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PHASEJ/OLTAGEPhase Voltage ReconstructionDescriptionThis software module calculates three phase voltages impressing to the 3-ph electric motor (i e., induction or synchronous motor) by using the conventional voltage-source inverter. Three phase voltages can be rec on structed from the DC-bus voltage and three switching fun ctions of the upper power switching devices in the inverter. In addition, this software module also in eludes the clarke transformation changing from three phase voltages into two stationary dq-axis phase voltages.MfuncVIMfuncV2MfuncVSDcBusVoEVphaseA.VphaseB”PHASE_VOL VphaseCy TAGE CALC_ Valpha .Vbeta 新AvailabilityThis IQ module is available in one interface formatModule Properties1) The C interface versionType: Target Independent, Application DependentTarget Devices: x281x or x280xC Version File Names: volt calc.c, volt calc.hIQmath library files for C: IQmathLib h. IQmath.libItemC versionCommentsCode Size0144/144 words(x281x/x280x)Data RAM0 words*xDAIS readyNoXDAIS componentNoIALG layer not implementedMultiple instancesYesReentrancyYes Each pre-initialized jq PHASEVOLTAGE structure consumes 22 words in the data memorya Code size mentioned here is the size of the calc() functionDigital Control Systems (DCS) GroupTexas Instruments2C InterfaceC InterfaceObject Definitiontypedef struct q DcBusVolt;q MfuncVI;q MfuncV2:q MfuncV3;Uint32 OutOfPhase; iq VphaseA;q VphaseB,jq VphaseC;q Valpha;q Vbeta, void (*calc)(); PHASEVOLTAGE;The structure of PHASEVOLTAGE object is defined by following structure definitionII Input DObus voltage/Input Modulation voltage phase AII Input. Modulation voltage phase BII Input Modulation voltage phase CII Parameter: Out of Phase adjustment (0 or 1)II Output. Phase voltage phase AII Output. Phase voltage phase BII Output Phase voltage phase CII Output Stationary d-axis phase voltageII Output Stationary q-axis phase voltageII Pointer to calculation function typedef PHASEVOLTAGEa PHASEVOLTAGE.handle;ItemNameDescriptionFormatRange(Hex)InputsDcBusVoltDC-bus voltageGLOBAL.Q80000000-7FFFFFFFMfuncVISwitching function of upper switching device 1GLOBAL_Q80000000-7FFFFFFFMfuncV2Switch!ng function of upper switching device 2GLOBAL_Q80000000-7FFFFFFFMfuncV3Switching function of upper switching device 3GLOBAL_Q80000000-7FFFFFFFOutputsVphaseAne-neutral phase voltage AGLOBAL Q80000000-7FFFFFFFVphaseALjnneutral phase voltage AGLOBAL.Q80000000-7FFFFFFFVphaseAUne-neutral phase voltage AGLOBAL.Q80000000-7FFFFFFFValphaStationary d-axis phase voltageGLOBAL Q80000000-7FFFFFFFVbetaStationary q-axis phase voltageGLOBAL.Q8000000Q-7FFFFFFFGLOBAL Q valued between 1 and 30 is defined in ttie IQmathLib h header fileSpecial Constants and Data typesPHASEVOLTAGEThe module defi nition is created as a data type. This makes it con vement to in stance an in terface to phase voltage reco nstructio n. To create multiple insta nces of the module simply declare variables of type PHASEVOLTAGEPHASEVOLTAGE_handleUser defined Data type of pointer to PHASEVOLTAGE modulePHASEVOLTAGE_DEFAULTSStructure symbolic constant to initialize PHASEVOLTAGE module. This provides the initial values to the terminal variables as well as method pointers.Methodsvoid phase_voltage_calc(PHASEVOLTAGE_handle);This definition implements one method viz, the phase voltage reconstruction computation function. The in put argument to thisfunctio n is the module handle.Module UsageInstantiationThe following example instances two PHASEVOLTAGE objectsPHASEVOLTAGE voltl, volt2；InitializationTo Instanee pre-initialized objectsPHASEVOLTAGE voltl = PHASEVOLTAGE.DEFAULTS;PHASEVOLTAGE volt2 = PHASEVOLTAGE DEFAULTS；Invoking the computation functionvoltl calc(&volt1);volt2.calc(&volt2);ExampleThe following pseudo code provides the information about the module usage.main()void interrupt