Design, analysis and prototyping of a low-cost monopole machine

Transcription

1 Published in IET Electric Power Applications Received on 1st August 2012 Revised on 2nd December 2012 Accepted on 2nd January 2013 Design, analysis and prototyping of a low-cost monopole machine Solmaz Kahourzade, Amin Mahmoudi, Hew Wooi Ping ISSN UM Power Energy Dedicated Advanced Centre (UMPEDAC), Wisma R&D UM, University of Malaya, Kuala Lumpur, Malaysia solmazkahourzade@gmail.com Abstract: This study presents the design, analysis and prototyping of a low-cost monopole machine capable of battery charging. The designed monopole machine encompasses a rotor disc including eight permanent magnets with the same magnetising direction and a stator consists of a magnetic core and three windings: power coil winding, trigger coil winding and recovery coil winding. This machine includes an electronic circuit as a trigger and a magnetic circuit that converts electrical energy to mechanical energy and vice versa. The machine captures energy in the form of back-electromagnetic force generated by a collapsing field in the stator and rotor to avoid wasting energy and stores it in a battery. To simulate the machine, electromagnetic and electrical analyses were conducted simultaneously to predict the design parameters and machine performance: three-dimensional finite element analysis via Vector Field Opera, and MATLAB/Simulink. To validate the simulation results accuracy, the machine was fabricated and tested. Experimental data were compared with simulation results, and showed good agreement with that of simulation. Nomenclature B magnetic flux density (T) B max maximum magnetic flux density (T) e electromotive force (EMF) (V) f frequency (Hz) H magnetic field intensity (A m 1 ) i g winding current during generating state (A) i m winding current during monitoring state (A) i i (t) instantaneous input current (A) i m (t) instantaneous motor current (A) i o (t) instantaneous output current (A) J current density (A m 2 ) j m moment of inertia (kg m 2 ) k e hysteresis constant k h eddy current constant l axial length of iron core (m) L winding inductance (H) n hysteresis coefficient P i input power (W) P cor core loss (W) P cu copper loss (W) P e eddy current loss (W) P h hysteresis loss (W) P o output power (W) R winding resistance (Ω) S conductor area of each winding turn (m 2 ) T L load torque (N m) T e electromagnetic torque (N m) u g generated voltage (V) u s applied source voltage (V) v m (t) instantaneous motor voltage (V) v o (t) instantaneous output voltage (V) V i average voltage of supply battery (V) η efficiency (%) ρ c core material density (kg m 3 ) μ magnetic permeability (A m 2 ) ψ magnetic vector potential (V s m 1 ) σ electrical conductivity (Ω m) θ s permanent-magnet skew angle (deg.) λ damping coefficient (kg s 1 ) ω mechanical speed (radian s 1 ) Ω e total cross-sectional area of conductors winding (m 2 ) 1 Introduction The world s total energy consumption rose from 4674 million tons of oil in 1973 to 8353 million tons of oil in 2011 according to the statistics documented in [1], with 66.5% of the total energy coming from fossil fuels (41.3% oil, 15.2% natural gas and 10% coal). The global concern regarding energy sources is only increasing because of all the industries depending on depleting fossil fuels besides the issues of global warming and air pollution [2]. Growing energy demand has made resorting to alternative sources inevitable [3]. Nuclear power is used as an alternative source of cheap energy. However, the nuclear disaster in Fukushima on 11 March 2011 because of the earthquake and tsunami has led to the closure of many nuclear power plants. Renewable energies are suggested as clean and free sources with lower contamination. Despite all its IET Electr. Power Appl., 2013, Vol. 7, Iss. 4, pp & The Institution of Engineering and Technology 2013

2 advantages, the widespread application of renewable energy faces serious obstacles, as it is challenging to provide a continuous supply because of its reliance on climate, complex inverters, planning, control and optimisation methods as well as the high cost of generation technologies [4]. A large portion of produced energy is converted to electrical energy, whereas electrical machines consume about 70% of the total electricity generated [5 7]. Moreover, CO 2 emitted from electrical machines is another matter of concern; with three-phase induction machines alone having a share of 17% of the emitted CO 2 in the UK [8]. Therefore increment in energy efficiency and improvements in conservation programmes are necessary. To explore the possibility of more