Rapid Modelling and Design of Variable Speed Permanent Magnet Generators for Maritime Applications J. M. Gutierrez-Alcaraz, N. Al-Fartusi, H. Polinder, J.A. Ferreira DELFT TECHNICAL UNIVERSITY Mekelweg 4 Delft, Netherlands Tel.: +31 / (15) – 27 86016 Fax: +31 / (15) – 27 82968. E-Mail:
[email protected] URL: http://ewi.tudelft.nl/epp
Keywords GenSet, Permanent Magnet Generator, Maritime applications, modelling, design, fractional pitch, 3 pole, 2 teeth.
Abstract Electrical power generation plays an important role in maritime vessels. This power is usually provided by a multi-component system where the generation begins with the rotational movement of a prime mover, usually and Internal Combustion Engine, an electric generator and an assortment of power electronic components to process and regulate electrical energy. Due to the requirements of the application, i.e. power-on-demand to reduce fuel consumption and increase user comfort, all components need to be adapted to perform efficiently within a wide range of output power levels. For such a purpose a Variable Speed Permanent Magnet Generator (VSPMG) is presented as a solution that fulfills most of the requirements of the power generation stage. However, the design of such of generator is a long process where multiple variables intervene. The following paper deals with a rapid modelling and design tool that helps evaluate a VSPMG with concentrated windings in a quick, and relatively accurate, manner. This tool can be used to obtain a first draft design that can be perfected after further analysis. Analytical equations and experimental data are presented for validation. A simplified thermal model is also presented with the corresponding experimental counterpart. Finally, conclusions are given and next steps are suggested.
Introduction Power generation in maritime vessels is an interesting and challenging topic. Stringent requirements are posed on the power plant of a marine ship starting from correct selection of materials to reduce the risk of corrosion and ending with the constant monitoring of multiple components distributed across the ship. The project in hand pursues the integration of such system into a very small volume that can substitute the many distributed components that are used nowadays. Our integrated Generator Set (GenSet), as shown in Figure 1, comprises all necessary components to produce high quality regulated energy: - A Diesel Internal Combustion Engine (Diesel ICE), - A Compact Permanent Magnet (PM) Generator/Motor, - An AC/DC converter/inverter, - A DC/DC bidirectional converter, - A high power/energy density battery pack, - A DC/AC inverter/converter, - A control system, - A system wide thermal management solution.
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Figure 1. Generator Set schematic
To increase fuel efficiency and reduce acoustic noise, the system produces energy-on-demand, which means that the speed of the Diesel ICE is increased when more energy is needed by the load. Since the induced electromagnetic force (emf) of the generator is dependant on the speed of the Diesel ICE, the PM Generator will produce a variable output voltage between its terminals. In addition, the battery pack provides energy when the system is in standby and during transients that exceed the generator’s response time or the PM Generator maximum output power. The PM Generator also starts the Diesel engine automatically when a big enough load is detected; i.e. a load that exceeds the continuous rated battery power. For very small loads the energy is taken from the batteries. The present paper focuses on the development for a PM Generator rapid design tool, which can provide a starting point for subsequent optimization. By means of analytical modelling a reliable rapid design tool is presented, simplifying and quickening the construction of VSPM Generators. This paper will present a brief introduction to concentrated windings PM Generators, a list of application requirements, the rapid design model, the validation results, our conclusions and next steps.
Variable Speed Permanent Magnet Generators As stated before the requirement of a GenSet PM generator is to perform efficiently under variable angular speed to minimize fuel consumption and maximize user comfort by generating only the power necessitated. A PM Synchronous Generator (PMSG) was considered as the best option due to its compact volume and efficiency [1]. Based on a model developed at the Delft University of Technology and described in this paper, two 9kW generators were constructed for test and validation purposes. The requirements and assumptions considered in the design of a 9kW PMS Generator have the following criteria: - A 3-teeth/2-pole combination was chosen. - Rare earth permanent magnets (NdFeB) were selected because they offer higher remanent flux density, even though these magnets are electrically conductive and prone to develop Eddy currents due to field changes caused by the coils on the stator’s teeth [2]. - Two alternatives are considered in respect to teeth geometry: o Rectangular-teeth/open-slots are easier to wind, i.e. they offer easier and faster fabrication time for the generator assembly, yet they produce higher Eddy current losses within the rare earth magnets and the magnets’ back iron [3]. o Semi-closed-slots/Tooth-tips help reduce the Eddy currents developed within the permanent magnets due to the pulsating field generated by the windings [4], but are difficult to wind. o Optimized versions of both designs will be prototyped and based on the comparison of their performance (higher efficiency) one of them will be selected for the application.
