Variable speed wind turbine

BACKGROUND OF THE INVENTION

Field of the Invention

0001This invention relates generally to wind turbines that operate at variable speed under varying wind conditions, and relates more particularly to a power converter for converting wind energy into AC electrical power at a controlled power factor and for controlling the torque generated by the wind turbine.

Description of the Relevant Art

0002Wind turbines provide a primary source of energy that can be converted into electricity and supplied to utility power grids. Conversion of wind energy to electrical energy is accomplished in a wind turbine by driving an electrical generator, commonly an AC induction generator. If the electrical power generated by a wind turbine is to be supplied to a utility power grid, then it is required to have a constant frequency, e.g., 60 Hertz, that is synchronized to the utility line frequency. This can be accomplished by driving the generator at a constant rotational speed, which, unless a variable speed transmission is used, requires that the wind turbine rotate at a constant speed. Unfortunately, constant speed operation of a wind turbine limits its energy conversion efficiency due to variable wind conditions. Turbine rotor speed needs to be proportional to wind speed for optimal energy recovery.

0003Variable speed wind turbines have been proposed as a way of increasing the energy conversion efficiencies of constant speed wind turbines. By varying the rotor speed in varying wind conditions, improved energy recovery can be achieved over a range of wind speed. Also importantly, the peak mechanical stresses caused by wind gusts can be reduced by limiting the torque reacted on the wind turbine by the generator and allowing the wind turbine to speed up in response to wind gusts. The increased kinetic energy of the rotor caused by wind gusts serves as a short term energy storage medium to further improve energy conversion. Such operation, however, requires a responsive torque control system.

0004Although variable speed wind turbines are advantageous from the perspective of increased energy conversion and reduced stresses, the electrical generation system is more complicated than that of a constant speed wind turbine. Since a generator is usually coupled to a variable speed rotor through a fixed-ratio gear transmission, the electrical power produced by the generator will have a variable frequency. This requires a conversion from the variable frequency AC output by the generator to a constant frequency AC for supplying the utility power grid. The conversion can be accomplished either directly by a frequency converter or through an intermediate conversion to DC by a rectifier and reconversion to fixed-frequency AC by an inverter.

0005An example of a prior art variable speed wind turbine is disclosed in US-A-4700081 (Kos et al) which includes speed avoidance logic to prevent the turbine lingering at a critical speed which would tend to cause excessive vibration. Such also discloses the use of a frequence converter for converting the variable frequency AC produced by the wind turbine to a fixed frequence AC for supply to the power grid. Further, PESC'86, 17th Annual IEEE Power Electronics Specialist Conference, pages 94 to 501, an article by BE.T.OOI et al, discloses "An integrated AC drive system using a controlled-current PWM rectifier/inverter link".

SUMMARY OF THE INVENTION

0006In accordance with the present invention there is provided a variable speed wind turbine comprising: <ul id="ul0001" list-style="none" compact="compact"><li>a turbine rotor including at least one blade mounted to a rotatable shaft;</li><li>a multiphase generator having a stator and a rotor coupled to the turbine shaft for rotation therewith;</li><li>a power converter for converting variable frequency electricity generated by the generator into fixed frequency electricity, the power converter including active switches operable for controlling stator electrical quantities for the generator;</li><li>torque command means for defining a torque reference signal; and</li><li>generator controller means coupled to the power converter for controlling the active switches, including</li><li>field orientation means responsive to the torque reference signal for defining a desired current in field coordinates, and</li><li>switch control means for controlling the active switches to produce stator electrical quantities that correspond to the desired current.</li></ul>

0007Also according to the present invention there is provided a method for controlling torque in a wind turbine having a generator coupled to a power converter with active switches, wherein the active switches establish a rotating flux field in the generator rotor, the method comprising of the steps of: <ul id="ul0002" list-style="none" compact="compact"><li>defining a torque reference signal indicative of a desired generator torque;</li><li>converting the torque reference signal into a desired quadrature axis current representing torque in rotating field coordinates normal to the rotor flux field; and controlling the active switches of the power converter to produce stator electrical quantities that correspond to the desired quadrature axis current.</li></ul>

BRIEF DESCRIPTION OF THE DRAWINGS

0008<ul id="ul0003" list-style="none" compact="compact"><li>Figure 1 is a block diagram of a wind turbine,</li><li>Figure 2 is a schematic diagram of a power converter circuit and block diagram of associated control circuits.</li><li>Figure 3 is a block diagram of the control system used to control generator torque.</li><li>Figure 4 is a graphical diagram illustrating the angular relationships between a fixed stator coordinate system, a rotating rotor coordinate system, and a rotating field oriented coordinate system.</li><li>Figure 5 is a block diagram of a generator control unit,</li><li>Figure 6 is a block diagram of a field orientation converter.</li><li>Figure 7 is a block diagram of a delta modulator current controller.</li><li>Figure 8 is a block diagram of a distortion index current controller.</li><li>Figure 9 is a block diagram of an alternative implementation of the distortion index current controller of Figure 8.</li><li>Figure 10 is a graphical representation, in α,β coordinates, of voltage vectors resulting from eight possible switch states of the active rectifier.</li><li>Figure 11 is a block diagram of a voltage controller.</li><li>Figure 12 is a block diagram of a computer program used in the generator control unit.</li><li>Figure 13 is a block diagram of an inverter control unit of the present invention.</li><li>Figure 14 is a block diagram of a current controller used in the inverter control unit of Figure 13.</li><li>Figure 15 is a block diagram of a computer program used in the inverter control unit of the present invention.</li></ul>

DETAILED DESCRIPTION OF THE INVENTION

0009Figures 1 through 15 of the drawings disclose various embodiments of the present invention for purposes of illustration only. One skilled in the art will readily recognize from the following discussion that alternative embodiments of the structures and methods illustrated herein may be employed without departing from the principles of the invention as claimed.

0010The preferred embodiment of the present invention is a variable speed wind turbine with a power converter that supplies constant frequency, high quality power at an adjustable power factor to a utility grid. As shown in Figure 1, the wind turbine 10 includes a variable pitch turbine rotor 12 that is mechanically coupled through a gear box 14 to two 3-phase AC induction generators 16 and 18. The gear box 14 includes a fixed-ratio, step-up transmission, so that the generator rotors rotate at a fixed multiple of the speed of the turbine rotor. The generators 16 and 18 produce 3-phase AC electricity at a variable frequency that is proportional to the speed of the turbine rotor. The electricity generated by each generator 16 and 18 is converted from variable frequency AC to fixed frequency AC by power converters that comprise active rectifiers 20 and 22, DC voltage links 24 and 26, inverters 28 and 30, and filters 32 and 34. The outputs of the filters 32 and 34 are combined at a transformer 36, the output of which is supplied to the utility grid.

0011The two generators, both of which rotate at all times whenever the turbine rotor rotates, are preferred over one generator in this embodiment in order to build a high capacity wind turbine while using readily available generators. The invention can, of course, be implemented in a wind turbine with only one generator or more than two generators.

0012Each of the generators 16 and 18 is controlled separately by generator controllers 38 and 40, which, as explained below, control the torque reacted by the generators by controlling the stator currents or voltages. Shaft speed sensors d? and 44 monitor the rotor speed of the two generators, respectively, and supply rotor speed information to the generator controllers 38 and 40 and to a torque command device 46. The inverters 28 and 30 are controlled separately by inverter controllers 50 and 52. A power factor controller 54 directs the inverter controllers 50 and 52 to provide power factor correction by shifting the output current with respect to the output voltage.

0013The torque command device 46 monitors wind turbine performance parameters and generates torque control signals to the generator controllers 38 and 40 and pitch angle control signals to a pitch control unit 48. Stored within the torque command device 46 is a table of optimal values of torque, pitch angle, and rotor speed for various operating conditions. These values are given as a function of an estimated wind speed, which is determined by an aerodynamic model of the wind turbine having inputs of rotor speed from the speed sensors 42 and 44, measured pitch angle from the pitch control unit 48, and measured torque from the generator controllers 38 and 40. In order to improve the dynamic stability of the overall control system, a speed control signal is used to adjust the optimal values of pitch angle and torque found from the table. The speed control signal is proportional to the difference between the optimal desired speed from the table and the measured speed from the speed sensors 42 and 44. The torque command device 46 thus determines desired values of torque and pitch angle based on the sensed operating conditions and supplies torque and pitch angle control signals to the generator controllers 38, 40 and pitch control unit 48, respectively.

