1ry multi-criterion design and 2d cosimulation model of 4
TRANSCRIPT
Multi-Criterion Design and 2D Cosimulation
Model of 4 kW PM Synchronous Generator
For Standalone Run-of-the-River Stations
Yucel Cetinceviz Mechatronics Dept.,
Kastamonu University
Kastamonu, Turkey
Durmus Uygun Electrical-Electronics Eng. Dept.,
Gediz University
Izmir, Turkey
Huseyin Demirel Electrical-Electronics Eng. Dept.,
Karabuk University
Karabuk, Turkey
Abstract— This study reports the analytical computation
including performance characteristics such like load line voltage
and output power in combination with coupled-field circuit
analysis of a 4kW direct drive permanent magnet synchronous
generator (PMSG) to be used in a micro-scale run-of-the-river-
station application. The specifications such like slot opening, pole
embrace and magnet length of PMSG are optimized by using
parametric approach including multi-criterion design
optimization. Based on the optimized design, the model has been
exposed to some transient coupled-field circuit analyses based on
variable river flow speed and variable ohmic load conditions. The
analytical studies related to finite element methods and
conducted parametric approaches verified the effectiveness of the
employed dynamic co-simulations.
Keywords—run-of-the-river-stations; coupled-circuit analysis;
PM generator; multi-criterion design optimization; parametric
approach
I. INTRODUCTION
The need for the energy is increasing day by day along with rapid population growth and industrialization. The fossil fuels such as coal, oil and natural gas which are used to meet these requirements are being replaced by renewable energy sources like sun, wind, geothermal, hydraulic and ocean resources [1, 2]. Energy cycle plants are obtained with the turbines placed in natural energy sources such like a river, wave or tidal areas which are using the power of liquid flow [3-5]. Compared to other renewable energy technologies, hydrokinetic systems are low-cost energy conversion systems due to their low investment expenditures and maintenance fees [6]. Accordingly, micro-scale run-of-the-river-stations are offering cost-effective solutions especially in rural areas [6, 7]. As long as the rivers and creeks don’t dry up, they offer the advantage of being a constant source [8]. Besides, these river plants relatively have higher kinetic-energy densities when water flow velocity exceeds 2 m/s and thus increase potential commercial investments [9].
In such kinds of power plants; commonly variable speed permanent magnet synchronous generators (PMSGs) [5, 6 and 8-13] and doubly-fed induction generators (DFIGs) [2] are employed. Variable-speed turbine structure housing PM generator offers appropriate solutions to meet the energy needs
of the rural areas.
The objective of this article is related to present the design and dynamic performance analysis of a 4kW PMSG in order to get maximum available energy from water flow. To gain maximum available energy, detailed design and analysis was carried out to cover the operational aspects such as start-up torque, cogging torque, ripple, flow interactions, efficiency, rated power and terminal voltage. The cogging torque is a common issue for permanent magnet machines [11]. The torque ripple in the cogging torque is related to the harmonics in the back-EMF. To reduce it, the effect of the slot opening, the magnet thickness and the pole arc/magnet arc ratio (embrace) of the cogging the torque were investigated parametrically. Thus, this study gives an opportunity analysis of dynamic performance of 4 kW PMSG supplying different loads and variable generator speeds related to water flow by using coupled two dimensional (2D) electromagnetic field -circuit model.
II. DESIGN SPECIFICATIONS
A. Background of the Design
Prior to preliminary prototyping of a custom electrical machine, the design can be initiated by defining basic parameters such as machine type (synchronous, asynchronous, DC, reluctance machine, etc.), structure, nominal power, rated speed, number of pole pairs and rated voltage and by determining additional characteristics like efficiency, cost and manufacturability [14]. A real machine design starts with the selection of main dimensions of the machine. These main dimensions indicate the air gap diameter (Ds) measured via stator slot tips and stack length (L) of the machine. In electrical machine design, there are some empirical definitions in the variation interval of current density and flux density parameters including the selection of magnetic loading values.
