A Comparative Efficiency Study of Silicon-basedSolid State Transformers

Hengsi Qin and Jonathan W. KimballDepartment of Electrical and Computer Engineering

Missouri University of Science and Technology141 Emerson Electric Co. Hall

301 W. 16th St., Rolla, MO 65409, USA

AbstractSolid state transformers (SSTs) have lower physicalprofiles than traditional 60 Hz transformers and provide activecontrol of power flow. However, they are not as efficient astraditional 60 Hz transformers because of the presence of powerelectronic converters. This work presents an analytical loss cal-culation model of an SST. It evaluates conduction loss, switchingloss and transformer loss in four candidate SST topologies. Lossbreakdown under both rated-load and light-load conditions arecompared for all four configurations.

Index TermsSolid State Transformer, Efficiency, Soft Switch-ing

I. INTRODUCTION

Power electronic converter-based solid state transformers(SSTs) have become attractive during recent years. Thanksto high-frequency modulation, the volume and weight ofSSTs can be much smaller than those of conventional 60 Hztransformers [1]. More importantly, SSTs provide active powerflow control and ports for distributed generation (DG) sourcesat the distribution level; such ports are essential to the futurerenewable energy power grid [2]. However, an SST must havea power efficiency profile similar to that of a conventionalpassive transformer (typically 97%).

In an SST, the presence of power converters reduces effi-ciency by introducing conduction and switching losses. Softswitching is one feasible solution, facilitated either by addingauxiliary devices (auxiliary resonant commutated pole, orARCP) [3] or by using leakage inductance of high-frequencytransformers (dual active bridge converter, or DAB) [4] [5].However, soft switching adds circulated energy, trading con-duction loss for switching loss.

Fig. 1 shows four potential 20 kVA 7.2 kV/240 V SSTconfigurations using silicon-based power device. All havepower electronic converters that can actively control powerflow; therefore, they are categorized as SSTs. These topologiesare: (1) a back-to-back voltage source converter (VSC) with aconventional 60 Hz transformer (SST1); (2) a three-stage SSTwith a two-level input-series front end (SST2); (3) a three-stage SST with four-level flying capacitor front end; and (4)a single-stage ac-ac DAB converter-based SST (SST4).

This paper first reviews the operational principles for allfour SST topologies and zero voltage switching (ZVS) com-mutations using ARCP or leakage inductance. It then presentsanalytical loss calculations of both semiconductor device and

transformer and illustrates the loss breakdown in the SST.Finally, it compares the efficiency of all four topologies underdifferent load conditions and identifies key targets for lossreduction.

II. OPERATION PRINCIPLEA. SST Configurations

The following briefly reviews the hardware configurationand operational principles of four SST topologies:

1) Back-to-back VSC with 60 Hz transformer (SST1): SST1is a cascade connection of a 60 Hz passive transformer anda low-voltage ac-dc-ac converter. It lacks the advantage of ahigh frequency transformer; however, it does have power flowcontrollability. So it is defined as an SST configuration. It setsa base line for evaluation of the efficiency of SSTs.

2) Three-stage SST with two-level rectifier (SST2): SST2uses input-series-output-parallel configuration because avail-able silicon-based devices are unable to block peak voltageon the 7.2 kV side. Each two-level rectifier converts one-third of the input voltage to a 4 kV dc bus. Three dc-dc DAB converters, whose outputs are parallel-connected,provide galvanically isolated power conversion to a 400 V dcbus. An inverter converts low voltage dc to utility ac voltage.SST2 is the most complex configuration. However, It has thefull features of an SST: compact high frequency transformer,power flow control, power factor correction, and a low voltagedc bus for DG connection.

3) Three-stage SST with multi-level rectifier (SST3): SST3is similar to SST2 at the DAB and inverter stages. Thedifference is at the rectifier stage. SST3 uses one flyingcapacitor multilevel ac-dc converter to provide a 12 kV dcbus for three paralleled-connected dc-dc DAB converters.

