15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad,
SerbiaExperimental Analysis on Precise CalorimetricPower Loss Measurement Using Two Chambers
Jun-ichi Itoh1, Atsushi Nigorikawa2

1

Nagaoka University of Technology, Nagaoka, Japan, itoh@vos.nagaokaut.ac.jp
Nagaoka University of Technology, Nagaoka, Japan, nigori@stn.nagaokaut.ac.jp

2

Abstract — In this paper, a low cost and simple structure
power measuring system for a high efficiency power
converter is proposed. The Calorimetric Power Loss
Measurement (CPLM) uses the heat quantity which is
generated by the power converter to measure losses. The
proposed system is a low cost and simple structure withoutcomplex control circuits, which will increase the cost of the
CPLM system. The measurement of the power consumption
can be calculated by the increased temperature. The
features of the proposed method are that the power
consumption of the power converter is measured from thetransient state of the rise in temperature. As a result, themeasurement time of the power loss of the power converter
is reduced by 86.1% in comparison with a conventional
method. In addition, all of the maximum errors of themeasuring power consumption are within 10%. Moreover,another method that can reduce the measurement time isdiscussed. In particular, the temperature in the container B
is controlled to follow in the temperature in the container A
for the transient state of the rise in temperature. As aconsequence, the measurement time of the power loss of thepower converter is reduced by 87.5% in comparison with aconventional method.
Keywords — Calorimetric determination, Power loss
analysis, Thermostatic chamberI.

INTRODUCTION

Recently, power converters become relatively highefficiency and high switching frequency due to theadvanced semiconductor devices, such as SiC and GaN,
and magnetic materials [1]. The power loss analysis of
the very high efficiency power converter becomesdifficult because the power losses are buried in themeasurement error. One of the loss measurement
methods is to measure the input and output power using a
power measurement instrument (EPM) [2]. The EPM
uses the products of voltage and current, which gives anelectrical quantity equivalent to power. The power
measurement can be performed by measuring the voltage
drop across the device and the current flowing through itusing electrical instruments. This method is commonlyused to measure power directly by using analog
electronic equipment. However, this method contains
certain error because the ratio of the power loss to thetotal power is very small. That is, the full scale error of
the measurement range is buried in measurement results.
Furthermore, the measurement results by EPM are also
affected by the delays between the probes. The phaseshifts between sampling channels of digitizer, sampling
errors, and voltage offset [3]. Even if the digital meter
which has the required resolution is used in this method,

problem such as the radio frequency interference andelectromagnetic interference are very sensitive to noise.
To overcome these problems, there is another power
loss measurement method, which uses two power
converters to measure losses [4]. Two power converters
are connected in parallel. The first converter is operated
as a generator. The second converter is used as a receptor.
The power is circulated by using two converters. The
input power is equal to two converter losses from thiscircuit configuration [5]. Therefore, the measurement
range of the power meter becomes smaller. As a result,the higher accuracy measurement results are obtained.
However, since this method requires two power
converters, consequently this method takes longer
configuration time and cause higher cost.
On the other hand, another loss measurements method
using the heat quantity of the power converter is known
as the Calorimetric Power Loss Measurement (CPLM)[6]. A measured power converter is activated in thethermostatic chambers. The water or air is circulated in
the thermostatic chambers. The power converter loss isobtained from the temperature change of the circulatingwater or air. This method can reduce the measurement
error because of measurement of only the power loss.
Therefore, this method provides higher accuracy than the
EPM. The advantage of this method is measuring thepower losses under normal operating conditions andindependent of electrical quantities of a measured
converter [7]. Moreover, the CPLM requires low
sensitivity and less complicated device [8]. This system
uses a thermostatic chamber to achieve the precise
measurement of heat quantity and use the circulatoryorgan to circulate the water or air inside the thermostaticchambers [9]. However, the thermostatic chamber isrequired complex control circuits to control the water orair. Therefor thermostatic chamber systems are expensive.
Also, the CPLM method takes longer time to complete ameasurement due to the low sensitivity.
This paper proposes a low cost and simple structure
CPLM system using two chambers to overcome thedisadvantage of the conventional CPLM. The proposedsystem uses two simple chambers [10]. Also, the complex
controlling water or air for measuring the temperature in
the thermostatic chambers is not required in the proposedsystem. Therefore, the proposed system becomes low costand simple structure. Besides, the power loss will becalculated by transient state data of the rise temperatureinside the chamber. Therefore, this method can bemeasure quickly. Moreover, the measurement time will be
short time to design the PI controller.

