc link. The action of controllers for the generator bridge and the network bridge (that is the generator bridge controller 32 and the network bridge controller 34 described in more detail below) may be capable of being coordinated in the event of a network voltage dip such that power is not drawn from the power network but, subject to the parameterisation and the level of the voltage dip, the power converter 20 is still capable of supplying power to the power network.

The generator and network bridges may be configured such that power flow may be from the power network to the generator 22 for maintenance purposes, for example.

The ac output voltage of the network bridge 30 is filtered by an ac filter 36 and supplied to the nominally fixed frequency power network via a step-up transformer 38. Protective switchgear (not shown) can be included to provide a reliable connection to the power network and to isolate the generator system from the power network for various operational and non-operational requirements.

Generator bridge control

The principal control of the generator bridge 26 is to manage the dc link voltage and the flux in the generator 22.

A generator bridge controller 32 receives a generator bridge active power reference POWER* and a flux reference φ*. (As described below, the generator bridge controller 32 may receive a power factor reference PF* instead of the flux reference φ*.) The generator bridge controller 32 also receives a voltage feedback signal Vdc indicative of the dc link voltage and a current feedback signal IJ3EN (comprising individual current measurements i _mR , i _mY and i _mB for red, yellow and blue phases,

respectively) that is derived from a current transducer on each of the three phase connections between the generator 22 and the generator bridge 26.

The positive sequence voltage angle θ _GEN is measured by a rotor position transducer that is initialised with the magnetic poles of the generator. The current feedback signal I GEN is supplied to a function block 40 which uses the signal θ _GEN , and its inverse signal - θ_GEN, to convert the individual current measurements for the red, yellow and blue phases into the positive and negative sequence current outputs

There is no direct measured equivalent to V_ NET for the generator bridge 26. However, because the generator 22 is a synchronous machine, for the purposes of the n-samples discrete-time current control scheme described below, the voltage outputs (which effectively represent the back emf voltage of the generator 22) can be calculated by the function block 40 from the rotor speed, parameters relating to the magnet characteristic (flux level) and unbalanced conditions represented by the current outputs derived from I_GEN. The frequency of the voltage and current outputs can be determined directly from the rotor speed ω_GEN defined as the rotating frequency of the generator 22. In most cases, the generator 22 will operate in well balanced conditions.

Once they have been calculated by the function block 40, the positive and negative sequence voltage and current outputs are supplied to a DT-VOC function block 42 of the generator bridge controller 32.

The generator bridge power reference POWER* can be derived from the output of a PI regulator which is driven by the error between a dc link voltage reference Vdc* and the voltage feedback signal Vdc indicative of the dc link voltage.

The flux reference φ* can be derived from a look up table relating turbine rotor speed and load level to the flux required in the generator 22 or may be a fixed constant for a particular wind turbine configuration. This allows the generator flux to be optimised for various reasons Although the generator 22 is a permanent magnet synchronous machine (PMSM) and therefore has in-built magnets providing the bulk of the flux, a flux reference is still needed for one or more of the following reasons: (i) to manage the terminal voltage of the generator presented to the ac terminals of the generator bridge, (ii) to compensate for magnet induction including temperature effects and (iii) to optimise the efficiency of the generator-generator bridge interaction.

Given a standard rotating reference frame with direct and quadrature axes (d, q), the relation between the flux (φ ) and voltage (v) components for the generator 22 is defined as follows:

where ω_GEN is the rotating frequency of the generator 22.

In the same rotating reference frame, the active power P of the equivalent network is defined as the following dot product:

The reactive power Q of the equivalent network is defined as the following cross product:

The torque T of the generator 22 is defined as the following cross product:

The associated flux φ of the generator 22 is defined as the following dot product:

Then, given the relation between flux and voltage components for the generator 22 replacing v _d and v _q by the resulting flux components we can obtain the following relations:

and

The relationship between the reactive power reference Q* and the flux reference φ* can be determined by:

It is therefore possible to control the generator bridge 26 using a DT-VOC scheme similar to that described above for the network bridge 2 by taking into account the relationship between the reactive power reference Q * and the flux reference φ*.