0014Broadly speaking, the power converter for each generator includes an active rectifier, a DC voltage link, an inverter, filters, and associated controls. Both power converters are identical; only one will be explained. More particularly, as illustrated in Figure 2, the active rectifier 20 includes three pairs of active switching devices 60 arranged in a bridge circuit between a +DC rail 68 and a -DC rail 70 of the DC voltage link 24 and each of three stator power taps 72-74 of the generator 16. Each pair of switching devices is coupled between the DC rails 68 and 70, and connected at an intermediate point to one of the stator power taps. Commutation signals that cause the active switching devices to switch on and off originate in a generator control unit 76, which supplies the signals to the switching devices through a drive circuit 78. The generator control unit 76 and drive circuit 78 are isolated from the rectifier 20 by optical isolators to minimize interference. The commutation signals are complementary for each pair of switching devices, causing one switching device of each pair to switch on and the other switching device of the pair to switch off, as appropriate to achieve the desired stator currents or voltages. The switching devices 60 of the rectifier 20 control the stator currents and voltages in the three phase stator windings.

0015The switching devices 60 of the rectifier can be any of a number of different types of active switches, including insulated gate bipolar transistors (IGBT), bipolar junction transistors, field effect transistors, Darlington transistors, gate turn-off thyristors, or silicon controlled rectifiers. In the preferred embodiment, the switching devices 60 of the rectifier are IGBTs, with two IGBTs connected in parallel for each one shown in Figure 2, for a total of twelve devices in the rectifier 20.

0016The generator control unit 76, which is part of the generator controller 38, receives sensor inputs of the stator currents i_s1, i_s2, i_s3, and rotor speed ω_r, receives a torque reference value T_ref from the torque command device 46 (Figure 1), and generates pulse width modulated (PWM) commutation signals that it supplies to the rectifier switches 60 through the drive circuit 78. Although Figure 2 shows sensing of all three stator currents, only two currents need to be sensed because the third can be found from the relationship i_s1 + i_s2 + i_s3 = 0. The operation of the generator control unit 76 will be explained in further detail below.

0017The DC voltage link 24 consists simply of the two rails 68 and 70, plus an energy storage capacitor 80 connected between the two rails. In the preferred embodiment, where each generator is rated at 150 kilowatts, the capacitance of the capacitor 80 is about 15,000 microfarads, and the nominal voltage of the DC link is about 750 volts.

0018Situated on the other side of the DC voltage link from the active rectifier 20, the inverter 28 also includes three pairs of active switching devices 82 arranged in a bridge circuit between the +DC rail 68 and -DC rail 70 of the DC voltage link 24. The intermediate points of the pairs of active switching devices 82 form three output taps 84-86 from which 3-phase electricity flows through the filters 32 and transformer 36 to the utility grid. Commutation signals for the active switching devices 82 originate in an inverter control unit 88, which supplies the signals to the switching devices through a drive circuit 90. The inverter control unit 88 and drive circuit 90 are isolated from the inverter 28 by optical isolators. The commutation signals are complementary for each pair of switching devices, causing one switching device of each pair to switch on and the other switching device of the pair to switch off at any given time. In the preferred embodiment, the switching devices 82 of the inverter 28 consist of twelve IGBTs arranged in parallel pairs, like the switching devices 60 of the rectifier.

0019The inverter control unit 88, which is part of the inverter controller 50, receives sensor inputs of the inverter currents i_o1, i_o2, i_o3, inverter voltages v_o1, v_o2, v_o3, and DC link voltage v_dc. The inverter currents are sensed at the output taps, while the inverter voltages are sensed at the output of the filters 32 and are isolated through potential transformers 92. The inverter control unit 88 also receives, from the power factor controller 54, a power factor signal, a reactive power signal, and an operation mode signal, which define the desired power factor. In response, as will be explained in further detail below, the inverter control unit 88 generates pulse width modulated commutation signals and supplies them to the inverter switches 82 through the drive circuit 90. In addition, the inverter control unit 88 also supplies a feedback signal, Q_fb, to the power factor controller 54 that indicates the reactive power being supplied by the inverter 50.

0020The control structure of the wind turbine is illustrated in Figure 3 for one of the generators 16. The generator control unit 76 includes a field orientation converter 94 that converts the torque reference, T_ref, and the rotor speed, ω_r, into field oriented control currents, i<maths id="math0001"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0001.tif" /></maths> and i<maths id="math0002"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0002.tif" /></maths>, and a rotor flux angle, θ<maths id="math0003"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0003.tif" /></maths>. These control variables, which are identified as control variables by the * superscript, are used by a PWM controller 95 along with the sensed 3-phase stator currents, i_s1, i_s2, i_s3, to generate the PWM commutation signals, D₁, <maths id="math0004"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0004.tif" /></maths>₁, D₂, <maths id="math0005"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0005.tif" /></maths>₂, D₃, <maths id="math0006"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0006.tif" /></maths>₃. The notation D_n and <maths id="math0007"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0007.tif" /></maths>_n for example, refers to the base drive signals for the upper (D_n) and lower (<maths id="math0008"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0008.tif" /></maths>_n) devices of one pair of rectifier switches 60. The PWM controller 95, as will be described in more detail below, controls stator electrical quantities, either the stator currents or the stator voltages, depending on the rotor monitor 97 monitors the stator currents, generates a signal indicative of actual torque, T_fb, and feeds it back to the torque command device 46.

0021Controlling the generator currents and voltages in terms of field coordinates is a key element of the present invention. The electric torque of an AC induction machine can be expressed in terms of the stator and rotor currents, but such an expression is difficult to use in a torque control system since the rotor currents of a squirrel-cage induction generator cannot be directly measured. Field orientation control eliminates that difficulty.

0022It is important to understand that, at any instant of time, the rotor flux of an induction machine can be represented by a radial vector λr with magnitude λr and angle θs. The field orientation principle defines the stator current in terms of a rotating d,q coordinate system, where a direct (d) axis is aligned with the instantaneous rotor flux vector <u>λ</u>r at angle θs and a quadrature (q) axis is perpendicular to the rotor flux vector. This is illustrated in Figure 4. The stator current vector, <u>i</u>_s, can be degenerated into a component, i_sd, that is parallel to the rotor flux <u>λ</u>r vector and a component, i_sq, that is perpendicular to the rotor flux vector. The currents i_sd and i_sq at angle θs, are the field coordinate representation of the stator current vector.

0023Figure 4 also illustrates that ω_r is defined as the rotor angular speed and ω_s is defined as the angular speed of the rotor flux vector. The machine slip speed, ω_sl, which is the speed of the stator current vector with respect to the rotor, is the difference between ω_s, and ω_r.

0024The d,q coordinate system isolates or decouples a current that creates the rotor flux field, i_sd, on the direct axis, from a current that creates torque, i_sq, on the quadrature axis. Defining the generator currents in field orientation coordinates permits the generator control unit 76 to convert the torque control commands directly into a desired quadrature axis current, i<maths id="math0009"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0009.tif" /></maths>, which is then used by the PWM controller 95 to carry out the torque commands of the torque command device 46.

0025Controlling the generator in this manner requires conversion between stationary stator coordinates and rotating field coordinates. The stator currents in a balanced, 3-phase coordinate system, as represented by the currents on the three stator power taps 72-74 (Figure 2), can be designated by the variables i_s1, i_s2, and i_s3. The balanced, 3-phase stator currents are equivalent to 2-phase stator currents, i_sα and i_sβ, defined by the following matrix equation:<maths id="math0010"><img file="EP1432115A2_D0010.tif" /></maths>

0026The 2-phase stator currents, i_sα, and i_sβ, can be converted into the field coordinate currents, i_sd and i_sq, as a function of the rotor flux angle, θ_s, by the following transformation:<maths id="math0011"><img file="EP1432115A2_D0011.tif" /></maths> Transformation from field coordinates to 2-phase coordinates is accomplished by inverting equation (2), which results in the following:<maths id="math0012"><img file="EP1432115A2_D0012.tif" /></maths> Transformation from 2-phase to balanced 3-phase coordinates is found by inverting equation (1):<maths id="math0013"><img file="EP1432115A2_D0013.tif" /></maths> Representations of the stator current vector in the rotating d,q field coordinate system, in the stationary 2-phase α,β coordinate system, and in the stationary balanced 3-phase coordinate system are shown in Figure 4.

