Accepted for presentation at IEEE IEMDC 2015, Coeur d’Alene, USA
Real-Time Sensorless Speed Estimation in Wound Rotor Induction Machines using a Dichotomous Search Algorithm K. Tshiloz, Student Member, IEEE, S. Djukanović, Member, IEEE and S. Djurović, Member, IEEE Abstract – This paper investigates the development and realtime implementation of a dichotomous search algorithm based sensorless speed estimation technique in wound rotor induction machines. To this end the authors present the description of the structure and implementation of the technique proposed to extract the desired slip dependent frequency and hence the rotor speed information from the machine stator current spectrum. The performance of the presented algorithm in delivering estimation rate and accuracy improvements is then assessed and validated in real-time speed estimation tests undertaken on a 7.5 kW induction generator operating in the nominal and extended slip range. Index Terms - Dichotomous search, real-time sensorless speed estimation, wound rotor induction generator.
I. INTRODUCTION The possibility of eliminating the need for a mechanical speed sensor through development of sensorless rotor speed estimation schemes has been investigated in conventional cage rotor induction (CRIM) machinery [1]-[5]. Wound rotor induction machines (WRIMs), extensively used in variable speed applications in the wind industry, have received significantly less attention in this respect [6]-[7]. Spectral components present in the current signals have been utilised to achieve real-time detection and tracking of CRIM rotor speed [1]. Rotor-slot and eccentricity harmonics were extracted in [1], [5] using the maximum entropy spectral estimation or interpolation method in combination with the Fast Fourier transform (FFT). The published real-time performance limitations of these methods state a steady-state estimation error of up to 1%, for which the reported estimation rates are limited at up to approximately 4 estimations per second [1], [5]. Spectral analysis based real-time sensorless speed estimation performance limitations during CRIM transient operating regimes have been less investigated in available literature. Model reference adaptive systems (MRAS) [8]-[9] provide an alternative for obtaining sensorless speed estimation. However, the performance of MRAS is sensitive to the accuracy of machine K. Tshiloz and S. Djurović are with the Power Conversion Group, School of Electrical and Electronic Engineering, The University of Manchester, Manchester M13 9PL, UK. (E-mail:
[email protected]). S. Djukanović is with the Faculty of Electrical Engineering, University of Montenegro, 20000 Podgorica, Montenegro.
parameters and prior knowledge of machine characteristics is required. Combined with FFT analysis, the dichotomous search algorithm [10] presents a potential alternative to spectral processing methods proposed in reported spectral frequency extraction based sensorless schemes [1], [5] as it provides an inherent advantage in the frequency estimation rate without compromising the estimation accuracy. This work investigates the application of a dichotomous search based frequency extraction method to provide improved rate real-time sensorless speed estimation on a laboratory WRIM in steady-state and transient operating regimes. The manuscript first describes the structure and the implementation of the dichotomous search based algorithm proposed for realtime extraction of slip-dependent WRIM stator line current spectral components reported in [11]-[13]. The performance of the presented method in delivering reliable real-time steady-state and transient speed estimation is assessed by direct comparison with synchronously recorded encoder speed measurements. The estimation algorithm is implemented on an NI CompactRIO (cRIO) real-time platform. The algorithm performance is evaluated on an industrial 7.5kW WRIM design operating as a generator. The laboratory machine is operated in the nominal but also in the -10% slip range to emulate a Type-II configuration wind turbine WRIM application [14]-[15]. The presented procedure is demonstrated to have a strong potential for providing a reduction in the required estimation time while maintaining good real-time estimation accuracy. II. DICHOTOMOUS SEARCH BASED REAL-TIME SPEED ESTIMATION The dichotomous search frequency estimation is a binary search approach that consists of the coarse and the fine search steps [10]. In the coarse search step, the periodogram is calculated using an L-samples long discrete Fourier transform (DFT) with a relatively large frequency resolution Δf, and the frequency fmax that maximises the periodogram is identified. In the fine search step, the frequency estimation is adjusted towards a larger of the two DFT coefficients from either side of the identified peak. A New DFT coefficient is then calculated halfway between the peak and the larger coefficient; its position represents an improved frequency estimation over that initially obtained in the coarse search step. The procedure is repeated Q times to refine the obtained frequency estimation. The dichotomous search frequency estimator can be described by the following steps:
Sense: Stator Line Current
Monitored Supply Frequency
FFT coarse search for slip-dependent frequency, Initial search
Extracted Frequency
Filter Bandwidth Containing SpeedDependent Component
r
9 p
f Estimated f s
Frequency estimation refirement using Dichotomous fine search, fEstimated
Calculate Speed Output Speed
Fig.1: Speed estimation algorithm
Step 1. Coarse search Calculate the periodogram I(f) at the grid of Fourier frequencies and find the position of the periodogram maximum fmax. Denote I 0 =I(f max ). Calculate I(f) at points f max ±Δf/2, i.e.