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-
The angular speed range varies from 1500 RPM to 3150 RPM with ± 5% variation (3400 maximum non-repetitive speed). The nominal speed of the Diesel Internal Combustion Engine (ICE) used as prime mover is set to 2600 RPM. At this speed the engine provides the highest torque for the lowest fuel consumption [5]. The nominal power at nominal speed is set at 9 kW. The Diesel flywheel will be integrated in the PMSG.
PM Generator – requirements and variable definitions Due to the many variables needed for the design some of them were defined in advance based on the requirements and common characteristics of PM Generator with 3teeth-2pole configuration. Table I lists most of the defined variables of the PM Generator including the ones needed for manufacturability, with a short explanation of the role that they play in the overall design. The table also defines the variables and constants used throughout the paper. Table I: PM Generator variable definitions Description
Variable used
Value
Number of phases
Phn
3
Number of teeth The relationship between teeth and pole number is a design aspect, results vary in different applications. Number of poles
Nt
27
Np p
18
Number of pole pairs Mechanical air-gap [mm] The mechanical air-gap between rotor and stator, it should be as shorter as mechanically possible to allow maximum transfer of flux. Copper fill factor The percentage of Copper that effectively fills the slots (due to the geometry of the wire and the insulation burnish). Slot width/slot pitch ratio The relation between the width of the slot and the total pitch. This ratio is used to determine the transfer of magnetic flux. Pole width/pole pitch ratio Relation between the width of the magnet and the total pitch. Appropriate values provide smooth flux density distribution from the permanent magnets. Winding factor The ratio of flux linked by an actual winding to flux that would have been linked by a full- pitch, concentrated winding with the same number of turns. Rotational speed range [RPM] The angular speed range at which the rotor is moving around the stator. Nominal Speed [RPM] The speed at which the engine has maximum fuel efficiency. Output power at Nominal Speed [W] Desired power at the given angular velocity. Maximum (peak) output voltage [V] (+ 8%) Maximum expected output line-to-line peak voltage at maximum non-repetitive rotational speed (3150RPM+8%, i.e. 3400RPM).
Np / 2
lg
0.002
K sfil
>0.25
bs / τ s
----
bp / τ p
----
Kω
0.866
RPM
1500 ~3400
RPM
2600
Pdes
9000
Vl 2l _ r
---
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r_s H _s
0.1075 ---
hsy
0.015
ls
0.045 1.2
Resistivity of Copper [Ω·m]
β rm μ0 μrm ρ mCu ρ mFe ρ mm ρCu
Hysteresis iron loss per unit mass @ 50 Hz [W]
PFe 0 h
2
Eddy current iron loss per unit mass @ 50 Hz [W]
PFe 0 e
0.5
Maximum radius of the stator [m] Slot height [m] Parameter that can be changed to accommodate sufficient space for the windings. Stator yoke height [m] The stator yoke has to be thick enough to close the magnetic circuit by providing a path for the flux to travel form one teeth to the other. Machine stack length [m] In a disk-shape design the stack length contributes to decrease the size of the stator/rotor diameter Magnets Remanent flux density [T] Permeability of air Recoil permeability of magnets Copper mass density [kg/m3] 3
Iron mass density [kg/m ] 3
Magnet mass density [kg/m ]
(4π)e-7 1.05 8900 7700 7500 2.4e-8
9kW PM Generator Design The Diesel ICE is used as the prime mover for the generator; this provides rotational motion and torque to the rotor of the PMSG. To find out the electrical frequency at which the generator is running, the mechanical speed needs to be established first; this is done with eq. 1 and 2: rpm ωm = 2π (1) 60 ωe = ωm ⋅ p (2) Knowing the electrical frequency is possible to continue the design of the dimensions of the PM. The radius of the rotor is a design variable, in our case a larger diameter of the generator is preferred because the engine to which the generator is attached already occupies considerable depth and height compared to the rest of the components. Setting the radius to 9 [cm] (could be smaller, but we take the depth measurement of the Diesel ICE) and with the total number of desired pole pairs, it is possible to calculate the pole pitch. Given the pole width/pole pitch ratio (eq. 3) it is possible to calculate the width of the permanent magnets (eq. 4) to achieve a smooth flux density in the air gap. The magnet length is either given or computed with an iterative procedure based on the magnetic flux in the air gap.
