Evaluation on Chamber Volume and Performance for
Simple Calorimetric Power Loss Measurement
by Two Chambers
Koji Orikawa, Atsushi Nigorikawa and Jun-ichi Itoh
Nagaoka University of Technology
Nagaoka, Japanorikawa@vos.nagaokaut.ac.jp

Abstract—In this paper, a calorimetric power loss measurement(CPLM) which is low cost and a simple structure using twocheap chambers. A feature of the proposed method is that thepower loss of the power converter is measured from thetransient state of the rise in temperature. As a result, themeasurement time of the power loss using heat conduction
equation formulas is reduced by 86.1% compared with aconventional method which uses the steady state of thetemperature due to the power loss. In addition, another methodthat can reduce the measurement time is discussed. In particular,
the temperature in one of two chambers is controlled to follow
the temperature in another chamber for the transient stat of therise in temperature. As a result, the measurement time of thepower loss is reduced by 87.5% in compared with theconventional method. In order to confirm the validity of the
proposed method for actual applications, a switching power
supply is used for an objective of the power loss measurement.
Moreover, the relationship among the measurement error rate,
the measurement time and the chamber volume. As a result, allof the maximum errors of the measured power loss were within
10%.

I.

INTRODUCTION

Recently, power converters become relatively highefficiency and high switching frequency due to wide-gap
semiconductor devices, such as silicon carbide (SiC) andgallium nitride (GaN), and improved magnetic materials [1].
As a result, the power loss analysis of very high-efficiency
power converters has been becoming difficult because verysmall power losses are buried in the measurement error.
However, it is very important to measure the power loss of
power converters precisely in order to improve the efficiencyof power converters certainly.
Fig. 1 shows power loss measurement methods using anelectrical power measurement (EPM) instrument. The mostcommon method shown in Fig. 1(a) is to measure the input
and output power using by EPM instrument. Especially, incase of very small power loss, the measurement results by

EPM instrument are affected greatly by the delays between
current probes and voltage probes, phase shifts between
sampling channels of an oscilloscope and voltage offsets andso on [2]. In this method, the full scale error of themeasurement range of the EPM instrument is included inmeasurement results because the power loss is calculated byusing the measured input power and output power. In order toovercome these problems, there is another power loss
measurement method, which uses two power converters areconnected in parallel shown in Fig. 1(b) [3]. The first power
converter is operated as a generator. The second power
converter is used as a receptor. The power is circulated
through two converters [4]. As a result, the input power isequal to power loss of two power converters due to theparallel connection. Therefore, the measurement range of the
EPM instrument becomes smaller. As a result, the higher
accuracy measurement result is obtained. However, since thismethod requires two power converters, consequently thismethod takes longer assembly time and causes high cost.
On the other hand, another power loss measurement
method using the heat quantity of the power converter isknown as the Calorimetric Power Loss Measurement (CPLM)[5], [6]. This system uses a thermostatic chamber in order tomeasure the heat quantity precisely. In addition, thecirculatory organ is also used in order to circulate the water or
air in the inside the thermostatic chamber [7]. This method canachieve high accuracy of power loss measurement because
only the power loss is measured using the heat quantity is
obtained from the temperature change of the circulating wateror air. Additionally, the measurement accuracy is affected by
the heat leakage through the walls of the chamber. Even if thepower loss is very small, the thermostatic chamber and thecirculatory organ are expensive. In addition, the structure ofthis method is complex due to these instruments. These
instruments cannot be changed easily depending on thevolume of the power converter, even if there are cases that themeasurement time could be reduced when the power converterwhich has very small power loss is tested.
In this paper, a low cost and simple structure CPLM
system using two chambers is described [8]. Two chambers
are made from the expanded polystyrene, which are cheaper
than instruments such as general thermostatic chambers andcirculatory organs. By locating two chambers under the sameenvironment, an effect of the heat leakage through walls of
two chambers to the measurement accuracy can be reduced.
This paper is organized as follows; first, the calorimetricprinciple is described, next, the proposed system is introduced
and a theoretical behavior of the temperature in the chamber isdiscussed based on equations of heat conduction; thirdly, themeasurement time and accuracy are evaluated when a resisterand a switching power supply is used as the measured objectof the proposed system. Finally, the relationship among thechamber volume, the measurement accuracy and themeasurement time is verified by changing the chamber
volume.
II.