This paper is organized as follows, firstly, thecalorimetric principle is described, next, the proposedsystem is introduced and the measurement principle ofthe proposed system is explained. At last, the prototype
system will be demonstrated with experimental results.
The experimental results indicate the validity of the
proposed system.
II. CALORIMETRIC PRINCIPLE
The measurement error ε of the power loss in the power
converter may be expressedε=ΔPloss ΔPin + ΔPout
=
Ploss
Ploss

(1)

(a)

where, ΔPloss is the error of the measured power loss of
power converter. Ploss is the error of the power
consumption of the power converter. ΔPin is themeasured input power and ΔPout is the error of themeasured output power. If a measured power converter
which has the 99% efficiency is measured to use thepower meter which have the 0.15% accuracy, the worst
case of the measurement error is 29.85%. Besides, thismethod does not provide high accuracy due to the limited
bandwidth and dynamic frequency response. Therefore, it
is required to measure the power loss directly.
The power consumption of the power converters is
exchanged to heat. Therefore, the calorimetric method
used the controlled water or air to take over the heat fromthe power converters. Ploss can be described by(2)
Ploss = ρ cp V (Tout − Tin )where, ρ is the mass density, cp is the specific heat
capacity of the fluid, V is the flow rate of the coolant, andTin and Tout are the temperature of the inlet and outlet
water.
In the past, several types of the calorimeters have been
proposed. Figure 1 shows the three basic calorimeters[11], [12]. Fig. 1. (a) depicts the open type calorimetersystem. In this system, the electrical power converter isplaced directly in the measurement circuit. Using air forthe coolant, this system is a simple construction and afast response time. However, this system has significant
defect that it is difficult to measure heat capacity, the risein temperature and the volume flow of the air.
Additionally, air is very sensitive to environmental
changes such as the humidity, the temperature anddensity. Therefore, the accuracy of this system is very
affected from the environment. This calorimeter type isoften used for measuring induction machines with power
losses up to several kilowatts [13], [14].
One the other hand, Fig. 1. (b) depicts closed and singlecased type calorimeter system. This system employs aseparate cooling loop for the heat exchange with theambient. Using water for a coolant, this system is higher
accuracy than the open type calorimeter.
Moreover, in order to increase the measurement
accuracy, closed and double-cased type calorimetersystem have been proposed as shown Fig. 1. (c) The
measurement accuracy is affected by the heat leakage
through the walls of the calorimeter [15]. The power
consumption for the heat leakage through the walls of the(b)Open type

Closed type, single-cased(c) Closed type, double-cased
Fig. 1. Three kind of conventional calorimeters systems.

calorimeter Pwall on closed and single-cased type isexpressed as
T − Tamb(3)
Pwall = test
Rth,wallwhere, Ttest is the temperature in the chamber, Tamb is theambient temperature, Rth,wall is the thermal resistance ofthe calorimeter walls. In the contrast, Pwall of the closed
and double-type system is expressed as
Pwall =

Ttest − Tgap
Rth,wall(4)

where, Tgap is the air temperature in the gap between the
inner chamber and outer chamber. The double-cased
calorimeter controls Tgap equal to the temperature in the
inner chamber. Therefore, the power consumption for theheat leakage through the walls of the inner chamber canbe zero. Therefore, the double-cased calorimeter ishighest accuracy in the three types. However, this system