0027The structure of the generator control unit 76 is shown in block diagram form in Figure 5. The generator control unit is preferably implemented in a digital signal processor ("DSP"), a Texas Instruments model TMS320C25. Computer code for implementing the invention in a DSP is disclosed in the microfiche appendix.

0028Functionally, the generator control unit 76 includes the field orientation converter 94, the torque monitor 97, and the PWM controller 95. In the preferred embodiment, the PWM controller 95 includes a current controller 96, a voltage controller 98, and a selector circuit 100. These components will be explained in more detail below, but generally, the field orientation converter 94 generates control parameters based on the rotor speed and torque reference signals, the current controller 96 or the voltage controller 98 generates PWM commutation signals for the active switching devices 60, and the selector circuit 100 chooses which of the PWM commutation signals to output to the drive circuit 78. The torque monitor 97 senses the actual stator currents, i_s1, i_s2, i_s3, converts them to field coordinate values using equations (1) and (2), and calculates a torque signal, T_fb, using equation (8) (see below) for feedback to the torque command device 46. The torque monitor 97 thus infers generator torque from the measured currents. The computations performed within the DSP of the generator control unit 76 are digital, which requires A/D conversion of the external signals.

0029The field orientation converter 94, illustrated in Figure 6, converts the torque control and rotor flux signals into field coordinates. Using a desired direct axis current, i<maths id="math0014"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0014.tif" /></maths>, the field orientation converter 94 computes the desired magnitude of the rotor flux, λ<maths id="math0015"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0015.tif" /></maths>. The desired flux-producing direct axis current, i<maths id="math0016"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0016.tif" /></maths>, is a function of the particular generator used, and can be predetermined and stored in the DSP. In the preferred embodiment, i<maths id="math0017"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0017.tif" /></maths> is assumed to be constant. Alternatively, i<maths id="math0018"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0018.tif" /></maths> can be varied to provide field weakening control, if desired. The notation * designates a desired value generated by the control system as opposed to an actual value.

0030The desired rotor flux, λ<maths id="math0019"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0019.tif" /></maths>, is defined by the following equation:<maths id="math0020" num="(5)"><math display="block"><mrow><msubsup><mrow><mover accent="true"><mrow><mtext>λ</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>-R</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msubsup><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></mfrac><mtext> + </mtext><mfrac><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msub><mrow><mtext> L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext> i</mtext></mrow><mrow><mtext>sd</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1432115A2_D0020.tif" /></maths> where: λ<maths id="math0021"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0021.tif" /></maths> = desired rotor flux;       λ̇<maths id="math0022"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0022.tif" /></maths> = time derivative of desired rotor flux;       R_r = rotor resistance;       L_o = mutual inductance;       L_r = rotor self inductance. In the general case, equation (5) can be represented by the following recursive equation:<maths id="math0023" num="(6)"><math display="block"><mrow><msubsup><mrow><mtext>λ</mtext></mrow><mrow><mtext>r(k)</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> = λ</mtext></mrow><mrow><mtext>r(k-1)</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> - </mtext><mfrac><mrow><msub><mrow><mtext>Δt R</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msubsup><mrow><mtext> λ</mtext></mrow><mrow><mtext>r(k-1)</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext></mtext></mrow><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></mfrac><mtext> + </mtext><mfrac><mrow><msub><mrow><mtext>Δt R</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msub><mrow><mtext> L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext> i</mtext></mrow><mrow><mtext>sd(k-1)</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1432115A2_D0023.tif" /></maths> where: λ<maths id="math0024"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>r(k)</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0024.tif" /></maths> = λ<maths id="math0025"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0025.tif" /></maths> at time = k;       λ<maths id="math0026"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>r(k-1)</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0026.tif" /></maths> = λ<maths id="math0027"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0027.tif" /></maths> at time = k-1;       i<maths id="math0028"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd(k-1)</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0028.tif" /></maths> = i<maths id="math0029"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0029.tif" /></maths> at time = k-1;       Δt = sample time period between time = k-1 and time = k. In the case where i<maths id="math0030"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0030.tif" /></maths> is constant, the time derivative λ̇<maths id="math0031"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0031.tif" /></maths> = 0, so that equation (6) simplifies to:<maths id="math0032" num="(7)"><math display="block"><mrow><msubsup><mrow><mtext>λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> = L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext> i</mtext></mrow><mrow><mtext>sd</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow></math><img file="EP1432115A2_D0032.tif" /></maths> Once the rotor flux is known, the torque reference can be converted into quadrature axis current. In field coordinates, the torque reacted by the generator is given by:<maths id="math0033" num="(8)"><math display="block"><mrow><mtext>T = </mtext><mfrac><mrow><msub><mrow><mtext>P L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msub><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msub><mrow><mtext> i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>3 L</mtext></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1432115A2_D0033.tif" /></maths> where: T = generator torque;       P = number of generator poles;       i_sq = quadrature axis current. Solving equation (8) for i_sq, yields the following expression for desired torque-producing quadrature axis current as a function of the torque reference supplied by the torque command device 46:<maths id="math0034" num="(9)"><math display="block"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>3 L</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msub><mrow><mtext> T</mtext></mrow><mrow><mtext>ref</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>P L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow></mfrac></mrow></math><img file="EP1432115A2_D0034.tif" /></maths> where T_ref is the torque reference signal supplied to the generator control unit by the torque command device 46.

0031Once the desired rotor flux, λ<maths id="math0035"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0035.tif" /></maths>, and desired quadrature axis current, i<maths id="math0036"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0036.tif" /></maths>, have been determined, the desired rotor flux angle, θ<maths id="math0037"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0037.tif" /></maths>, at a particular instant of time can be found. This is accomplished by solving the following equations:<maths id="math0038" num="(10)"><math display="block"><mrow><msubsup><mrow><mtext>ω</mtext></mrow><mrow><mtext>sl</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msub><mrow><mtext> L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext> i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext></mtext></mrow><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msubsup><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow></mfrac></mrow></math><img file="EP1432115A2_D0038.tif" /></maths><maths id="math0039" num="(11)"><math display="block"><mrow><msubsup><mrow><mtext>ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> = ω</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msubsup><mrow><mtext> + ω</mtext></mrow><mrow><mtext>s1</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow></math><img file="EP1432115A2_D0039.tif" /></maths><maths id="math0040" num="(12)"><math display="block"><mrow><msubsup><mrow><mtext>θ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> = ∫ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> dt,   0 ≤ θ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> ≤ 2π</mtext></mrow></math><img file="EP1432115A2_D0040.tif" /></maths> where: ω<maths id="math0041"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sl</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0041.tif" /></maths> = desired machine slip speed;       ω<maths id="math0042"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0042.tif" /></maths> = desired rotor flux speed;       ω_r = actual rotor speed;       θ<maths id="math0043"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0043.tif" /></maths> = desired instantaneous rotor flux angle. Machine slip speed, ω<maths id="math0044"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sl</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0044.tif" /></maths>, is found from the calculated values of desired rotor flux, λ<maths id="math0045"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0045.tif" /></maths>, and desired quadrature axis current, i<maths id="math0046"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0046.tif" /></maths>, using equation (10). The measured rotor speed, ω_r, is then added to the machine slip speed, ω<maths id="math0047"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sl</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0047.tif" /></maths>, to find the desired rotor flux speed, ω<maths id="math0048"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0048.tif" /></maths>, according to equation (11). The desired rotor flux speed, ω<maths id="math0049"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0049.tif" /></maths>, is then integrated modulo 2π to find the desired instantaneous rotor flux angle, θ<maths id="math0050"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0050.tif" /></maths>.