Ploss  Pin  Pout(a) Input and output powers measurement.

(b) Opposition method.

Figure 1. Electrical methods of power loss measurement.

CALORIMETRIC PRINCIPLE

The measurement error  of the power loss in the power
converter can be expressed by (1),(a) Open type.

(b) Closed type, single-cased.

  Ploss / Ploss  Pin  Pout  / Ploss 

Tout

where, Ploss is the measured power loss of power converter,
Ploss is the power consumption of the power converter, Pin is
the measured input power and Pout is the measured output
power. If the power loss of a power converter which has theefficiency of 99% is measured by using a power meter which
has an accuracy of 0.15%, the worst case of the measurement
error is 29.85%. Besides, a measurement method does notprovide high accuracy due to the limited bandwidth anddynamic frequency response. Therefore, it is required tomeasure the power loss directly.

Heatexchanger

The power consumption of the power converters is
exchanged to heat. Therefore, the calorimetric method
controls water or air in order to take over the heat from thepower converters. Ploss can be described by (2),

Tin

Ploss
Power
converter
Pwall

Ttest
Tgap
Tamb

(c) Closed type, double-cased.
Figure 2. Conventional calorimeter systems.

the walls of the calorimeter Pwall because the temperature in
the chamber Ttest is different from the ambient temperature
Tamb. Therefore, the accuracy of this system is very affectedfrom the environment. This calorimeter type is often used formeasuring induction machines with power losses up to several
kilowatts.
Ploss   c p V (Tout  Tin ) 
On the other hand, Fig. 2 (b) shows closed and singlecased
type calorimeter system. This system employs awhere,  is the mass density, cp is the specific heat capacity of
the fluid, V is the flow rate of the coolant, and Tin and Tout are separate cooling loop for the heat exchange with the ambient.
Using water for a coolant, this system is higher accuracy than
the temperature of the inlet and outlet water.
the open type calorimeter. However, the measurement time
Fig. 2 shows several types of the conventional calorimeters becomes long because heat capacitance of water is higher
have been proposed so far [9-11]. Fig. 2 (a) shows an open compared with that of air.
type calorimeter system. In this system, a power converter isFig. 2 (c) shows a closed and double-cased typeplaced directly in a measurement chamber. Using air for thecalorimetersystem can increase the measurement accuracy.
coolant, this system is a simple construction. In addition,measurement time of this system is short. However, this Tgap is the air temperature in the gap between the inner
system has significant defect that it is difficult to measure heat chamber and outer chamber. In this method, Tgap is controlled
capacity, the temperature rise and the volume flow of the air. to be equal to Ttest. Therefore, the power consumption for the
Air is very sensitive to environmental changes such as the heat leakage through the walls of the inner chamber Pwall canhumidity, the temperature and density. Additionally, the be zero. Therefore, the double-cased calorimeter is the highest
measurement accuracy is affected by the heat leakage through accuracy in the three types as mentioned above. However, thissystem uses the circulatory organ for the coolant, complex
control circuits and sensor. As a result, these systems are
expensive. Moreover, this method is also required to take thelong measurement time due to high heat capacitance of water.
III.

CPLM SYSTEM USING TWO CHAMBERS

Fig. 3 shows the control block diagram of proposed system
which is composed by two chambers and a heater. The
chambers which are made from insulator materials, areillustrated as the chamber A and chamber B in Fig. 1. A power
converter as the measured object of the proposed system isplaced in the chamber A. The temperature in the chamber A
TinA is increased by the power loss of the power converter. TinA
saturates when the amount of heat consumption from heater
equals to the amount of heat consumption from the chamber
surface.