The machine constant (C) of a well-designed power conversion system is the basic element in construction. The machine constant jointly expresses apparent power Si or active power Pi presented with given rotor volume. Another factor affecting the power of the machine is Dis
2.L multiplication [15-
17]. So, the problem is to separate these two parameters as air gap diameter (Dis) and equivalent stack length (L). In the
This work is funded by The Scientific and Technological Research Council of Turkey (TUBITAK) under grant numbers 113E782 and 113E577.
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literature, various ratios like stack length/pole arc [15, 18 and 19] and stack length/air-gap diameter (or stator inner diameter) have been used to separate these parameters. In other study, the stack length/air-gap diameter ratio has been used as L=Dis/4. Additionally, stator outer diameter/stator inner diameter ratio is an important parameter to declare and meet temperature effects, loss and efficiency requirements. Various values are indicated for that ratio in the literature as well. While it is given as 1.24-1.26 for the machines with high number of poles in [18], it is approximately indicated as 1.66 in [14] and as √3 in [20]. The generator taken into consideration will have 24 poles due to high energy harvesting requirements even in low shaft speeds and it is not clear which value or interval is appropriate for this application.
Owing to this complex processes mentioned above, the necessity is increasing for the verification of the design and optimum solution delivery. This also leads the process to be more complex, expensive and time consuming. Therefore, there is a need for simulation and analysis model to address this complexity [21]. So, in this study, an integrated field-circuit model was used for analysis of the dynamic performance of the machine combined with electromagnetic field solution.
B. Analytical Modelling Study
In many direct drive application, high torque and low speed
are required. Thus, a multiple pole, inner rotor-structured
machine topology has been considered by using NdFeB
magnets with high magnetic flux density. Besides, another
reason for choosing an inner-runner structure is shorter
manufacturing process and easy mounting of the generator.
This configuration is also suitable for cooling since the
windings where copper losses (heat) are taking place are
formed around the rotor. In this section, analytical calculations
for the design of the machine according to the specifications
given in Table II are performed.
TABLE I. GIVEN TECHNICAL DATA FOR THE GENERATOR
Parameter Data
Rated Output Power (kW) 4
Rated speed (rpm) 250
Frequency (Hz) 50
Number of phases 3
Rated Voltage (V) 400
Rated Power Factor 0.95
Target Efficiency >= %92
If the design of the generator is initiated with machine
constant, the following equation can be derived;
2
0 1 1 2
1
60 gap
f i w g
is
SC K K A B
D Ln (1)
where Kf is the form factor, αi is the magnetic flux density
form factor based on magnetic saturation on stator tooth, Kw1
is the winding factor, A1 is the specific electrical loading and
Bg is the magnetic loading values.
As insisted before, Dis which is the air-gap diaemeter (or
stator inner diameter in other words) is one of the most
important parameter of both inner and outer runner PM
generators and can be obtained as;
2 2
3 32is is
is
D L p D LD
x (2)
But, these two equations are not enough to give a
comprehensive volume expression of the machine. So, stator
outer diameter must be taken into consideration in terms of
slot dimension as follows [22];
2( )o is s csD D h h (3)
where Do is the outer diameter of the generator, hs is the
slot depth and hcs is the stator core height. These two
parameters can been calculated as [17, 18];
1 16 1n
s
g giscon fill con fill
ts ts
W I Ah
B BDj K j K
B B
(4)
12 2 2
gi is
cs
cs cs
BDh
LB p B
(5)
Additionally; the following ratio can be given to declare
and meet temperature effects, loss and efficiency
requirements;
1
21 1
2
aspect g go
is s ts cs
K B BD i
D N B p B
(6)
where Kaspect is the limitation factor. The ratio of stack
length to air gap diameter is another significant parameter
which is also known as L/D [23];
12; 0.6 3.0
p
is
LL
D
(7)
With respect to all parameters calculated by using
analytical method, the initial design parameters of the
generator can be demonstrated in Table II.
TABLE II. COMPUTED OUTPUT DATA FOR 4KW GENERATOR
Parameter Data
Load Line Voltage 405 V
RMS Line Current 6.49 A
Specific Electrical Loading 28699.9 A/m
Armature Current Density 3.94 A/mm2
Iron Core Loss 36.56 W
Armature Copper Loss 338.52 W
Total Loss 375.08 W
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Output Power 4539 W
Input Power 4914 W
Efficiency (%) 92. 36
Power Factor 0.9851
Rated Torque 188.707 Nm
Short Circuit Current 27.38 A
As a result of analytical calculations, the generator model which is consisting of calculated analytical dimensions can be illustrated as seen Fig.1.