In a similar manner, it is possible to control the generator bridge 26 using a DT-VOC scheme where the flux reference φ* supplied to the generator bridge controller 32 is replaced by a power factor reference PF*. In this case, the power factor reference PF* may be converted to a reactive power reference Q * as follows:

Given the active power POWER (in W) and reactive power Q (in Var) then:

POWER = S cos(φ)

Q = Ssin(φ)

where cos(φ) is defined as the power factor PF and S is the total power (in VA).

Then using the following equations:

POWER ^* = S x PF*

Q' = S χ sin(Arc cos(PF*))

the relationship between the reactive power reference Q* and the power factor reference PF* can be determined by:

The DT-VOC function block 42 uses the voltage feedback signal Vdc, the active power reference POWER*, the flux reference φ* or power factor reference PF*, the oscillating component references 01 * and 02*, the positive and negative sequence voltage and current outputs the value of the sampling period δ and the rotating frequency of the generator ω_GEN to calculate direct and quadrature axis modulation indexes for each sampling period.

The individual upper (U) and lower (L) gate drive command signals for the three phases red, yellow and blue resulting in individual signals RU, RL, YU, YL, BU and

BL of the generator bridge 26 are calculated in the PWM controller 44 using the total modulation index magnitude m (as derived from the four modulation indexes rovided by the DT-VOC function block 42), the sum of the angles θ ₀ and θ GEN and the PWM frequency. Since the voltage feedback signal Vdc is included in the discrete-time model there is no need to factor it into the calculation of the PWM controller 44. Once again, third harmonic enhancement can be included in the PWM controller 44 for the generator bridge 26 to maximise the phase to phase output voltage that can be achieved for a given dc link voltage.

A DT-VOC scheme for the DT-VOC function block 42 will now be described in more detail with reference to Figure 7. The scheme uses an ^-samples discrete-time current controller (Block 4 of Figure 7). However, it is possible that an «-samples discrete- time power controller similar to that shown in Figure 5 might also be used. The DT- VOC function block 42 represents a discrete-time model of the generator bridge and generator system for both balanced and unbalanced operating conditions. In other words, the discrete-time model for the generator side of the power converter 20 can cope fully with unbalanced operating conditions.

It will be noted that a reactive power reference Q* is shown within the DT-VOC function block 42 and will in practice be derived using a function block (not shown) from the flux reference φ* or the power factor reference PF* using the relationships given above. In other words, the flux reference φ* or the power factor reference PF* provided to the generator bridge controller 32 is first converted into a reactive power reference Q* which is then used by the DT-VOC function block 42 to derive the modulation indexes. It will therefore be readily appreciated that the main discrete- time equations below are expressed with reference to a reactive power reference Q* rather than a flux reference φ* or power factor reference PF*.

The DT-VOC function block 42 includes four separate function blocks.

Block 1 :

Block 1 calculates current references for each sampling period δ from the positive and negative sequence voltage outputs and the active power reference POWER*, the reactive power reference Q* and the oscillating component references O1 * and 02* as follows:

Block 2: Block 2 calculates the continuous-time matrice and as follows:

Positive sequence state matrix

Negative sequence state matrix

Input matrix

where:

R is the stator resistance of the generator 22; L is stator inductance of the generator; and GEN is the rotating frequency of the generator.

The continuous-time state matrices [A ⁺ ] and [A- ] must be calculated every time ω_ GEN changes and will normally be calculated for each sampling period δ.

Block 3: Block 3 calculates the discrete-time matrices that are used by the n-samples discrete- time current controller described below with reference to Block 4. It is possible to adjust the time response as an expected integer number. "Dead-beat" control can be achieved for n = 1.

