DEVELOPMENT OF A BATTERY STEP VOLTAGE TO DETERMINE PARAMETERS OF LARGE PMG W.E. Kuchenbecker*, J.C. Teixeira † *WEG Electric Equipments, Brazil †UFABC Universidade Federal do ABC, Brazil Contact: walterk@weg.net; juliocarlos.teixeira@ufabc.edu.br
Keywords: Permanent Magnet Generators (PMG), DC Step Voltage Test, wind energy.
Abstract
On the contrary, for PMG with fixed rotor flux, these methods are not applicable. A measurement of the machine electrical parameters requires the adoption of procedures that differ from classical methods applied to wound field machines.
Permanent magnet generators (PMG) parameters cannot be determined by using conventional test procedures due to the impossibility to control the magnetic field created by the rotor, so that new procedures need to be developed and standardized taking into account that the power of new PMG for large wind farms is increasing as is the need for power in laboratory facilities. A DC step voltage is an equivalent method that, analyzed with others, makes the determination of important PMG parameters possible. To validate the new method, it was also applied to a well know conventional synchronous machine using the IEC and IEEE methods. The comparison of results showed that de DC step voltage can help the parameter identification of large PMG for wind applications.
Given the fact that PMG standardized tests are not available at present, some alternative approaches have been proposed to determine PMG parameters: the DC decay at Standstill [12], and the use of both, the short circuit test and load tests in a small machine (until some kVA) [6,7], bearing in mind that this procedure requires special laboratory facilities.
1 Introduction
2 Battery step voltage testing procedure
Wind power is a promising renewable energy source. Many studies have been focused on the improvement of efficiency to convert wind energy into electrical energy [1]. Part of these efforts has been directed to the design of new electrical wind generators [8]. In the past years, PMG have become popular among suppliers as alternative machines due to their high density torque, efficiency and very low maintenance costs as it does not require an excitation system. Newer PMG wind energy systems have the ability to operate at low speeds without gearbox, thus reducing the maintenance cost [1]. In a typical three-phase synchronous machine, the rotor has the field winding, while the stator has the armature windings. After being manufactured, the machine functionality is verified through standardized laboratory tests. Worldwide standards for larger generators were developed to enable different laboratories to perform equivalent tests in their facilities. In classical machines, determination of the model parameters may be derived from results of standards as IEC 60034-4 [10] and IEEE 115 [5], using methods in which the field current of synchronous machine is adjusted.
PMG machines are recently designed electrical machines so that their specificities may still need changes. Considering that there is no worldwide standardized procedure for PMG synchronous generators to retrofit design processes, it is important to improve experimental tests. The aim of this work is to adapt a DC step voltage on direct and quadrature axes to determine typical parameters of large PMG.
2.1 Method Electrical machines can be represented by means of equivalent circuits in “d” and “q” axes [11]. The performance can be calculated by a mathematical model as shown in figure 1 (direct axis) and figure 2 (quadrature axis).
Figure 1 – The classical electrical synchronous machine model on d axes
with several frequencies, including higher ones. The experimental voltage and current were applied to a model developed in the MATLAB® platform, so as to enable the identification of “d” and “q” axes parameters.
Figure 2 – The classical electrical synchronous machine model on q axes
In order to determine the parameters of the two circuits, the rotor must be positioned at a maximum flux (direct axis) and a minimum flux (quadrature axis). On PMG machines, the rotor position can be defined by applying the DC current into two terminals of the stator winding. The rotor aligns with the flux created by the DC current fed phase coils. If the polarity of the DC current is changed, the rotor should align accordingly. The q-axis is located in the middle of two d-axes positions [6]. After the rotor has been positioned, shaft must be locked at desired test points to avoid any movement that could generate measuring fluctuations on the graphic responses. The battery cables must be connected to the same stator terminals used for rotor positioning. The circuit connection was performed as indicated in figure 3 and 4. By means of an accurate oscilloscope, the DC step voltage and current responses were recorded in all six possibilities.
