Evaluation on Chamber Volume and Performance for Simple Calorimetric Power Loss Measurement by Two Chambers

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1 Evaluation on Chamber Volume and Performance for Simle Calorimetric Power Loss Measurement by Two Chambers Koji Orikawa, Atsushi Nigorikawa and Jun-ii Itoh Nagaoka University of Tenology Nagaoka, Jaan Abstract In this aer, a calorimetric ower measurement (CPLM) whi is low cost and a simle structure usg two ea ambers. A feature of the roosed method is that the ower of the ower converter is measured from the transient state of the rise temerature. As a result, the measurement time of the ower usg heat conduction equation formulas is reduced by 86.1% comared with a conventional method whi uses the steady state of the temerature due to the ower. In addition, another method that can reduce the measurement time is discussed. In articular, the temerature one of two ambers is controlled to follow the temerature another amber for the transient stat of the rise temerature. As a result, the measurement time of the ower is reduced by 87.5% comared with the conventional method. In order to confirm the validity of the roosed method for actual alications, a switg ower suly is used for an objective of the ower measurement. Moreover, the relationshi among the measurement error rate, the measurement time and the amber volume. As a result, all of the maximum errors of the measured ower were with 10%. I. INTODUCTION ecently, ower converters become relatively high efficiency and high switg frequency due to wide-ga semiconductor devices, su as silicon carbide (SiC) and gallium nitride (GaN), and imroved magnetic materials [1]. As a result, the ower analysis of very high-efficiency ower converters has been becomg difficult because very small ower es are buried the measurement error. However, it is very imortant to measure the ower of ower converters recisely order to imrove the efficiency of ower converters certaly. Fig. 1 shows ower measurement methods usg an electrical ower measurement (EPM) strument. The most common method shown Fig. 1(a) is to measure the ut and outut ower usg by EPM strument. Esecially, case of very small ower, the measurement results by EPM strument are affected greatly by the delays between current robes and voltage robes, hase shifts between samlg annels of an oscilloscoe and voltage offsets and so on [2]. In this method, the full scale error of the measurement range of the EPM strument is cluded measurement results because the ower is calculated by usg the measured ut ower and outut ower. In order to overcome these roblems, there is another ower measurement method, whi uses two ower converters are connected arallel shown Fig. 1(b) [3]. The first ower converter is oerated as a generator. The second ower converter is used as a recetor. The ower is circulated through two converters [4]. As a result, the ut ower is equal to ower of two ower converters due to the arallel connection. Therefore, the measurement range of the EPM strument becomes smaller. As a result, the higher accuracy measurement result is obtaed. However, sce this method requires two ower converters, consequently this method takes longer assembly time and causes high cost. On the other hand, another ower measurement method usg the heat quantity of the ower converter is known as the Calorimetric Power Loss Measurement (CPLM) [5], [6]. This system uses a thermostatic amber order to measure the heat quantity recisely. In addition, the circulatory organ is also used order to circulate the water or air the side the thermostatic amber [7]. This method can aieve high accuracy of ower measurement because only the ower is measured usg the heat quantity is obtaed from the temerature ange of the circulatg water or air. Additionally, the measurement accuracy is affected by the heat leakage through the walls of the amber. Even if the ower is very small, the thermostatic amber and the circulatory organ are exensive. In addition, the structure of this method is comlex due to these struments. These struments cannot be anged easily deendg on the volume of the ower converter, even if there are cases that the measurement time could be reduced when the ower converter