uses the circulatory organ for the coolant, complex
control circuits and sensor. Therefore, these systems are
expensive. Additionally the controlling the coolant andTgap on this system is difficult. Moreover, these closed
systems (Fig. 1. (b) and Fig. 1. (c)) are required to takethe long measurement time because the heat capacity of
the water is higher than that of the air.
To overcome this drawback, we propose the unique
technic and simple structure CPLM system. In the
proposed CPLM system, the heat quantity is obtained bycomparing between the two chambers. Therefore, themeasurement accuracy of the proposed system is notaffected by Pwall and the coolant parameter. As a result,the proposed system becomes significant low cost andsimple structure. Moreover, the proposed system can bemeasured accurately the heat quantity to use the air as thecoolant. Therefore, the proposed system becomes highaccuracy and a fast response time. The specific is
described in the next chapter.
III. CPLM SYSTEM USING TWO CHAMBERS
Figure 2 shows the control block diagram of proposedsystem which is composed by two chambers and a heater.
The chambers, which are made from insulator materials,
are illustrated as the container A and container B in Fig. 2.
A measured power converter is placed in the container A.
The temperature in the container A is increased by power
loss of the power converter. The temperature in thecontainer A saturates when the amount of heatconsumption from heater equals to the amount of heatconsumption from the container surface.
The temperature in the container B is controlled by a
feedback control using the PI regulator. It should be notedthat the air in the container B is heated by a heater, whichis controlled by the buck converter. The temperature in
the container A is set to the command temperature ofcontainer B. The sensitivity error of the temperature
sensor is corrected in the control circuit. When thetemperature in the container B reaches the command
value that is the saturated temperature in the container A,
the heat generation from the heater in the container B
equals to the heat generated from the power converter inthe container A. In this way, the power consumption of
the heater equals to the power loss of the power converter.
This system does not require complex control circuit.
Therefore, the proposed system becomes significant low
cost and simple structure. The heat leakage of the walls of
the container B is same the container A. Therefore, in the
proposed system, the measurement accuracy of the power
consumption does not be influenced by the heat leakage
through the walls of the container.
The room temperature and the heat discharge for the twochambers must be the same in order to ensure highaccuracy measurement. Therefore, in this paper, thedevelopments of the measurement system will be
discussed from the theoretical formula in the next
chapter.
IV. THEORETICAL DISCUSSION
The power converter is put and works in the container A.

Fig. 2. System configuration of proposed CPLM
using two chambers.

The temperature of the air in the container A rises, due tothe heat quantity produced by the power loss of the power
converter. The air in the container A is circulated by a fan
in order to balance out the temperature in the container A.
From heat conduction equation, the heat quantity Qin is
led todT(5)ρ air c pair Vcon inA = Qin − Q R − Qcool
dt

where, the density of the air is ρair (kg/m3), the specificheat of air is cpair (J/gK), the inner volume of thecontainer A is Vcon (m3), the temperature of the air in thecontainer A is TinA (K) and Qin is the heat quantity fromthe inside of the power converter to the converter surface
in the container A. QR is the heat quantity from theconverter surface to the measurement point of the airtemperature in the container A. Qcool is the heat discharge
from the container A.
Then QR and Qcool can be expressed asρ air c pair Vcon

dTinA
T −T
T −T
= Qin − R inA − inA amb
dt
Rr
RconA

(6)

(Q R + T ) − Tamb
= Q − in r inA
inR

where, TR is the inner temperature of power converter, Rr
is the thermal resistance from inside of the power
converter to the measurement point of the room
temperature, RconA is the thermal resistance of thecontainer A, R is the total thermal resistances.
Eq. (6) is then transformed with Laplace transformationand presented asQ ⎛R ⎞ T (s ) T(7)ρ c V (s T (s ) − T ) = in ⎜1 − r ⎟ − inA − amb
air

pair

con

inA

o

s ⎝

R ⎠

R

sR

where, To is the initial temperature in the container A. The
heat quantity of the power converter is assumed as thestep input. Eq. (7) is derived in term of the Tin, and then it
is applied with inverse Laplace transformation, which isshown in (8).
⎧⎪
⎛
⎞⎫⎪
1
TinA = {Qin (R − Rr ) + Tamb } ⋅ ⎨1 − exp⎜ −
t ⎟⎬
⎜
⎟
⎪⎩
⎝ ρ air c pair Vcon R ⎠⎪⎭⎛⎞1+ To exp⎜ −t⎟⎜ ρ air c pair Vcon R ⎟
⎝
⎠

(8)

If the parameters are known except Qin, (9) is derived bydifferentiating (8) and translating into logarithm.

1
Q (R − Rr ) + Tamb − To
⎛ dT ⎞−
Ln ⎜ inA ⎟ = ln in
t
dt
c
V
R
c
ρ
ρ
⎠
⎝
air pair con
air pair Vcon R(9)

As a result, the Qin can derive by (9) before temperature
becomes saturated. The rise of the measured temperature
is differentiated and both sides of equation are expressed
logarithmically. Moreover, the regression curve isanalyzed from the experimental results. The measurement
results are expressed by 1st order equation. The R and the
Rr is showed by (10) and (11) by using the slope a and theintercept b, respectively.
1
(10)
R=−
ρ air c pair Vcon aρ air c pair Vcon R exp (b )Rr = R −Qin(11)

V. EXPERIMENTAL RESULTS

Fig. 3. Prototype of proposed CPLM using two chambers.

