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