0032The computed values for desired field oriented currents, i<maths id="math0051"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0051.tif" /></maths> and i<maths id="math0052"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0052.tif" /></maths>, rotor flux, λ<maths id="math0053"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0053.tif" /></maths>, rotor flux speed, ω<maths id="math0054"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0054.tif" /></maths>, and rotor flux angle, θ<maths id="math0055"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0055.tif" /></maths>, are available to the current and voltage controllers 96 and 98 (Figure 5) for determination of the PWM commutation signals. Transformation of the desired stator currents from field coordinates into stationary 2-phase α,β coordinates or balanced 3-phase coordinates, if required by the PWM controller, can be accomplished either in the field orientation converter or in the PWM controller. Here, it is assumed that the transformations occur outside of the field orientation converter 94.

0033In response to the values computed by the field orientation converter 94, either the current controller 96 or the voltage controller 98, depending on which is selected, determines switch states for the active switching devices (Figure 5). The current controller 96 generates PWM commutation signals by choosing a switch state that causes stator currents to approximate the desired currents defined by the field orientation converter. The voltage controller 98 generates PWM commutation signals by converting the desired field oriented currents into desired field oriented voltages, transforming them into stator coordinates, and then selecting the appropriate switch state to obtain the desired stator voltages.

0034One simple method of current control is illustrated in Figure 7, a delta modulator current controller. The delta modulator current controller converts the desired field oriented currents into stationary 2-phase stator coordinates, and then to 3-phase stator coordinates to generate desired 3-phase stator currents, i<maths id="math0056"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s1</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0056.tif" /></maths>, i<maths id="math0057"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s2</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0057.tif" /></maths>, i<maths id="math0058"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s3</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0058.tif" /></maths>.

0035Transforming the desired currents from rotating field coordinates to stationary 2-phase α,β coordinates is achieved by equation (3), which reduces to the following:<maths id="math0059" num="(13)"><math display="block"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> = i</mtext></mrow><mrow><mtext>sd</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> cosθ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> - i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> sinθ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow></math><img file="EP1432115A2_D0059.tif" /></maths><maths id="math0060" num="(14)"><math display="block"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> = i</mtext></mrow><mrow><mtext>sd</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> sinθ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> + i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> cosθ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow></math><img file="EP1432115A2_D0060.tif" /></maths> The desired stator currents are then transformed into 3-phase coordinates using equation (4).

0036After converting the desired stator currents from field coordinates into 3-phase coordinates, the delta modulator current controller then periodically compares each desired stator current i<maths id="math0061"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s1</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0061.tif" /></maths>, i<maths id="math0062"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s2</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0062.tif" /></maths>, i<maths id="math0063"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s3</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0063.tif" /></maths>, with the corresponding actual stator current i_s1, i_s2, i_s3, using compare and hold devices 102. If the desired stator current for a phase is greater than the actual stator current, then the upper switching device is switched on and the lower switching device is switched off, otherwise, the upper device is switched on and the lower device is switched off. The compare and hold devices 102 set the PWM commutation signals, D₁, <maths id="math0064"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0064.tif" /></maths>₁, D₂, <maths id="math0065"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0065.tif" /></maths>₂, D₃, <maths id="math0066"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0066.tif" /></maths>₃ to accomplish the desired switching. The switch state so selected remains in effect until the next sample period occurs, at which time the comparisons are performed with updated actual and desired values.

0037Another method of current control, one that minimizes a distortion index, is illustrated in Figures 8-10. This method generates PWM signals by periodically minimizing a distortion index related directly to total harmonic distortion (THD). In comparison with the delta modulator current controller or with a linear controller with triangular crossing, this method is preferable due to lower THD at comparable frequencies, while requiring fewer switching events and, consequently, less power loss due to switching. The distortion index that is minimized may be defined as the sum of the squares of the current errors:<maths id="math0067" num="(15)"><math display="block"><mrow><msub><mrow><mtext>J</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msubsup><mrow><mtext> = (i</mtext></mrow><mrow><mtext>s1</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - i</mtext></mrow><mrow><mtext>s1</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msubsup><mrow><mtext> + (i</mtext></mrow><mrow><mtext>s2</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - i</mtext></mrow><mrow><mtext>s2</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msubsup><mrow><mtext> + (i</mtext></mrow><mrow><mtext>s3</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - i</mtext></mrow><mrow><mtext>s3</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></math><img file="EP1432115A2_D0067.tif" /></maths> where, i<maths id="math0068"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s1</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0068.tif" /></maths>, i<maths id="math0069"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s2</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0069.tif" /></maths>, i<maths id="math0070"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s3</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0070.tif" /></maths> are the desired 3-phase stator currents, and i_s1, i_s2, i_s3 are the actual 3-phase stator currents. Alternatively, the distortion index can be defined as the sum of the absolute values of the current errors.<maths id="math0071" num="(16)"><math display="block"><mrow><msub><mrow><mtext>J</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext> = </mtext><mfenced open="|" close="|"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>s1</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>-i</mtext></mrow><mrow><mtext>s1</mtext></mrow></msub></mrow></mfenced><mtext> + </mtext><mfenced open="|" close="|"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>s2</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>-i</mtext></mrow><mrow><mtext>s2</mtext></mrow></msub></mrow></mfenced><mtext> + </mtext><mfenced open="|" close="|"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>s3</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>-i</mtext></mrow><mrow><mtext>s3</mtext></mrow></msub></mrow></mfenced></mrow></math><img file="EP1432115A2_D0071.tif" /></maths>

0038Minimizing the distortion index, J, involves determining which of eight possible switch states of the rectifier switches will produce actual stator currents nearest in value to the desired stator currents. One way to accomplish this is shown in Figure 8. Switching decisions are made periodically, based on the most recently measured stator currents. The actual stator currents i_s1(k), i_s2(k), and i_s3(k), are measured at time = k, and a projection is made of the stator currents i_s1(k+1), i_s2(k+1), and i_s3(k+1) at the next interval of time, for each possible switch state. Since there are two possible switch settings for each of the three switch pairs, there are eight (2³) possible switch states for the rectifier switches. The projected stator currents i_s1(k+1), i_s2(k+1), and i_s3(k+1) are found by modeling the generator and rectifier according to the following equation derived from a simplified model:<maths id="math0072" num="(17)"><math display="block"><mrow><munder accentunder="true"><mrow><mtext>V</mtext></mrow><mo>̲</mo></munder><mtext> = </mtext><munder accentunder="true"><mrow><mtext>E</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext> + L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><mfrac><mrow><mtext>d</mtext></mrow><mrow><mtext>dt</mtext></mrow></mfrac><mtext>(</mtext><munder accentunder="true"><mrow><msub><mrow><mtext>i</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow><mo>̲</mo></munder><mtext>)</mtext></mrow></math><img file="EP1432115A2_D0072.tif" /></maths> where <u>V</u> = voltage vector resulting from a particular switch state;       <u>E</u> = generator emf vector;       <u>i</u>_s = stator current vector. Evaluating the derivative over a discrete time interval, At, yields the following for the projected currents:<maths id="math0073" num="(18)"><math display="block"><mrow><munder accentunder="true"><mrow><mtext>i</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><mtext>(k+1) = </mtext><mfrac><mrow><mtext>Δt</mtext></mrow><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub></mrow></mfrac><mtext></mtext><munder accentunder="true"><mrow><mtext>V</mtext></mrow><mo>̲</mo></munder><mtext>(k) - </mtext><munder accentunder="true"><mrow><mtext>E</mtext></mrow><mo>̲</mo></munder><mtext>(k)) + </mtext><munder accentunder="true"><mrow><mtext>i</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><mtext>(k)</mtext></mrow></math><img file="EP1432115A2_D0073.tif" /></maths> The projected stator currents can thus be found for each switch state by evaluating equation (18) using the voltage vector that would result from that switch state.

0039After the projected stator currents are found, the distortion index, J, can be computed by equations (15) or (16) for each possible switch state. The switch state that yields the minimum value of J is output to the selector 100.