The space-state representation of a linear continuous-time model can be represented by:

x(t) = [A] c(t) + [B]u(t)

where: x(t) is defined as the derivative f the state x(t) ; u(t) is defined as the control inpu ; [A] is the continuous-time state matrix; and [B] is the continuous-time input matrix.

Given the sampling period δ, and under the assumption that a sample and hold is used for the sampling of the state x(t) and the control input u{f) then the discrete-time state- space representation of the previous model can be represented by:

where: x _k+1 is the state calculated for the next sample, associated with the instant t _k+1 ; u _k is the input available at the instant t _k ;

is the discrete-time state matrix; and is the discrete-time input matrix, with defined as the identity matrix.

The discrete-time model can be interpreted as a "one-sample" prediction model for unbalanced operating conditions.

In the case where: is the time constant of the generator side circuit then the discrete-time state matrix [F ^± J and the discrete-time input matrix can be calculated from: Negative sequence discrete-time state matrix

which could be written as:

Positive sequence discrete-time state matrix

which could be written as:

and

Positive sequence discrete-time control matrix

which could be written as:

and Negative sequence discrete-time control matrix

which could be written as:

Thus, the discrete-time state matrix [F ^± J used in Block 4 is defined by:

and the associated discrete-time input matrix [G ^± J used in Block 4 is defined by:

which could be simplified as follows:

Block 4:

Block 4 uses the current outputs and the discrete-time state and input matrices [F ^± ] and [G ^± ], respectively, and the current references and derived in Block 1 to calculate the four modulation indexes and that are used by the PWM controller 44 to derive the gate drive command signals for the semiconductor power switching devices of the generator bridge 26. The modulation indexes are represented by the following modulation vector:

Given the adjustment gain matrix [J] where:

where j = gain and "dead-beat" control is obtained for the case where j = 0 and the identity matrix [l _d ] defined by:

then the calculation of the four modulation indexe are defined by the main discrete-time equation:

It will be noted that the discrete-time input matrix [G ^± ] must be inverted for each sampling period δ. Any suitable method for inverting the discrete-time input matrix can be used. Examples would include the Gauss-Jordan elimination, Gaussian elimination and LU decomposition methods.

In general terms it is possible to use a pole placement tracking error method to set value of j. For "dead-beat" control where n = 1 then the poles of the DT-VOC function block 42 must be placed at the centre of the unit circle in the z-plane (discrete-time plane). For other values of n (i.e. two or more sampling periods) then j is calculated using the desired time-response in closed-loop of the active rectifier/inverter and network system setting poles of the DT-VOC function block 42 inside the unit circle.

For the particular case with "dead-beat" control (i.e. where j = 0) then the main discrete-time equation can be simplified to:

The sampling period δ may be fixed and optionally set to be the same as the PWM switching period of the generator bridge 26. However, the sampling period δ may also be variable, either independently or with changes in the PWM switching period.

Taking one operating example, for a change in speed of the generator 22 then Block 2 of the DT-VOC function block 42 calculates the new values for the continuous-time state matrices [A ⁺ ] and [A-] and corresponding changes to the discrete-time state matrix [F ^± ] and the discrete-time input matrix [G ^± ] These changes are then acted on by Block 4 and the subsequent summing blocks to calculate the new modulation indexes and hence the gate drive command signals to be applied to the generator bridge 26 by the PWM controller 44 during the next sampling period to achieve the levels of active power and flux (or power factor) specified in the active power and flux (or power factor) references POWER* and φ* (or PF*), respectively, in the presence of a speed change.

Network bridge control

The control of the network bridge 26 will be as described generally above and corresponding parts have been given the same reference numerals.

A rotor speed feedback signal N can be derived from a speed sensor (or alternatively from an observed rotor speed signal) and then filtered to provide a first filtered speed signal N' and a second filter speed signal N'2. The second filtered speed signal N'2 provides damping for any shaft resonance via a damping gain KD. The first filtered

speed signal N' provides a pointer to a pre-calculated look-up table of power demand versus filtered speed. The look-up table may be combined with a PI regulator. The resulting active power reference P*, which is the sum of the damping and look-up table power demand signals, is applied to the network bridge controller 34 as shown in Figure 6.

