INTRODUCTION
Recently, a great attention has been paid to the pollutionfree renewable energy
sources to be an alternative source for oil, gas, Uranium and coal sources that
will last no longer than one century. Boldea and Nasar (1987)
introduce the wind energy as one of the most important types of renewable energy
sources that have been used widely in electricity generation. The fact is that
the cost of energy supplied by wind turbines is continuously decreasing.
Wind generators using radial flux configuration become more and more popular.
Joorabian and Zabihinejad (2009) and Kang
et al. (2000) showed that drop in prices of rareearth Permanent
Magnet (PM) materials and progress in power electronics have played an important
role in the development of PM synchronous machines in the last three decades.
Mirzayee et al. (2005) and Kang
et al. (2000) compared the traditional machines using gearbox to
couple to wind turbines with directdrive generators which present some advantages
such as producing higher efficiency, operating with similar magnetic flux density
in all the magnetic circuit and allowing the construction of compact generators
with a large number of poles.
Boldea and Nasar (1987) and Muljadi
et al. (1999) introduce the conventional generators which are installed
at the top of the towers and require stepup gearbox so that the type of generator
for this application needs to be compact and light. The gearbox of a wind generator
is expensive, subject to vibration, noise and fatigue and needs lubrication
as well as maintenance at appreciable cost.
Joorabian and Zabihinejad (2009), Chen
et al. (2000), Gieras and Gieras (2002) and
Gieras et al. (2004) showed that Radial flux permanent
magnet generator has higher efficiency in comparison with conventional doubly
fed induction generators. But design of these generators is so complex. Kessinger
and Robinson (1997) and Kessinger et al. (1998)
proved that it is more difficult to design a high mechanical integrity rotorshaft
mechanical joint in the higher range of the output power. A common solution
to the improvement of the mechanical integrity of the rotorshaft joint is to
design multidisc (multistage) machine. In the Radial structures, output power
can increase easily by increasing the stator length.
Dorigo et al. (1991, 1996)
and Dorigo (1992) presented Ant Colony Optimization (ACO)
such as a pattern solution for combinatorial optimization problems. The first
algorithm which can be classified with in this framework was presented by Dorigo
et al. (1991) and Di Caro and Dorigo (1998)
and since then, many diverse variants of the basic principle have been reported
in the literature.
The characteristic of ACO algorithms is their explicit use of elements of previous
solutions. In fact, they drive a constructive lowlevel solution. But including
it in a population framework and randomizing the construction in a Monte Carlo
way. Stutzle and Hoos (1998) and Tsekouras
et al. (2001) suggested a Monte Carlo combination of different solution
elements also by Genetic Algorithms but in the case of ACO the probability distribution
is explicitly defined by previously obtained solution components.
So far no significant effort has been made to develop high power Radial Flux Permanent Magnet (RFPM) synchronous generators for directly coupling with wind turbines. In this study, complete design and optimization procedures for such electric machine are developed and the manufacturing aspects for the construction of a 20 kW, 150 rpm, 50 Hz prototype are discussed. Since, this generator is a directdrive generator, a rectifierconverter set is required to connect it with the power system.
Ant Colony Optimization (ACO): ACO algorithms simulate the behavior
of real ants. They are based on the principle that using simple communication
mechanisms, an ant group is able to find the shortest path between any two points.
During their trips, a chemical trail (pheromone) is left on the ground. The
pheromone guides other ants toward the target point. For one ant, the path is
chosen according to the quantity of pheromone. The pheromone evaporates over
time. If many ants choose a certain path and lay down pheromones, the quantity
of the trail increases and thus, this trail attracts more and more ants. The
artificial ants simulate the transitions from one point to another point, according
to the improved version of ACO, namely the MaxMin AS (MMAS) algorithm presented
by Stutzle and Hoos (1998) as follows:
In the ant colony optimization algorithms, ants move in search space to arrive
to optimum point. The search space of the ant colony has been shown in Fig.
1. The ant k maintains a black list (N^{k}_{r}) in memory
that defines the set of points still to be visited when it is at point r. The
ant chooses to go from point r to point s during a tour with relation Eq.
1 given by Di Caro and Dorigo (1998).
where, matrix represents the amount of the pheromone trail (pheromone intensity) between points r and s.