Figure 3. System configuration of proposed CPLM
using two chambers.

The temperature in the chamber B TinB is controlled by a
feedback control using the PI regulator. It should be noted thata heater in the chamber B is controlled by the buck converter.
TinA is set to the command temperature of chamber B. When
TinB reaches the command value that is the saturated
temperature in the chamber A, the power consumption of theheater in the chamber B equals to that which is generated fromthe power converter in the chamber A.
Fig. 4 shows the prototype of the proposed CPLM system.
The measurement accuracy is evaluated using the prototype.
Table I shows the used materials for the calorimeter. Twochambers are made from the expanded polystyrene. The heater
Figure 4. Prototype of proposed CPLM using two chambers.
cement resistor of 10 is used. For simplicity of theexperiment, a heater is used instead of the power converter.
TABLE I.
USED MATERIALS FOR THE CALORIMETER.
The power converter runs in the chamber A. The power loss
measurements with the power consumption between 5 W and
25 W are demonstrated. The volume of the chamber is Vchamb1= 3.17×10-2 m3 (inner dimension of chamber; long 447 mm,
width 322 mm, height 220 mm). The error rate set up within
10% based on the power consumption between 5 W and 25 W.
The power loss of the power converter is evaluated from thepower consumption of a heater in chamber B. The
temperatures of the air in the two chambers are affected by thesame ambient temperature because two chambers are placed in(W) is the heat quantity from the inside of the power convertersame place.
to the converter surface in the chamber A, QR (W) is the heat
quantity
from the converter surface to the measurement point
IV. THEORETICAL DISCUSSIONof the air temperature in the chamber A, Qcool (W) is the heat
In this section, the relationship between the chamber discharge from the chamber A. QR and Qcool is expressed byvolumes and measurement time is discussed using the (4) and (5).
theoretical equation of heat conduction. The power converter
is operated in the chamber A. The temperature of the air in
QR  TR  TinA  / Rr  Qcool  TinA  Tamb  / Rchamb  
the chamber A rises, due to the heat quantity produced by thepower loss of the power converter. The air in the chamber A
is circulated by a fan. Based on the heat conduction equation, Here, Eq. (3) is also expressed by Eq. (6).
the heat quantity Qin (W) is led todT  c p V inA  Qin  Qin  Rr  TinA   Tamb / R  dTinAdt
 Qin  QR  Qcool 
dt
where, TR (K) is the inner temperature of power converter, Rr
where,  (kg/m3) is the density of the air, cp (J/gK) is the (K/W) is the thermal resistance from inside of the power
specific heat of air, V (m3) is the inner volume of the chamber converter to the measurement point of the room temperature,
A, TinA (K) is the temperature of the air in the chamber A, Qin

 cp VTamb (K) is the ambient temperature, Rchamb (K/W) is thethermal resistance of the chamber A, R (K/W) is the total
thermal resistances (=Rr +Rchamb).
Eq. (5) is transformed with Laplace transformation andpresented as  c p V s TinA s   To  

Qin  Rr  TinA s  Tamb


1 

s 
R
R
sR

45

40
Chamber B(Heater)


30





where Rchamb (K/W) is the thermal resistance of thechamber A, Tamb (K) is the ambient temperature and  is thetime constant.  is expressed by (8).
   1 /  c p Vch R  

If the parameters are known except Qin, (9) is derived bydifferentiating (7) and translating into logarithm.

Q R  Rr   Tamb  To
1
 dT 
t 
ln  inA   ln in air c pair V ch R air c pair Vch R
 dt 
As a result, the Qin can derive by (9) before the temperature
is saturated. The rise of the measured temperature isdifferentiated and both sides of equation are expressed
logarithmically. Moreover, the regression curve is analyzed
from the experimental results. The measurement results are
expressed by 1st order equation. The R and the Rr is showedby (10) and (11) by using the slope a and the intercept b,
respectively.