2 whi has very small ower is tested. In this aer, a low cost and simle structure CPLM system usg two ambers is described [8]. Two ambers are made from the exanded olystyrene, whi are eaer than struments su as general thermostatic ambers and circulatory organs. By locatg two ambers under the same environment, an effect of the heat leakage through walls of two ambers to the measurement accuracy can be reduced. This aer is organized as follows; first, the calorimetric rcile is described, next, the roosed system is troduced and a theoretical behavior of the temerature the amber is discussed based on equations of heat conduction; thirdly, the measurement time and accuracy are evaluated when a resister and a switg ower suly is used as the measured object of the roosed system. Fally, the relationshi among the amber volume, the measurement accuracy and the measurement time is verified by angg the amber volume. P P P out (a) Inut and outut owers measurement. (b) Oosition method. Figure 1. Electrical methods of ower measurement. II. CALOIMETIC PINCIPLE The measurement error of the ower the ower converter can be exressed by (1), (a) Oen tye. (b) Closed tye, sgle-cased. P / P / P Pout P T out T where, P is the measured ower of ower converter, P is the ower consumtion of the ower converter, P is the measured ut ower and P out is the measured outut ower. If the ower of a ower converter whi has the efficiency of 99% is measured by usg a ower meter whi has an accuracy of 0.15%, the worst case of the measurement error is 29.85%. Besides, a measurement method does not rovide high accuracy due to the limited bandwidth and dynamic frequency resonse. Therefore, it is required to measure the ower directly. The ower consumtion of the ower converters is exanged to heat. Therefore, the calorimetric method controls water or air order to take over the heat from the ower converters. P can be described by (2), P c V ( T T ) out where, is the mass density, c is the secific heat caacity of the fluid, V is the flow rate of the coolant, and T and T out are the temerature of the let and outlet water. Fig. 2 shows several tyes of the conventional calorimeters have been roosed so far [9-11]. Fig. 2 (a) shows an oen tye calorimeter system. In this system, a ower converter is laced directly a measurement amber. Usg air for the coolant, this system is a simle construction. In addition, measurement time of this system is short. However, this system has significant defect that it is difficult to measure heat caacity, the temerature rise and the volume flow of the air. Air is very sensitive to environmental anges su as the humidity, the temerature and density. Additionally, the measurement accuracy is affected by the heat leakage through Heat exanger P Power converter P wall T test T ga T amb (c) Closed tye, double-cased. Figure 2. Conventional calorimeter systems. the walls of the calorimeter P wall because the temerature the amber T test is different from the ambient temerature T amb. Therefore, the accuracy of this system is very affected from the environment. This calorimeter tye is often used for measurg duction maes with ower es u to several kilowatts. On the other hand, Fig. 2 (b) shows closed and sglecased tye calorimeter system. This system emloys a searate coolg loo for the heat exange with the ambient. Usg water for a coolant, this system is higher accuracy than the oen tye calorimeter. However, the measurement time becomes long because heat caacitance of water is higher comared with that of air. Fig. 2 (c) shows a closed and double-cased tye calorimeter system can crease the measurement accuracy. T ga is the air temerature the ga between the ner amber and outer amber. In this method, T ga is controlled to be equal to T test. Therefore, the ower consumtion for the heat leakage through the walls of the ner amber P wall can be zero. Therefore, the double-cased calorimeter is the highest accuracy the three tyes as mentioned above. However, this

system uses the circulatory organ for the coolant, comlex control circuits and sensor. As a result, these systems are exensive.

CPLM SYSTEM USING TWO CHAMBES Fig. 3 shows the control block diagram of roosed system whi is comosed by two ambers and a heater.

A ower converter as the measured object of the roosed system is laced the amber A.

T A saturates when the amount of heat consumtion from heater equals to the amount of heat consumtion from the amber surface.

It should be noted that a heater the amber B is controlled by the buck converter. T A is set to the command temerature of amber B.

whi is generated from the ower converter the amber A. Fig. 4 shows the rototye of the roosed CPLM system.

Two ambers are made from the exanded olystyrene. The heater cement resistor of 10 is used.

The ower measurements with the ower consumtion between 5 W and 25 W are demonstrated. The volume of the amber is V amb1 = 3.

The error rate set u with 10% based on the ower consumtion between 5 W and 25 W.

The temeratures of the air the two ambers are affected by the same ambient temerature because two ambers are laced same lace. IV.

equation of heat conduction. The ower converter is oerated the amber A.

The air the amber A is circulated by a fan.