Fig. 1: 
Search space for an optimization problem 
Then, the pheromone trail on coupling is updated according to Eq.
2:
where, α with 0<α<1 is the persistence of the pheromone trail, so that (1α) to represent the evaporation and is the amount of pheromone that ant k puts on the trail. The pheromone update Δγ^{k}(r,s) reflects the desirability of the trail (r,s), such as shorter distance, better performance, etc., depending on the application problem. Since, the best tour is unknown initially, an ant needs to select a trail randomly and deposits pheromone in the trail, where the amount of pheromone will depend upon the pheromone update rule. The randomness implies that pheromone is deposited in all possible trails, not just in the best trail. The trail with favorable update, however, increases the pheromone intensity more than other trails. After all ants have completed their tours, global pheromone is updated in the trails of the ant with the best tour executed. In the next section, the MMAS algorithm is extended and modified to find optimal or near optimal generator parameters.
Machine structure: In this study, a low speed, Yconnected RFPM generator has been designed and investigated. The generator structure is formed from stator, rotor, winding and PMs. The machine consists of an intermediate rotor with 40 rareearth PMs and nonmagnetic supporting structure. As a result, the used PM volume is efficiently applied in this structure. The structure of directdrive generator is shown in Fig. 2.
Because of using low speed generator, the topology shown in Fig.
2 does not need any gearbox to couple to wind turbine.

Fig. 2: 
The structure of the directdrive RFPM generator 
The machine is free of mechanical noise and losses. The cogging torque is decreased
with accurate design. In this generator, current density is chosen so that the
natural cooling system is sufficient to work in the thermal limit.
Because of the absence of gearbox, it was estimated that considerable input
wind energy could be saved for electrical generation. Malekian
and Monfared (2007) presented computerprogrammed inverter which controlled
the hybrid system, the use of normal damp structure is not necessary in the
machine. Reliable and simple mechanical construction makes this sort of machine
compact and easy to be installed on the top of a tower.
The parameters of the RFPM generator structure, such as PM dimensions and rotor diameter, are optimized.
OPTIMIZATION
Ant colony Optimization (ACO) algorithms are exploratory search and optimization procedures that work base on the behavior of real ants. In this study, ACO and FEM structural programs are used to achieve high power density and efficiency. In the other words, the permanent magnet dimensions and diameter of stator and rotor are optimized using ACO to achieve the abovementioned objectives. The generator parameters which should be optimized are the thickness, the width and the length of PM as well as the diameter of stator and rotor. The relation Eq. 3 shows fitness function which is utilized to cover such objectives.
where, H is a large positive constant and f is the objective function which is defined in relation Eq. 4:
where, η is the generator efficiency; ξ is the normalized power density which is defined in relation Eq. 5:
where, P is the rated power of generator; m is the total mass of generator and ξ_{max} is the maximum possible ξ according to the constraints of the optimization problem which is considered as follows:
where, T_{PM} is the thickness of PM; W_{PM} is the width of
PM; L_{PM} is the length of PM and D is the diameter of stator and rotor.
These constraints are chosen by considering some practical purposes like the
mechanical strength requirements, etc.
A decision variable x_{i} is represented by a real number within its lower limit a_{i} and upper limit b_{i}, i.e., x_{i} ε [a_{i}, b_{i}].
A twopoint crossover operator has been employed in this study. The nonuniform
mutation operator has been applied in this work. The new value x'_{i}
of the parameter x_{i} after mutation at generation t is given in relation
Eq. 6 and 7:
and
where, τ is a binary random number, r is a random number r ε [0,1], g_{max} is the maximum number of point and β is a positive constant chosen arbitrarily. In this study, β =5 was selected. This operator gives a value x'_{i}ε[a_{i},b_{i}] such that the probability of returning a value close to x_{i} increases as the algorithm advances. This makes uniform search in the initial stages and very locally at the later stages.
After running ACO algorithm, the following optimal parameters have been obtained for constructing the generator:
FEM simulation: For the modeling purpose, the equivalent 2dimensional
(2D) model for FEM analysis is used. Figure 3 shows the triangular
sections for finite element analysis. The sections density in air gap is more
than others. The 2D FEM analysis is applied to this model. Simulation software
generates flux line distribution, flux density distribution which is obtained
by PMs. The distribution of flux line is shown in Fig. 4 in
noload conditions. We can see the maximum flux density in air gap section.
The maximum flux value in air gap section is between 7.2 and 7.8 mWb. Also,
Fig. 5 shows the flux density in no load condition. The maximum
flux density in air gap is about 0.7 T. This value is completely ideal in coreless
schemes. Because of the optimized design, we can have the maximum flux density
in air gap section. In this condition, Rareearth magnets are able to create
an average working flux density of about 1.2 T at the winding.
In order to calculate the induced EMF, an external circuit is connected so
that deriving characteristics at a resistive load is analyzed. In the no load
state, software calculated the flux linkage and electromagnetic force in winding
position. The phase voltage and flux linkage for the resistive load are shown
in Fig. 6a and b. The differential angel
between voltage and flux is about 89.4 degree. Figure 6 proves
that EMf is the integral of the flux linkage. Figure 6 shows
that the shape of phase voltage is almost sinusoidal and has more less harmonics
in compare to conventional generators.
Using 2D FEM analysis, both mutual and leakage fluxes can be taken into account.
The only remaining part is the end winding leakage flux which is thoroughly
discussed by Atallah et al. (1998) and Kamper
et al. (1996).