* Red line – Battery voltage / * Blue line – Battery current
Figure 5 – Graphic response of the step voltage The procedure was applied in a classical synchronous machine, with wound rotor and damper windings. For one large traditional synchronous generator, the values of parameters are obtained by standardized methods in direct and quadrature axes. Results are analyzed to identify which parameters could be obtained by a DC step. After this validation, a PMG prototype with no damper winding was tested.
2.2 Estimation of parameters Figure 3: Electrical connections and rotor position, modified from [3].
The voltage and current of the DC step test was recorded at the oscilloscope, and converted to a MATLAB® variable. The parameters of the model presented in figure 6 were estimated using a last-square error method.
Figure 4: DC step voltage circuit. In this work, a battery voltage was applied to the machine. Initially, a peak voltage appears as shown in figure 5. As the current increases, there is a reduction of the terminal voltage. This transitory can be translated as an excitation of the model
Figure 6: Electrical circuit for parameters identification.
The main objective to determine PMG parameters without damper winding is the incremental inductance [4] on both, the direct axis (Ld) and the quadrature axis (Lq). These inductances can be calculated using equations 1 and 2, by the summing of the leakage reactance and the incremental magnetization reactance [4].
Ld = Ll + Lmd
Lq = Ll + Lmq
(1) (2)
The stator resistance was measured by a Kelvin bridge. As its value can interfere with other machine parameters, a sensitivity analysis was performed. A single inductance can represent the circuit of figure 6 during the first instants of a fast transitory [2]: L” = LL + Lmd//Lkd
(3)
Figure 7 (b) – Final Measured versus Simulated Responses
This sub transient inductance can be obtained for the direct and the quadrature axes.
3 Testing results Based on measured responses, routine iteration parameters on the machine electrical model were tuned to match simulated responses, as figure 7(a) initial and figure 7(b) final process. The figure 8 shows the trajectory of nine iterations beginning with the input values of LL, Lmd and Rkd from the conventional synchronous generator, which were tested using worldwide standards. Initial and final errors can be followed in figure 9.
Figure 8 – Trajectories of estimated Parameters
Figure 9 – Iteration errors of simulating responses
Figure 7 (a) – Initial Measured versus Simulated Responses
3.1 Sensitivity analyses of parameters estimation As the parameter R1 is measured conventionally, it is important to analyze the sensitivity of others parameters for the resistance variation at +/-5%. Figure 10 shows that the sub transient inductance (eq. 3) is almost independent of the assumed R1 parameter. All other estimated parameters are R1-dependent.
procedures by means of IEC and IEEE. Each method has the respective parameter to be determined, as follows: R1 – Kelvin Bridge or Method of Ohm’s Law (voltage / current); LL – Applied voltage test with rotor removed Lmd=Ld – LL (Ld is determined from the Saturation and short circuit curves). The parameters of table 1 were used as reference and acceptance criteria of the proposed method.
Figure 10: Analyzes of the effect of R1 on Ld” The sensitivity results show that the proposed method is able to correctly identify sub transitory inductances, but is not able to separate all the parameters that represent a machine with damper windings. As in the tested PMG, there are no damper windings and the method is able to identify the important parameters. The sensitivity analysis of LL into Lmd shows that they are well correlated, as expected. Figure 11 shows that a 1% dispersion inductance accuracy results in 10% of mutual inductance accuracy. As the relationship between Lmd and LL is approximately 10, even if LL is incorrect (or Lmd), their sum tends to be correct. As their sum is defined as the direct inductance, the method can also be used to determine this important value, even in a machine with a damper winding.