0040While the above-described method will define a switch state that minimizes the distortion index, another equivalent method is preferable due to its reduced computational overhead. The alternative method of computing the switch state that minimizes the distortion index is illustrated in Figures 9 and 10. This method converts the desired stator current vector into an equivalent desired voltage vector, and then finds the switch state that would most closely approximate the desired voltage vector. This method in effect minimizes an equivalent distortion index defined in the α,β coordinate system with respect to voltage error:<maths id="math0074" num="(19)"><math display="block"><mrow><msub><mrow><mtext>J</mtext></mrow><mrow><mtext>3</mtext></mrow></msub><msubsup><mrow><mtext> = (v</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - v</mtext></mrow><mrow><mtext>sα</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msubsup><mrow><mtext> + (v</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - v</mtext></mrow><mrow><mtext>sβ)</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></math><img file="EP1432115A2_D0074.tif" /></maths> or<maths id="math0075" num="(20)"><math display="block"><mrow><msub><mrow><mtext>J</mtext></mrow><mrow><mtext>4</mtext></mrow></msub><mtext> = </mtext><mfenced open="|" close="|"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - v</mtext></mrow><mrow><mtext>sα</mtext></mrow></msub></mrow></mfenced><mtext> + </mtext><mfenced open="|" close="|"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - v</mtext></mrow><mrow><mtext>sβ</mtext></mrow></msub></mrow></mfenced></mrow></math><img file="EP1432115A2_D0075.tif" /></maths> where v<maths id="math0076"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0076.tif" /></maths> = desired α axis voltage;       v<maths id="math0077"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0077.tif" /></maths> = desired P axis voltage;       v_sα = actual α axis voltage;       v_sβ = actual β axis voltage. It can be shown that minimizing the voltage differences of equations (19) or (20) is equivalent to minimizing the current differences of equations (15) or (16), since the distortion indices vary only by constant or proportional factors. Due to this equivalence, minimizing the distortion index defined by equations (19) or (20) does control the stator currents, even though the desired currents are converted into desired voltages for evaluating the distortion index.

0041As shown in Figure 9, computations are carried out using the 2-phase α,β coordinate system instead of the 3-phase coordinate system in order to eliminate some redundant computational steps. The measured 3-phase stator currents, i_s1, i_s2, and i_s3, are converted into the 2-phase α,β coordinate system using equation (1). The desired field coordinate currents, i<maths id="math0078"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0078.tif" /></maths> and i<maths id="math0079"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0079.tif" /></maths>, as received from the field orientation converter 94 (Figure 5), are converted into desired α,β stator currents at time (k), i<maths id="math0080"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0080.tif" /></maths>(k) and i<maths id="math0081"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0081.tif" /></maths>(k), using equation (3). These values are projected forward in time using the formulas:<maths id="math0082" num="(21)"><math display="block"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext>(k+1) = 2i</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext>(k) - i</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext>(k-1)</mtext></mrow></math><img file="EP1432115A2_D0082.tif" /></maths><maths id="math0083" num="(22)"><math display="block"><mrow><msubsup><mrow><mtext>i</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext>(k+1) = 2 i</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext>(k) - i</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext>(k-1)</mtext></mrow></math><img file="EP1432115A2_D0083.tif" /></maths> The generator emf, in α,β coordinates, is estimated by:<maths id="math0084" num="(23)"><math display="block"><mrow><msub><mrow><mtext>E</mtext></mrow><mrow><mtext>α</mtext></mrow></msub><msubsup><mrow><mtext> = λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext></mtext><mfrac><mrow><mtext>d</mtext></mrow><mrow><mtext>dt</mtext></mrow></mfrac><msubsup><mrow><mtext> (cos θ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext>) = ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> sin (ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> t)</mtext></mrow></math><img file="EP1432115A2_D0084.tif" /></maths><maths id="math0085" num="(24)"><math display="block"><mrow><msub><mrow><mtext>E</mtext></mrow><mrow><mtext>β</mtext></mrow></msub><msubsup><mrow><mtext> = λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext></mtext><mfrac><mrow><mtext>d</mtext></mrow><mrow><mtext>dt</mtext></mrow></mfrac><msubsup><mrow><mtext> (sin θ</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext>) = ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> cos (ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> t)</mtext></mrow></math><img file="EP1432115A2_D0085.tif" /></maths> The desired voltages in α,β coordinates, v<maths id="math0086"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0086.tif" /></maths> and v<maths id="math0087"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0087.tif" /></maths>, are estimated by the generator model of equation (17), which defines the following equations:<maths id="math0088" num="(25)"><math display="block"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext> (i</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k+1) - 1</mtext></mrow><mrow><mtext>sα</mtext></mrow></msub><mtext>)</mtext></mrow><mrow><mtext>Δt</mtext></mrow></mfrac><msub><mrow><mtext> + E</mtext></mrow><mrow><mtext>α</mtext></mrow></msub></mrow></math><img file="EP1432115A2_D0088.tif" /></maths><maths id="math0089" num="(26)"><math display="block"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext> (i</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k+1) - 1</mtext></mrow><mrow><mtext>sβ</mtext></mrow></msub><mtext>)</mtext></mrow><mrow><mtext>Δt</mtext></mrow></mfrac><msub><mrow><mtext> + E</mtext></mrow><mrow><mtext>β</mtext></mrow></msub></mrow></math><img file="EP1432115A2_D0089.tif" /></maths>

0042Next, instead of solving equation (19) or (20) for each possible switch state, the desired α and β axis voltages, v<maths id="math0090"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0090.tif" /></maths> and v<maths id="math0091"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0091.tif" /></maths>, are compared to the limited number of voltage vectors that could result from the eight possible switch states. These voltage vectors, shown in Figure 10, have a magnitude of either zero or the DC link voltage, v_dc, and are aligned with the s₁, s₂, and s₃ axes. The voltage vectors are defined according to the following table: <tables id="tabl0001" num="0001"><table frame="all"><tgroup cols="3" colsep="1" rowsep="0"><colspec colnum="1" colname="col1" colwidth="52.50mm" /><colspec colnum="2" colname="col2" colwidth="52.50mm" /><colspec colnum="3" colname="col3" colwidth="52.50mm" /><thead valign="top"><row rowsep="1"><entry namest="col1" nameend="col1" align="center">State</entry><entry namest="col2" nameend="col2" align="center">Switch Setting</entry><entry namest="col3" nameend="col3" align="center">(v_sα, v_sβ)</entry></row></thead><tbody valign="top"><row><entry namest="col1" nameend="col1" align="center">0</entry><entry namest="col2" nameend="col2" align="center">[<maths id="math0092"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0092.tif" /></maths>₁, <maths id="math0093"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0093.tif" /></maths>₂, <maths id="math0094"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0094.tif" /></maths>₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (0, 0)</entry></row><row><entry namest="col1" nameend="col1" align="center">1</entry><entry namest="col2" nameend="col2" align="center">[D₁, <maths id="math0095"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0095.tif" /></maths>₂, <maths id="math0096"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0096.tif" /></maths>₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (1, 0)</entry></row><row><entry namest="col1" nameend="col1" align="center">2</entry><entry namest="col2" nameend="col2" align="center">[D₁, D₂, <maths id="math0097"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0097.tif" /></maths>₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (1 /2, <maths id="math0098"><math display="inline"><mrow><msqrt><mtext>3</mtext></msqrt></mrow></math><img file="EP1432115A2_D0098.tif" /></maths>/2)</entry></row><row><entry namest="col1" nameend="col1" align="center">3</entry><entry namest="col2" nameend="col2" align="center">[<maths id="math0099"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0099.tif" /></maths>₁, D₂, <maths id="math0100"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0100.tif" /></maths>₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (-1/2, <maths id="math0101"><math display="inline"><mrow><msqrt><mtext>3</mtext></msqrt></mrow></math><img file="EP1432115A2_D0101.tif" /></maths>/2)</entry></row><row><entry namest="col1" nameend="col1" align="center">4</entry><entry namest="col2" nameend="col2" align="center">[<maths id="math0102"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0102.tif" /></maths>₁, D₂, D₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (-1,0)</entry></row><row><entry namest="col1" nameend="col1" align="center">5</entry><entry namest="col2" nameend="col2" align="center">[<maths id="math0103"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0103.tif" /></maths>₁, <maths id="math0104"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0104.tif" /></maths>₂, D₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (-1/2,-<maths id="math0105"><math display="inline"><mrow><msqrt><mtext>3</mtext></msqrt></mrow></math><img file="EP1432115A2_D0105.tif" /></maths>/2)</entry></row><row><entry namest="col1" nameend="col1" align="center">6</entry><entry namest="col2" nameend="col2" align="center">[D₁, <maths id="math0106"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0106.tif" /></maths>₂, D₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (1/2,-<maths id="math0107"><math display="inline"><mrow><msqrt><mtext>3</mtext></msqrt></mrow></math><img file="EP1432115A2_D0107.tif" /></maths>/2)</entry></row><row rowsep="1"><entry namest="col1" nameend="col1" align="center">7</entry><entry namest="col2" nameend="col2" align="center">[D₁, D₂, D₃]</entry><entry namest="col3" nameend="col3" align="center">v_dc (0, 0)</entry></row></tbody></tgroup></table></tables> Since states 0 and 7 define the same zero voltage, there are seven possible stator voltages that could result from the eight possible switch settings of the active switching devices of the rectifier.