I 1 I f max f / 2
Pole Number
Speed Estimation
fs
I1 I f max f / 2 .
Step 2. Iterations Iterate Q times f f / 2 if I1 I 1 then I -1 I 0 and f max f max f else I1 I 0 and f max f max f calculate I ( f max ) and set I 0 I ( f max ).
The final frequency estimation is the fmax value obtained in the Q-th iteration. While the estimation accuracy improves with the increase of Q, this improvement is typically not significant above Q=10 [9]. The WRIM real-time speed estimation algorithm employed in this work is based on the analysis presented in [6], [10], [11], [16]-[18]. This work has shown that the fundamental supply induced WRIM stator current slipdependent components, f, can be expressed as a function of rotor slip, s, by: f = [6k(1-s)±1]fs (1) where fs is the supply fundamental frequency and k = 1,2,3… This work utilises the k = 3 upper component in the laboratory machine’s stator current to extract the information on rotor speed from (1), as proposed in [6]. The slip dependent component’s frequency is extracted in real-time in an algorithm containing the following general steps: 1) Coarse Fast-Fourier transform (FFT) search in a set bandwidth, constant duration, time window of the stator line current signal. 2) Extraction of the low resolution narrow-band current spectrum containing the spectral frequency that carries information on rotor speed. 3) Execution of the iterative Dichotomous algorithm based fine search in the extracted narrow-band spectrum to obtain accurate
information on slip-dependent current component frequency. The extracted frequency value is used to obtain the realtime rotor speed estimation. The extraction algorithm flowchart is presented in Fig.1. III. EXPERIMENTAL SETUP AND REAL-TIME ALGORITHM IMPLEMENTATION Experimental work was performed on a laboratory test rig comprising of a 7.5 kW, 4 pole, 50 Hz star connected VEM 160M4 WRIM [19] driven to operate in the generating mode by a speed controlled 15.5 kW DC machine prime mover, shown in Fig.3. The prime mover speed can be regulated to follow a desired steady-state or transient time profile using the DC drive controller. The WRIM rotational speed is measured using a 1024 ppr stub shaft mounted incremental encoder. The stator line current was measured with an LEM LA 305-S current transducer. The measured signals are recorded and processed with an NI-9024 cRIO real-time platform: the NI-9205 analog input module was used to record the measured stator line current and the NI-9401 digital module to monitor the encoder output signals. The cRIO utilises the LabVIEW FPGA and real-time modules in a reconfigurable platform enabling practical execution of real-time applications through development of an appropriate LabVIEW virtual instrument (VI) code architecture. The cRIO embedded real-time frequency extraction algorithm is divided into two sections in this work: data collection and FFT processing on the FPGA module and the execution of the coarse and the fine search algorithms hosted on the cRIO controller. The
WRIM
DC MACHINE
Fig.3: 7.5 kW Laboratory test rig
FPGA VI was developed to execute a 2n data point FFT of the measured current in consecutive, non-overlapping, constant length Hanning windows, extract the supply frequency (fs), and perform the time and frequency domain data transfer to the cRIO controller for further processing. The developed controller VI executes the proposed estimation algorithm for tracking a known slipdependent stator line current spectral component in a predefined bandwidth, according to the information presented in Fig.1. A simplified schematic of the realtime estimation algorithm practical implementation is shown in Fig.2. NI-9205 analog input module