efficient energy, monopole machines may be reviewed as one potential with acceptable efficiency, that is independent of inverters and do not emit any CO 2. However, present monopole machine technology does not produce sufficient torque capacity to fulfil most machine application needs, but it can be used to charge batteries that are available in most renewable energy storage systems. Monopole machines are also potential in low-power constant-speed applications such as fans. Moreover, developing and improving this machine can potentially facilitate off-grid independent householders/ customers with limited access to the power network as they are located in remote areas. In the last two decades, the monopole machine, designed by Bedini [9], has been portrayed as a clean and affordable energy converter. Monopole machines rely on repulsion between two north poles or two south poles. The winding around the electromagnetic core has opposite polarity to that of the permanent magnets. Monopole machines use the system s existing electromagnetic energy to generate electromagnetic force (EMF) by applying a small amount of energy from a battery. The produced energy is then rectified and stored through a high-voltage capacitor, which can then charge a battery. Achieving recovered energy with less contamination is the most important feature of the monopole machine. This energy is delivered based on the fact that the monopole machine applies a supply battery for rotation while charging a separate battery. To the best of the authors knowledge, no work has been published on the design and analysis of the monopole machine. Designed monopole machine uses back-emf generated by a collapsing field in the stator and rotor and stores it in a battery. Modelling of the proposed machine is based on the equivalent circuit for the machine. A three-dimensional (3D) finite element analysis (FEA) is conducted to determine machine parameters, predict the results and validate their accuracy. The simulation includes coupled electromagnetic and electrical analysis via Vector Field Opera 15R1 and MATLAB/Simulink, respectively. To validate the accuracy of the simulation results, the machine was fabricated and tested. The machine meets the design requirement and both simulation and experimental results agree well. The paper is organised as follows: Section 2 presents the monopole machine concept, and structure; Section 3 describes finite element analysis of the monopole machine along with its equivalent circuit, and connection with MATLAB/Simulink; Section 4 outlines the results and discussion; Section 5 contains the conclusions. 2 Monopole machine The main objective is to design a monopole motor; however, the capability of battery charging is also considered as a second purpose to improve the efficiency of the machine. The monopole machine consists of two parts: an electronic circuit that works as a trigger and an electromagnetic circuit that converts electrical energy to mechanical energy and vice versa. Fig. 1 shows the schematic of the proposed system for the monopole machine capable of battery charging. The stator is a coil that entails three windings: a power coil winding, a trigger coil winding and a recovery coil winding. The rotor comprises of eight permanent magnets with the same polarity embedded in a rotating plastic disc. The rotor creates variable flux in the coil and Fig. 1 Schematic diagram of the proposed monopole machine capable of battery charging 288 IET Electr. Power Appl., 2013, Vol. 7, Iss. 4, pp & The Institution of Engineering and Technology 2013

3 has no more effect on the machine s performance. The application of the plastic rotor is to avoid electromagnetic interference of steel bearings and shaft on the rotor. It also significantly decreases rotor weight enabling smooth rotation; however, the power may be reduced that can be compensated with the application of multiple rotors and stators at the expense of sacrificing simplicity and power density. Fig. 2 illustrates the structure of the proposed monopole machine. The permanent-magnet s magnetising direction is north-pole outward (Fig. 2a). In the standstill state, one of the permanent magnets is aligned in the direction of the winding core. Once the power coil is energised, the produced electromagnetic field repels the permanent magnet and the rotor begins rotation. However, the rotor can start rotation manually or by any prime mover. When the rotor is moved so that the poles approach the stator pole piece, it is magnetised as the south pole (opposite polarity of permanent magnets) and generates magnetic flux in the windings. Core magnetisation also