0043Minimizing the distortion index is accomplished by finding which stator voltage vector is closest to the desired voltage vector defined by v<maths id="math0108"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0108.tif" /></maths> and v<maths id="math0109"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0109.tif" /></maths>. Graphically, the α,β coordinate space can be divided into seven regions: an inner circle 104 of radius v_dc/2, plus six 60° sectors 106-111 of outer radius v_dc surrounding the inner circle, each sector having a switch state centered at the outer radius thereof.

0044Determining the closest voltage vector is a matter of finding into which region the desired voltage vector falls. To do so, the magnitude of the desired voltage vector is first compared to v_dc/2 to determine whether the desired voltage vector falls within the inner circle 104. If the magnitude of the desired voltage vector is less than one-half of v_dc, then state ○ or state 7 is the desired switch state. Choosing between state ○ and state 7 is accomplished by selecting the state that requires the fewest number of switches to change state from the previous switch setting.

0045Next, if the magnitude of the desired voltage vector exceeds v_dc/2, then the signs of v<maths id="math0110"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0110.tif" /></maths> and v<maths id="math0111"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0111.tif" /></maths> are examined to determine in which quadrant the voltage vector falls. If the sign of v<maths id="math0112"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0112.tif" /></maths> is positive, then states 1, 2, or 6 are candidates, and, if negative, then states 3, 4, or 5 are candidates. If both v<maths id="math0113"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0113.tif" /></maths> and v<maths id="math0114"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0114.tif" /></maths> are positive, for example, then either state 1 or state 2 is the closest voltage vector. For v<maths id="math0115"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0115.tif" /></maths> and v<maths id="math0116"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0116.tif" /></maths> positive, state 1 is closest if v<maths id="math0117"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0117.tif" /></maths> > <maths id="math0118"><math display="inline"><mrow><msqrt><mtext>3</mtext></msqrt></mrow></math><img file="EP1432115A2_D0118.tif" /></maths> v<maths id="math0119"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0119.tif" /></maths>, otherwise state 2 is closest. This is so because a dividing line 112 between sector 106 of state 1 and sector 107 of state 2 is inclined at 30° to the α axis, and because:<maths id="math0120" num="(27)"><math display="block"><mrow><mtext>tan 30° = </mtext><mfrac><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext></mtext></mrow><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow></mfrac><mtext> = </mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><msqrt><mtext>3</mtext></msqrt></mrow></mfrac><mtext> .</mtext></mrow></math><img file="EP1432115A2_D0120.tif" /></maths>

0046The selections between states 3 and 4,4 and 5, and 1 and 6 in the other quadrants are developed in the same manner. Once the closest voltage vector is found, the switch state associated with that voltage vector is output to the selector 100.

0047Referring back to Figure 5, operation with the current controller 96 generating the PWM commutation signals occurs at relatively low speeds, where the DC voltage link offers substantial ceiling voltage. In that situation, the current controller 96 keeps the stator currents in close agreement with the desired stator current values. This operation effectively results in current sources for the stator windings, which allows the current controller to ignore the stator voltages.

0048At higher speeds, however, where the generator emf approaches the voltage of the DC voltage link, the stator voltages can no longer be ignored. In this operating region, the voltage controller 98 takes the stator voltages into consideration.

0049The selector 100 senses the rotor speed, ω_r, and selects the voltage controller 98 instead of the current controller 96 when the rotor speed exceeds a predetermined value. This value can be determined empirically by observing the distortion of the current waveform during operation of the current controller at various speeds. In the preferred embodiment, using a four pole squirrel-cage induction generator with a 1800 rpm synchronous speed and operating at a nominal voltage of 750 volts, the switching point is about 1780 rpm. Preferably, some hysteresis is built into the switching point of the selector 100 so that small oscillations of the rotor speed about the switching point do not cause repeated switching between current control and voltage control. As an alternative to or in addition to monitoring the rotor speed, the DC link voltage and the generator emf can be monitored to determine at which point to switch between current control and voltage control. Monitoring the DC link voltage is not necessary in the preferred embodiment because the inverter control unit 88 maintains that voltage at a fairly constant value.

0050Like the current controller 96, the voltage controller 98 periodically generates a set of PWM commutation signals for switching on and off the active switches of the rectifier. The voltage controller monitors the desired and actual torque and flux, as defined by the field oriented currents, i<maths id="math0121"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0121.tif" /></maths> and i<maths id="math0122"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0122.tif" /></maths>, compensates for the stator voltages, and generates field oriented control voltages, v<maths id="math0123"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0123.tif" /></maths> and v<maths id="math0124"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0124.tif" /></maths>, which are used to generate the commutation signals.

0051The stator voltages, in field coordinates, are defined by the following equations:<maths id="math0125" num="(28)"><math display="block"><mrow><mfrac><mrow><msub><mrow><mtext>σ L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><mtext></mtext><msub><mrow><mover accent="true"><mrow><mtext>i</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>sd</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac><msub><mrow><mtext> + i</mtext></mrow><mrow><mtext>sd</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>v</mtext></mrow><mrow><mtext>sd</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac><mtext> - </mtext><mfrac><mrow><msub><mrow><mtext>(1-σ) L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><mtext></mtext><msub><mrow><mover accent="true"><mrow><mtext>λ</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>r</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub></mrow></mfrac><mtext> + </mtext><mfrac><mrow><msub><mrow><mtext>σ L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> ω</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1432115A2_D0125.tif" /></maths><maths id="math0126" num="(29)"><math display="block"><mrow><mfrac><mrow><msub><mrow><mtext>σ L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><mtext></mtext><msub><mrow><mover accent="true"><mrow><mtext>i</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>sq</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac><msub><mrow><mtext> + i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>v</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac><mtext> - </mtext><mfrac><mrow><msub><mrow><mtext>(1-σ) L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> ω</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msub><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub></mrow></mfrac><mtext> - </mtext><mfrac><mrow><msub><mrow><mtext>σ L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> ω</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> i</mtext></mrow><mrow><mtext>sd</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1432115A2_D0126.tif" /></maths>    where: σ = total or global leakage factor;       L_s = stator inductance;       R_s = stator resistance. The last two terms on the right sides of equations (28) and (29) are coupling terms for which compensation is required to eliminate cross coupling between the direct and quadrature axes. The goal is to generate v<maths id="math0127"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0127.tif" /></maths> as a function of i<maths id="math0128"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0128.tif" /></maths> and v<maths id="math0129"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0129.tif" /></maths> as a function of i<maths id="math0130"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0130.tif" /></maths>. Eliminating the cross coupling terms allows v<maths id="math0131"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0131.tif" /></maths> to control rotor flux and v<maths id="math0132"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0132.tif" /></maths> to control torque.

