Unbalanced Loading Behaviour

Abstract —Portable AC generators directly driving isolated AC loads require tight voltage regulation, good voltage waveform quality and high efficiency. This paper studies the performance of a 4 pole, 16 kW interior permanent-magnet generator under balanced 3ph and unbalanced 1ph resistive loading conditions. For the unbalanced 1ph condition, the use of star and delta winding connections is compared. The results of analytical and finite-element simulations have been compared with experimental results.

I. Introduction

This paper examines the application of an interior permanent-magnet generator (IPMG) to replace a conventional wound-field synchronous generator in a small portable generator. This generator is driven by a speed-regulated prime mover such as a diesel or petrol engine, and provides power to an isolated AC load. Some of the advantages of an IPMG over a conventional generator are: lower size and weight, higher efficiency, no requirement for field excitation, and higher reliability and lower maintenance [1].

The key requirement for the generator when driving isolated AC loads is to maintain tight voltage regulation, good voltage waveform quality and high efficiency over a wide range of load conditions including unbalanced operation such as running single-phase loads. The voltage regulation should be within . In addition, the 3ph voltages should be balanced when driving induction machines to minimize negative sequence currents which can otherwise cause overheating and shorten their life. The total harmonic distortion (THD) of the voltage waveform should also be less than 5%.

There are some published works on voltage regulation issues of AC permanent magnet generators. Oversizing the machine, saturating the stator and using high-saliency designs are possible solutions to the tight voltage regulation requirement [1-4]. However, to the best of authors’ knowledge, no work has been presented on the analysis of the IPMG under the single-phase loading condition. The present paper focuses on the behavior of the IPMG under balanced and single-phase unbalanced loading conditions with the especial attention to the voltage regulation and THD requirements.

This paper is organized as follows: section II explains the equivalent circuit and the response of the machine under balanced condition (see Fig. 1(a)). Section III includes the behavior of the machine under the unbalanced single-phase load condition (see Fig. 1(b)). In section IV, the alternative delta winding connection is considered to improve performance under single-phase loads (see Fig. 1(c)) and section V concludes. For all the above conditions, analytical calculations, finite element (FE) analysis and experimentally measured results will be presented.

Figure 1. Equivalent diagram of the IPMG. (a) 3-phase balanced loading condition. (b) single-phase star connection. (c) single-phase delta connection.

II. Balanced Resistive Load

Analysis, simulation and modelling of a 16-kW, 4-pole, 36-slot IPMG for a portable generator application had been presented previously [5]. It included the effects of various factors such as saliency ratio, stator resistance and saturation on the voltage regulation and efficiency. In addition, the superiority of the designed IPMG as compared to the wound-field generator had been demonstrated by experimental measurement of the efficiency and fuel consumption.

Fig. 2 shows the indicative cross-section of the spoke-type IPMG and its flux plot when operating under load. It uses a split-magnet design with carefully designed rotor voids and slots to improve the AC output voltage waveform under load. Table I shows a summary of its key design information.

Figure 2. Calculated flux plot of spoke-type interior PM generator under the loaded condition [5].

In this paper a time-stepping transient 2D FE simulation with a coupled electric circuit was used to model the machine. The stator skew was approximating by averaging the results over one stator slot pitch.

Fig. 3 compares the time-stepping FE simulation results with the analytical and measured results presented earlier in [5] for the IPMG with a balanced 3-phase resistive load (Fig. 1(a)). The analytical results are presented for an ideal model and then with saturation and stator resistance. The results indicate that stator resistance and saturation have a significant impact on the voltage regulation and efficiency of the machine.

The machine shows acceptable voltage drop (approx. 5%) at the 16 kW rated output condition. Even at 20 kW output power, the machine shows about 8% voltage drop.

The FE results are in excellent agreement with the measured ones. In addition, the difference in efficiency between the FE and experimental results may be due to neglecting the mechanical and windage losses in the simulation.

Figure 3. Comparison of analytical, FE simulation and measured characteristics of the IPMG at 1,500 rpm. (a) voltage regulation and (b) efficiency.

III. Unbalanced Load

In this section the single-phase loading case (Fig. 1 (b)) is considered as it is one of the most common and extreme sources of unbalanced operation of isolated generators. In this case, although the currents in the other phases is zero, the voltage change in the other phases is still significant due to the effect of mutual inductance.