LEM LA 305-S Current Sensor
Dichotomous search on 800 MHz cRIO Controller
FFT on 40 MHz FPGA cRIO
Fig.2: Simplified block diagram of the real-time algorithm implementation
IV. REAL-TIME ESTIMATION EXPERIMENTAL RESULTS A. Performance Evaluation
1520 1500
1620 Encoder Dichotomous 1600 FFT 1580
Speed [rpm]
Encoder 1560 Dichotomous 1540 FFT
Speed [rpm]
Speed [rpm]
The real-time performance of the developed algorithm was tested in a series of laboratory experiments. The laboratory machine was first operated in steady-state to obtain an initial evaluation of the estimation algorithm performance. The machine was then operated as a generator in a range of no-load to full load speed ramps of 0.25, 0.5, 1, 2, 4, 8, 16 and 32 second duration, covering the nominal (-3.3%) or extended (-10%) slip range. During the tests in the nominal slip range the machine was operated with short circuited rotor windings and with the stator windings connected to the grid. The 10% slip range was achieved by coupling the rotor windings via slip rings to an external 0.5 Ω/phase three-phase resistor bank and keeping the stator windings connected to the grid. The comparison of experimental results for the measured and the estimated speed signals recorded synchronously during tests is shown in Figs.4-21. To enable the evaluation of the proposed algorithm’s performance against a conventional FFT only based frequency extraction method, the real-time speed
estimation was simultaneously obtained using two procedures: a 2n point FFT routine executed on the FPGA module and the proposed 2n FFT+dichotomous search extraction algorithm. For operation in the nominal speed range a pre-determined optimal FFT window size of 28 data points was used, while the optimal value of n was investigated for the extended speed range, as reported in section IV.B. The estimation accuracy for the considered operating scenarios was then evaluated by investigating the standard deviation and maximum error levels in comparison to the synchronously obtained encoder measurement, shown in Tables 1-3. In order to include the bandwidth containing the spectral information of interest the current was sampled at 2 kHz for the nominal slip range experiments and at 2.15 kHz for the extended slip range experiments. The proposed dichotomous algorithm was first executed with 10 iterations, which is a conventionally used iteration number level in dichotomous search applications [10]. In addition, a 100 iteration search was also executed in the experiments in order to evaluate the possibility of refining the estimation performance. The real-time platform execution time of a single window FFT+dichotomous algorithm search, excluding the FPGA module to controller data transfer time, was measured on the cRIO platform to require ≈0.326 ms for the maximum considered iteration number. The measured single search execution time compares favourably to the applied FFT window duration at sampling rates used in this work. The results of steady-state experiments for no-load and nominal operating points are shown in Figs.4-5. The corresponding measured estimation error and its deviation rates for the considered dichotomous search iteration numbers are presented in Table1. Both sets of steady-state results clearly show a marked performance improvement to that obtained from an FFT only estimation. The proposed estimation algorithm delivers a ≈35% improvement in the estimation maximum error and a ≈72% improvement in the standard deviation error, reflecting the steadier nature of the FFT+dichotomous obtained results in Figs.4-5.