τp =
π ⋅ (rs + lg ) p
bp = (bp / τ p ) ⋅τ p
(3) (4)
The slots in the stator will have a trapezoidal shape, i.e. the teeth will have a constant width. Because we are working close to saturation point of the teeth, a bigger area of the teeth in the stator translates into higher transfer of magnetic flux from the permanent magnets to the windings on the teeth. Equations 5-9 show the procedure to calculate the area of the slots under the assumption that they are open slots as shown in Figure 2.
τs =
2π rs Nt
(5)
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bs = τ s ⋅ bsτ s
(6)
bt = τ s − bs
(7)
bsi =
2π ( rs − hs ) N t − bt
Aslot =
(8)
(bsi + bs ) ⋅ hs 2
(9)
Figure 2. Geometry of rectangular teeth
For the calculation of the area of the slot in a semi-closed slot configuration, the geometry changes and a tooth-tip is added at the end of the teeth, the corrected equation to find the total area available in this configuration is given by eq. 14. In Figure 3, the height and the width of the tips of the teeth were taken based on measurements of teeth from other available stators and were found to be 10% of the total height of the teeth and the width of the tip was extended 60% of the width of the teeth on each direction:
hs 0 = 0.1 ⋅ hs
(10)
btt = 2.2 ⋅ bt
(11)
bs 0 = 0.4 ⋅τ s
(12)
bsi _ cap
r −h = 2 ⋅ π ⋅ s s 0 − bt Nt
Aslot _ cs =
(bsi _ cap + bsi ) ⋅ (hs − hs 0 ) 2
bsi_cap
(13) (14)
btt hso
bso
bsi
bt
hs τs
Figure 3. Geometry of semi closed slots and tooth tips
The calculation of the Carter factor and the effective air gap is based on a very simplified model of the magnetic path in the air gap from the teeth to the magnets’ back iron. The result of such modeling will provide a very rough approximation of the fundamental flux density space harmonic due to the permanent magnets (eq. 19). The calculation of the Carter coefficient and the Carter factor itself are based on the same premises as in [2] and [3]: where magnets are replaced by a smooth surface placed at a distance g eff from the teeth, therefore the Carter factor is a correction factor that takes into account the slotting of the stator. Although the equations presented are not necessarily applicable to the design of a VSPM Generator they provide a good starting point for its subsequent optimization.
⎛ ⎛ bs ⎜ bs ⎜ 4⎜ 2 2 ⋅ arctan ⎜ γ= ⎜ l π l + m ⎜ l + lm ⎜ g ⎜ g μ μ rm ⎜ rm ⎝ ⎝ K carter =
τs
⎛ l ⎞ τ s − γ ⋅ ⎜ lg + m ⎟ μ rm ⎠ ⎝ ⎛ l ⎞ g eff = ⎜ l g + m ⎟ ⋅ K carter μ rm ⎠ ⎝ lm ⋅ Brm Bg = g eff ⋅ μ rm
⎞ ⎛ bs ⎟ ⎜ 2 ⎟ − log 1 + ⎜ ⎟ ⎜ l + lm ⎟ ⎜ g μ rm ⎠ ⎝
⎞ ⎟ ⎟ ⎟ ⎟ ⎠
2
⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
(15)
(16)
(17) (18)
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4 ⎛ π ⋅ bb ⎞ Bg1 = Bg ⋅ sin ⎜ ⎟ π ⎜⎝ 2 ⋅τ p ⎟⎠
(19)
With the value of the fundamental harmonic of the flux density, it is possible to calculate the flux fundamental component (eq. 20) which in turn is used to calculate the electrical parameters of the generator. The flux component is dependant on the flux density and the geometry of the magnets and the width of the teeth; e.g. saturation of the magnetic path through the teeth will occur in narrower teeth. 2
Φ pm max = B g 1 ⋅
π
⋅τ p ⋅ ls ⋅ k w
(20)
Equations 21 and 22 are used to calculate the reluctance of the air gap as well as the reluctance due to the slotting of the stator for the rectangular version of the stator. The equations were derived from the general reluctance expression given in [6], the constant given in eq. 22 is an empirical constant.