Fig. 3: 
Mesh distribution in 2D FEM analysis 
With the 2D finite element solution, the magnetic vector potential
has only a z component, i.e., where,
is the unit vector in z direction. The total stator flux of a phase winding
ψ_{abc} that excludes the endwinding flux leakage can be readily
calculated by using Stokes’ theorem, i.e.,
where,
is magnetic flux density.
In the case that the coil is not very thin, magnetic vector potential varies
in the coil crosssection area. Therefore, the average magnetic vector potential
values should be used. For first order triangular elements, the flux linkage
of a coil with N_{1} turns, area S and length l is calculated
with relation Eq. 9 which is given by Atallah
et al. (1998):

Fig. 4: 
Flux line distribution in optimized RFPM generator 

Fig. 5: 
Flux density in optimized RFPM generator 

Fig. 6: 
(a) Back EMF and (b) Flux leakage in optimized RFPM generator 
where, A_{ij} is the nodal value of the magnetic vector potential of
the triangular element j, ζ = +1 or ζ = 1 indicates the direction
of integration either into the plane or out of the plane, Δ_{j}
is the area of the triangular element j and n is the total number of elements
of the ingoing and outgoing areas of the coil. It follows that for an AFPM
machine with only one pole modeled, the total flux linkage of a phase winding
is calculated by relation Eq. 10:
where, u is the total number of elements of the meshed coil areas of the phase in the pole region and a_{p} is the number of parallel circuits (parallel current paths) of the stator windings.
If the 5th and 7th and higher harmonics are ignored, the fundamental total
phase flux linkages can bee calculated by using the ralation Eq.
11 which is given by Atallah et al. (1998),
i.e.,
where, the cophasal 3rd harmonic flux linkage, including the higher order triple harmonics, can be obtained from relation Eq. 12:
With the fundamental total phase flux linkages and rotor position known, the
d and qaxis flux linkages are calculated using Park’s transformation
as relation Eq. 13 and 14 which is given
by Hughes and Miller (1997):
where,
In this type of generator, the daxis and qaxis synchronous inductances are equal and are defined as relation Eq. 15,
where, L_{i} is the leakage inductance; L_{m} is mutual inductance and L_{ew} is the end winding inductance. Sum of the leakage and mutual inductances is calculated using relation Eq. 16:
where, ψ_{d} and ψ_{q} are the d and qaxis flux, respectively; i_{ad} and i_{ad} are the d and qaxis current, respectively; ψ_{f} is the flux of PM on the daxis.
The end winding inductance, L_{ew}, can be calculated using relation Eq. 17 from numerical evaluation of the energy stored in the end connection.
where, q_{1} is the number of coil sides per pole per phase; l_{lew} is the length of the onesided end connection and λ_{lew} is the specific permeance for the leakage flux about the end connection.
IMPLEMENTATION
In this study, a low speed, Yconnected RFPM generator rated at 20 kW, 150 rpm has been constructed after designing and optimizing. The stator threephase winding fixed to the stator frame is assembled as flower petals. Multiturn coils for each pole are arranged in overlapping layers around the shaftaxis of the machine. The whole winding is then embedded integrity resin. Forty averagequality nickelcoated sintered NdFeB PMs with B_{r} = 1.2 T and H_{c} = 950 kA/m have been used in rotor surface. Table 1 shows specifications of the constructed optimized RFPM directdrive generator.
The constructed AFPM generator has been tested as a stand alone a.c. generator.
The experimental setup for testing this generator is shown in Fig.
7. The shaft of the generator and the shaft of the prime mover, which is
a d.c. machine, are coupled together via a torque meter. The open circuit characteristic,
i.e., EMF (linetoline), as a function of speed is shown in Fig.
8.
Table 1: 
Specifications of the constructed rfpm directdrive generator 


