Simulations Analysis with Comparative Study of a PMSG Performances for Small WT Application by FEM

Permanent magnet synchronous generators (PMSGs) have a bright prospect in the small wind turbine (WT) applications; PMSGs compared to the conventional electrically excitated generators have many advantages, that’s why they have attracted many and a strong interest of research. In this paper, a comparative PMSG performance study's is presented, these performances is studied as a function of physical material like the type of permanent magnet (high, poor, average and linear), as a function of the environmental conditions as rotor speed, finally, as a function of the design and geometrical parameters (rotor length, number of poles, number of stator slots). These results are obtained by finite element method (FEM); this approach is a powerful and useful tool to study and design PMSGs, as represented in this paper.


Introduction
There is now general acceptance that the burning of fossil fuels is having a significant influence on the global climate. Effective mitigation of climate change will require deep reductions in greenhouse gas emissions, with UK estimates of a 60-80% cut being necessary by 2050 [1], Still purer with the nuclear power, this last leaves behind dangerous wastes for thousands of years and risks contamination of land, air, and water [2]; the catastrophe of Japan is not far. Wind power can contribute to fulfilling several of the national environmental quality objectives decided by Parliament in 1991. Continued expansion of wind power is therefore of strategic importance [3], hence, the energy policy decision states that the objective is to facilitate a change to an ecologically sustainable energy production system [3], as examp le the Swedish Parliament adopted new energy guidelines in 1997 following the trend of moving towards an ecologically sustainable society. The decision also confirmed that the 1980 and 1991 guidelines still apply, i.e., that the nuclear power production is to be phased out at a slow rate so that the need for electrical can be met without risking employ ment and welfare. The first nuclear reactor of Barseback was shut down 30th of November 1999; Nuclear power production shall be replaced by improving the efficiency of electricity use, conversion in the renewable forms of energy and other environmentally acceptable electricity production technologies [3].
On the indiv idual scale in Den mark Poul la Cour, who was among the first to connect a wind mill to a generator [4]. The development of modern wind power conversion technology has been going on since 1970s, and the rapid development has been seen from 1990s. Various WT concepts have been developed and different wind generators have been built [5]. In real wind power market, three types of wind power system for large WTs exist. The first type is fixed-speed wind power (SCIG), directly connected to the grid. The second one is a variable speed wind system using a DFIG o r SCIG. The third type is also a variable speed WT, PMSG [6].

PMSG in Wind Turbine Application
In literatures many types of generator concepts have been proposed and used. Most of the low speed WT generators presented are PMSGs [7]. Fig. 1 shows the scheme of PMSG for direct-drive WTs connected o grid. Recent studies show a great demand for small to mediu m rating (up to 20 kW) wind generators for stand-alone generation-battery systems in remote areas. The type of generator for this application is required to be compact and light so that the generators can be conveniently installed at the top of the towers and d irectly coupled to the WTs [7]. In addition there are several reasons for using variable-speed operation of WTs; the advantages are reduced mechanical stress and optimized power capture. Because of the variab le speed operation, the direct-drive PM SG system can produce 5-10% mo re energy than the fixed two-speed concept, or 10-15% more than the fixed single-speed concept [8].
Co mpared to a conventional, gearbox coupled WT generator, directly coupled generators has a series of advantages, such as a much reduced size o f the overall system, a rather lo w installation and maintenance cost, flexib le control method, quick response to the wind fluctuation and load variations, etc. However, a directly coupled generator needs to have a very lo w-speed operation to match the WT speed and, at the same time, to produce electricity in a normal frequency range (10-60 Hz) [7].
Co mpared with electrically excited machines, PM SG have a number o f economical and technical advantages, so that they are becoming more attractive for direct-d rive WTs, these advantages can be summarised as follows according to literatures [5][6][7][8]: • higher efficiency and energy yield, • no additional power supply for the magnet field excitation, • imp rovement in the thermal characteristics of the PMM due to the absence of the field losses, • higher reliability due to the absence of mechanical components such as slip rings, • lighter and therefore h igher power to weight ratio. However, PMMs have some d isadvantages, which can be summarised as follows: • Relatively new and unknown technology for applications in larger MW-range • high cost of PM material, • difficult ies to handle in manufacture, • Low material reliability in harsh atmospheric conditions (offshore) • demagnetisation of PM at high temperature. On the other hand, in recent years, the use of PMs is more attractive than before, because the performance of PMs is improving and the cost of PM is decreasing [8].
Currently, Zephyros (currently Harakosan) and Mitsubishi are using this concept in 2 MW WTs in the ma rket.
PMM are not standard off-the-shelf mach ines and they allo w a great deal of flexibility in their geo metry, so that various topologies may be used [8].
One can noticed two p roblems of PMSG used in wind power. First is the inherent cogging torque due to magnet materials naturally attractive force. This kind of torque is bad for operation, especially stopping WT starting and making noise and vibration in regular operation. The other one is the risk of demagnetization because of fault happening and overheating of magnets. This risk is very dangerous and the cost for replacing bad magnets is much higher than the generator itself [5].