periodicjnterrupt_isr()voltl DcBusVolt = dc_volt1;II Pass irputs to voltlvoltl MfuncVI = M1 1;II Pass irputs to voltlvoltl MfuncV2 = M2J;II Pass irputs to voltlvoltl ,MfuncV3 = M3 1;II Pass irputs to voltlvolt2.DcBusVolt = de volt2;II Pass irputs to volt2volt2.MfuncV1 二 M1 2;II Pass irputs to volt2volt2.MfuncV2 二 M2 2;II Pass irputs to volt2volt2.MfuncV3 = M3_2;II Pass irputs to volt2voltl .calc(&volt1);II Call compute function for voltlvolt2.calc(&volt2);II Call compute function for volt2Vd1 = voltl Valpha;II Access the outputs of voltlVq1 = voltl Vbeta;/ Access the outputs of voltlVd2 = volt2.Valpha;II Access the outputs of volt2Vq2 = volt2 Vbeta;II Access the outputs of volt2Digital Control Systems (DCS) GroupTexas Instruments4Technical BackgroundTechnical BackgroundThe phase voltage of a general 3-ph motor (Van? Vbn, and V) can be calculated from the DC-bus voltage (Vdc) and three upper switching fjnctions of inverter (Si, S2, and S3). The 3-ph windings of motor are connected as the Y connection without a neutral return path (or 父ph, 3-wire system). The overall system can be shown in Figure 1.Figure 1: Voltage-source inverter with a 3-ph electric motorDigital Control Systems (DCS) GroupTexas Instruments#Technical BackgroundDigital Control Systems (DCS) GroupTexas Instruments#Technical BackgroundEach phase of the motor is simply modeled as a series impedance of resista nee and inductance (r, L) and back emf (ea, eb, ej Thus three phase voltages can be computed asan a n=1 1 + L + ea3 dt 3(1)dt+ ebcncn= ici + Lc dt+ ecSumming these three phase voltages, yieldsVa4-Vb+Vc-3Vn = (ia+ib+ic + L毗 +%+ )(4)Without a neutral return path, according to KCL, i.e., i3 +ib +ic = 0, and the back emfsare bala need and symmetrical due to the 3-ph win ding structures, i.e., e3 +eb +ec = 0, so (4) becomesV3n + Vbn + vcn = 0(5)Furthermore, the neutral voltage can be simply derived from (4)-(5) asNow three phase voltages can be calculated as2= Va-(Va+Vb + Vc)=-Va-Vb-Vc(6)(7)an(8I7I产+；+；)育：_产_尹(9)Three voltages V, Vb, Vc are related to the DC-bus voltage (Vdc) and three upper switching functions (S1( S2. S3) as the following relation.(10) Vb = S2 Vdc(11)V = S3vdc(12)where Si, S2, S3 二 either 0 or 1, and S4= 1-S1t S5 = 1-S2r and Se = I-S3(13)As a result, three phase voltages in (7)(9) can also be expressed in terms of DC-bus voltage and three upper switching functions as follows(14)(15)(16)Digital Control Systems (DCS) GroupTexas Instruments6Technical BackgroundDigital Control Systems (DCS) GroupTexas Instruments#Technical BackgroundIt is emphasized that the S2, and S3 are defined as the upper switching functions. If the lower switch i ng functio ns are available in stead, then the out-of-phase correction of switching functions is required in order to get the upper switching functions as easily computed from equation (13).Next the clarke transformation changing from three phase voltages (Vanf Vbn, and V/ to the stationary dq-axis phase voltages (V；, and V；) are applied by using the following relationship Because of the balanced system (5), V is not used in clarke transformation.(17)V；=-(VM + 2Vbn)(18)Figure 2 depicts the abc-axis and stationary dq-axis components for the stator voltages of motor. Notice that the notation of the stationary dq-axis is sometimes used as the stationary aP-axis, accordingly.Figure 2: The abc-axis and statio nary dq-axis comp on ents of the stator phase voltagesNext, Table 1 shows the correspondence of notations between variables used here and variables used in the program (i.e., volt_calc.c, volt_calc.h). The software module requires that both in put and output variables are in per unit values.Equation VariablesProgram VariablesInputsSiMfuncVIS2MfuncV2SoMfuncV3VdcDcBusVoltOutputsV.nVphaseAvbnVphaseBVCnVphaseCVsVdsValphaVs VVbetaTable 1: Correspondence of notationsDigital Control Systems (DCS) GroupTexas Instruments7