Rmg =
g eff
(21)
μ 0 ⋅ τ s ⋅ ls
Rσ = 2 ⋅
bs μ 0 ⋅ hs ⋅ ls
(22)
To calculate the reluctance due to the slotting of the stator in the semi-closed version of the stator equation 22 becomes a set of 3 equations when substituting the appropriate expressions for equations 10 to 14. In this case, the reluctance due to the slotting comprises the reluctance due to the tooth-tip and the reluctance of the tooth.
bs
Rσ s = 2 ⋅
b μ 0 ⋅ ( hs − hso − so ) ⋅ ls 3 bso Rσ so = b μ 0 ⋅ ( hso + so ) ⋅ ls 1.5 1 Rσ = 1 1 + Rσ s Rσ so
(23)
(24)
(25)
The maximum values of the flux density in the teeth that flows through the stator yoke can be calculated with eq. 26 and 27.
Bt max =
Φpmmax
(26)
bt ⋅ ls
By max = Bg1 ⋅τ p ⋅
2 2 ⋅π ⋅ hsy
(27)
To calculate the number of turns per teeth to get a maximum line to line peak output of Vl 2 l _ r [V], we can use eq. 28-29 and solve it for N s and N c using the desired voltage value at maximum speed. With the number of turns, the final back emf is calculated again and the new peak line-to-line voltage is compared with the maximum expected.
Ns =
Nt ⋅ Nc 3
emf = Ns ⋅ωe ⋅
(28) Φpmmax 2
(29)
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Once the total number of turns is found the total inductance of the generator can be calculated with the help of eq. 30; low inductance values will make the current flowing through the generator fluctuate [1].
L=
N 6 ⋅ Rm g + 2 ⋅ Rmσ 3 ⋅ N c2 ⋅ t ⋅ 2 3 3 ⋅ Rm g ⋅ Rmσ
(30)
A power factor of 0.9 is considered. In addition, the wire will generate losses due to the intrinsic resistance of the conductor; these losses will produce heat that needs to be removed from the generator. At speeds lower than the nominal speed the generator will be less efficient because power is generated through the production of low voltage at high current; therefore, higher losses on the conducting wire will be present for a given current density (J). At higher speeds, the voltage increases and the losses in the iron core also increase. However, the core has more volume to dissipate the generated heat, thus the effect of this increase on the losses is not critical. Eq. 36 gives the total loss in the wire:
π ⋅τ s ⎞ ⎛ lCus = 2 ⋅ N s ⋅ ⎜ ls + ⎟ 2 ⎠ ⎝ A ACus = K sfil ⋅ slot 2 ⋅ Nc Rs =
(31) (32)
ρCu ⋅ lCus
(33)
ACus
I s = ACus ⋅ J
(34)
Pgen = 3 ⋅ emf ⋅ I s ⋅ 0.9
(35)
PCus = 3 ⋅ I s2 ⋅ Rs
(36)
To calculate the losses in the iron core of the stator, due to Eddy currents in the teeth and flux flowing through the stator yoke that is lost in transit, eq. 37 to 41 are used. The loss is proportional to the mass of the iron core, the frequency of operation and the flux density flowing through the stator core. Eq. 41 gives the losses in the iron; however, this is a very optimistic approach because it does not take into account other sources of losses, from empirical data a factor of 1.6 is multiplied to the total losses to have a better approximation of the real losses in the stator core.
M Fest = Nt ⋅ hs ⋅ ls ⋅ bt ⋅ ρmFe ⎛B ⎞ PFestnom = M Fest ⋅ ⎜ t max ⎟ ⎝ 1.5 ⎠
(
2
⎛ P ⋅ω ⋅ ⎜ Fe0h e ⎜ 2 ⋅ π ⋅ 50 ⎝
(37) ⎛ ωe ⎞ +⎜ ⎟ ⎝ 2 ⋅ π ⋅ 50 ⎠
2
)
⎞ ⎟ ⎟ ⎠
M Fesy = ls ⋅ π ⋅ ( rs − hs ) − ( rs − hs − hsy ) ⋅ ρmFe 2
2
2
⎛ P ⋅ω ⋅ ⎜ Fe0h e ⎜ ⎝ 2 ⋅ π ⋅ 50 PFe = 1.6 ⋅ ( PFestnom + PFesynom ) ⎛ By max ⎞ PFesynom = M Fesy ⋅ ⎜ ⎟ ⎝ 1.5 ⎠
⎛ ωe ⎞ +⎜ ⎟ ⎝ 2 ⋅ π ⋅ 50 ⎠
(38) (39)
2
⎞ ⎟⎟ ⎠
(40) (41)
The thermal modeling represents a challenge on its own due the multiple variables involved. Our approach is based on a break down model of a single tooth and coil pair. The model assumes that the distribution of losses is balanced across each pair ( ( PFe + PCus ) / 27 ), and that the power loss generated by Eddy currents in the laminations of the teeth is uniform ( Pgen / N laminations ). It is also assumed that, as a result of this simplification, there will not be temperature changes within the tooth, and all generated heat will be transferred to the outer sidewalls in direct contact with the coil former and air, behaving like fins in a heatsink. Identically, we assume that the tooth width is a lot smaller