PM Material Used in PMSG Design
The application requirement decides the type of PM material used due to cost, size and weight. It is very important to consider operating temperature range, weight constraint, external demagnetizing field and space limitat ion at design stage itself. Co mmercial type PMM uses ceramic or poly mer-bonded neodymiu m-iron boron magnets [7].
The first known apparatus exp loiting magnetism was a magnetic co mpass, invented by the Chinese around 3000 BC. An important milestone in the research field of magnetis m was set in 1600 when William Gilbert published his book "De Magnete" [9]. Fig. 2 shows the historical development of the rare earth magnets.
In 1931 T. M ishima patented the first hard magnetic alloy, based on alu min iu m, nickel and iron. Th is was the start of the development of the PM family known as AlNiCo. In the 1950s, another PM family, known as ferrites, became commercially available. The development of rare earth PM materials started in the 1960's with the Samariu m-Cobalt alloys. The material properties of SmCo 5 and Sm2Co 17 make these PM materials very suitable to be used in electric motors and generators, but they are expensive due to the rare raw material Cobalt [9]. Historical development of the rare earth magnets [9] In 1983 is the most important development in PM used in PMM it is the invention of the high-performance Neodymiu m-Iron-Boron (Nd -Fe-B), since that, the development of the PMSM has been fast, especially low-speed and variable speed industrial applications [9], this material has a very lo w Curie temperature and high temperature sensitivity. It is often necessary to increase the size of magnets to avoid demagnetizat ion at high temperatures and high currents [10], Recently, Nd-Fe-B magnet material with remanence a flu x density Br of 1.52 T and a maximu m energy product of 440 kJ/ m3 was reported. An Nd-Fe-B magnet material of this grade has become commercially available since the year 2004.The best Nd-Fe-B grades, capable of tolerating temperatures up to 200℃, have remanence flu x densities of about 1.2 T and have their maximu m energy product of 300 kJ/ m3 at a 20°C temperature [9].

Methodology Design Used in PMSG Software
Traditionally, the study and design of PMSGs is based on the equivalent magnetic circuit method (EM CM). The EM CM is of advantages of simplicity and fast computation, but its disadvantage is also marked : it relies too much on emp irical design experience, such as flu x leakage coefficient, armature react ion factor, etc. Meanwhile, under certain circu mstances, EMCM is not co mpetent for the analysis and design of PMSGs. Fo r examp le, EM CM cannot be employed to study the cogging torque of PMSGs with fractional stator slots [11]. Nu merical methods, such as fin ite-element analysis (FEA), have been extensively used in study and design PMSGs [11][12], Fu rthermore, o wing to its precision and simplicity, the two-d imensional (2-D) FEM has approximately do minated the FEM study of PMSGs. By using FEM, many design curves and data, such as the PMSGs' output voltage, no-load leakage flu x coefficient, and cogging torque etc., can be obtained and used to design PMSGs [11], In addit ion, many co mmercially available co mputer-aided design (CAD) packages for PM motor designs, such as SPEED, Rmxprt, and flu x2D, require the designer to choose the sizes of magnets. The performance of the PM motor can be made satisfactory by constantly adjusting the sizes of magnets and/or repeated FEA analyses [12].