Fig. 7: 
Constructed RFPM generator setup 
The main output of the generator is the voltage waveform which must be sinusoidal.
The linetoline EMF at rated speed (i.e., 150 rpm) is shown in Fig.
9. The actual value in Fig. 9 shows that we will have
less harmonic and iron losses in comparison with conventional generators.
MACHINE LOSSES AND EFFICIENCY
Since, the gearbox is not used, in the directdrive generators, the losses pertaining to the gearbox will be omitted. The aerodynamic loss is proportional to the cube of speed. As a result, compared to the conventional RFPM generators, the aerodynamic loss is considerably less because the rated speed for directdrive generators is approximately onetenth of the rated speed of the conventional ones. The main loss in an RFPM generator is the copper loss, RI2. Eddycurrent loss in the winding conductors is important because the conductors are exposed in the main field.

Fig. 8: 
Open circuit characteristic of the ironless AFPM generator 

Fig. 9: 
The linetoline EMF at 150 rpm for no load condition 

Fig. 10: 
The theorical and practical efficiencies versus mechanical
speed 
If the wind speed reduces to kxthe rated value (k<1), then each of the abovementioned
loss component varies as follow:
• 
The input power varies as k3 
• 
The copper loss varies approximately as k4 
• 
The eddycurrent loss varies as frequency, hence k4 
• 
The aerodynamic loss varies with the cube of speed, k3 
According to the relations between losses and speed variation, the efficiency of an ironless AFPM generator can be written in relation Eq. 18:
where, P_{in} is the rated input power; P_{cu} is the rated copper loss; P_{ed} is the rated eddycurrent loss and P_{ae} is the rated aerodynamic loss. Efficiency of the generator changes with the change in rotor speed. Figure 10 shows the theorical curve for efficiency versus speed. Also, in some speeds, the efficiency is practically calculated by measuring the output and input power of the generator. The practical data are also shown in Fig. 9. As shown in Fig. 9 there is an appropriate concordance between theorical and practical efficiency.
CONCLUSION
Design and optimization of a high power directdrive RFPM generator for wind applications are presented in this study. Operation of this generator has been investigated in both finite element simulation and implementation. Also, proper efficiency and power density have been achieved using Ant colony optimization algorithm. Such a high efficiency is a result of decreasing core losses and cogging torque in this ironless structure. These initially promising results were followed by further work involving the development of a prototype generator to validate the design methodology with experimental results and the development of a finite element.
ACKNOWLEDGMENTS
Authors would like to acknowledge the active participation and financial support of the Mapna Electrical and Control Engineering and Manufacturing Company.