0

1000
2000
3000
4000
Measurement time [s]Figure. 5. Temperature control results for constant temperature commandusing PI control.
8
7
6
5
4
3
2
1
0
0
5
10
15
20
25
30
Power consumption Ploss [W]Figure. 6. Measurement error rate of the power loss measurement basedon steady state condition. When power consumption is 5 W and 25 W,
measurements were done three times.
Error rate [%]Ambient

35

where, To is the initial temperature in the chamber A. The heat
quantity of the power converter is assumed as the step input.
Eq. (6) is derived in term of the TinA, and then it is applied withinverse Laplace transformation, which is shown in (7).
 TinA  Qin Rchamb  Tamb  1  e t  To e t 

Chamber A(Converter)

A. Power loss measurement based on steady state condition
Two chambers are made from the expanded polystyrene.
For simplicity of the experiment, a heater is used instead of
the power converter in the chamber A.
Fig. 5 shows the experimental result of the temperature
control by using PI regulator at Ploss = 5 W. From Fig. 5, it isconfirmed that the temperature in the chamber B is equaled tothe temperature in the chamber A by using PI control.

Fig. 6 shows the fluctuation band of the power loss
measurement error rate when the temperature is saturated on
the steady state. The power consumption of the power
converter is measured three times at the each power
consumption. From Fig. 2, it is confirmed that the maximum
error of power loss is 8.0% at Ploss = 5 W. In this case, allmeasurement accuracy becomes within 0.08% when the R  1 /  air c pair Vch a  converter that has the efficiency of 99% at 1kW. In theory,when the temperature deviation of the chamber A andchamber B is 0 degrees Celsius, the heater power consumption
in the chamber B perfectly agrees with the power loss in the Rr  R  air c pair Vch R expb / Qin   chamber A in the proposed system. However, there aremeasurement errors in the experimental results. This reason is
From (10) and (11), when the chamber volume Vch is small, the difference of the ambient temperature between thethe surface area of the chamber is decreased. Then, the time chamber A and the chamber B.
constant of the temperature rise is increased by increasing ofFig. 7 and Fig. 8 show the surface temperature of the
Rchamb. Therefore, the measurement time will be long because chambers. Before the measurement, it is confirmed that it is
the time of the temperature saturations becomes long when the low. In the steady state after them temperature was saturated,chamber volume Vch is small.
the surface temperature becomes around 13 degree Celsius.
From the results, it is seen that there are variations of the
V. EXPERIMENTAL RESULTS
surface temperatures of the chambers. However, from the
In order to valid the theoretical analyses of the proposed results of Fig. 6, Fig. 7 and Fig. 8, the measurement error ismethod, experiments are conducted by using prototype within 8% even if there are variations of the temperature.
experimental setup.









Temperature ( degree )Temperature ( degree )(a) Before a measurement.

(b) Chamber A

Chamber B

Temperature ( degree )15.0
Chamber A

14.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0

(b) After temperature was saturated.
Figure. 7. Surface temperature of two chambers.

(b) Chamber B
Figure. 8. Surface temperature of two chambers after temperature was saturated.

B. Power loss measurement using heat conduction equation
formulaFig. 9 shows the error rate of the power consumption of
the heater between the measurement value of the calculated
values which is obtained by (10) and (11). As a result, it isconfirmed that the error rate of the power consumption iswithin 10%. In addition, it is confirmed that the measurement
time is shortened by 86.1% compared with the method basedon the steady state condition.
C. Power loss measurement by transient response of
temperature rise
In this section, the temperature in the chamber B iscontrolled to follow in the temperature in the chamber A for
the transient state of the temperature rise.

