Interpolation Procedures
for the Determination of
Losses and Energy Efficiency
of Electrical Machines
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Karlsruhe Institute of Technology (KIT)
Institute of Electrical Engineering (ETI)
Germany
Chairman of IEC TC2 WG31
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Efficiency Contour Plot Over Speed And Torque
Efficiency Contour
1
0,9
0,8
0,9000-0,9500
0,7
0,6
0,8500-0,9000
0,8000-0,8500
Torque
0,7500-0,8000
0,5
0,7000-0,7500
0,6500-0,7000
0,4
0,3
0,6000-0,6500
0,5500-0,6000
0,5000-0,5500
0,2
0,1
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Speed
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Determination of Relative (Related) Losses
• Losses are more meaningful than efficiency
• Losses have a smoother behavior than efficiency and are better suited for
interpolation
• Losses, power, speed, frequency and torque will always be regarded as relative to
the nominal values:
T=1
is rated torque
n=1
is rated speed
f=1
is rated frequency
η=1
is 100% efficiency
P=1
is rated output (mechanical) power
• Operation of machine limited to constant flux (U/f = const), i.e. T = 0…1, f = 0…1
• No overload operation (T > 1)
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Development of Interpolation Formula Based on Equivalent Circuit Calculations
Stator and rotor
winding losses (PLS + PLR)
Iron losses (PLfe)
Additional load losses (PLL)
Friction and windage losses (PLfw)
Additional harmonic losses (PLHL)
Simple, physical/mathematical interpolation formula using 7 parameters:
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Efficiency
Determining the 7 Parameters
From 7Contour
Operating Points
1
0,9
90% speed to avoid loss of flux
at 100% speed due to voltage
0,9000-0,9500
limitations
of the frequency
0,8500-0,9000
converter!
0,8
0,7
0,8000-0,8500
0,6
Torque
0,7500-0,8000
0,5
0,7000-0,7500
0,6500-0,7000
0,4
0,6000-0,6500
0,5500-0,6000
0,3
0,5000-0,5500
0,2
0,1
0
0
0,1
0,2
0,3
0,4
0,5
Speed
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
0,6
0,7
0,8
0,9
1
P1
P2
P3
P4
P5
P6
P7
f
0.9
0.5
0.9
0.5
0.25
0.5
0.25
Interpolation Procedure Motor Losses
T
1
1
0.5
0.5
1
0.25
0.25
P
0.9
0.5
0.45
0.25
0.25
0.125
0.0625
Comment
Also included
Also included
Also included
Also included
in
in
in
in
IEC 61800-9-2
IEC 61800 -9-2
IEC 61800 -9-2
IEC 61800 -9-2
Also included in IEC 61800 -9-2
September 2015
Determination of the 7 Parameters
• Analytically from measurement of losses at the 7 standardized operating points
• Analytically from measurement of losses at the 7 alternate operating points
(measurements at 90% speed replace by measurements at 100% speed)
• Numerically from measurement of losses at 16 operating points
(search for least overall error – Interpolation stability index QISI)
• Any other method chosen by the manufacturer
Regardless of how the interpolation parameters were determined:
The application (the formula) for the user is always the same !
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Analytical Determination of 7 Parameters from the 7 Operating Points
Solving a system of linear equations:
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Analytical Determination of 7 Parameters from the 7 Operating Points
Losses at:
P1 = (90,100)
P2 = (50,100)
P3 = (90,50)
P4 = (50,50)
P5 = (25,100)
P6 = (50,25)
P7 = (25,25)
(speed, torque)
Px = 0...1
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Analytical Determination of 7 Parameters from 7 Alternate Operating Points
Losses at:
P1* = (100,100)
P2 = (50,100)
P3* = (100,50)
P4 = (50,50)
P5 = (25,100)
P6 = (50,25)
P7 = (25,25)
(speed, torque)
Px = 0...1
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Interpolation Stability Index – Based on 16 Measured Operating Points
QISI is the standard deviation of the interpolated values from the real values
across all 16 points, i.e. the average interpolation error:
QISI <= 5 %
QSI <= 10%
QISI > 20%
very good
Acceptable
not usable
The determination of the 7 parameters (A…G) is performed by a numerical search for
the minimum QISI.
An EXCEL-Sheet with a VBA algorithm will be provided through IEC.
Alternatively, EXCEL’s built-in Solver (optional installation) or MATLAB can be used.