3 system uses the circulatory organ for the coolant, comlex control circuits and sensor. As a result, these systems are exensive. Moreover, this method is also required to take the long measurement time due to high heat caacitance of water. III. CPLM SYSTEM USING TWO CHAMBES Fig. 3 shows the control block diagram of roosed system whi is comosed by two ambers and a heater. The ambers whi are made from sulator materials, are illustrated as the amber A and amber B Fig. 1. A ower converter as the measured object of the roosed system is laced the amber A. The temerature the amber A T A is creased by the ower of the ower converter. T A saturates when the amount of heat consumtion from heater equals to the amount of heat consumtion from the amber surface. The temerature the amber B T B is controlled by a feedback control usg the PI regulator. It should be noted that a heater the amber B is controlled by the buck converter. T A is set to the command temerature of amber B. When T B reaes the command value that is the saturated temerature the amber A, the ower consumtion of the heater the amber B equals to that whi is generated from the ower converter the amber A. Fig. 4 shows the rototye of the roosed CPLM system. The measurement accuracy is evaluated usg the rototye. Table I shows the used materials for the calorimeter. Two ambers are made from the exanded olystyrene. The heater cement resistor of 10 is used. For simlicity of the exeriment, a heater is used stead of the ower converter. The ower converter runs the amber A. The ower measurements with the ower consumtion between 5 W and 25 W are demonstrated. The volume of the amber is V amb1 = m 3 (ner dimension of amber; long 447 mm, width 322 mm, height 220 mm). The error rate set u with 10% based on the ower consumtion between 5 W and 25 W. The ower of the ower converter is evaluated from the ower consumtion of a heater amber B. The temeratures of the air the two ambers are affected by the same ambient temerature because two ambers are laced same lace. IV. THEOETICAL DISCUSSION In this section, the relationshi between the amber volumes and measurement time is discussed usg the theoretical equation of heat conduction. The ower converter is oerated the amber A. The temerature of the air the amber A rises, due to the heat quantity roduced by the ower of the ower converter. The air the amber A is circulated by a fan. Based on the heat conduction equation, the heat quantity Q (W) is led to dt c V dt A Q Q Q cool where, (kg/m 3 ) is the density of the air, c (J/gK) is the secific heat of air, V (m 3 ) is the ner volume of the amber A, T A (K) is the temerature of the air the amber A, Q Figure 3. System configuration of roosed CPLM usg two ambers. Figure 4. Prototye of roosed CPLM usg two ambers. TABLE I. USED MATEIALS FO THE CALOIMETE. (W) is the heat quantity from the side of the ower converter to the converter surface the amber A, Q (W) is the heat quantity from the converter surface to the measurement ot of the air temerature the amber A, Q cool (W) is the heat disarge from the amber A. Q and Q cool is exressed by (4) and (5). T TA r Q cool T A Tamb / amb Q / Here, Eq. (3) is also exressed by Eq. (6). A c V Q Q T dt r A Tamb/ dt where, T (K) is the ner temerature of ower converter, r (K/W) is the thermal resistance from side of the ower converter to the measurement ot of the room temerature,

4 T amb (K) is the ambient temerature, amb (K/W) is the thermal resistance of the amber A, (K/W) is the total thermal resistances (= r + amb ). Eq. (5) is transformed with Lalace transformation and resented as Q r T s T A amb c V sta s To 1 s s where, T o is the itial temerature the amber A. The heat quantity of the ower converter is assumed as the ste ut. Eq. (6) is derived term of the T A, and then it is alied with verse Lalace transformation, whi is shown (7). t t T A amb amb o Q T 1 e T e where amb (K/W) is the thermal resistance of the amber A, T amb (K) is the ambient temerature and is the time constant. is exressed by (8). 1/ c V If the arameters are known excet Q, (9) is derived by differentiatg (7) and translatg to logarithm. dt ln dt A Q ln c air r air T V T amb o 1 c V air air t As a result, the Q can derive by (9) before the temerature is saturated. The rise of the measured temerature is differentiated and both sides of equation are exressed logarithmically. Moreover, the regression curve is analyzed from the exerimental results. The measurement results are exressed by 1st order equation. The and the r is showed by (10) and (11) by usg the sloe a and the tercet b, resectively. 1/ c V a air air c V ex b / Q r air air From (10) and (11), when the amber volume V is small, the surface area of the amber is decreased. Then, the time constant of the temerature rise is creased by creasg of amb. Therefore, the measurement time will be long because the time of the temerature saturations becomes long when the amber volume V is small. V. EXPEIMENTAL ESULTS In order to valid the theoretical analyses of the roosed method, exeriments are conducted by usg rototye exerimental setu Chamber A(Converter) Chamber B(Heater) Ambient Measurement time [s] Figure. 5. Temerature control results for constant temerature command usg PI control Power consumtion P [W] Figure. 6. Measurement error rate of the ower measurement based on steady state condition. When ower consumtion is 5 W and 25 W, measurements were done three times. Error rate [%] A. Power measurement based on steady state condition Two ambers are made from the exanded olystyrene. For simlicity of the exeriment, a heater is used stead of the ower converter the amber A. Fig. 5 shows the exerimental result of the temerature control by usg PI regulator at P = 5 W. From Fig. 5, it is confirmed that the temerature the amber B is equaled to the temerature the amber A by usg PI control. Fig. 6 shows the fluctuation band of the ower measurement error rate when the temerature is saturated on the steady state. The ower consumtion of the ower converter is measured three times at the ea ower consumtion. From Fig. 2, it is confirmed that the maximum error of ower is 8.0% at P = 5 W. In this case, all measurement accuracy becomes with 0.08% when the converter that has the efficiency of 99% at 1kW. In theory, when the temerature deviation of the amber A and amber B is 0 degrees Celsius, the heater ower consumtion the amber B erfectly agrees with the ower the amber A the roosed system. However, there are measurement errors the exerimental results. This reason is the difference of the ambient temerature between the amber A and the amber B. Fig. 7 and Fig. 8 show the surface temerature of the ambers. Before the measurement, it is confirmed that it is low. In the steady state after them temerature was saturated, the surface temerature becomes around 13 degree Celsius. From the results, it is seen that there are variations of the surface temeratures of the ambers. However, from the results of Fig. 6, Fig. 7 and Fig. 8, the measurement error is with 8% even if there are variations of the temerature.