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than its depth and that most of the heat will be transferred to the sidewalls of a tooth, which in combination with other teeth will form canals that will allow the air to flow. An experimental approach was used to measure the thermal conductivity of the coil former in commercial generators. The model can be cast as a resistor network, and the equations for the thermal model are based on the analysis presented in [7]. The thickness of the coil former and the conformal coatings on the wire and the tooth is assumed to be known ( coil _ fthickness ). This preliminary test will help us define the best cooling method for the VSPM Generator, i.e. forced air or water cooling. RAir1
Tamb
RFec3
Rcoil_f=2.66 K/W Tooth
RFec1 C3
RAir2
RCu1
Aslot bs
C1
RCu2
C3
hs
RFec2
C3
RAir3
Tamb
Tamb RFec4
Stator Yoke
RY RAir4
PM Generator: Stator Teeth – Simplified
Rair=4.42 K/W Tamb
Aslot Pslot
Dhyd _ slot = 4 ⋅ Rn =
Figure 4. Thermal model – Stator Teeth simplified
(42)
Vair ⋅ Dhyd _ slot
ARslot =
bs hs
J Colburn _ slot =
(44) 0.023 ( Rn )0.2
⎛ air ⋅ µ hslot = J Colburn _ slot ⋅ aircp ⋅Vair ⋅ ⎜ cp air ⎜ K ⎝ th _ air 1 Rth _ slot = hslot ⋅ Aslot Rcoil _ f =
(43)
µair
coil _ f thickness K th _ coil _ f ⋅bs ⋅ ls
(45) ⎞ ⎟⎟ ⎠
−2
3
(46) (47) (48)
Solving the resistor network, the final temperature of the generator is obtained, assuming an ambient temperature of 50 ºC inside the containment box. If the temperature is too high for the use of forced air with the current dimensions of the generator; another cooling medium needs to be used. The modeling procedure is simple, solving the analytical model with the available data certain parameters are predicted: the output emf, individual losses of the core and the windings and the machine inductance. In addition, the efficiency of the machine can also be computed.
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Model Validation – 9 kW Permanent Magnet Generator To optimize the design of a VSPM Generator, multiple iterations are required, and multiple variables can be changed to obtain similar results. In our case, we set a fixed geometry based on the available space next to the engine casing. Next the thickness of the magnets, the number of turns in each winding and the cross section of the wire were continuously iterated until the best combination was found. The labels on the plots below correspond to a description of the slots geometry, where ‘os’ stands for open-slots and ‘scs’ stands for semi-closed-slots. 5.A 100 50
100
0
50 0
0
500
Meas ured
1000
1500
2000
2500
3000
3500
4000
0
5.C
5.D Iron loses [W]
Iron losses (G9k_os) 60 0,000 40 0,000 P
0,000 0
50 0
100 0
1 500
2000
2500
300 0
3 500
400 0
3000
4000
Iron losses (G9k_scs)
800 600 400 200 0 0
1000
P_F e M eas ured
Speed [rpm]
P _Fe M eas ured
2000 Speed [rpm]
Simulated (B rm =1. 2T)
80 0,000
20 0,000
1000
Meas ured
speed [rpm]
Si m ulated (Brm =1. 2T)
P_ Fe [w]
N o Loa d induce d e mf (G9 k_ sc s)
150 V_ph [V]
V_ph [ V]
5.B
No Load induc ed em f (G9k _os )
150
2000
3000
4000
Speed [rpm]
P_F e S im ulat ed
P _Fe S im ulated
5.F Efficiency (G9k_os)
100
Efficiency [%]
Efficiency [%]
5.E
80 60 40 20 0 0
500
E f f . (M eas ur ed: T _cal c. ) E f f . (s i mul at ed)
1000
1500
2000
Spe e d [ r pm]
2500
3000
3500
Efficiency (G9k_scs)
100 80 60 40 20 0 0 Ef f . (measur ed) Ef f . (si mul ated)
1000
2000
3000
4000
Speed [rpm ]
Figure 5. Comparison between expected and measured values (A, C, E – open slots, B, D, F – semi closed slots.