causes attraction between opposite poles and assures rotation. Rotation increases the magnetic flux and voltage which is proportional to the speed of rotation. When the voltage exceeds a certain threshold, the electrical energy can be stored in the capacitor and battery, and also turns on the transistor. The trigger voltage is determined by adjusting the potentiometer. In addition, depending on the voltage level across the capacitor, the voltage across the winding may be high enough to cause energy recovery current to flow through the winding, rectifier and capacitor. Thus, when the recovery current flows, the winding is converting magnetic energy from the rotating pole into electrical energy. When the transistor turns on, current drawn from the battery through the switch and transistor generates increasing magnetic flux that opposes the magnetic flux from the rotor s permanent magnets. When the opposing flux reaches a higher value than the generated flux through the rotation, the pole piece s magnetising direction is changed to the north pole, which repels the rotor s pole and assures rotation. If changing the pole piece s magnetising direction happens when the permanent magnet is exactly aligned with the pole piece, maximum efficiency is obtained. This can be set by adjusting the trigger voltage. By exceeding the opposing flux from the rotor flux, the transistor turns off, causing a voltage spike in the recovery windings, which shows energy generation. The voltage spikes can reach up to several times of source voltage [9]. The released energy is stored through a rectifier and capacitor, after that it can charge the battery. Fig. 2b indicates the structure of the proposed monopole machine. Any number of rotors and stators can be incorporated in the design. In the multiple rotors/stators combination, the number of rotors, magnets and stator are dependent on the amount of required power. Each stator may be energised at one time or all stators may be energised simultaneously. The desired machine size and power determine whether the stator will be in parallel or fired sequentially. Fig. 2 Structure of the proposed monopole machine a Magnetising direction of the permanent magnets b Various components of the monopole machine IET Electr. Power Appl., 2013, Vol. 7, Iss. 4, pp & The Institution of Engineering and Technology 2013

4 3 Finite element analysis To determine the machine s characteristics, FEA is applied. The basic FEA equations are as follows [10] B = mj (1) J = s db dt (2) B = c (3) Fig. 3 Monopole machine equivalent circuit where B is the magnetic flux density, J is the current density and ψ is the magnetic vector potential. σ and μ are the electrical conductivity and magnetic permeability, respectively. Considering H as the magnetic field intensity, (1) (3) can be summarised as 1 B ( H) + s t = 0 (4) The result is a formula where vector fields are represented by first-order edge elements and scalar fields by secondorder nodal unknowns. Field equations are coupled with the circuit equations for the conductors, because in the transient simulations, supply voltages are applied and currents are unknown. The circuit equation during motoring is given by u s = Ri m + L di m dt + e (5) e = l c dv S V e t (6) where u s is the applied source voltage, R is the winding resistance, L is the winding inductance, e the electromotive force (EMF), i m is the winding current, l is the axial length of iron core, S is the conductor area of each winding turn and Ω e is the total cross-sectional area of conductors winding. In generation state, the circuit equation is u g = e Ri g L di g dt where u g is the generated voltage. It can be seen that the circuit equation is similar to that for motoring, except the direction of current. The motion equation of the machine is given by (7) j m dv dt = T e T L lv (8) where j m is the moment of inertia, ω is the mechanical speed, T L is the load torque, T e is the electromagnetic torque and λ is the damping coefficient. The above mentioned operating equation is based on the equivalent circuit shown in Fig. 3. It provides performance analysis of the proposed machine in both motoring and generation statues. Therefore after discretisation, the three types of aforementioned equations (electromagnetic, electrical and mechanical) can be solved at each time step simultaneously. Consequently, both steady-state and transient performances of the proposed machines can be calculated. 