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Proposed Testing Points – Numerical Determination of 7 Parameters = 16 Points
Efficiency Contour
1
0,9
0,8
0,9000-0,9500
0,7
0,6
0,8500-0,9000
0,8000-0,8500
Torque
0,7500-0,8000
0,5
0,7000-0,7500
0,6500-0,7000
0,4
0,3
0,6000-0,6500
0,5500-0,6000
0,5000-0,5500
0,2
0,1
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Speed
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
A Practical Example
Measurement results of a 37 kW, 4-pole induction machine:
Torque
1
0,75
0,5
0,25
0,7950
0,8183
0,8221
0,7678
0,25
0,8709
0,8786
0,8725
0,8250
0,5
0,9009
0,9047
0,8967
0,8508
0,75
0,9131
0,9193
0,9126
0,8729
1
Speed
From the grey shaded operating points the 7 interpolation
coefficients were determined to be:
A = 0,00511
B = 0,04368
C = -0,01829
D = -0,00858
E = 0,02300
F = 0,00487
G = 0,04540
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
A Practical Example
Measurement results:
Torque
1
0,75
0,5
0,25
0,7950
0,8183
0,8221
0,7678
0,25
0,8709
0,8786
0,8725
0,8250
0,5
0,9009
0,9047
0,8967
0,8508
0,75
0,9131
0,9193
0,9126
0,8729
1
Speed
Compared to the interpolated efficiency values (analytically from 7 points):
Torque
1
0,75
0,5
0,25
0,7950
0,8111
0,8144
0,7678
0,25
0,8709
0,8774
0,8725
0,8250
0,5
0,8989
0,9030
0,8972
0,8541
0,75
0,9131
0,9171
0,9126
0,8758
1
Speed
QISI = 2,31 %
Compared to the interpolated efficiency values (numerically from 16 points):
Torque
1
0,75
0,5
0,25
0,7952
0,8146
0,8193
0,7665
0,25
Univ.-Prof. Dr.-Ing. Martin
0,8708
0,8786
0,8733
0,8199
0,5
Doppelbauer
0,8988
0,9033
0,8966
0,8478
0,75
0,9130
0,9171
0,9114
0,8693
1
Speed
Interpolation Procedure Motor Losses
QISI = 1,92 %
September 2015
A Practical Example
Losses over Speed - analy cal 7 points
Losses over Speed - XSOLVE 16 points
0,100
0,120
0,090
0,100
0,080
100% Torque
100% Torque
0,080
75% Torque
0,060
50% Torque
0,050
25% Torque
0,040
100% Interpola on
0,030
75% Interpola on
Losses
Losses [%]
0,070
75% Torque
50% Torque
0,060
25% Torque
Datenreihe6
0,040
Datenreihe7
50% Interpola on
0,020
Datenreihe8
0,020
25% Interpola on
0,010
0,000
Datenreihe9
0,000
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0
0,1
0,2
0,3
0,4
Speed [%]
0,5
0,6
0,7
0,8
0,9
1
Speed
Losses over Torque - analy cal 7 points
Losses over Torque - XSOLVE 16 points
0,100
0,120
0,090
0,100
0,080
100% Speed
100% Speed
0,080
75% Speed
0,060
50% Speed
0,050
25% Speed
0,040
100% Interpola on
0,030
75% Interpola on
Losses
Losses [%]
0,070
75% Speed
50% Speed
0,060
25% Speed
Datenreihe5
0,040
Datenreihe6
50% Interpola on
0,020
25% Interpola on
0,010
0,000
Datenreihe7
0,020
Datenreihe8
0,000
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0
0,1
0,2
0,3
Torque [%]
0,4
0,5
0,6
0,7
0,8
0,9
1
Torque
Losses are linearly depending on speed – typical for ASM
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Another example : PM-motor
Losses over Torque - XSOLVE 7 points
0,060
0,050
100% Speed
Losses
0,040
75% Speed
50% Speed
0,030
25% Speed
Datenreihe5
0,020
Datenreihe6
Datenreihe7
0,010
Datenreihe8
0,000
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Torque
Losses are rapidly increasing at high speeds – typical for PMSM
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015
Mass Testing of the Interpolation Formula
A total of 128 motors were analyzed:
• Data from Leroy Somer, Quebec Hydro, KSB, Siemens, Grundfos, WILO
• Induction machines (ASM), Permanent Magnet SM, Reluctance SM
• IE2, IE3, IE4
• 0,12 … 1000 kW
• 2-, 4-, and 6-pole
Interpolation procedures:
• Proposed interpolation formula – analytically determined parameters (7 points)
• Proposed interpolation formula – numerically determined parameters (16 points)
• EN 50598-2 linear interpolation (G.2.3) (8 points)
7-coeff
analytical
7 points
7-coeff
numerical
16 points
EN 505982 linear
interpol.
Average error all 128 motors
1,7 %
1,8 %
8,6 %
Max error all 128 motors
7,8 %
10,8 %
20,6 %
Average error 76 IE2 ASM
0,4 %
0,9 %
7,9 %
Average error 32 SynREL
3,2 %
2,7 %
8,7 %
Average error 9 PMSM
4,3 %
4,4 %
11,4 %
Univ.-Prof. Dr.-Ing. Martin
Doppelbauer
Interpolation Procedure Motor Losses
September 2015