Temerature ( degree ) Temerature ( degree ) (a) Before a measurement. (b) Chamber A Chamber A Chamber B 15.0 14.0 13.0 12.

(b) Chamber B Figure. 8. Surface temerature of two ambers after temerature was saturated. Temerature ( degree ) B.

9 shows the error rate of the ower consumtion of the heater between the measurement value of the calculated values whi is

In addition, it is confirmed that the measurement time is shortened by 86.

Power measurement by transient resonse of temerature rise In this section, the temerature the amber B is controlled to

10 shows that the temerature of the amber B T B is controlled to the temerature of the amber A T A a short time.

3, it is confirmed the temerature the amber B reaes to the temerature the amber A the transient states of the temerature

11 shows the ower consumtion of the ower converter and the heater when the temerature of the amber B is controlled as shown

As a result, it is confirmed that the measurement time is shortened by 87.

Measurement accuracy comarison with EPM In this section, the rototye system is exerimentally tested usg a switg (SW) ower

5 Temerature ( degree ) Temerature ( degree ) (a) Before a measurement. (b) Chamber A Chamber A Chamber B (b) After temerature was saturated. Figure. 7. Surface temerature of two ambers. (b) Chamber B Figure. 8. Surface temerature of two ambers after temerature was saturated. Temerature ( degree ) B. Power measurement usg heat conduction equation formula Fig. 9 shows the error rate of the ower consumtion of the heater between the measurement value of the calculated values whi is obtaed by (10) and (11). As a result, it is confirmed that the error rate of the ower consumtion is with 10%. In addition, it is confirmed that the measurement time is shortened by 86.1% comared with the method based on the steady state condition. C. Power measurement by transient resonse of temerature rise In this section, the temerature the amber B is controlled to follow the temerature the amber A for the transient state of the temerature rise. Fig. 10 shows that the temerature of the amber B T B is controlled to the temerature of the amber A T A a short time. Note that the ower consumtion of the ower converter is 25 W. Accordg to Fig. 3, it is confirmed the temerature the amber B reaes to the temerature the amber A the transient states of the temerature rise. Fig. 11 shows the ower consumtion of the ower converter and the heater when the temerature of the amber B is controlled as shown Fig. 11. The ower consumtion of the heater is equaled to the ower consumtion of the converter on 1350 s. As a result, it is confirmed that the measurement time is shortened by 87.5% comare with the ower measurement based on the steady state. D. Measurement accuracy comarison with EPM In this section, the rototye system is exerimentally tested usg a switg (SW) ower suly that has the maximum efficiency of 67% whi was measured by the EPM. The ower of the SW ower suly used this Figure. 9. Error rate of the ower consumtion between the measurement values and the calculation values. Figure. 10. Temerature of the amber B is controlled to the temerature of the amber A a short time. exeriment 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 the accuracy of the roosed CPLM. Outut ower of the SW ower suly P out is set to 1, 5, 20, 30 and 40 W. The ower es of the SW ower suly P SW are measured by the rototye three times at ea P out.