0052The operation of the voltage controller 98 is shown in Figure 11. The actual 3-phase stator currents, i_s1, i_s2, i_s3, are converted into field oriented coordinates by equations (1) and (2). The desired voltage on the quadrature axis, v<maths id="math0133"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0133.tif" /></maths>, is generated by first subtracting the actual quadrature current, i_sq, from the desired quadrature current, i<maths id="math0134"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0134.tif" /></maths>, and then running the resultant through a proportional-integral (PI) controller 114 to generate v<maths id="math0135"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>'</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0135.tif" /></maths>, which is a measure of quadrature axis current error. The PI controller supplies a proportional/integral output of the form:<maths id="math0136" num="(30)"><math display="block"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><msub><mrow><mtext> = k</mtext></mrow><mrow><mtext>p</mtext></mrow></msub><msubsup><mrow><mtext> (i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub><msub><mrow><mtext>) + k</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msubsup><mrow><mtext> ∫(i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub><mtext>) dt</mtext></mrow></math><img file="EP1432115A2_D0136.tif" /></maths> where k_p and k_i are coefficients selected to provide adequate stability. Equation (30) can be evaluated in discrete time by the following:<maths id="math0137" num="(31)"><math display="block"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><msubsup><mrow><mtext>(k) = v</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><msub><mrow><mtext>(k-1) + (k</mtext></mrow><mrow><mtext>p</mtext></mrow></msub><msub><mrow><mtext> + Δt k</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msubsup><mrow><mtext>) (i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k) - i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub><mtext>(k)) -</mtext><mspace linebreak="newline" /><msub><mrow><mtext> k</mtext></mrow><mrow><mtext>p</mtext></mrow></msub><msubsup><mrow><mtext> (i</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k-1) - i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub><mtext>(k-1))</mtext></mrow></math><img file="EP1432115A2_D0137.tif" /></maths> The value of v'_sq is then compensated by adding a decoupling factor consisting of the two voltage coupling terms on the right side of equation (29), which results in v<maths id="math0138"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0138.tif" /></maths> as follows:<maths id="math0139" num="(32)"><math display="block"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> = v</mtext></mrow><mrow><mtext>sq</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><mtext> + </mtext><mfrac><mrow><msub><mrow><mtext>(1-σ) L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msubsup><mrow><mtext> ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> λ</mtext></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub></mrow></mfrac><mtext> + </mtext><mfrac><mrow><msub><mrow><mtext>σ L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msubsup><mrow><mtext> ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> i</mtext></mrow><mrow><mtext>sd</mtext></mrow></msub><mtext></mtext></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1432115A2_D0139.tif" /></maths>

0053Similarly, the desired voltage on the direct axis, v<maths id="math0140"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0140.tif" /></maths>, is generated by first subtracting the rotor flux divided by the mutual inductance, λ<maths id="math0141"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0141.tif" /></maths>/L_o, from the desired direct axis current, i<maths id="math0142"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0142.tif" /></maths>. The resultant is then input to another PI controller 116, which generates v'_sd as a measurement of direct axis current error. PI controller 116 is similar to the PI controller 114 for the quadrature component. The value of v'_sd is then compensated by adding a decoupling factor consisting of the two voltage coupling terms on the right side of equation (28), which results in v<maths id="math0143"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0143.tif" /></maths> as follows:<maths id="math0144" num="(33)"><math display="block"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>sd</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msubsup><mrow><mtext> = v</mtext></mrow><mrow><mtext>sd</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><mtext> + </mtext><mfrac><mrow><msub><mrow><mtext>(1-σ) L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><mtext></mtext><msubsup><mrow><mover accent="true"><mrow><mtext>λ</mtext></mrow><mo>̇</mo></mover></mrow><mrow><mtext>r</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext> L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub></mrow></mfrac><mtext> - </mtext><mfrac><mrow><msub><mrow><mtext>σ L</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msubsup><mrow><mtext> ω</mtext></mrow><mrow><mtext>s</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> i</mtext></mrow><mrow><mtext>sq</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>R</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP1432115A2_D0144.tif" /></maths>

0054Once the desired field coordinate voltages, v<maths id="math0145"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sd</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0145.tif" /></maths> and v<maths id="math0146"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0146.tif" /></maths>, have been generated, they are transformed into 3-phase stator voltages by equations (3) and (4), resulting in v<maths id="math0147"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s1</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0147.tif" /></maths>, v<maths id="math0148"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s2</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0148.tif" /></maths>, and v<maths id="math0149"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>s3</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0149.tif" /></maths>. These reference voltages are modulated by a triangular carrier wave to generate the PWM commutation signals, D₁, <maths id="math0150"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0150.tif" /></maths>₁, D₂, <maths id="math0151"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0151.tif" /></maths>₂, D₃, and <maths id="math0152"><math display="inline"><mrow><mover accent="true"><mrow><mtext>D</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1432115A2_D0152.tif" /></maths>₃ that are sent to the selector 100 (Figure 5). In the preferred embodiment, the triangular carrier wave has a frequency of about 8 kHz, while the comparisons between the reference voltages and the carrier wave are performed continuously or at a rate much higher than 8 kHz.

0055Figure 12 illustrates how a computer program is structured for execution in the digital signal processor of the generator control unit. The program consists primarily of a main loop and an interrupt service routine. The main loop initializes the necessary variables, and then loops until it is interrupted, which occurs periodically, at about 8 kHZ in the preferred embodiment. The interrupt service routine performs the calculations necessary for generating the PWM commutation signals, and then updates the control variables. Upon interrupt, the interrupt service routine first reads the stator currents, and then executes the code of either the current controller or the voltage controller to generate and output the appropriate switch states. The interrupt routine then reads a value for the torque reference, T_ref, and updates the corresponding value of the desired quadrature axis current, i<maths id="math0153"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>sq</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0153.tif" /></maths>. The routine then reads the speed sensor and computes a new value for the rotor speed, ω_r. The routine updates the value for desired rotor flux, λ<maths id="math0154"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>r</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0154.tif" /></maths>, and the desired instantaneous rotor flux angle, θ<maths id="math0155"><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>*</mtext></mrow><mrow><mtext>s</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0155.tif" /></maths>. The interrupt routine then returns to the main loop, which waits until the next periodic interrupt, at which time the updated values will be used to compute the switch states. All constants used in the calculations are computed in advance, and the expressions are arranged to avoid division, which executes relatively slowly in a DSP. The steps performed in the computer program can be executed in different order than is shown in Figure 12, but it is important to calculate and output the switch states as soon as possible after reading the actual stator currents.

0056Turning now to the inverter side of the wind turbine system, the details of the inverter control unit 88 are shown in Figures 13-15. Like the generator control unit 76, the inverter control unit is preferably implemented with a digital signal processor, a Texas Instruments model TMS320C25. Computer code for implementing the inverter control function in a DSP is disclosed in the microfiche appendix.

0057The inverter control unit controls the inverter switch matrix to supply to the utility grid power with adjustable power factor and low THD. The inverter and its control unit can supply or absorb reactive power as needed by adjusting the phase difference between the output voltage and current. Low harmonic distortion is achieved in the same way as in the current controller of the generator control unit, by periodically minimizing a distortion index. In addition, the inverter control unit also controls the voltage of the DC voltage link, to maintain it at a desired value.

0058As shown in Figure 13, the inverter control unit uses the output voltage as a sinusoidal waveform reference, rotates the reference waveform by a certain phase angle to generate a rotated reference waveform, or "template", then multiplies the template waveform by a factor, I_ref, derived from the DC link voltage, v_dc, to generate a desired current waveform. The actual currents are compared to the desired currents to generate the PWM commutation signals for the inverter switches. All of the calculations of the inverter control unit are performed periodically. In the preferred embodiment, the DSP cycles through its calculations every 125 microseconds, equal to a rate of 8 kHz.