1560 1540
1480
Encoder 1560 Dichotomous FFT 1540 1520 1500
1520 1460 2
4
6 Time [Sec]
8
1500 0
10
2
1520 1500 1480 0
2
4
6 8 Time [Sec]
1480 0
8
Fig 5: Nominal speed
Encoder 1560 Dichotomous FFT 1540
Speed [rpm]
Speed [rpm]
Fig.4: No-load speed
4 6 Time [Sec]
10
12
Fig 7: 0.5 sec speed ramp, nominal slip range
1520 1500 1480 0
2
4
6 Time [Sec]
2
4
6 8 Time [Sec]
10
12
14
Fig.6: 0.25 sec speed ramp, nominal slip range
Encoder 1560 Dichotomous FFT 1540
Speed [rpm]
0
8
10
Fig 8: 1 sec speed ramp, nominal slip range
Encoder 1560 Dichotomous FFT 1540 1520 1500 1480 0
5
10 Time [Sec]
15
20
Fig 9: 2 sec speed ramp, nominal slip range
1500 1480 0
5
10 15 Time [Sec]
1520 1500 1480 0
20
Encoder 1560 Dichotomous FFT 1540
1650
1520 1500
20
30 40 Time [Sec]
50
1500
2
4
6 Time [Sec]
8
4 6 Time [Sec]
8
1700
Speed [rpm]
1650
1600 1550
Fig 16: 1 sec speed ramp, -10% slip range
Speed [rpm]
1600 1550 1500
2
4 Time [Sec]
6
5
10 Time [Sec]
15
Fig 19: 8 sec speed ramp, -10% slip range
1700 1650
1600 1550
5
10
Dichotomous (10 & 100)
Max Error Standard Deviation
Max Error [%]
Max Error Standard Deviation
1.20, 1.01
0.39, 0.41
0.77, 0.67
0.11, 0.11
Dichotomous to FFT Performance Comparison
-35.9%, -34.2%
15 20 Time [Sec]
25
30
Fig 20: 16 sec speed ramp, -10% slip range
Max Error [%]
Max Error [% change]
5
10 Time [Sec]
15
Dichotomous Encoder FFT
1600 1550 1500
Table 1: Measured real-time steady-state performance FFT (256)
1550
Fig 18: 4 sec speed ramp, -10% slip range
Dichotomous Encoder 1650 FFT
1450 0
Dichotomous Encoder FFT
1450 0
8
1500
1450 0
4
1500
1700
Dichotomous Encoder 1650 FFT
2 3 Time [Sec]
1600
Fig 17: 2 sec speed ramp, -10% slip range
1700
1
Fig 15: 0.5 sec speed ramp,-10% slip range
Dichotomous Encoder 1650 FFT
1450 0
10
Dichotomous Encoder FFT
1550
1450 0
10
1500 2
40
1600
Fig 14: 0.25 sec speed ramp, -10% slip range
Speed [rpm]
Speed [rpm]
1550
20 30 Time [Sec]
1500
1700
1600
10
Fig 12: 16 sec speed ramp, nominal slip range
1650
1550
1700
Speed [rpm]
Dichotomous Encoder FFT
1450 0
60
Dichotomous Encoder 1650 FFT
1500
1700
1500
10
1520
1480 0
25
1600
Fig 13: 32 sec speed ramp, nominal slip range
1450 0
20
Speed [rpm]
1480 0
10 15 Time [Sec]
Encoder 1560 Dichotomous FFT 1540
Fig 11: 8 sec speed ramp, nominal slip range 1700
Speed [rpm]
Speed [rpm]
Fig 10: 4 sec speed ramp, nominal slip range
5
Speed [rpm]
1520
Encoder 1560 Dichotomous FFT 1540
Speed [rpm]
Speed [rpm]
Speed [rpm]
Encoder 1560 Dichotomous FFT 1540
Max Error Standard Deviation [% change] -72.1, -72.2
The difference in estimation performance between execution of 10 and 100 dichotomous search iterations is seen to be minimal for the investigated steady-state scenarios. No significant improvement was observed for a further increase in the iteration number. The presented measurements indicate that accurate real-time speed estimation is achieved by the proposed algorithm in the steady-state mode operation. The experimental results for the transient tests in the nominal slip range are shown in Figs.6-13. A number of
1450 0
10
20 30 Time [Sec]
40
50
Fig 21: 32 sec speed ramp,-10% slip range