Figure. 9. Error rate of the power consumption between the measurement
values and the calculation values.

Fig. 10 shows that the temperature of the chamber B TinB iscontrolled to the temperature of the chamber A TinA in a shorttime. Note that the power consumption of the power converter
is 25 W. According to Fig. 3, it is confirmed the temperaturein the chamber B reaches to the temperature in the chamber A
in the transient states of the temperature rise.
Fig. 11 shows the power consumption of the power
converter and the heater when the temperature of the chamber
B is controlled as shown in Fig. 11. The power consumptionof the heater is equaled to the power consumption of theconverter on 1350 s. As a result, it is confirmed that themeasurement time is shortened by 87.5% compare with thepower loss measurement based on the steady state.

Figure. 10. Temperature of the chamber B is controlled
to the temperature of the chamber A in a short time.

experiment can be measured by the EPM at high accuracy
because the full scale error is small. Thus, the measured value
with an EPM can be used as a reference value to evaluate theD. Measurement accuracy in comparison with EPM
In this section, the prototype system is experimentally accuracy of the proposed CPLM. Output power of the SW
tested using a switching (SW) power supply that has the power supply Pout is set to 1, 5, 20, 30 and 40 W. The power
maximum efficiency of 67% which was measured by the EPM. losses of the SW power supply PSW are measured by the
The power loss of the SW power supply used in this prototype three times at each Pout.

Fig. 12 shows the measurement error of the PSW at each
Pout. The maximum measurement error is 6.1% at PSW = 10.7
W (Pout = 1 W). On the other hand, the minimum
measurement error is 0.6% at PSW = 16.8 W (Pout = 30 W).
E. Relationship among the chamber volume, measurement
accuracy and measurement time
The measurement accuracy and measurement time aredetermined by the chamber volume in CPLM methods. The
chamber volume is approximately 30 times the volume of the
SW power supply used in the previous section. In this section,
the chamber with twice volume is used for measuring the PSW.
Figure. 11. Power consumption of converter and heater when thetemperature of the chamber B is controlled as show in Fig. 10.
7
Pout = 1W

Fig. 13 shows the measurement accuracy and themeasurement time when the chamber volume varies at PSW is10.7 W. When the Vchamb2 is used, the maximum measurement
error is 3.74%. However, the measurement time is extended
from 4380 s to 6600 s.

VI.

CONCLUSION

In this paper, the low cost CPLM system for a highefficiency converter is proposed. The proposed system isconstructed at a low cost without the thermostatic chambers
which cause a high cost of the CPLM system. The method formeasurement of the power loss by the temperature rise withthe loss of power converter is discussed. The maximum errorof the measured power consumption was within 6.1%.
Moreover, the relationship between the measurement accuracy
and the measurement time was experimentally verified byusing the prototype with the reduced volume of the chamber.
As the result, it was confirmed that the measurement accuracy
and time becomes higher and longer by decreasing thechamber volume.

4
3

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Pout = 20W
Pout = 40W
Pout = 30W

2
1
0
10

12
14
16
18
Power consumption PSW [W]20

Figure. 12. Measurement error rate of the power consumptionof a switching power supply with the proposed CPLM system based ontransient response of temperature rise. Measurements were done twotimes or three times at each power consumption.
7.0
Vchamb1/Vsw
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=2
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Measurement time [s]Figure. 13. Relationship among the measurement error rate, themeasurement time and the chamber volume.
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[1]

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5

Measurement error rate[%]The high measurement accuracy is obtained by decreasing
the chamber volume. In contrast, the measurement time
becomes longer. The thermal resistance Rchamb increases due tothe decreasing of a surface area. From (8), the value of thetime constant is increased by increasing of Rchamb. It meansthat the period of the temperature saturation also becomes
long. As a result, the decrease of the chamber volume helps toachieve the high measurement accuracy because thetemperature dispersion in the chamber is decreased bydecreasing the chamber volume.

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