A. Identification of the Thermal Resistance
Figure 3 shows the prototype of the proposed CPLM
system. The measurement accuracy is evaluated using theprototype. Table I shows the used materials for thecalorimeter. Two chambers are made from the expanded
polystyrene. The heater cement resistor of 10 Ω is used.
For simplicity of the experiment, a heater is used insteadof the power converter. The power converter runs in thecontainer A. The power loss measurements with thepower consumption between 5 W and 25 W aredemonstrated. The thermal resistances are identified fromthe experimental results of the rise in temperature in thecontainer A. The volume of the container is Vcon =3.17×10-2 m3 (inner dimension of container; 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.
Figure 4 shows the temperature characteristic of thecontainer A that the power converter is placed. Figure 5
shows the natural logarithm of differential rise intemperature at Ploss = 25 W where Ploss is the power
consumption of the power converter in the container A.
The noise of the rise temperature is removed by themoving average method. The slope a and the intercept b
is obtained by using the regression analysis. The thermal
resistances are obtained by using (10) and (11).
Table II shows the slope a and the intercept b which is
obtained from the temperature characteristic of thecontainer A. The thermal resistances are obtained fromthis experimental result by (10) and (11).
The permissible temperature deviation range (ΔTinA) is
derived by substituting the permissible power
consumption range and the thermal resistances to (8).
Table III shows the thermal resistances and thepermissible temperature deviation range. Then, it isassumed that To equal to Tamb. From Table III, if thepower consumption is small, the control of thetemperature is shown accurately. When the temperature issaturated, (8) become (12).
(12)
TinA = Qin (R − Rr )ΔTinA is obtained by substituting the acceptable range ofthe power loss (error rate:10%). R and Rr that are shownin Table III are used.

TABLE I
USED MATERIALS FOR THE CALORIMETER.

Fig. 4. Temperature characteristic of the container A.

Fig. 5. Relation between the differential of temperatureand time in log scale.

(13)ΔTinA = ± 0.1Qin (R − Rr )When the power consumption is 5 W, the allowance ofthe temperature deviation is ±0.635 degrees Celsius inorder to keep within 10% measurement accuracy.
B. Power Loss Measurement Based on Steady State
Condition
The power loss of the power converter is evaluated fromthe power consumption of a heater in container B. The
temperatures of the air in the two containers are affectedby the same ambient temperature because two containers
are placed in same place.
Figure 6 shows the experimental result of thetemperature control by using PI regulator at Ploss = 5 W.
From Fig. 6, it is confirmed that the temperature in thecontainer B is equaled to the temperature in the container
A by using PI control.
Figure 7 shows the fluctuation band of the measurement
error rate. The power consumption of the power converter
is measured three times at the each power consumption.
The ambient temperature is different with respect to eachmeasurement. As a result, the measurement error rate ischanged. From Fig. 7, it is confirmed that the maximum
error of power loss is 8.0% at Ploss = 5 W. The
measurement error rate of the power consumption iswithin 10% in the proposed system.
In theory, when the temperature deviation of thecontainer A and container B is 0 degrees Celsius, themeasurement error became 0% in this system. However,there are measurement errors in the experimental results.
This reason is the difference of the ambient temperature
between the container A and the container B.

TABLE II
THE SLOPE AND THE INTERCEPT (0 – 7200 S).

TABLE IIITEMPERATURE ALLOWANCE ΔT TO KEEP WITHIN ±10%
MEASUREMENT ACCURACY.

Fig. 6. Temperature control results for constant temperature commandusing PI control.

C. Power Losses Measurement Using Heat Conduction
Equation Formula
The CPLM methods spend a lot of measurement time
until the temperature in the container A is saturated. In
the experiment shown in previous section, themeasurement is over three hour. In this section, themethod that can reduce the measurement time isdiscussed. In particular, the power consumption of thepower converter is introduced from the transient state of
the rise in temperature.
However, the error of the measurement power loss
increases because the thermal resistance of the container
varies with the power loss of the power converter.
Therefore, the thermal resistance of the container A canbe corrected by using the rise in temperature of thecontainer B in order to reduce the error of themeasurement power loss.
From Fig. 4, the temperature saturation time isapproximately 7200 s. In addition, the change of thetemperature is confirmed from 0 s to 4000 s. The power
consumption of the power converter is obtained by (10)and (11) in the measurement time of up to 4000 s. It
should be noted that the measurement results below 500 s
is not accurate because time delay occurs in the results.
Some variations occur in the measurement results.
Therefore, the measurement results of the rise intemperature are approximated by the regression curve.
After that, the regression curve is differentiated and bothFig. 7. Measurement error rate.