Fig. 1. Objective 4kW PM generator for run-of-the-river station application.
C. Multi-Criterion Parametric Optimization
Parametric analysis is employed in the case of optimizing the model that is preconfigured via theoretical computations in electric machine design process. In design process, there are many software and modules realizing simulations in order to shorten the development period prior to construction of the real model. Due to comprising numerous sub-modules, ANSYS RMxprt software is used in detailed parametric analyses.
Optimization problem is to find an acceptable design which fulfils all the requirements. However, there are many possibilities for selecting an objective function. Due to the fact that a PMSG is including many parameters, it is useful to use a multi criterion optimization approach of which main idea is presented in the following equation;
1 1 1 1
2 2 1 2
1
( , , )
( , , ): : :
( , , )
n
n
n m n m
x f x x Q
x f x x QX Q
x f x x Q
(19)
Where x1 and x2 are two feature vectors and Q is the evaluation criteria. Besides, the optimization based on the analytical model which is implemented in order to obtain the optimal geometric structure and field distributions of PMSG is also preferred to minimize total losses at nominal operation
conditions. In that case some parameters like outer diameter of the stator and rotor, stack length of PMSG, slot opening and magnet thickness which are forming the basic of the generator are chosen to be optimized of which computation way is presented below;
0
min max 0
, , ,
, , , ,
( )
loss o s mag
o s mag
min P D L B t
Functions x x x x D L B t
f x
(20)
In the scope of the above mentioned explanations, slot
opening, magnet thickness and the pole embrace parameters have been optimized within acceptable ranges.
Slot opening must be in the size of the conductor. In the case of using very small slot opening, it may be possible to see leakage flux from one tooth to another. Therefore, the length of the slot opening must be higher than air gap length. On the other hand; for wider slot opening values, cogging torque parameter increases. In accordance with all these limits, it is necessary to determine an optimum slot opening value. In the literature, it is stated to choose a slot opening value between 2 and 3 mm [18, 24]. So, the value of slot opening has been recalculated for better efficiency and output voltage level and lowest cogging torque as a result of multi-criterion parametric analyses between 1mm and 3mm length with a sensitivity of 0.1mm. And the derived results are illustrated in Fig.2. It can be easily seen on the graph that especially cogging torque is very close to zero for the selected slot opening value (optimum region).
Optimum
region
Fig. 2. Effect of variable slot opening on load line voltage, output power,
efficiency and cogging torque parameter of generator.
In direct drive generators, the effect of cogging torque is considerably significant since the designed generators may be used in very low speed application. One of the methods to eliminate cogging torque is “skewing of either stator slots or magnets” in which we preferred magnet skewing owing to easy manufacturing cases. Another way to decrease cogging torque and make some improvements in parameters like output power and load line voltage is to vary magnet arc/pole arc ratio (embrace) within an acceptable range. So, embrace has been parametrically solved between 0.5 and 1 with 0.02 steps and the effect of that variation on load line voltage, efficiency, output power and cogging torque is illustrated in Fig.3.
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Optimum
region
Fig. 3. Effect of variable pole arc/magnet arc ratio (embrace) on load line
voltage, output power, efficiency and cogging torque parameter of generator.
Nowadays, the magnets with high energy density are generally used in electrical machine applications. N40SH type NdFeB magnets will be preferred in this generator design due to their high energy density and effective operational functions in applications with high temperature. The magnetic flux density (Bm) of these magnets is around 1.23T. One of the most significant factors in selecting magnet type is the thickness of the magnet not allowing demagnetization in a short time [22]. But on the other hand, thickness is a factor which is increasing the cost of the machine.
Since cost/efficiency ratio is to be considered as a design parameter, a reasonable magnet thickness should be chosen. A parametric study between 3mm and 10mm thickness with 0.2mm steps has been achieved and the effect of that variation on load line voltage, efficiency, output power and cogging torque is illustrated in Fig.4.
Fig. 4. Effect of variable magnet thickness on load line voltage, output
power, efficiency and cogging torque parameter of generator.