4) Single stage ac-ac DAB converter (SST4): SST4 usesan direct ac-ac version of a DAB converter [5]. It comprisesthree ac-ac DAB converters in an input-series-output-parallelconnection. This simple topology controls only active powerand lacks a dc port for renewable energy.

B. Soft Switching Process1) ARCP: ARCP adds a bi-directional switch pole between

the neutral point of dc bus and the midpoint of a mainswitch leg. Auxiliary switches are turned on during the mainswitching transient and they provide enough inductive energy

978-1-4244-5287-3/10/$26.00 2010 IEEE 1458

(a) SST1 (b) SST2

(c) SST3

iVPr

outC

SecVinL

outLN:1

inCleakL

High-freq transformer

1Q

2Q

3Q

4Q

5Q

6Q

7Q

8Q

leakL

N:1

inCleakL

High-freq transformer

1Q

2Q

3Q

4Q

5Q

6Q

7Q

8Q

leakL

N:1

inCleakL

High-freq transformer

1Q

2Q

3Q

4Q

5Q

6Q

7Q

8Q

leakL

(d) SST4

Fig. 1. Four candidate SST topologies

to resonate with snubber capacitors. This limits the dv/dt ofthe main switches during transients and achieves ZVS for boththe main switches and auxiliary switches. There is fixed andvariable timing for ARCP [6]. For simplicity, only fixed-timingis analyzed here. ARCP is always used for switching transientsfrom a diode to a transistor (Fig 2(a)). For transistor to diodeswitching, the auxiliary switches are not used at heavy loads,when there is adequate inductive energy to achieve ZVS (Fig2(c)). At light loads, the auxiliary circuit provides the extraenergy required to complete the ZVS transient.

2) DAB: Similar to ARCP, leakage inductance resonateswith snubber capacitors to achieve ZVS. By resonating leakageinductance and snubber capacitors, ZVS is achieved oncethere is enough energy circulating in transformer leakageinductance.

III. LOSS EVALUATIONThe design of a distribution level 20 kVA SST was per-

formed for all four candidate configurations. The key param-eters of switching device in each stage are listed in Table I.Three major sources of loss were evaluated: conduction loss,switching loss, and transformer loss. This study did not addresspower losses in the gate driver, controller, and other accessorycircuits.A. Conduction Loss

1) PWM Voltage Source Converter: Each power semi-conductor device in the current conduction path has forwardvoltage drop, which contributes to conduction loss. The for-ward voltage can be modeled as

vce = vce0 +Ron,tif (1)for a transistor and

vf = vf0 +Ron,dif (2)

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(a) Diode to Transistor (b) Transistor to Diode without ARCP (c) Transistor to Diode with ARCP

Fig. 2. ARCP switching transisent

TABLE ISWITCHING DEVICE PARAMETERS

HV Rectifier and DAB LVDAB HV side LV side Inverter

Transistor Ron 64 m 25 m 3.7 mTransistor Vce0 2.6 V 1.05 V 0.9 V

Diode Ron 17 m 10 m 3 mDiode Vf0 2.67 V 0.9 V 0.95 V

Eon 61.2 mJ 2.5 mJ 8.5 mJ

Eoff 30.2 mJ 1.8 mJ 5.5 mJ

Err 35.1 mJ 1.2 mJ 3.5 mJ

for a diode.When using SPWM, the duty ratios of transistor and diode

are dT =12 (1 +m sin (t)) and dD =

12 (1m sin (t)),

respectively [7]. Integrating instantaneous conduction loss v i d over one grid period, the conduction loss of transistor is

Pcond,T =

(1

2+

4

3m cos

)I2mRon,t

4pi+(2 +

pi

2cos

) vce0Im4pi

,

(3)and the conduction loss of diode is

Pcond,D =

(1

2 4

3m cos

)I2mRon,d

4pi+(2 +

pi

2cos

) vf0Im4pi

.