3D-FEA is applied to model the proposed monopole machine because of the machine s structure and permanent-magnet skewing. An advantage of 3D-FEA is that various components of flux density can be calculated with high accuracy. The design is simulated on commercial Vector Field Opera 15R1 [11]. Corresponding materials and circuit currents are assigned to each segment of the model. For simulation, input parameters to be considered are permanent-magnet dimensions, air-gap length and electromagnetic properties of all the active materials. Table 1 lists the machine s design dimensions. Within each region, finite element mesh generation is conducted automatically, using the subdivisions of the sides to control mesh density. Fig. 4 shows the FEA model of the monopole machine: (a) 3D tetrahedral elements auto-mesh generation, and (b) flux density distribution of the monopole machine. Magnetic flux density evaluation in various sectors of the machine is important in order to avoid saturation and hence loss reduction. It is to be noted that the objective is to improve efficiency as much as possible; however, conventional machines may operate at somewhere beyond the knee-cap of the B H curve. Opera-3D can be used as a block in MATLAB/Simulink analysis. It provides a dynamic-link library that exports a set of functions which can be called to create and control Opera application objects; it also has the ability to start and communicate with the Opera-3D solvers. Fig. 5 shows the model s Simulink block diagram including the external library used to model the electronic part of the machine and battery charging. The details of the electronic circuit presented in Fig. 1 are: a 1N4148 diode, a GBPC3504 diode bridge rectifier, two 12 V batteries used as supply battery and recovery battery, potentiometer, 2N3055 transistor, a capacitor and a switch. The total cost of this prototype monopole machine is about $75 whereas permanent magnets have the highest portion in cost. Mass production can decrease the cost depending on the shape and size of permanent magnets up to 50%. It should be noted that Opera and the Simulink solver are independent from each other and only exchange the results. The Opera analysis block starts the simulation first with input values at time zero given by initialisation commands. To analyse the model at the end of each time step the following happens: Table 1 Proposed monopole machine dimensions Item Material Dimension rotor disc plastic Radius = 10 cm permanent magnet NdFeB cm coil copper wire 150 turns core mild still Radius = 0.5 cm 290 IET Electr. Power Appl., 2013, Vol. 7, Iss. 4, pp & The Institution of Engineering and Technology 2013

5 Fig. 4 FEA model of the monopole machine generated on Vector Field Opera 15R1 software a 3D auto-mesh generation b Flux density plot Fig. 5 Simulink block diagram of the model including external library 1. The output values are sent to the analysis block outputs. 2. Simulink runs at the same time as Opera does, whereas the time step in Simulink is chosen smaller. Simulink can then run enough steps to reach Opera time. 3. The user variables in the Opera model are updated from the analysis block inputs. 4. The analysis block runs Opera for the next time step. The time step can be either fixed or adaptive. In this analysis, the value of the fixed time step is chosen to be the same as the Simulink time step, but it is not necessary. Adaptive time stepping requires a variable time step to be set in Simulink s options. It is applied to limit the maximum time step in Opera to a reasonable value, as any change in the Simulink model is taken into account only in the next Opera time step. 4 Results and discussion After a computer-aided design (CAD) procedure based on FEM and MATLAB Simulink, the main concerns are extracting the designed machine parameters and evaluating the machine s performance with the focus on battery charging. Then the designed machine is fabricated and the IET Electr. Power Appl., 2013, Vol. 7, Iss. 4, pp & The Institution of Engineering and Technology 2013

6 results are compared with those from simulation. It is to be mentioned that as the motor, fan type load is considered in both simulation and experiment and as the generator, the recovery battery is considered as the load. Table 2 lists the designed monopole machine specifications. One of the characteristics that should be considered in machine design is cogging torque. Cogging torque of an electrical machine is the torque caused by the interaction between the rotor s permanent magnets and the stator slots. It results from the permanent-magnet s tendency to align itself at the position of minimum magnetic reluctance path between the rotor and stator. It is especially prominent at lower speeds, with the symptom of jerkiness. Cogging torque results in torque as well as speed