A number of wind turbines as represented by the entirety of Figure 6 can be connected together to define a wind farm. In this case the voltage control scheme may include two levels of control. The first is defined at the wind farm level and is responsive to a wind farm voltage demand signal that is typically set by the utility company who controls the wind farm. This wind farm voltage demand signal is compared to a wind farm voltage feedback signal and the error between the two signals is applied to a proportional plus integral controller to define a turbine voltage demand signal VTURB* that is transmitted to all of the wind turbines in the wind farm. A second level of control is then applied to each of the individual wind turbines to regulate its own output voltage in response to the turbine voltage demand signal VTURB*.

With reference to Figure 6, the reactive power demand Q* can be derived from the output of a PI regulator which is . driven by the error between the turbine voltage demand signal VTURB* and the quadrature axis positive sequence measure of the network voltage

The individual upper (U) and lower (L) gate drive command signals for the three phases red, yellow and blue resulting in individual signals RU, RL, YU, YL, BU and

BL of the network bridge 30 are calculated in the PWM controller 18 using the total modulation index magnitude m (as derived from the four modulation indexes provided by the DT-VOC function block 14), the sum of the angles θ _o and θ_NET and the PWM frequency as described above. More particularly, the DT-VOC function block 14 may use an n-samples discrete-time current controller (Block 4 of Figure 4) or an n-samples discrete-time power controller (Block 6 of

Figure 5). The DT-VOC function block 14 represents a discrete-time model of the network bridge and network system for both balanced and unbalanced operating conditions. In other words, the discrete-time model for the network side of the power converter 20 can cope fully with unbalanced operating conditions.

Operation of the power converter for wind turbine applications

The overall control of the power converter 20 using the combination of a generator bridge controller 32 and a network bridge controller 34 operates as follows.

In response to an increase in wind speed, the turbine rotor accelerates as the power absorbed by the power converter 20 does not equal the aerodynamic power into the turbine rotor. As the turbine rotor accelerates, the value of the rotor speed feedback signal N increases. A first filtered speed signal N' is used as a pointer pre-calculated look-up table and defines a new active power reference P* that is to be exported by the network bridge 30 under the control of the network bridge controller 34. Exporting more power from the dc link 28 through the network bridge 30 causes the dc link voltage Vdc to reduce. Reductions in the dc link voltage Vdc causes the generator bridge active power reference POWER* to increase and so more power is taken from the generator 22 through the generator bridge 26 under the control of the generator bridge controller 32. Power is taken from the turbine rotor to balance that being exported from the network bridge 30 until dc link voltage is again returned to its reference value and an equilibrium (or steady state) is achieved where aerodynamic power equals exported power. Additional trimming of the active power reference P* can carried out by the filter function on rotor speed feedback signal N to dampen any drive train resonances.

The power converter 20 will respond to a deceleration of the turbine rotor (i.e. for a reduction in wind speed) in a corresponding but opposite manner.

The power converter .20 will also respond to other operating situations, such as a change in the turbine voltage demand signal VTURB* or the dc link voltage reference

Possible modifications to the power converter topology

Typically, the generator will be a three-phase machine but other phase numbers can be employed. The power converter can also be arranged to operate with multi-level inverters instead of the two-level inverter arrangement described above.

The controller arrangement described above proposes two independent controllers for the network bridge and generator bridge. It would be equally suitable to integrate the functionality of the controllers on to one physical controller. Similarly, the functionality could be spread across more than two controllers if this is convenient to the practical implementation of the power converter.

