Parameters Determination of Grid Connected Interior Permanent Magnet Synchronous

Generator

Rania Assem Mona F. Moussa* Yasser G. Dessouky Barry W. Williams * Arab Academy for Science and Technology, Alexandria, (Egypt), ygdessouky@yahoo.com

** Strathclyde University, Scotland (United Kingdom), barry.williams@eee.strath.ac.uk

Abstract — Renewable energy sources are being utilized as a reliable alternative to the traditional energy sources for electricity production. Among these renewable sources, wind energy has the largest and fastest penetration into power systems. This paper introduces a method for measurement of the equivalent-circuit parameters of an interior permanent magnet synchronous generator (IPMSG) used in a wind energy system. A brief introduction on the methods used for parameter determination of IPMSG. The conventional two-axis IPMSG model is modified to include the saturation effect of the inductance in the q-axis including self-inductance values in the d- and q-axes, the stator resistance and also the PM flux-linkage.

Keywords — Interior permanent magnet machines, d-and q-axis inductances, parameter measurement.

I. INTRODUCTION Permanent magnet machines have gained wide interest

with applications ranging from small high speed servo drives, fans, pumps to large mega watt generators. With almost all the electricity generated in the world today from synchronous generators, permanent magnet generators seem appealing due to their high efficiency, fall of permanent magnet prices and magnetic material characteristics improvement. Along with the increased demand on environmental sustainability and the depletion of ordinary energy sources, wind power has gained notable emphasis in electrical power generation. Wind power is invariable in nature, thus variable- speed generation using synchronous generators has a larger market share, higher energy capturing and higher converting efficiency compared to fixed-speed generation [1]. For all reasons mentioned, synchronous-machine stability-constant determination has become a topic of considerable research interest by the power utility industry [2, 3]. Part of the reason, is due to the increasing demand for more accurate performance evaluation of electric generators and other components of the power system networks, to ensure stability and reliable operation of the power system as a whole. Today, power generator models describe the transient and sub transient behavior of the rotor and armature flux linkages in response to stator currents and field excitations. However, the problem posed by this complex description is that the required parameters are often inaccurate or completely unknown [4]. International Electrotechnical Committee (IEC) Standards provide guidelines of the conventional parameter measurement methods for wound

rotor synchronous machine. Unfortunately, these test procedures cannot be used with permanent magnet machines as the value of the quadrature axis synchronous reactance (Lq) becomes very irregular over a load range where the armature reaction in quadrature axis is changing from magnetizing to demagnetizing regions. This irregularity is due to the assumption of constant value of induced EMF due to the magnets [5]. There have been a number of papers describing test methods for synchronous-machine parameters determination which can be classified into two board categories depending on the operating condition of the machine --- (a) Standstill test and (b) Running (load) test [6]. Running tests are considered to be more accurate but it requires zero rotor fields, which requires removal of the permanent magnets from the rotor during the tests which may not be easy in any IPM machine. Standstill tests as the name implies, require no rotor movement and include DC test, instantaneous flux linkage test, standstill torque test and AC standstill test. The main drawback for the standstill tests is that the dq axis inductances are inaccurate as they don’t take into account saturation. Other tests using sensorless control techniques have been introduced in the past few years which have drawn much attention especially with the advancement in the field of signal processing and data acquisition. Since machine parameters are affected by the machine’s rotor position, sensorless identification techniques are well characterized with their high accuracy and optimal performance when used with an electrical drive system. Besides, the lack of position sensors makes sensorless techniques more appealing in terms of cost, size and reliability. Senorless identification techniques can be divided into those using high-frequency voltage or current signals (such as standstill frequency response test) and those using fundamental components of voltage and current signals (such as standstill time domain response test) [7].Standstill frequency response test (SSFR) procedure can be found in the IEEE standard 115A-1983 [8] and IEEE Standard 1110-2002 [9]. By supplying the winding with a low-frequency single phase alternating voltage, a low-frequency magnetic flux is obtained in the rotor. Rotor position in changed in small steps for repeated consecutive measurements, the d- and q-axes reactances can be determined from measurements of voltage and current. Compared with the locked rotor and the DC test, SSFR provides accurate equivalent circuit parameters

15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia

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with low risk for the machine under test [10]. The main drawback for the SSFR is its time-consuming nature due to the high number of measurements required. The SSFR is effective in low-speed ranges because the amplitude of high-frequency signals used for position estimation does not depend on rotating velocity [10]. As for the standstill time domain response test (STR), it is useful in middle- and high-speed ranges because it uses the fundamental components of control signals for position estimation and does not generate torque ripple or noises. Stator windings are subjected to a voltage step and the current transients are analyzed, thus the inductance for a certain position can be obtained at different rotor positions. The STR tests require a very short execution time and a simple setup. But on the other hand needs very accurate modeling for the machine’s equivalent circuit for accurate identification [11], [12].