(4)A high-voltage rectifier is a voltage source converter controlledby PWM with a power factor correction loop. Therefore, itsconduction pattern is similar to that of a VSC inverter with afixed load power factor at steady state. Thus, the conductionloss of high-voltage rectifier can also be calculated using (3)and (4).

2) Dual Active Bridge Converter: DAB converters transferactive power from the leading bridge to the lagging bridge.Once the amount of transferred power is determined, the phaseshift angle can be calculated as

=pi

2

(1

1 4NLrP

piViVo

). (5)

Then the boundary currents between switching states (Fig. 3)are:

i0 =(pi 2) Vo piVi

2Ll, (6)

andi =

piVo (pi 2)Vi2Ll

. (7)

For dc-dc DAB converters used in the SST2 and SST3,transistors are conducting when transformer instantaneouscurrent is positive, and diodes are conducting at negativecurrent. Finally, the conduction loss of leading bridge is

Pcond,lead = 2

(i0vfd1 + ivce

(d2 +

pi pi

)), (8)

and conduction loss of lagging bridge is

Pcond,lag = 2

(i0vf

(d1 +

pi pi

)+ ivced2

), (9)

where d1 = i0i0+i and d2 =i

i0+i.

The conduction loss of ac-ac DAB converters (SST4) canbe calculated in a different way. Note that there are alwaysseries-connected IGBT-diodes in the conduction path of eachswitching cell in the ac-ac DAB converters.The current wave-form showed in Fig. 3 is triangular from 0 to and from to, and trapezoidal from to pi. Using the symmetry of currentwaveform, the RMS current during one switching period is

Irms =13

2i20 + 2i

2 +

pi

(i2o i0i + i2

). (10)

Finally, the conduction loss of one bridge is

Pcond = I2rms (Ron,t +Ron,d) + Irms (vce0 + vf0) . (11)

B. Switching Loss1) Hard Switching: When hard switching is applied to the

inverter and rectifier stages, the average IGBT turn-on/turn-off energy and the diode reverse recovery energy can bedetermined from the device datesheets. Since the number of

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Fig. 3. Current waveforms of DAB converter during one switching cycle

commutation from IGBTs to diodes is equal to the number ofcommutation from diodes to IGBTs, switching loss is

Psw =fsw

pi(Eon + Eoff + Err) , (12)

where turn-on loss Eon, turn-off loss Eoff , and diode reverserecovery loss Err are linearly related to load current and busvoltage.

2) ARCP Soft Switching: The switching loss of ARCPconsists of three parts: main switch soft switching loss, extramain switch conduction loss, and auxiliary switch conductionloss.

(i) During ZVS transient, the dv/dt of IGBT is limited by itssnubber capacitor. IGBT turn-off energy under ZVS is Ezvs =t2f i

2

c

6Cr. Thus, IGBT turn-off loss is given by

Psw,ARCP = 2fot2f

6Cr

Ki=1

(i2t + i

2d

), (13)

where K = fswfo , turn-off current for diode switching is id =Im sint + Iboost,d, and turn-off current for IGBT switchingis

it =

{Im sint, for ARCP disabled(14a)Im sint+ Iboost,t, for ARCP enabled .(14b)

A detailed explanation can be found in [6].(ii) Beside conducting load current, the main switches must

conduct extra boost current from the auxiliary switches. Theextra current is used to provide the inductive energy to achieveZVS. Using waveform symmetry, this extra conduction loss is

PAux1 = 2fswLr

Vdc

(i2d + i

2t

)(Vf + Vce) . (15)

(iii) Auxiliary switching turns on-and-off at zero currentduring ARCP transients. Therefore, the switching loss of aux-iliary switches is neglected. However, the auxiliary switchesdo conduct a significant amount of current to realize ZVS forthe main switches. For diode-to-IGBT commutation, there arethree portions of current through the auxiliary switches: linearcharging current, half-period resonant transient current, andlinear discharging current. For IGBT-to-diode commutation,

there is an auxiliary circuit conduction loss only when ARCPis enabled. Combining these two scenarios, the power loss inthis portion is given by

PAux2=2fswid

(Lr

Vdcid + pi

2LrCr

)(Vce + Vf )+

2fo

Nit

(Lr

Vdcit + pi

2LrCr

)(Vce + Vf ) .(16)

where N is the number of switching transients when ARCPis enabled for transistor-to-diode switching.