Practical implementations

The power converter topology arrangements can be implemented as follows. The generator bridge 26 and network bridge 30 can each be implemented using a MV3000 liquid cooled DELTA inverter module of suitable power rating. This is an IGBT- based voltage source inverter suitable for operation on a 690 V ac network with a resulting dc link voltage of 1100 V. The generator bridge controller 32 and the network bridge controller 34 can each be implemented using a MV3000 DELTA controller. This is a microprocessor-based electronic controller, the firmware for which incorporates the functionality necessary to realise the above power control schemes. The microprocessor operates on a fixed or variable time base, sometimes referred to as "scan time", relating to the PWM frequency of the controller and or the chosen sampling period δ. All these products are supplied by Converteam Ltd of Boughton Road, Rugby, Warwickshire, CV21 IBU.

Power converter for motoring applications

With reference to Figure 8, a power converter 50 can be used for motoring

) applications. The power converter 50 can be used a part of an electric marine propulsion system or a drive system for pumps, fans, compressors or other industrial type loads, for example.

More particularly, a propeller assembly 52 of an electric marine propulsion system can be driven by the rotor of a variable speed ac permanent magnet synchronous motor 54. The propeller assembly 52 will normally consist of a number of blades mounted on a rotating shaft with a fixed pitch. The rotating shaft may be directly connected to the rotor of the motor 54 or indirectly through a gearbox (not shown) that is used to adjust the shaft speed. The speed at which the propeller assembly 52 must rotate will depend on the speed of the marine vessel and the level or direction of thrust required for propulsion. However, because the speed of rotation varies, the voltage and frequency applied to the terminals of the motor 54 must also vary. The generator bridge 26 of the power converter 20 of Figure 6 is therefore replaced by a three-phase motor bridge 56 which in normal operation operates as an inverter to supply power to the motor from a dc link 58. The motor bridge 56 has a conventional three-phase two-level topology with a series of semiconductor power switching devices fully controlled and regulated using a PWM strategy. The derivation of the gate drive command signals that are used to control the semiconductor power switching devices of the motor bridge 56 is described in more detail below.

A power network of the marine vessel operates at a nominally fixed frequency and includes a common ac supply bus (labelled "BUS") that receives power from an ac generator (not shown). The ac terminals of the network bridge 60 of the power converter 50 are therefore connected to the supply bus via an ac filter 62 and a step- down transformer 64. In normal operation the network bridge 60 will operate as an active rectifier to supply power from the supply bus to the dc link 58. Protective switchgear (not shown) can be included to provide a reliable connection to the supply bus and to isolate the propulsion system from the power network for various operational and non-operational requirements.

The principal control for the dc input voltage of the motor 54 is achieved by controlling the motor bridge 56. The network bridge 60 is controlled to meet two principal objectives, namely active power and supply bus voltage. A detailed description of how this control is achieved is provided below.

The derivation of the gate drive command signals that are used to control the semiconductor power switching devices of the network bridge 60 is also described in more detail below.

In a conventional marine propulsion system, the desired power network voltage would typically be set by a power management system (not shown) and provided to the automatic voltage regulator (AVR) of each generator (not shown). The power management system may also supply a voltage reference VBUS* to the power converter 50. The voltage reference VBUS* represents the desired voltage to be achieved at the network terminals of the ac filter 62 during normal operation of the power converter 50.

Motor bridge control

The principal control of the motor bridge 56 is to manage the dc link voltage and the flux in the motor 54.

A motor bridge controller 66 receives a generator bridge active power reference POWER* and a flux reference φ* or power factor reference PF*. The generator bridge controller 66 also receives a voltage feedback signal Vdc indicative of the dc link voltage and a current feedback signal I MOT (comprising individual current measurement for red, yellow and blue phases, respectively) that is derived from a current transducer on each of the three phase connections between the motor 54 and the motor bridge 56.

