# Power losses in pulsed voltage source inverters/rectifiers with sinusoidal currents

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1 ree-wheeling diode Turn-off power dissipaion: off/d = f s * E off/d (v d, i LL, T j/d ) orward power dissipaion: fw/t = 1 T T 1 v () i () d Neglecing he load curren ripple will resul in: fw/d = i Lavg * v (i Lavg, T j/d ) * (1-D T ) = i Lavg * v (i Lavg, T j/d ) * (D D ) D D = diode duy cycle The calculaion of IGBT and diode forward power dissipaion is based on an ideal duy cycle (neglecing he share he swiching ime conribues o he oal cycle duraion). Seleced raings for energy dissipaions during swiching as well as for he IGBT and diode forward volage drop are indicaed in he daashees (see chaper 2) ower losses in pulsed volage source inverers/recifiers wih sinusoidal currens Basic circui: igure 3.5 shows ideal characerisics of an inverer phase for a sinusoidal modulaion according o he sinusoidal pulse-widh modulaion. 140

2 i C1 i 1 V d /2 IGBT T1 Diode D1 V 1 i 1 V d /2 IGBT T2 Diode D2 i C2 i 2 v ref ; v h v ref () v h () i 1 ; v 1 1/f S 1/fou v 1 () v 1(1) () i 1 () i C1 ϕ 2 fou fw/t1 i 2 fw/d2 igure 3.5 Converer phase wih sinusoidal modulaion according o sinusoidal pulse-widh modulaion In he sinusoidal pulse-widh modulaion he pulse paern is generaed by comparison of a reference volage v ref o an auxiliary conrol volage v h, whereby he fundamenal frequency of he AC-parameers f ou is deermined by he reference volage and he swiching or pulse frequency of he swiches f s by he auxiliary conrol volage. The inersecions of reference and auxiliary conrol volage are he basis for commuaion imes in he converer phase. If vˆ ref vˆ h, his is called linear modulaion mode of he inverer. The following explanaions refer o he linear modulaion mode. urhermore, i is presupposed ha he fundamenal frequency of he AC-parameers is exceeded by he pulse frequency by far. Volage uilizaion of he converer may be expressed by he degree of modulaion m. I indicaes he raio beween fundamenal harmonics ampliude of he AC-volage and 50 % of he DC-link volage. In case of a pure sinusoidal reference volage, he degree of linear modulaion will be 0 m

3 The phase shif beween he fundamenal harmonics of AC curren and volage is described by he angle ϕ. The curren and volage characerisics for IGBTs and diodes, which are ime-shifed, will urn ou o be idenical due o he symmerical srucure of he inverer circui. Therefore, i is enough o consider jus one IGBT (here T1) and one diode (here D2) wih reference o he calculaion of power dissipaion (he resul is hen muliplied by he corresponding number of IGBTs/ diodes inegraed in he inverer). In conras o he calculaions under chaper duy cycle, load curren and juncion emperaure are no consan under saic operaion, bu vary depending on he fundamenal frequency of he AC side (e.g. 50/60 Hz). This means ha swiching and forward power dissipaions of IGBTs and diodes are subjec o emporal variabiliy and require a exensive calculaion of sysem power losses. Consequenly, exac resuls canno be produced wih grealy simplified calculaion procedures. Two calculaion possibiliies are o be inroduced in he following. 1. Approximaion of componen characerisics by polynominal equaions (deailed in [194]) In his calculaion procedure, he dependencies of ransisor and diode forward on-sae volages on load curren and juncion emperaure as well as of ransisor and diode swiching energy dissipaions on load curren, DC-link volage and juncion emperaure are approximaed by polynominal equaions of he ype y = f(x) = A + Bx + Cx². or his, he available componen parameers have o be aken from he daashees or deermined by simple pulse converer es circuis, which, however, requires considerable effor. The following se-up of he polynominal equaions may be done by using convenional curvefiing sofware. The coefficiens A-C of a following equaions comprise he deermined dependencies of he parameers. Accordingly, equaions may be se up o calculae he average energy dissipaion. The following simplificaions have been presupposed: - ransisor and diode swiching imes are negleced, - emporally consan juncion emperaures (permissible if f ou =..50 Hz), - linear modulaion of he converer, - neglecing he swiching frequency ripple of he AC-curren. orward power dissipaion Including forward characerisic approximaion of IGBT and diode according o y = A + Bx and considering he emperaure coefficiens of he forward on-sae volages, resuls in he following equaions: 1 dead A fw/t Bfw/T A fw/t Bfw/T fw/t1 = - î1 + m cosϕ î1 (3.1) 2 TS π 4 8 3π 142