0059The multiplication factor, I_ref, is calculated as follows. The measured DC link voltage, v_dc, is subtracted from a desired value of the DC link voltage, v<maths id="math0156"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>dc</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0156.tif" /></maths>, to generate an error, which is then input to a PI controller 130. The PI controller supplies a proportional/integral output of the form:<maths id="math0157" num="(24)"><math display="block"><mrow><msub><mrow><mtext>I</mtext></mrow><mrow><mtext>ref</mtext></mrow></msub><msub><mrow><mtext> = k</mtext></mrow><mrow><mtext>p</mtext></mrow></msub><msubsup><mrow><mtext> (v</mtext></mrow><mrow><mtext>dc</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - v</mtext></mrow><mrow><mtext>dc</mtext></mrow></msub><msub><mrow><mtext>) + K</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msubsup><mrow><mtext> ∫ (v</mtext></mrow><mrow><mtext>dc</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext> - v</mtext></mrow><mrow><mtext>dc</mtext></mrow></msub><mtext>) dt</mtext></mrow></math><img file="EP1432115A2_D0157.tif" /></maths> where k_p and k_i are coefficients selected to provide adequate stability. In discrete time, equation (34) can be evaluated as follows:<maths id="math0158" num="(35)"><math display="block"><mrow><msub><mrow><mtext>I</mtext></mrow><mrow><mtext>ref</mtext></mrow></msub><msub><mrow><mtext>(k) = I</mtext></mrow><mrow><mtext>ref</mtext></mrow></msub><msub><mrow><mtext>(k-1) + (k</mtext></mrow><mrow><mtext>p</mtext></mrow></msub><msub><mrow><mtext> + Δt k</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msubsup><mrow><mtext>) (v</mtext></mrow><mrow><mtext>dc</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k) - v</mtext></mrow><mrow><mtext>dc</mtext></mrow></msub><mtext>(k))</mtext><mspace linebreak="newline" /><msub><mrow><mtext> - k</mtext></mrow><mrow><mtext>p</mtext></mrow></msub><msubsup><mrow><mtext> (v</mtext></mrow><mrow><mtext>dc</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k-1) - v</mtext></mrow><mrow><mtext>dc</mtext></mrow></msub><mtext>(k-1))</mtext></mrow></math><img file="EP1432115A2_D0158.tif" /></maths>

0060The rotational transformation of the reference waveform can be accomplished in either 3-phase or 2-phase coordinates. In 3-phase coordinates, the template waveform, rotated by an angle φ, is calculated as follows:<maths id="math0159"><img file="EP1432115A2_D0159.tif" /></maths><maths id="math0160"><img file="EP1432115A2_D0160.tif" /></maths><maths id="math0161" num="(38)"><math display="block"><mrow><msub><mrow><mtext>v</mtext></mrow><mrow><mtext>t3</mtext></mrow></msub><msub><mrow><mtext> = -v</mtext></mrow><mrow><mtext>t1</mtext></mrow></msub><msub><mrow><mtext> - v</mtext></mrow><mrow><mtext>t2</mtext></mrow></msub></mrow></math><img file="EP1432115A2_D0161.tif" /></maths> These values can be transformed into the 2-phase α,β coordinate system using equation (1). The result is v_tα and v_tβ. The template values that result from the rotational transformation, v_tα and v_tβ, are then multiplied by the value of I_ref to generate the desired 2-phase output currents, i<maths id="math0162"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0162.tif" /></maths> and i<maths id="math0163"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0163.tif" /></maths>. The desired output currents are input into a current controller 132, which compares them to the actual currents and generates the appropriate PWM commutation signals for the inverter switches.

0061The current controller 132 of the inverter control unit can be implemented in the several ways described above for the current controller 96 of the generator control unit, including the delta modulator. Preferably, however, the current controller 132 generates switch states that minimize the distortion index, J, in a manner similar to that described above with respect to Figures 9 and 10. Referring to Figure 14, the inverter current controller generates desired output voltages, v<maths id="math0164"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0164.tif" /></maths> and v<maths id="math0165"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0165.tif" /></maths>, according to the following equations:<maths id="math0166" num="(39)"><math display="block"><mrow><msubsup><mrow><mtext>v</mtext></mrow><mrow><mtext>oα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext>(i</mtext></mrow><mrow><mtext>oα</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k+1)-i</mtext></mrow><mrow><mtext>oα</mtext></mrow></msub><mtext>) </mtext></mrow><mrow><mtext>Δt</mtext></mrow></mfrac><msub><mrow><mtext> + v</mtext></mrow><mrow><mtext>oα</mtext></mrow></msub></mrow></math><img file="EP1432115A2_D0166.tif" /></maths><maths id="math0167" num="(38)"><math display="block"><mrow><msub><mrow><mtext>v*</mtext></mrow><mrow><mtext>oβ</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msub><mrow><mtext>L</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><msubsup><mrow><mtext>(i</mtext></mrow><mrow><mtext>oβ</mtext></mrow><mrow><mtext>*</mtext></mrow></msubsup><msub><mrow><mtext>(k+1)-i</mtext></mrow><mrow><mtext>oβ</mtext></mrow></msub><mtext>) </mtext></mrow><mrow><mtext>Δt</mtext></mrow></mfrac><msub><mrow><mtext> + v</mtext></mrow><mrow><mtext>oβ</mtext></mrow></msub></mrow></math><img file="EP1432115A2_D0167.tif" /></maths> where: L_o is the output impedance;       i<maths id="math0168"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0168.tif" /></maths>(k+1) and i<maths id="math0169"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0169.tif" /></maths>(k+1) are the desired output currents at time = k+1 in α,β coordinates;       i_oα and i_oβ are the measured output currents in α,β coordinates;       v_oα and v_oβ are the measured output voltages in α,β coordinates; and       Δt is the sample period.

0062The desired output voltages, v<maths id="math0170"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oα</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0170.tif" /></maths> and v<maths id="math0171"><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>*</mtext></mrow><mrow><mtext>oβ</mtext></mrow></mfrac></mrow></math><img file="EP1432115A2_D0171.tif" /></maths>, are then compared to the seven available voltage vectors, and the switch state associated with the nearest voltage vector is selected and output to the inverter switches. Determining the nearest voltage vector is accomplished in the same manner as explained above with respect to the generator current controller of Figures 9 &amp; 10.

0063A computer program directs the operation of the digital signal processor of the inverter control unit to perform the calculations described above. As shown in Figure 15, the computer program is structured like that of the generator control unit in that a main loop executes until periodically interrupted, and then an interrupt service routine updates the sensed inputs, PWM switch state, and calculated variables. The interrupt service routine running on the inverter control unit DSP first reads the output currents, output voltages and DC link voltage. Then it calculates the optimal switch state, which it outputs to the inverter switches. Then the interrupt routine performs calculations necessary for the next calculation of switch state by rotating the voltage reference to define the template waveform, computing the multiplication factor I_ref, and multiplying the template waveform by I_ref to compute the desired currents for the next interrupt. Then control passes to the main loop, where it waits until interrupted again. In the preferred embodiment, interruptions occur at a rate of about 8 kHz.

0064Referring back to Figure 2, the power factor controller 54 can control either the power factor angle, φ, or the magnitude of reactive power to supply VARs (Volt-Ampere-Reactive) to the utility. The type of power factor control is specified by the operation mode signal that is input into the power factor controller. If the power factor angle is controlled, the power factor controller 54 outputs to the inverter control unit 88 a constant value of φ that is defined by the power factor input signal. If the reactive power is controlled, the power factor controller monitors the reactive power feedback signal, Q_fb, compares it to a desired reactive power level defined by the reactive power input signal, and adjusts the power factor angle, o, to obtain the desired reactive power.

0065The power factor correction facility of the inverter control unit can be utilized even when the wind turbine is not operating, by operating in a static VAR mode. To do so, the power factor controller 54 sets the power factor angle φ equal to 90°. After the DC link is charged up by the utility through the inverter, the inverter control unit operates as described above to rotate the output current to lead the voltage by 90°. This supplies reactive power to the utility to counteract reactive loads drawing power from the utility grid.

0066From the above description, it will be apparent that the invention disclosed herein provides a novel and advantageous variable speed wind turbine. The foregoing discussion discloses and describes merely exemplary methods and embodiments of the present invention. As will be understood by those familiar with the art, the invention may be embodied in other specific forms without departing from essential characteristics thereof. For example, some aspects of the current controller can be performed in various ways equivalent to those disclosed herein, including using hysteresis control or forced oscillation with triangular intersection. The generator need not be a 3-phase squirrel-cage induction generator, but may be any multiphase generator, including a synchronous generator. Certain aspects of the generator control could be performed open-loop, instead of the closed loop control disclosed herein. Also, the power converter could have a DC current link, or could be a cyclo-converter instead of a DC voltage link. In addition, the torque monitor could directly measure torque with a transducer, instead of inferring torque from the measured stator currents. Accordingly, the disclosure of the present invention is intended to be illustrative, but not limiting, of the scope of the invention, which is set forth in the following claims.