The positive sequence voltage angle θ MOT is measured by a rotor position transducer that is initialised with the magnetic poles of the motor. The current feedback signal I MOT is supplied to a function block 68 which uses the signal θ MOT , and its inverse signal -θ_ MOT , to convert the individual current measurements for the red, yellow and blue phases into positive and negative sequence current outputs Voltage outputs (which effectively represent the back emf voltage of the motor 54) can be calculated by the

function block 68 from the rotor speed, parameters relating to the magnet characteristic (flux level) and the current output derived from I_MOT.

The motor bridge power reference POWER* can be derived from the output of a PI regulator which is driven by the error between a dc link voltage reference Vdc* and the voltage feedback signal Vdc indicative of the dc link voltage. The flux reference φ* and the dc link voltage reference Vdc* may be set constants for a particular drive configuration. Although the motor is a permanent magnet synchronous machine and therefore has in-built magnets providing the bulk of the flux, a flux reference is still needed for one or more of the following reasons: (i) to manage the terminal voltage of the motor presented to the ac terminals of the motor bridge, (ii) to compensate for magnet induction including temperature effects and (iii) to optimise the efficiency of the motor-motor bridge interaction.

The DT-VOC function block 70 uses the voltage feedback signal Vdc, the active power reference POWER*, the flux reference φ* or power factor reference PF*, the oscillating component references O1 * and 02*, the positive and negative sequence voltage and current outputs the value of the sampling period δ and the rotating frequency of the motor ω_MOT to calculate direct and quadrature axis modulation indexes for each sampling period.

The individual upper (U) and lower (L) gate drive command signals for the three phases red, yellow and blue resulting in individual signals RU, RL, YU, YL, BU and

BL of the motor bridge are calculated in a PWM controller 72 using the total modulation index magnitude m (as derived from the four modulation indexes provided by the DT-VOC function block 70), the sum of the ang es θ ₀ and θ _M0T and the PWM frequency as described above. More particularly, the DT-VOC function block 70 may use an n-samples discrete-time current controller

(Block 4 of Figure 7) but where in the derivation of the main discrete-time equations (EQ5) and (EQ6):

R is the stator resistance of the motor 54; L is stator inductance of the motor; ω_M0T is the rotating frequency of the motor and is used in place of ω_GEN; and is the time constant of the motor side circuit.

The flux reference φ* or power factor reference PF* are used to derive a reactive power reference Q* within the DT-VOC function block 70 using the relationships given above.

The DT-VOC function block 70 might also use an n-samples discrete-time power controller similar to that shown in Figure 5.

The DT-VOC function block 70 represents a discrete-time model of the motor bridge and motor system for both balanced and unbalanced operating conditions. In other words, the discrete-time model for the motor side of the power converter 50 can cope fully with unbalanced operating conditions.

Network bridge control

A network bridge controller 74 supplies gate drive command signals to the network bridge 60 which cause the semiconductor power switching devices to be switched on and off resulting in a particular voltage being applied to the ac filter terminals. The network bridge controller 74 will select the voltage to be applied based on an active power reference P* that represents the level of power to be transferred to the dc link from the common ac supply bus through the motor bridge 56 and is provided by a speed/power controller 76, a voltage reference VBUS* that represents a desired voltage to be achieved at the network terminals of the ac filter 62 and is provided by the power management system, and the voltage and current feedback signals V_NET

and I_NET. A reactive power reference Q* is derived from the voltage reference VBUS*.

The network bridge controller 74 includes a function block 16, a DT-FOC function block 14 and a PWM controller 18 that operate as described above for the network bridge controller 34 of Figure 6. The individual upper (U) and lower (L) gate drive command signals for the three phases red, yellow and blue resulting in individual signals RU, RL, YU, YL, BU and BL for the network bridge 60 are calculated in the

PWM controller 18 using the total modulation index magnitude m (as derived from the four modulation indexes provided by the DT-VOC function block 14), the sum of the angles θ ₀ and θ _NET and the PWM frequency as described above. More particularly, the DT-VOC function block 14 may use an n- samples discrete-time current controller (Block 4 of Figure 4) or an n-samples discrete-time power controller (Block 6 of Figure 5). The DT-VOC function block 14 represents a discrete-time model of the network bridge and network system for both balanced and unbalanced operating conditions. In other words, the discrete-time model for the network side of the power converter 50 can cope fully with unbalanced operating conditions.