different gradient no-load to full load speed ramps were investigated in order to evaluate the potential and the limitations of the proposed algorithm for real-time estimation during realistic transient conditions with a range of different dynamics. The considered acceleration ramps ranged from a slow ≈32 second noload to full load transient to a rapid ≈0.25 second ramp. Identical to the steady-state analysis, a 10 and a 100 iteration dichotomous search algorithms were executed in real-time tests to investigate the optimal algorithm settings. The measured estimation error and its deviation values corresponding to results in Figs.6-13 are shown in Table2. The presented time domain data demonstrate a good level of performance for the slower ramps, while the transient regime estimation performance is not as accurate for the faster 0.25, 0.5 and 1 second duration ramps. The measured error values indicate that the maximum error for the investigated 2, 4, 8, 16 and 32 second transient profiles remains within the 1% margin. However, the maximum estimation error level increases to up to 2.70% for the fast 0.25, 0.5 and 1 second ramps. In comparison to the
Table 2: Measured real-time estimation performance, transient operation in the nominal slip range FFT (256) Ramps [Sec]
Max Error [%]
32 16 8 4 2 1 0.5 0.25
Dichotomous (10 & 100)
0.84, 0.64
Max Error Standard Deviation 0.11, 0.09
Dichotomous to FFT Performance Comparison Max Error Max Error [% change] Standard Deviation [% change] -23.58, -31.18 -53.32, -63.18
0.85, 0.68 0.90, 0.80 0.80, 0.81 1.09, 0.85 1.56, 1.41 2.52, 2.22 2.85, 2.70
0.13, 0.11 0.13, 014 0.15, 0.12 0.19, 0.14 0.24, 0.22 0.30, 0.31 0.42, 0.36
-28.40, -26.80 -26.26, -33.14 -23.90, -31.50 -18.81, -33.23 -21.46, -23.20 -8.90, -11.58 -0.08, -7.90
Ramps [Sec]
Max Error [%]
1.10, 1.18
Max Error Standard Deviation 0.25, 0.30
32
1.20, 0.93 1.22, 1.20 1.08, 1.19 1.35, 1.28 1.99, 1.85 2.81, 2.88 2.85, 2.94
0.29, 0.35 0.38, 0.40 0.32, 0.38 0.40, 0.43 0.50, 0.48 0.37, 0.34 0.44, 0.36
16 8 4 2 1 0.5 0.25
-53.05, -68.90 -63.73, -64.96 -51.04, -65.9 -51.36, -68.7 -51.42, -54.1 -13.3, -12.8 -2.32, -1.5
Table 3: Measured real-time estimation performance, transient operation in the -10% slip range FFT (256) Ramps [Sec]
Max Error [%]
32 16 8 4 2 1 0.5 0.25
1.13, 1.10 1.33, 1.09 1.41, 1.22 1.53, 1.62 2.76, 3.35 4.81, 5.88 8.92, 9.31 11.53, 11.68
Dichotomous (10 & 100) Max Error Standard Deviation 0.32, 0.28 0.48, 0.23 0.53, 0.46 0.62, 0.63 1.08, 0.72 1.30, 1.36 1.93, 1.77 2.01, 2.25
Ramps [Sec]
Max Error [%]
32 16 8 4 2 1 0.5 0.25
0.96, 0.75 1.01, 0.78 1.10, 1.08 1.27, 1.15 2.50, 3.10 4.91, 6.07 8.63, 9.13 11.63, 11.89
FFT algorithm, the FFT+dichotomous search estimation provides a clear improvement in the maximum error margin and a significant improvement in the estimation error deviation. Increasing the search iteration number to 100 was found to result in a general useful improvement of real-time performance parameters. However, a further increase in the iteration number did not yield significant performance benefits. The real-time speed estimation results for the WRIM -10% slip range tests are shown in Figs.14-21 and Table3. The considered no-load to full-load transients are identical in duration to those investigated for the nominal speed range. The measured data demonstrate a reasonable real-time performance of the estimation algorithm, with the 4, 8, 16 and 32 second ramps’ measured maximum estimation error of up to 1.15% and a sizeable 11.89% error for the rapid 0.25 second ramp. Increasing the search iteration number to 100 was discovered to result in a decrease in the estimation maximum error and deviation for the slower ramps. However, no significant changes in estimation performance were observed for the faster 0.25, 0.5, 1 and 2 sec ramps where, as expected, an increase in the number of executed iterations can compromise the estimation accuracy due to the high rate continuous real-time change in the monitored frequency value.