Simulation Results
The FEA model of electro magnetic field is built by Maxwe1l2D, Th is simulat ion is obtained by Terra pc (QuadroFX380, i7 CPU, 3.07 GHZ, 8 CPU, 4 G RAM), and the simu lation time is take some hours. Our model of PMSG used in Maxwell environ ment has 2138 triangles.

Infl uence of S peed Variati on in PMS G Performance
In this simu lation case, the objective is to see the effect of speed variation on the PMSG characteristics. Fig. 9 shows the waveform o f the one coil voltage vs electrical degree as a function of rotor speed, we can say that the relation between the rotor speed and one coil voltage is proportional, but the curvatures are similar. Fig. 10 Illustrate the efficiency vs rotor position angle at different rotor speed, so that more than the rotor turns at a high speed the efficiency increases in amplitude and broad in axis of the angles.     Fig. 12 depicts three-dimensional representation in terms of the power for our PMSG. The results show the power become higher as the rotational speed increase. Fig. 13 shows simu ltaneously the effect of rotor speed on the power and the efficiency of PMSG, an increasing in rotor speed of the PMSG which is turned by the turbine causes an increasing in the power and the output at the same time.

Rotor Length
Fig. 14 illustrate simultaneously the power and the efficiency vs rotor length, the power increases almost linearly with the increasing of rotor length, but the efficiency increases nonlinearly with the increasing of the rotor length up to the value 60mm, because the active surface was increased, practically the efficiency is constant between 60mm and 70mm, the efficiency decreases if the length of the rotor is increased because the rotor is longer than the stator, so more the losses additive.

Infl uence of pole-Number on PMS G Characteristics
Cogging torque is due to the non-uniformity of the airgap reluctance due to slotting. It is independent of current excitation and proportional to the square of the flu x-density [14], this is particularly important in wind generators since it raises the cut-in wind speed, thereby lowering the energy captured yield for a given installed capacity. Pulsating torques also produces noise and mechanical v ibrations which accelerate the wear of the mach ine and its support structure [14].
The simu lation results of cogging torque for six PM SG structures; when one varies only the nu mber o f poles by the FEA are shown in figure 15, one can see clearly that the number of poles influence direct ly the cogging torque in pulsations and magnitudes.
The following figure show the effect of the number of stator slots on cogging torque, according to our results one can say that the increase in number of stator slots gives an increase in amp litude of cogging torque, but does not change its frequency as we can equally be observed. Fig. 17 shows the efficiency as a function of electrical degree and the number of poles, no variation of curvatures is remarked, but a variation in amp litude is found, or the efficiency increases by 76.9% to 86% for the increase in number of poles fro m 2 to 10 respectively.
On the other hand the efficiency decreases if the number of poles increases; the efficiency reached the value 84.8% if the number of poles is 14.
The variation power of PM SG as a function of number of poles and mechanical angle is showed in figure 18, it is noticed that the wave form is similar, but one sees a power peak of 7KW if our PMSG designed by 8 nu mber of poles.

Conclusions
Nu merical analysis of magnetic field, e.g. FEA, can take into account the detailed structure and dimensions of the machine and the nonlinearity of the ferro magnetic materials, and hence can accurately compute the mach ine parameters and performances.
The type of PM used in the design of PMSG masters the majority of performances; it was found that among the PMs used the best performance is given by NDFE. It was found that the rotor speed influences proportionally on the power and the efficiency. The efficiency and power increase with the increasing of rotor length, but the efficiency decreases with the increasing of the rotor length, if it is bigger than the stator length, therefore its optimal value is 65mm.
According to showed results, the magnitude of the PMSG's cogging torque is affected by number of poles and number of stator slots, but the frequency of the PMSG's cogging torque is affected only by the number of stator slots, the optimal value of the nu mber of poles and nu mber of stator slots which guaranteed simultaneously these performances is 4 and 24 respectively.
FEM has proved to be a co mpetent and valuable tool to study and design of PMSGs used in small wind power generation systems. The analysis results help to improve the generator design aspects.