III. ELECTROMAGNETIC FIELD AND COUPLED CIRCUIT
ANALYSES
In this section, the dynamic design results of 4kW PMSG which will be manufactured in the project have been presented by using the model derived from optimization studies. The main idea behind executing a coupled electromagnetic analysis is that the results obtained via simulations will provide comprehensive information and data related to the behaviour of the machine in different conditions. Moreover, it is possible to confirm the accuracy and precision of analytical calculations.
Related model given in Fig.5 is used to carry out simulations in two steps. Primarily; the generator was operated for a time period of 100ms at varying speed rates ranging from 100rpm to 450 rpm for constant load condition (Rload is 44Ω as a result of analytical calculations).
RIVER STATION
PMSG
General arguments
for any application:
Size / Weight
Efficiency
Torque
Speed
Cost
Manufacturability
Power Density
Generator speed regime
related to water flow speedTransient
Analysis
using
FEA Variable load
Rectifier Block Inverter Block2D Electromagnetic Model of
PMSGLoad
CO-SIMULATION RESULTS
Fig. 5. Design methodology for complete co-simulation process.
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The dynamic performance of the PMGS relating to consant load and varying speed conditions have been summarized in Fig.6.
Fig. 6. Load line voltage and generator output power parameters for varying
generator speeds and constant load.
For varying generator shaft speeds (herein simulated as variable water flow speed), it can be clearly resulted that load line voltage and output power of the generator are curvaceously increasing as long as the shaft speed of the generator steps up.
For another study with Rload is 36Ω in which generator
operation regime with variable speed is shown in Fig.7,
transient coupled circuit field results demonstrated in Fig.8
have been obtained for a 200ms time period through 100µs
time steps. In the case that this time step is decreased which is
also leading more complex and longer simulation time, better
results can be derived.
Fig. 7. Generator speed regime related to water flow speed.
(a)
(b)
Fig. 8. Simulation results derived from variable speed operation, a) Generator side measurements b) Load side measurements
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Besides, the output characteristic of the machine related to simulation results realized separately for different load conditions (22-26-30-36-40-44-50-56Ω) and rated speed (250rpm) has been derived as seen in Fig.9.
Fig. 9. Load line voltage and generator output power parameters for varying
load conditions at 250rpm rated speed.
Different from the analyses derived before, the output characteristic of the machine has been pointed by defining an operation cycle related to time in which variable load conditions have been saved as 44-28-8-22Ω and illustrated in Fig.10 at rated speed and the results have been shown in transient variation in Fig.11 for both generator and load sides, respectively.
Fig. 10. Operating variable load(ohmic).
(a)
(b)
Fig. 11. Simulation results derived from variable load and constant flow operation, a) Generator side measurements b) Load side measurements.
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It can be noted that the reaction of the generator with in
predefined operation cycle is quite good but especially at the
points where value of the load is increased unexpectedly and
instantly, some ripples are observed on generator phase and
line voltage due to instant torque variation. On the other hand,
the observation on load side measurements indicates that the
generator is quite powerful to supply appropriate line voltage
for the load at the moments where the load is varied.
IV. CONCLUSION AND FUTURE STUDIES
In this paper, the design of a 4kW permanent magnet synchronous generator suitable for standalone or off-grid run-of-the-river-station turbine application has been developed. The results of analytical PMSG design and concerned optimization methods are reported in the paper. Thereto, the effectiveness of the proposed electrical machine configuration in terms of output power, efficiency, cogging torque and load line voltage have been demonstrated via 2D dynamic transient co-analysis approach by indicating compliance of simulated and real load conditions prior to the fabrication of the designed and optimized machine. But, the study on 380V, 4kW generator design with in-runner configuration is not yet complete. As a part of project; the testing, verification and advanced analysis studies need to be performed posterior to completion of prototyping process. Next to this, future studies on optimized machine are going to focus on eddy current loss minimization in permanent magnets as well as copper loss optimization in stator windings.
ACKNOWLEDGMENT
This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under grant numbers EEEAG-113E782 and partially EEEAG-113E577 since similar design methods and approaches have been utilized. The authors would like to thank TUBITAK for their financial supports.
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