B.Performance for emulated wind driven conditions In order to evaluate the potential of the proposed algorith to be used in a realistic WRIM Type-II wind turbine application the test rig prime mover was controlled to provide a transient speed profile in the generating region representative of the machine
Max Error Standard Deviation 0.18, 0.20 0.38, 0.19 0.35, 0.34 0.54, 0.44 0.89, 0.58 1.27, 1.34 1.44, 1.77 1.99, 2.28
Dichotomous to FFT Performance Comparison Max Error Max Error [% change] Standard Deviation [% change] -18, 1-27.01 -16.1, -17.2 -16.9, -26.0 -14.9, -14.4 -16.4, -25.7 -13.7, -14.8 -16.8, -25.1 -13.1, -15.8 +9.42, +8.52 -5.3, -4.3 +2.25, +3.1 -1.14, -1.3 +1.51, +2.1 -1.06, -1.2 +0.86, +1.8 -1.01, -1.2
operating dynamics found in MW size variable speed wind turbines [18], [20]. The profile was scaled for the -10% slip laboratory machine operating region to match a typical operating speed range found in industrial Type-II WRIM Opti-Slip and Flex-Slip drives [14]-[15]. Real-time estimation experiments were performed for estimation rates ranging from 2 to 14 speed estimates per second, to evaluate the performance parameters of the proposed technique during wind driven representative transient operating conditions. The dichotomous search algorithm was executed with 100 iterations during this investigation. The laboratory WRIM was operated in an identical generating variable speed profile for each considered estimation rate test. A comparison of typical real-time speed estimation results and encoder measured speed data achieved at a rate of 4, 8 and 12 rotor speed estimates per second is shown in Figs.22-24 for illustration purposes. The measured estimation performance parameters for all undertaken tests are summarised in Table4. The data demonstrate a satisfactory performance level for real-time speed estimation during WRIM operation on a representative wind driven profile; for all considered rates up to and including 10 estimates a second the estimation error was measured to be lower than 1% in comparison to the synchronously obtained encoder speed measurement. For the considered faster estimation rates of 12 and 14 estimates per second the measured data report a rise in the maximum estimation error level to 1.55%. As expected, the data indicate that the estimation rate increase is followed by a clear increase in the estimation error.
Speed [rpm]
1700 1600 Estimated Measured 150 Time [Sec]
1500
Absolute Error [%]
0
50
100
50
100
200
250
300
200
250
300
1.5 1 0.5 0 -0.5 0
150 Time [Sec]
Fig 22: Real-time speed estimation, 4 estimates per second, -10% slip wind turbine driven profile
Speed [rpm]
1700 1600 Estimated Measured 150 Time [Sec]
1500
Absolute Error [%]
0
50
100
50
100
200
250
300
200
250
300
1.5 1 0.5 0 -0.5 0
150 Time [Sec]
Fig 23: Real-time speed estimation, 8 estimates per second, -10% slip wind turbine driven profile
Speed [rpm]
1700 1600 Estimated Measured 150 Time [Sec]
1500
Absolute Error [%]
0
50
100
50
100
200
250
300
200
250
300
1.5 1 0.5 0 -0.5 0
150 Time [Sec]
Fig 24: Real-time speed estimation, 12 estimates per second, -10% slip wind turbine driven profile
Table 4: Measured real-time estimation performance, -10% slip wind turbine driven profile Estimates per second Absolute Error [%] Average Error [%]
2
4
8
10
12
14
0.63
0.77
0.91
0.98
1.23
1.55
0.22
0.19
0.24
0.21
0.31
0.34
V. CONCLUSION This paper proposes a dichotomous search based algorithm for real-time slip-dependent current frequency extraction in WRIMs. The algorithm’s performance is evaluated in real-time experiments by comparing the estimated speed signal with that
measured using an incremental encoder. The presented results demonstrate a strong potential of the proposed algorithm for accurate real-time speed estimation and report estimation rates and transient accuracy that deliver an improvement on published spectral frequency extraction based solutions. While performance limitations exist for rapid transient regimes and fast estimation rates, the proposed solution is shown to provide reliable performance at estimation rates of up to ten estimates per second for lower dynamics WRIM transient operation regimes representative of those found in wind turbine industry applications.
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