Load tests on the other hand, require the knowledge of the load angle for the determination of d and q axes inductances. Load tests performed according to the IEEE Standard 115-2009 [13] either using position encoder or stroboscope [14]. Sometimes load tests are used along with the SSFR or STR tests for the acquisition of additional information on the saturation of the motor inductances values [11]. As noted, load tests require additional hardware for measurement and recording.

PM synchronous generators sometimes have a complicated structure, and numerical or analog modeling is necessary to obtain an accurate distribution of the magnetic field. This distribution is very helpful to correctly estimate the form factors of the rotor and stator magnetic flux densities. The finite element method (FEM) makes it possible to find the d-and q-axis synchronous reactances and mutual (armature reaction) reactances by computing the corresponding inductances, e.g., [15, 16]. This method of parameter determination requires detailed knowledge of the machine geometry and for this reason it is rather complex compared to the other mentioned techniques. FEM can be made by using the flux linkage and magnetic vector potential concept or energy stored in the winding [17]. Recently, two modern FEM techniques in ac machines analysis have emerged: current/energy perturbation method [18] and time-stepping analysis [19]. These methods are especially suitable for transient analysis of converter-fed PM synchronous machines [20].

This paper introduces a method for calculating the equivalent-circuit parameters of an interior permanent magnet synchronous generator (IPMSG), by considering the cross saturation between direct-axis (d-axis) and quadrature-axis (q-axis). The conventional two-axis IPMSG model is modified to include the saturation effect of the q-axis inductance. Therefore, the parameters of the machine should be evaluated to estimate its performance.

The simulated IPMSG model is used for a medium voltage grid coupled wind turbine where the active and reactive power of the grid is controlled via the grid side converter. The control of the active and reactive power is done through the control of the d-axis and q-axis grid currents.

II. IPMSG WIND TURBINE CONNECTED TO MEDIUM VOLTAGE GRID

A. Overall System Description

As mentioned earlier, to examine the behavior of IPMSG both in transient and steady state operation require full knowledge of the machine’s parameters. A block diagram of an IPMSG wind energy system used for a 1.5MW medium voltage (MV) grid interfacing is shown in Fig. 1.

A 1.5kW experimental IPMSG scaled down prototype is used to demonstrate how parameters are being measured. The tests conducted show how saturation affects the parameters under investigation.

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Fig. 1. IPMSG Grid Connected Wind Energy System.

III. PARAMETER MEASUREMENT

A. Stator resistance Ra

The armature resistance can be measured by DC test at the ambient temperature with subsequent correction to obtain the AC value [21-23]. From the test, the value of the stator resistor was found to be Ra = 2.6Ω.

B. PM flux linkage

The flux linkage of the permanent magnet, can be obtained by measuring the no-load line-to-line r.m.s voltage VnL of the generator while it is driven through the shaft at a constant speed of . The flux linkage is the slope of the plot between the no-load voltage and the angular speed. The measured value of the permanent magnet flux linkage was found to be 0.36wb.

C. D-Q axis inductances Ld and Lq

A scheme is proposed to measure the load angle δ of the machine by coupling the proposed IPMSG with a DC motor from one side and with an externally excited synchronous machine (EESG) from the other side as shown in Fig. 3. Thus, the DC motor will drive the two synchronous generators, where the no-load voltage of the two machines will be recorded and synchronized on a dual beam scope. The no-load EMF’s of IPMSG and of EESG operating as generators should be in phase. Thus, the same positions of the IPMSG and EESG rotors with regard to the same phase windings can be found. When the IPMSG is loaded with a resistive load in which case, and in the absence of wattmeter, the load angle (which

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indicates rotor position) will be the difference between the output load voltage of the IPMSG machine and the no load voltage of the EESG.

(a)

(b)

Fig. 2. Connection diagram of the proposed method to measure the load angle δ.

The stator voltage equations of an IPMS Generator at steady- state are:

(1)

(2)

The relationship between load angle and d- and q-axis stator voltages and currents can be given as follows [20]: δ δ (3) δ δ (4)

Thus, the d-and q-axis inductances can be calculated as follows:

(5) (6)

Using the above results, the relationship between the d-axis linkage d and the d-axis current id at speed=1500 rpm is shown in Fig. 3. Taking the best fit of the two curves of Fig. 3, the relation between d and id can be described by the following equation: 0.085 0.36 (7)

Since, (8)

From the above equations, the measured value of the d-axis inductance Ld is found to be 0.083H. The measured d-axis inductance of the prototype IPMSG is shown in Fig. 4, where Ld is almost constant. Fig. 3 shows how much L is affected by the air gap.