3) DAB Soft Switching: When designed properly, dc-dcDAB converters allow ZVS over a wide operating range.Switching devices are turned on and off with ZVS. ZVSturn-on energy is close to zero, and turn-off energy can becalculated as

PDAB,dcdc = 4fswt2f

6Cr

(i20 + i

2

), (17)

where tf is the fall time of IGBT, Cr is resonant capacitance,and fsw is switching frequency.

The switching loss of an ac-ac DAB converter is slightlydifferent from that of its dc-dc counterpart. Both i0 and ivary sinusoidally. ZVS is valid when instantaneous current ishigh. Therefore, switching energy can be calculated as

Esw,soft =t2f

6Cr

(i2sw). (18)

When ZVS is not valid around zero-crossing points, hardswitching energy is

Esw,hard = Eon + Eoff +1

2CrV

2, (19)where the turn-on and turn-off energy of switching devicescan be found in the manufactures datasheets and the last termof (19) represents the energy lost in resonant capacitors. Theswitching loss of ac-ac DAB converter is

PDAB,acac =fsw

N(NsoftEsw,soft +NhardEsw,hard) ,

(20)where N is the number of switching commutation events isa single 60-Hz cycle, Nsoft and Nhard are the numbers ofsoft-switching and hard-switching events, respectively, in onemains cycle.

C. Transformer Copper LossThe transformer in a DAB converter operates at a frequency

range of several kilo-hertz where the skin depth of wire isclose to the wire diameter. Therefore, the high-frequency effecton winding resistance can be significant. The ac windingresistance of a high-frequency transformer is calculated usingthe orthogonality between skin effect and proximity effect [8].Ac resistance is the product of dc resistance and a factorrepresenting skin and proximity effects:

k =sinh () + sin ()

cosh () cos ()+2 (2m 1) sinh () sin ()

cosh () + cos (),

(21)

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where () =pi

2d

() and () =1

pif0/. The dc

component of winding resistance is Rdc = NlTA where Nis the total number of turns and A is the copper area of thewire. Copper loss is calculated using winding ac resistanceand RMS current:

Pcu = I2rms,priRac,pri + I

2rms,secRac,sec. (22)

D. Transformer Core LossAccording to [9], peak flux density is

Bac =Vrms 1044.44NfAe

, (23)

where Ae is the core area of the magnetic core. Core loss de-pends on magnetic flux, operating frequency, the core weight,and the voltage waveform. For simplicity, it is given by

Pcore = kfmBnac (24)

where parameters k, m, and n for a given core material canbe found in [9] or the manufacturers datasheets.

IV. RESULTS

This study evaluated seven cases: SST1, SST2 and SST3with hard switching and with soft switching, respectively, andSST4 with soft switching. Fig. 4(a) and Fig. 4(b) show the lossbreakdown for these seven cases. Table II and Table III showloss and efficiency at full load and 33 % load, respectively.

Fig. 5 shows the efficiency of SST2 with hard switchingunder different load apparent power and load power factor.In Fig. 5, SSTs efficiency drops drastically at light loadconditions.

The efficiency of all four SST topologies is lower than thatof conventional magnetic transformer due to the addition ofpower electronic converters. Among all four configurations,SST1 is the most efficient topology; however, it lacks thesize advantage of a high-frequency transformer. Efficiencydecreases as the power converters become more complex. Theefficiency of SST3 is slightly better than that of SST2 due tothe reduction of switching frequency by using a multilevelfront-end rectifier. SST4 has higher efficiency because itbenefits from less energy circulation and less number of powerconversion stages; however, it lacks a low voltage dc port andreactive power control.