From Figures 5.A and 5.B, we see that the induced emf in absence of load presents similar characteristics for both generators. However, on one hand it gives a closer approximation to measured values for the open-slot (OS) design but a greater difference for the semi-closed-slot (SCS) design. The average difference between the expected value and the obtained measurement is 10% of the simulated value in the OS stator; the difference is higher for the SCS design. At this stage we are working to find the reason for this difference. Iron losses present higher disparity in the results, shown in Figures 5.C and 5.D. Unfortunately, the last three test points couldn’t be completed because at the time of the test the only available prime mover could only provide a maximum output of 9 kW at 2600 RPM. The model seems to work fine for the SCS version of the VSPM Generator, but not accurately for the OS version of it. The disparity among the results for the OS case suggest that our approach is far from accurate in the calculation of the iron losses; however Copper losses seem to take up the slack of the total losses in our model, as it can be seen in figure 5.E. To test the efficiency of both VSPM Generators (Figures 5.E and 5.F) we measured the mechanical input, by means of a torque transducer, and the output power, using a single phase power analyzer, when connected to a balanced resistive load. The open slots stator outperforms the semi closed slots stator by 15% on average for different rotational speeds. At the same time we can notice that the model performance in predicting the total efficiency is better for the open slots case, especially around the nominal speed. For values close to the maximum Generator’s speed the model losses convergence,
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with a difference similar to the one found on the SCS case. Due to the better performance of the open slots configuration, thermal tests were not performed on the semi-closed slots stator.
Temperature [C]
Open Slots Stator Temperature 3,00E+02
Stator Yoke
2,50E+02
Winding Winding Winding
2,00E+02 1,50E+02
Winding HC_wall (back) Simulated Temperature
1,00E+02 5,00E+01 0,00E+00 0
500
1000 Time [s]
1500
2000
Figure 6. Stator temperature, tooth/winding, yoke and heat collector.
From the plot in Figure 6 we can se that the approximate model temperature is very high. Because the final temperature surpasses the thermal limit of the conformal coating of the wires and laminations, the test was stopped at 145 ºC. The assumed thermal conductivity of the coil former plus the coating seems to be good, since there is also a 40 ºC difference between the coil and the teeth. It is possible to see that the assumption made about the homogeneous temperature distribution on the teeth is also valid since temperatures measured on different teeth are similar. The high temperature developed by the teeth/coil pair when running at nominal speed requires a different approach in the cooling system, in other words liquid based cooling seems to be the only solution to control the temperature of the stator of the given geometry. To make liquid cooling a viable solution there is need to improve the thermal conduction from the coils’ windings to the iron core, where most likely a cold plate can be attached.
Conclusion We introduced an analytical rapid modelling and design tool that aims to speed up the process of designing a Variable Speed Permanent Magnet Synchronous Generator. Due to the complexity of the machine many variables have been simplified, trading off accuracy in the results. However, we showed with experimental data that our model can be used as a quick starting point to design VSPM Generators for maritime applications. Further work will be done to adjust certain equations and variables in the model, improve the thermal model and include the model of liquid based cooling system to cool down a VSPM Generator.
References [1] Boldea, Ian: Variable Speed Generators, Chapter 10: Permanent Magnet Synchronous Generator Systems, CRC Press, Boca Raton, FL, USA, 2006. [2] Sawhney, A.K.: A Course in Electrical machine Design, Dhanpat Rai & Co. Ltd., 1999. [3] Polinder, H.; Hoeijmakers, M.J.; Scuotto, M.: Eddy-Current Losses in the Solid Back-Iron of PM Machines with Concentrated Fractional Pitch Windings, Proc. of the 2006 International Conference on Power Electronics, Machines and Drives, Dublin, Ireland, 4-6 April 2006. [4] Polinder, H., Hoeijmakers, M.J.: Eddy-current losses in the segmented surface-mounted magnets of a PM machine. IEE-Proc. Electric Power Applications, 1999, vol. 146, no3, pp. 261-266. [5] Kubota Diesel Engine Model D722 Datasheet. http://www.kubotaengine.com/products/pdf_en/04_d722_36.pdf [6] Polinder, H., Slootweg, J.G., Hoeijmakers, M.J., Compter, J.C.: Modeling of a Linear PM Machine Including Magnetic Saturation and End Effects: Maximum Force-to-Current Ratio. IEEE Transactions on Industry Applications, 2003, vol. 39, pp. 1681-1688. [7] Remsburg, R.: Advanced Thermal Design of Electronic Equipment. Champan & Hall. USA. 1998.
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