Table 1: DC step voltage parameter determinations on a conventional synchronous machine Parameters Reference DC Step Standard (***) (**) Deviation R1 (ohm) 0.3294 --LL (H) 0.0112 0.0184* -39 % Lmd (H) 0.190 0.183 4% Lmq (H) 0.094 0.112 -14 % Ld (H) 0.201 0.202 -0.5 % Lq (H) 0.105 0.127 -18 % * Leakage inductance (LL) was determined on direct axis estimation and the result was fixed to estimate the quadrature parameters. ** For each phase the rotor was positioned at maximum and minimum flux and the test was performed six times. The results are the mean of the six obtained values. *** Lq reference was taken from design. Other reference values were obtained by IEC and IEEE procedures. Both methods yielded the same value for Ld. The difference of Lq values can be justified by the fact that reference is not experimental. Differences between the classical and the DC step method for the determination of the damping winding parameters were almost 100%. Previous studies [12] have improved this method measuring the field winding current. However, as these currents cannot be measured in PMG, it is not possible to correctly identify all the inductances of figure 5 by the proposed method.
Figure 11: Graphic of Lmd versus leakage inductance in pu of mean value.
3.2 DC step voltage applied to a conventional synchronous generator In order to verify the proposed test procedure to determine electrical parameters of PMG, the DC step voltage method was applied to a conventional synchronous generator. The parameter references were listed at table 1. The first column is related to the determination of standardized traditional
In this condition, an initial verification of the system order is necessary. To this end, a parameter estimation using a first order model can be performed. Figure 12 shows that if R1 is well known, the method does not converge to a good solution if the system order is not correct. The comparison between the current behavior displayed in figure 12 and in figure 7.b shows that it is possible to verify the system order prior to the identification of parameters.
PMG parameters were freely estimated on direct axis (Ld). As LL and Lmd are serial connected according to the model of figure 7, during the estimation process it is only possible to correctly define the sum of LL and Lmd. In the proposed method, LL was obtained in the direct axis estimation and used in the quadrature axis estimation. For better results, LL can be determined by means of IEC or IEEE methods. Results show that the Lq is almost three times the Ld. This significant difference is uncommon in conventional synchronous machines. According to Miller [9], PMG should have inductances Ld < Lq due to the high reluctance of the permanent magnets. When the rotor is positioned on quadrature axis between the permanent magnets where flux is facing laminated steel with low reluctances, inductances increase. However, the design of this particular machine does not completely explain the difference. Figure 12- First order model results
3.3 DC Step voltage on a PMG synchronous generator The Wind Power PMG generator prototype was designed without damper coils; the equivalent circuit is demonstrated at figure 13; the parameters to be identified are: Stator Resistance (R1) Leakage Inductance (LL) Magnetization Inductance (Lmd or Lmq)
It is necessary to consider that the DC step voltage test determines incremental inductances, i.e., the flux variation occurs in the tangential point of the saturation curve [4]. As direct axis inductances are mainly saturated due to the high reluctance of permanent magnets, Ld results are smaller than the synchronous inductance.
4 Conclusions Due to many limitations to perform electrical tests on PMG, a method based on DC step voltage was developed and allowed the determination of direct and quadrature axes in a 660kW PMG. This method proved to be equivalent to conventional ones regarding the parameters results in a large classical machine.
Acknowledgements Figure 13: Electrical circuit of a PMG. Table 2: PMG synchronous machine parameters through DC step voltage. Parameters Values Standard (mean) Deviation R1 12,7 mΩ 1% LL 0,36 mH 12% Lmd 0,71 mH 2% Lmq 2,60 mH 7% 1,06 mΩ Ld 5% 2,97 mΩ Lq 5% The DC step voltage was applied to the three phases (1-2, 1-3 and 2-3) with the rotor positioned on direct and quadrature axes position. The mean values of phase results are listed at table 2. In order to analyze the results, the standard deviations of the parameters were calculated. These standard deviations show that the proposed method has a useful precision.
The authors would like to thank WEG Equipamentos Eletricos S.A. for the tested machines and also for the use of their laboratory facilities to perform the tests.
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Walter Evaldo Kuchenbecker is Engineering Supervisor with expertise in electrical machines at WEG Equipamentos Elétricos S.A. and MsC student of the PostGraduation program at the UFABC University. His work and research topics are Large PMG performing tests.
Julio Carlos Teixeira member of IEEE, professor at Universidade Federal do ABC (UFABC). His graduation (1983). and MSc title in Electrical Engineering from USP, Brazil He obtained his Ph.D. degree in INPG, France (1994).