ripple; however, at high speeds the motor moment of inertia filters the effect of cogging torque. To measure the cogging torque value, an open circuit test is conducted for the designed monopole machine. Fig. 6 displays the optimisation process of cogging torque for the proposed monopole machine. The cogging torque was reduced by skewing the permanent Table 2 Proposed monopole machine specifications rated power 15 W rated voltage 12 V rated speed 375 rpm rated torque 38.2 Ncm number of magnets 8 magnets. Fig. 6a portrays the permanent-magnet s skew diagram. Permanent-magnet skew angle θ s is the angle between the central axis of each permanent magnet before and after skewing. Cogging torque is measured based on the simulation for skew angle between 0 and 90. Simulation results show that at five-degree of permanent-magnet skewing, cogging torque is minimum (Fig. 6b). Pre-skewing peak value of cogging torque was 8.8 N cm. At five-degree skewing, peak cogging torque reduced to 5.2 Ncm (a 41% reduction). Fig. 7 compares the simulated cogging torque with five-degree skew and without skew. To validate the simulation results, the cogging torque of prototyped monopole machine with five-degree of permanent-magnet skewing was measured and the result is presented in Fig. 8. It shows good agreement with the simulation result. Back-EMF is a voltage that occurs in an electrical machine where there is relative motion between the armature of the motor and the external magnetic field. Back-EMF is measured when the machine is operated in open circuit as a generator. It is equal to the terminal voltage when the terminal current is zero. By skewing permanent magnets to reduce cogging torque, the value of back-emf decreases slightly. Fig. 9 shows the simulation results of back-emf without skew and because of five-degree permanent-magnet skew for the designed monopole machine that shows a 3% Fig. 7 skewing Cogging torque with and without permanent-magnet Fig. 6 Cogging torque optimisation a Permanent-magnet skewing diagram for cogging torque reduction b Maximum value of cogging torque against permanent-magnet skew angle Fig. 8 Experimental measurement of cogging torque for the prototyped monopole machine 292 IET Electr. Power Appl., 2013, Vol. 7, Iss. 4, pp & The Institution of Engineering and Technology 2013

7 Fig. 9 Back-EMF with and without skewing in the open circuit test reduction. Fig. 10 presents the measured back-emf of the prototyped monopole machine with five-degree of permanent-magnets skewing. Practical results confirmed the simulation results. The conservative field inside the monopole machine is divided into two phases. Producing a conservative field involves net symmetry between the power-out phase from the permanent magnets to the rotor and the power-back-in phase from the rotor back to the permanent magnets. Those two flows of energy are identical in magnitude but opposite in direction when each phase alone is asymmetrical. In the power-out phase, energy is delivered from the EMF existing between the stator pole piece and incoming rotor pole in the attraction mode. In this phase, the rotary motion (angular momentum and kinetic energy) of the rotor is increased. For the power-back-in phase, energy fed back into the permanent magnets from the rotor (and the load) to overcome the attraction force existing between the stator pole and the outgoing rotor pole. In this phase, energy is returned to the internal magnetic system from the rotary motion of the rotor (angular momentum). Therefore the generated EMF is asymmetrical because of unequal energy in the power-out and power-back-in phase while unusable available potential energy is saved. It should be noted that monopole motor efficiency is rather low because of poor application of permanent magnets. Hence, improving the efficiency makes this motor practically acceptable. That is why an electrical storage system is added to capture the collapsing field and utilise the permanent-magnets capability. Therefore the capability of battery charging is the key issue. The machine performance during battery charging was tested via both CAD and experimental results. The voltage and current waveforms of the recovery battery via simulation and experiment are shown in Figs. 11a and b, respectively. The experimental and simulation results are in agreement; however, they differ slightly because of fabrication deviation of windings and permanent-magnet shape. It is found that the generated voltage is almost three times the source voltage. The recovery battery is a 12 V, 2.16 A battery that was charged to full capacity in 6 h and 32 min. It is worth mentioning that, the