6 Fig. 12 shows the measurement error of the P SW at ea P out. The maximum measurement error is 6.1% at P SW = 10.7 W (P out = 1 W). On the other hand, the mimum measurement error is 0.6% at P SW = 16.8 W (P out = 30 W). E. elationshi among the amber volume, measurement accuracy and measurement time The measurement accuracy and measurement time are determed by the amber volume CPLM methods. The amber volume is aroximately 30 times the volume of the SW ower suly used the revious section. In this section, the amber with twice volume is used for measurg the P SW. Fig. 13 shows the measurement accuracy and the measurement time when the amber volume varies at P SW is 10.7 W. When the V amb2 is used, the maximum measurement error is 3.74%. However, the measurement time is extended from 4380 s to 6600 s. The high measurement accuracy is obtaed by decreasg the amber volume. In contrast, the measurement time becomes longer. The thermal resistance amb creases due to the decreasg of a surface area. From (8), the value of the time constant is creased by creasg of amb. It means that the eriod of the temerature saturation also becomes long. As a result, the decrease of the amber volume hels to aieve the high measurement accuracy because the temerature disersion the amber is decreased by decreasg the amber volume. VI. CONCLUSION In this aer, the low cost CPLM system for a high efficiency converter is roosed. The roosed system is constructed at a low cost without the thermostatic ambers whi cause a high cost of the CPLM system. The method for measurement of the ower by the temerature rise with the of ower converter is discussed. The maximum error of the measured ower consumtion was with 6.1%. Moreover, the relationshi between the measurement accuracy and the measurement time was exerimentally verified by usg the rototye with the reduced volume of the amber. As the result, it was confirmed that the measurement accuracy and time becomes higher and longer by decreasg the amber volume. EFEENCES [1]. Kamei, A. kawamura, T. kim, Discussion on Highly Accurate Calorimetric for Power Loss Measurement, Annual Conference of I.E.E. of Jaan, Industry Alications Society,.I-363-I-366 (2011) [2] A. Stafiak, G. Kosobudzki, Sources of Error AC Losses Measurement Usg V-I Method, IEEE tran. VOL. 19, NO. 3, (2009) [3] W. Yu, H. Qian, J. S. Lai, Design of High-Efficiency Bidirectional DC DC Converter and High-Precision Efficiency Measurement, IEEE tran. VOL. 25, NO. 3, (2010) [4] F. Forest, J. J. Huselste, S. Fauer, M. Elghazouani, P. Ladoux, T. A. Meynard, F. iardeau, C. Tur, Use of Oosition Method the Test of High-Power Electronic Converters, IEEE tran. VOL. 53, NO. 2, (2006) [5] B. Szabados, A. Mihalcea, Design and Imlementation of a Calorimetric Measurement Facility for Determg Losses Electrical Maes, IEEE tran. VOL. 51, NO. 5, (2002) Figure. 11. Power consumtion of converter and heater when the temerature of the amber B is controlled as show Fig P out = 1W 6 P out = 5W 5 4 P out = 20W P out = 40W 3 P out = 30W Power consumtion P SW [W] Figure. 12. Measurement error rate of the ower consumtion of a switg ower suly with the roosed CPLM system based on transient resonse of temerature rise. Measurements were done two times or three times at ea ower consumtion. 7.0 Measurement error rate[%] V amb1 /V sw = 30 V SW : 1075cm 3 V amb1 : 31700cm 3 V amb2 : 2280cm 3 V amb2 /V sw = Measurement time [s] Figure. 13. elationshi among the measurement error rate, the measurement time and the amber volume. [6] D. Christen, U. Badstuebner, J. Biela, J.W.Kolar : Calorimetric Power Loss Measurement for Highly Efficient Converters, I PEC2010, (2010) [7] S. Weier, M. A. Shafi,. McMahon Precision Calorimetry for the Accurate Measurement of Losses Power Electronic Devices, IEEE tran. VOL. 46, NO. 1, (2010) [8] J. Itoh, A. Nigorikawa: "Exerimental Analysis on Precise Calorimetric Power Loss Measurement Usg Two Chambers", EPE-PEMC 2012, DS2b (T2) (2012) [9] G. Chen, C. Xiao, and W. Odendaal, An aaratus for measurement of tegrated ower electronics modules: design and analysis, Conference ecords of the 37 th Annual Industry Alications Conference (IAS), 2002, [10] P. Wolfs and Q. Li, Precision calorimetry for ower measurement of a very low ower maximum ower ot tracker, Australasian Universities Power Engeerg Conference (AUPEC), 2007,.1-5. [11] D. Christen, U. Badstuebner, J. Biela, J.W.Kolar : Calorimetric Power Loss Measurement for Highly Efficient Converters, I PEC2010, (2010)

The extreme case of the anisothermal calorimeter when there is no heat exchange is the adiabatic calorimeter.

The extreme case of the anisothermal calorimeter when there is no heat exchange is the adiabatic calorimeter. .4. Determination of the enthaly of solution of anhydrous and hydrous sodium acetate by anisothermal calorimeter, and the enthaly of melting of ice by isothermal heat flow calorimeter Theoretical background