The flux linkage of the permanent magnet Φ , can be obtained from the proposed scheme used to measure the load angle δ of the machine. From Fig. 3, it is clear that the relation between Φ and can be described by (8). Therefore, by comparing (7) with (8), the measured value of the permanent magnet flux linkage is found to be 0.357wb. This matches well with the value obtained from the no-load test.

Similarly, the relationship between the q-axis flux linkage q and the q-axis stator current iq is drawn, as shown in Fig. 5. The measured q-axis inductance of the prototype IPMSG is shown in Fig. 6. It is found that, Lq depends on the q-axis current. Thus, before magnetic saturation (iq < 0.4A), Lq is almost constant, where,

(9)

Therefore, the average value of the measured q-axis inductance Lq is found to be 0.86H. The relation between measured q-axis inductance and q-axis current after magnetic saturation is determined by:

0.86 0.6173 (10)

Fig. 3. Relationship between measured Φd and id

Fig. 4. Relationship between measured and

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Fig. 5. Relationship between measured and

Fig. 6. Relationship between measured Lq and iq

Fig. 7 shows the Simulink model of the IPMSG while

taking into account the saturation effect of the q-axis inductance. The input to this system is the speed, where both the d-axis inductance Ld and the PM flux- linkage

are practically constants.

The machine is loaded experimentally at nominal speed and loaded with R, L and C loads, where the external characteristics (relation between the load voltage and current) from theoretical and experimental tests are compared and showed good matching.

IV. GRID CONNECTION WITH ACTIVE AND REACTIVE

POWER CONTROL

For a direct driven PM generator wind power generation system, the amplitude and frequency of the output voltage are not constant due to the variable speed and fixed excitation of the permanent magnets. Therefore, the output power should be converted into AC power with constant voltage and constant frequency through AC/DC/AC converter as seen in Fig. 1 for grid coupling. Several topologies have been adopted in literatures for the possible configurations of the AC/DC/AC [24-25].

The simulation is based on a 1.5 MW PMSG wind turbine using the mathematical model described earlier with the MV system parameters. The control topology in the synchronous reference frame is being adopted in this paper is based on using a 3-phase diode rectifier for the AC/DC conversion and a sinusoidal PWM voltage source inverter (VSI) for the DC/AC conversion for grid interfacing with MV network. The VSI is interfaced to the MV grid through an L- filter and a three phase Δ-Y transformer. As seen from Fig. 1, the use of phase locked loop (PLL) along with the desired active and reactive power command, sets the desired current being injected into the grid through and .The simulation results of the MV grid connected PMSG can be seen in Fig. 8 to Fig. 12 which shows the generator current as well as the DC link voltage, active and reactive power exported to the grid.

Fig. 7. Simulink model of the IPMSG

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15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia

Fig. 8. Grid Current (pu)

Fig. 9. IPMSG Current (pu)

Fig. 10. Grid Active Power (pu)

Fig. 11. Grid Reactive Power (pu)

Fig. 12. DC Link Voltage (pu)

V. CONCLUSION This paper presents a practical method for deriving the synchronous machine parameters including the self-inductance values in the d- and q-axes, the stator resistance and also the PM flux-linkage. On the basis of simulation results from the machine model using Simulink and experimental work, the identified models have shown good agreement with the machine responses obtained from the experimental results. The simulated model has been used for simulation of a 1.5 MW IPMSG based wind energy system, where grid active and reactive power are controlled.

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[11] I. Kamwa, et al., "Identification of generalized models of synchronous machines from time-domain tests," IEE Proceedings Generation, Transmission and Distribution,, vol. 138, pp. 485-498, 1991.

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[26] Hua Geng, Geng Yang, Dewei (David) Xu, and Bin Wu, “Unified Power Control for PMSG-Based WECS Operating Under Different Grid Conditions,” IEEE Transactions on Energy Conversion, this article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

APPENDIX

TABLE I DATA FOR 1.5 MW PMSG WAS OBTAINED FROM [26]:

Parameter Rating Base power P (MVA) 1.5

Base voltage V (V) 690/ √3 Base frequency f (Hz) 11.5

Pole pairs of PMSG 40 WT inertia constant (pu) 4.8

PMSG inertia constant (pu) 0.5 Shaft stiffness (pu) 2

Rated generator torque (pu) 1 Rated generator line voltage (pu) 1

Generator inductance in the d frame (pu) 0.4 Generator inductance in the q frame (pu) 0.76

Generator stator resistance (pu) 0.01 Flux of the permanent magnets (pu) 0.9

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