initial purpose of the designed monopole machine is to run the motor that can be applied in low-power constant-speed applications whereas charging the battery is considered a plus benefit. The monopole machine captures energy in the form of back-emf, generated by a collapsing field in a coil comprised of multiple windings and a pole piece to avoid wasting energy in generation cycle. Therefore the monopole machine is neither battery charger nor DC DC converter and should not be compared with them in terms of cost, size and efficiency. Fig. 10 Experimental measurement of back-emf for the prototyped monopole machine Fig. 11 Voltage and current waveform of recovery battery in both simulation and experiment a Voltage b Current IET Electr. Power Appl., 2013, Vol. 7, Iss. 4, pp & The Institution of Engineering and Technology 2013

8 Fig. 12 shows the fabricated monopole machine based on data delivered from simulation. It includes a primary battery, recovery battery, rotor disc, stator with winding coil around the mild steel core, electronic circuit and measuring equipment. An important factor for assessing machine function is its efficiency defined as the ratio of output power to input power. Owing to machine losses, efficiency is always less than 100%. The proposed monopole machine losses include copper loss, mechanical loss, core loss and diode bridge rectifier loss. To accurately assess machine efficiency, it is vital to calculate the losses. Core loss and copper loss are calculated from the equations below P cor = P h + P e, and P cu = RI 2 (9) Copper loss (P cu ) is responsible for most of the total losses. Hysteresis loss (P h ) and eddy current loss (P e ) comprise the motor core losses (P cor ) and can be calculated based on the Steinmetz equation P h = k h B n max f r c, and P e = k e B 2 maxf 2 r c (10) where k h, k e, B max and ρ c are the hysteresis constant, eddy current constant, maximum flux density and core material density, respectively. Hysteresis coefficient (n) depends on the lamination material, thickness, conductivity and core material density. The maximum efficiency of a full-wave rectifier is 81.2% and mechanical loss is negligible as the motor is small and runs at low speed. Overall machine efficiency for the designed monopole machine is calculated as 1 T h = P v o T o (t) i o (t) dt + 1 T v 0 T m (t) i m (t) dt 0 = P i V i 1 T i T i (t) dt 0 (11) where P o (output power) is the summation of electrical energy of running machine and the recovery battery charging, and P i Fig. 12 Prototype monopole machine (1) Supply battery (2) Recovery battery (3) Rotor (4) Voltage of recovery battery (5) Winding coil around the mild steel core (6) Voltage and current waveforms of recovery battery (7) Electronic circuit (input power) is the power derived from the supply battery. v o (t) and v m (t) are the instantaneous voltage of recovery battery and machine, respectively; V i is the average voltage of supply battery; i i (t), i m (t) andi o (t) are the instantaneous input current, instantaneous motor current and instantaneous output current, respectively. The efficiency of the proposed monopole machine considering the capability of battery charging is 71% which is acceptable considering the size of the machine. As mentioned before, the monopole machine alone has rather low efficiency (in this prototype machine 50%); however the added storing system significantly improves efficiency and makes this motor practically acceptable. Moreover, in order to improve the application of the permanent magnets, more stators can be added to the system, at the expense of sacrificing the simplicity of the system. 5 Conclusion The design, analysis, fabrication, simulation and testing of a low-cost monopole machine was presented. The main objective was to design a monopole motor; however the capability of battery charging was added as a plus to the motor in order to retrieve the collapsing electromagnetic field and increase machine efficiency. The entire system was modelled based on the proposed machine equivalent system. 3D-FEA and MATLAB/Simulink was employed to predict and analyse both electromagnetic and electrical performance of the designed machine. The prototyped machine was tested and experimental results confirmed the validity of the simulated model. The designed machine achieved the required machine specifications. The efficiency of the entire system was 71% and the designed monopole machine charged a 12 V, 2.16 A battery in 6 h and 32 min. 6 Acknowledgment The authors thank the University of Malaya for the High Impact Research grant no. 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