4 Diode D2: 1 dead A fw/d Bfw/D A fw/d Bfw/D fw/d2 = + î1 m cosϕ î1 (3.2) 2 TS π 4 8 3π igure 3.6 explains he influence of swiching deadime dead on forward energy dissipaions ( dead deermines he effecive duy cycles) wih he example of a 1200 V/50 A-IGBT-module. Especially if high pulse frequencies are involved, he arm-inerlock-deadime dead has o be considered in he calculaion of he average power forward dissipaion. fwreal - fwideal fwreal [%] IGBT Diode ,02 0,04 0,06 dead /T S 0,08 igure 3.6 orward power dissipaions versus swiching deadimes (i 1eff = 25 A; m = 0.8; cos ϕ = 0.8) Swiching losses The following equaions resul from he approximaion of he dependency of swiching losses on he curren according o y = Bx + Cx² in consideraion of emperaure and volage coefficiens of he swiching losses: Diode D2: Bon+ off/t Con+ off/t on+ off/t1 = f s î1 π 4 (3.3) Boff/D Coff/D off/d1 = f s î1 π 4 (3.4) igure 3.7 shows one resul of his calculaion mehod wih he example of a 1200 V/50 A- IGBT-dual module in an inverer. 143

5 fw [W] m * cosφ= IGBT Diode I RMS [A] sw [W] V d =700 V 500 V IGBT Diode I RMS [A] igure 3.7 a) orward power dissipaions ( dead = 5 µs, T j = 125 C) b) Swiching losses (f s = 10 khz, T j = 125 C) The produc of m * cos ϕ deermines how he oal power dissipaion is divided up on IGBT and diode (see also chaper ). m * cos ϕ = 0.64 m * cos ϕ = 0.1 m * cos ϕ = represens an operaing poin in inverer mode (moor load) represens an operaing poin in moor saring mode represens an operaing poin in recifier mode The procedure for calculaion of IGBT and diode power dissipaion described above shows very exac resuls, however he deerminaion of parameers requires grea effors. Therefore, he following grealy simplified calculaion mode o produce a rough calculaion can be recommended. 2. Simplified, linear approach [274] Assumpions: - ransisor and diode swiching imes as well as swiching inerlocking imes are negleced, - emporally consan juncion emperaures (permissible if f ou =..50 Hz.), 144

6 - linear modulaion of he converer, - neglecing swiching frequency ripple of he AC curren (sinusoidal curren), - f s >> f ou. orward on-sae power dissipaion: If he oupu characerisics are linearized wih y = A + Bx, he emporal dependency of he sauraion volage v CEsa may be expressed as follows: vcesa () = VCE0 + rce i C () = VCE0 + rce î1 sin ω wih: V CE0 = hreshold volage of he oupu characerisic wih i C = 0 r CE = on-sae resisance of he IGBT (rae of rise of he oupu characerisic) Considering he sinusoidal dependency of duy cycles versus ime, he forward power dissipaion of IGBT T1 may be calculaed according o 1 VCE0 rce VCE0 rce fw/t1 = î1 + m cosϕ î1 + î1 (3.5) 2 π 4 8 3π Diode D2: If he oupu characerisics are linearized wih y = A + Bx, he emporal dependency of he foward on-sae volage v may be expressed as follows: v () = V0 + r i () = V0 + r î1 sin ω wih: V 0 = hreshold volage of he forward characerisic wih i = 0 r = on-sae resisance of he diode (rae of rise of he oupu characerisic) Considering he sinusoidal dependency of duy cycles versus ime, he forward power dissipaion of diode D2 may be calculaed according o 1 V0 r V0 r fw/d2 = î1 m cosϕ î1 + î1 (3.6) 2 π 4 8 3π Swiching losses rovided ha he energy dissipaion during swiching is linearly dependen on he collecor curren, he oal power dissipaion of an IGBT may be calculaed wih [ E on/t ( î1 ) E off/t ( î1 )] 1 on+ off/t1 = f s + π Equaion 3.7 is acually based on he assumpion ha he IGBT swiching losses generaed during one sine half-wave are abou idenical o he swiching losses generaed if an equivalen direc curren is applied, which would correspond o he average value of he sine half-wave. IGBT swiching losses are approximaely converible linearly o oher DC-link volages. (3.7) 145

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