Comparing hard switching and soft switching, ARCP in-creases efficiency at the expense of increasing circuit complex-ity even further. It is costly to implement ARCP at the 7.2 kVhigh voltage side. Furthermore, the effect of loss reductionbecomes less significant at light loads for fixed timing ARCP.DAB converters achieve soft switching without introducingextra switching devices. However, the soft switching rangedepends on the converter parameters. Under light load condi-tions, the soft-switching range of DAB converters (both dc-dcand ac-ac) is narrower, resulting in more switching loss.

(a) Full load

(b) Light load

Fig. 4. Loss breakdown

0 2 4 6 8 10 12 14 16 18 2020

30

40

50

60

70

80

90

100

Load Apparent Power (kVA)

Effic

ienc

y (%

)

pf=0.7pf=0.86pf=1.0

Fig. 5. SST2 efficiency under different load conditions

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TABLE IIEFFICIENCY ESTIMATION AT 100% LOAD

SST1 SST1 ARCP SST2 SST2 ARCP SST3 SST3 ARCP SST4HV Conduction Loss (W) 107.8 107.8 19.53 19.53 24.9 24.9 N/A

Rectifier Switching Loss (W) 262.5 125.2 344.7 166.0 229.2 110.9 N/ADAB Conduction Loss (W) N/A N/A 151.5 151.5 151.5 151.5 231.1

Converter Switching Loss (W) N/A N/A 692.9 692.9 692.9 692.9 662.0LV Conduction Loss (W) 107.8 107. 8 107.8 107.8 107.8 107.8 107.8

Inverter Switching Loss (W) 262.5 125.2 262.5 125.2 262.5 125.2 N/ATransformer Loss (W) 600 600 746 746 746 746 746Power Efficiency (%) 93.7 94.9 89.6 90.8 90.0 91.1 92.4

TABLE IIIEFFICIENCY ESTIMATION AT 33% LOAD

SST1 SST1 ARCP SST2 SST2 ARCP SST3 SST3 ARCP SST4HV Conduction Loss (W) 24.5 24.5 5.9 5.9 6.5 6.5 N/A

Rectifier Switching Loss (W) 86.6 75.3 207.0 137.3 137.6 91.6 N/ADAB Conduction Loss (W) N/A N/A 41.9 41.9 41.9 41.9 62.5

Converter Switching Loss (W) N/A N/A 444.2 444.2 444.2 444.2 512.3LV Conduction Loss (W) 24.5 24.5 24.5 24.5 24.5 24.5 24.5

Inverter Switching Loss (W) 86.6 75.3 86.6 75.3 86.6 75.3 N/ATransformer Loss (W) 322 322 378 378 378 378 378Power Efficiency (%) 92.5 92.8 84.8 85.7 85.6 86.3 87.4

V. DISCUSSION AND CONCLUSIONAlthough the power efficiency of the current generation of

SSTs is not competitive with conventional passive transform-ers, SST is still attractive by increasing the overall efficiencyof the distribution system. An SST (except SST4) can increasepower factor by reactive power control. In this way the losscaused by reactive current is reduced, which can fully orpartially compensate the increased loss by SST itself.

The power efficiency of all three stages in an SST needsimprovement.

1) For the low voltage inverter, it might be advantageousto replace IGBTs with high voltage MOSFETs, suchas those with SuperMESH technology.

2) For the high voltage rectifier, the key issue is availabil-ity of new generation of power semiconductor device.

3) For the DAB stage, it is necessary to develop a controlmethod to increase efficiency at low power conditions.It is also interesting to find a circuit parameter opti-mization method.

It is necessary to develop a system-level loss estimationframework to analyze the effect of SSTs power flow controland power factor correction capability on the overall efficiencyof a distribution grid.

ACKNOWLEDGMENTThis work was supported by ERC Program of the National

Science Foundation under Award Number EEC-08212121.REFERENCES

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