To analytically calculate the voltages of the three phases it is necessary to find the self and mutual inductances. The IPMG has a low saliency ratio and can be approximated as a non-salient machine [5]. Its inductances can be found using finite-element analysis or experimental testing. One phase (phase A) of the machine is connected to the AC current source where the other phases (B and C) are open

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while the machine is stationary. As the machine is symmetrical V_b = V_c. The self (L) and mutual (M) inductances can be calculated [6] as:

 

where I_a is the a-phase current and R is the stator resistance. Therefore, the voltages of the three phases can be calculated as follow:

 

 

 

Fig. 4 shows some example calculated phasor diagrams for the machine at rated output using the self and mutual inductances calculated from (1) and (2). The four phasor diagrams are for the 3-ph balanced case and for the loaded phase with single-phase loading, both with and without resistance. As the resistance voltage drop is in-phase with the output voltage, the voltage regulation is more sensitive to stator resistance than the inductance. Also under single-phase loading, the voltage regulation would be expected to be slightly improved due to lack of induced mutual voltage from other phases.

 

Figure 4. Example calculated phasor diagrams for balanced 3-phase and single phase loading, both with and without stator resistance.

 

Figs. 5(a), (b), and (c) compare the analytically calculated, FE simulation, and measured results of the voltage regulation of the three phases of the IPMG when a single-phase resistive load is applied to phase A. The analytical model predicts phase A to have the largest voltage drop, with phase B having a smaller voltage drop and phase C having a small voltage increase. The experimental results show a reasonable correspondence to the analytical model except with approximately twice the voltage magnitude changes. The finite-element results show a good correspondence to the experimental results for phases A and C, but predicts a much larger drop (a factor of two) in phase B than was observed experimentally.

Fig. 5(d) compares the voltage regulation of the loaded phase in 3-phase and single-phase loading conditions. As indicated above, it is expected that in the 3-phase loading condition, the voltage change would be more than that of the single-phase loading. This was found in the analytical and FE results however, the experimental results show the reverse trend. The reason for this is being investigated.

 

Figure 5. Voltage regulation of the IPMG under unbalanced loading condition at 1,500 rpm: (a) analytical, (b) FE simulation and (c) experimental measurement. (d) Comparison of voltage regulation of the loaded phase in 3-phase and single-phase loading conditions for analytical, FE and measurements.

 

IV. Star-Delta Connection

If the generator only needs to drive single-phase loads, it is possible to reconnect the stator winding in a delta configuration (Fig. 1 (c)). The voltage regulation and THD of this configuration is compared with the star configuration in this section.
Fig. 7(a) compares the FE and measured voltage regulation of the loaded phase with the generator stator windings connected in star and delta. The FE results predict that the delta-connected configuration should have an approximately 1% better voltage regulation at full load. The measurements show similar voltage regulation for the two configurations up to about 3 kW with an approximate 0.5% improvement at full-load.

The delta connection has a more substantial effect on the THD value as shown in Fig. 7 (b). The FE results predict the general trend found in the measured results. The delta connection shows about 2 to 3% improvement in THD over the full range of loads and allows the generator to meet the 5% THD requirement at full-load.

One of the issues with a delta connection for permanent magnet machines is circulating current.  The FE simulation showed that this circulating current was 3.3A (about 14% of rated current) and was largely 3rd harmonic. The measured circulating current was 2.9A.

Figure 7. FE and experimental result comparison of the loaded phase in star/delta connection: (a) voltage regulation and (b) THD.

 

V. Conclusions

In a portable AC generator application, voltage regulation, THD, and efficiency are important. This paper focusses on the  performance of a 3ph, 4 pole, 16 kW interior permanent-magnet generator under unbalanced 1ph resistive loading. The results show the importance of the stator resistance and mutual inductance on the voltage regulation of the three phases under single-phase loading. It also compared the star and delta stator winding connections and showed a small measured improvement (0.5%) in the voltage regulation but a significant improvement in the THD (2%) of the loaded phase when using a delta connection.

 

References

[1]    R. M. Saunders and R. H. Weakley, “Design of Permanent-Magnet Alternators,” American Institute of Electrical Engineers, Transactions of the, vol. 70, pp. 1578-1581, 1951.
[2]    B. J. Chalmers, “Performance of interior-type permanent-magnet alternator,” Electric Power Applications, IEE Proceedings -, vol. 141, pp. 186-190, 1994.

[3]    W. Wu, E. Spooner, and B. J. Chalmers, “Design of slotless TORUS generators with reduced voltage regulation,” Electric Power Applications, IEE Proceedings -, vol. 142, pp. 337-343, 1995.

[4]    K. Kurihara, T. Kubota, K. Saito, N. Kikuchi, and H. Iwamoto, “High-efficiency interior permanent-magnet synchronous generators with minimal voltage regulation for nano and pico hydro generation,” in Electrical Machines and Systems (ICEMS), 2012, pp. 1-4.

[5]    “Interior PM generator for portable AC generator sets,” Energy Conversion Congress and Exposition (ECCE), IEEE 2014.

R. Dutta, M. F. Rahman, and L. Chong, “Winding Inductances of an Interior Permanent Magnet (IPM) Machine With Fractional Slot Concentrated Winding,” IEEE Trans. Magnetics., vol. 48, no. 12, 2012, pp. 4242-4849.