Operation of the power converter for motoring applications

The overall control of the power converter 50 for a marine propulsion system using the combination of a motor bridge controller 66 and a network bridge controller 74 operates as follows.

When a thrust requirement is made to the marine propulsion system this will either be supplied directly to the network bridge controller 74 as an active power reference P* or as a speed reference. The power and speed references can be provided to the speed/power controller 76 directly from control levers on the bridge of the marine vessel or from a vessel control system and represent vessel control commands. A speed reference will be converted to an active power reference P* by the speed/power controller 76 as part of a speed control loop with reference to the actual speed of the

motor 54 detected by a speed sensor. Applying the active power reference P* to the network bridge controller 74 will cause the dc link voltage to increase. Once the dc link voltage reaches the level set by the dc link voltage reference Vdc* the motor bridge controller 66 will begin to request power in an attempt to limit the dc link voltage at the desired level and will start to accelerate the shaft of the propeller assembly 52.

The magnitude of the power transfer through the network bridge 60 can be limited by a signal derived from the power reference P*.

Once an initial steady state has been achieved, the power converter 50 operates in a dynamic manner to accommodate changing thrust requirements. For example, for an increasing thrust requirement (i.e. for an increasing reference signal P*) the network bridge controller 74 causes the network bridge 60 to import more power from the supply bus to the dc link 58. Increasing the amount of power that is imported to the dc link 58 leads to an increase in the dc link voltage. The motor bridge controller 66 responds to this increase in the dc link voltage to cause the motor bridge 56 to draw more power out of the dc link 58 and provides this to the motor 54 until a new steady state is achieved (i.e. where the amount of power that is supplied from the supply bus to the dc link 58 is equal to the amount of power that is supplied from the dc link to the motor 54). In this steady state, the dc link voltage has matched the level set by the dc link voltage reference Vdc*.

For a reducing thrust requirement then opposite control actions take place.

Other potential applications for DT-VOC

STATCOM:

In many power network or supply grid applications, it necessary to perform reactive power compensation in order to control voltage magnitude at a specific point along an overhead line. One solution is to use shunt compensation such as static reactive compensation (STATCOM) or static VAR compensation (SVC) to enable the power network to operate in unbalanced conditions. The STATCOM arrangement will

normally include a VSC active rectifier/inverter whose ac terminals are connected to the power network via an ac filter and a transformer. The active rectifier/inverter can be controlled using a DT-VOC scheme as described above. One of the advantages of DT-VOC for STATCOM applications is the ability to satisfy low voltage ride through in unbalanced operated conditions.

VSC-HVDC:

High voltage direct current (HVDC) links are used to connect two power networks or supply grids together. In a typical back-to-back VSC-HVDC link the dc terminals of a pair of VSC active rectifier/inverters are joined together by a dc link and used to connect two power networks having different operating frequencies, for example. The pair of VSC active rectifier/inverters can also be joined together by an overhead line or long-distance dc cable. Each active rectifier/inverter operates as a network bridge and can be controlled using a DT-VOC scheme under unbalanced conditions to provide the best power dynamics for a given switching frequency, synchronised with the sampling period of the associated network bridge controller.

Renewable energy devices:

A VSC active rectifier/inverter can be used as a network bridge to interface a renewable energy device to a fixed frequency power network or supply grid. In the case of a photovoltaic cell that converts sunlight into useful electrical energy then the dc terminals of the network bridge can be connected to the photovoltaic cell via dc link and a dc-dc converter. In the case of a fuel cell (i.e. an electrochemical energy conversion device) then the dc terminals of the network bridge can be connected directly to the fuel cell via a dc link. The network bridge can be controlled using a DT-VOC scheme as described above.