sides of equations are expressed logarithmically.
Moreover, the regression curve is analyzed from theexperimental results. The measurement results are
expressed by 1st order equation.
Figure 8 shows the experimental results of theregression analysis at Ploss = 25 W. The regression curveis approximated by 1st order equation. The power
consumption of the power converter is obtained from (10)and (11) by using the slope a and the intercept b of the 1storder equation. Similarly, the power consumption of thepower converter is obtained when the measurement timeis decreased.
Table IV shows the slope a and the intercept b which is
obtained from the regression analysis. It is noted that thepower consumptions of the power converter arecalculated when the data ranges of the rise in temperature
are in the measurement times between from 500 s to 4000
s, 500 s to 2000 s and 500 s to 1500 s.
Figure 9 shows the error rate of the power consumptionof the converter between the measurement values and thecalculation values which is obtained by (10) and (11). As
a result, the power consumption of the power converter isobtained from 500 s to 4000 s, the maximum error of thepower consumption occurs as 5.8% at Ploss = 15 W. On
the other hand, when the measurement range is from 500
s to 2000 s, the maximum error of the power consumption
is 6.7% at Ploss = 15 W. Similarly, when the measurement
range is from 500 s to 1500 s, the maximum error of thepower consumption is 6.2% at Ploss = 25 W.
These results are compared with the experimental resultsin chapter B. As a result, the measurement accuracy byusing the (10) and (11) is lower than that is measured
from the steady state of the temperature described in theprevious section. However, it is confirmed that themeasurement error rate can be achieved within 10%.
Therefore, a long measurement time is not required in the
proposed method compared with conventional method.
Moreover, it is confirmed that the measurement time isshortened by 86.1%.

Fig. 8. Relation between the differential of temperatureand time in 4000 s.
TABLE IV
THE SLOPE AND THE INTERCEPT (500 – 4000 S)

D. Power Loss Measurement by Transient Response of
Temperature Controller

VI. CONCLUSION
In this paper, a low cost and simple structure to measure
the converter losses is discussed. The CPLM uses theheat quantity which is generated by the power converter

Fig. 9. Error rate of the power consumption between the measurement
values and the calculation values.
55

Container
A(Converter)

50
Temperature [℃]As already mentioned, the CPLM methods spend a lotof measurement time until the temperature in thecontainer A is saturated. In this section, another method
which can reduce the measurement time is discussed. In
particular, the temperature in the container B is controlled
to follow in the temperature in the container A for thetransient state of the rise in temperature. The overshoot ofcontrolled temperature response in the container A
happens easily because the heater does not have a cooling
function. Therefore, the response should be the first orderlag system, which has no overshoot. In order to achieve
the response of first order lag system, the time constant of
PI controller is design to the time constant of the heater.
As a result, the transfer function of temperature response
becomes the first order system.
Figure 10 shows that the temperature of the container B
is controlled to the temperature of the container A for ashort time. Note that the power consumption of the power
converter is 25 W. According to Fig. 10, it is confirmed
the temperature in the container B reaches to thetemperature in the container A in the transient states ofrise in temperature.
Figure 11 shows the power consumptions of converterand heater when the temperature of the container B iscontrolled as shown in Fig. 10. In this experiment, thepower consumption of the heater is equaled to the power
consumption of the converter on 1350 s. As a result, it isconfirmed that the measurement time is shortened by
87.5%.

45
Container B(Heater)
40
35
30
25
0

2000

4000
Measurement time [s]6000Fig. 10. Temperature of the container B is controlled tothe temperature of the container A for a short time.

to measure losses. The proposed system is a low cost andsimple structure without complex control circuits. The
measurement method of the power consumption based on
the rise in temperature is discussed. When themeasurement
uses
temperaturesaturation,themeasurement time becomes longer. In the proposedsystem, the power consumption measurement of thepower converter is achieved from the transient state of therise in temperature. As a result, when the measurement
ranges are from 500 s to 4000 s, 500 s to 2000 s and 500 s
to 1500 s, the maximum error of the power consumption
are 6.2% at 25 W, 6.7% at 15 W and 5.8% at 5 W,
respectively. In other words, the proposed method
achieves approximately 10% measurement error rate.
Moreover, the measurement time of the power loss of thepower converter is reduced by 86.1% in comparison witha conventional method. Moreover, another method thatcan reduce the measurement time is discussed. In
particular, the temperature in the container B is controlled
to follow in the temperature in the container A for thetransient state of the rise in temperature. As a result, themeasurement time of the power loss of the power
converter is reduced by 87.5% in comparison with aconventional method.
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