energies Article
Research on Operation Principle and Control of Novel Hybrid Excitation Bearingless Permanent Magnet Generator Huangqiu Zhu and Yamin Hu * School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China;
[email protected] * Correspondence:
[email protected]; Tel.: +86-511-8878-0088 Academic Editor: David Wood Received: 24 May 2016; Accepted: 8 August 2016; Published: 24 August 2016
Abstract: Under the condition of load changing, the magnetic field of traditional permanent magnet generators (PMG) is hard to be adjusted, and the mechanical bearings are significantly worn. To overcome the drawbacks above, a novel hybrid excitation bearingless permanent magnet generator (HEBPMG) is proposed in this paper, which has integrated the merits of hybrid excitation permanent magnet generators and magnetic bearings. Firstly, the structure and winding configuration of the HEBPMG are introduced, and then the principles of radial suspension and power generation are presented. The suspension principle as well as power generation principle is analyzed in this paper. Then, the flux linkage and induced voltage equations are derived, and the accurate mathematical model of radial suspension force is built based on the Maxwell tensor method. Subsequently, by means of the finite element analysis software-ANSYS Maxwell, the corresponding electromagnetic characteristics are analyzed to verify the correctness of the mentioned models. In addition, a compensation control strategy based on flux-linkage observation is proposed to solve the problems of unstable suspension force and generating voltage under variable load condition in this paper. Meanwhile, the corresponding control system is constructed and its feasibility is validated by simulation results. Finally, an experimental prototype of a 2.2 kW HEBPMG is tested. Experimental researches show that the HEBPMG can operate steadily under variable load condition and possess good suspension performance and power generation quality. Keywords: permanent magnet generator; bearingless motor; hybrid excitation; mathematical model; compensation control
1. Introduction Traditional permanent magnet synchronous generators (PMSGs) have the advantages of simple structure, high efficiency, high power factor, reliable operation and so on. They are widely applied in the wind turbine, gas turbine generator, aviation electric power source, hybrid vehicles, and flywheel energy storage system, with the operation reliability of the PMSG paramount [1]. However, in conventional PMSGs, the mechanical bearing is used to support the shaft, which causes heavy mechanical wear with the increase of rotation speed and limits the load capacity [2]. The bearing represents a bottleneck in achieving high-speed and ultra-high speed operation of the transmission system. Until the 1980s, the emergence of the bearingless motor extended the bearing service life of the generator and reduced the maintenance costs, while weakening the influence of bearing failure. Current researches mainly focus on the electromotion-state of the bearingless permanent magnet synchronous motors (BPMSMs) [3]. Because of their excellent starting and generating performance, the generating state is another working pattern for the BPMSM, namely bearingless permanent magnet generator (BPMSG), which is still in a preliminary exploratory stage and will be a hotspot in the future. Energies 2016, 9, 673; doi:10.3390/en9090673
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Due to the poor field adjustment ability of PMSG, the regulation of magnetic fields has been a hot research topic. It is an effective way to solve the problem by increasing the auxiliary electric excitation to adjust the magnetic field. In [4], a hybrid excitation type synchronous machine is presented by Nobuyuki Naoe et al., which has both permanent magnet and wound fields on the same shaft. Xiaogang Luo and Lipo A [5] proposed a synchronous permanent magnet hybrid AC machine. Juan A. Tapia et al. [6] designed a consequent pole permanent magnet machine with field weakening capability. However, there exists a coupling effect between permanent magnetic field and electric excitation magnetic field caused by the magnetic circuit structure of these motor. In addition, in [7,8], a hybrid excitation claw-pole synchronous generator with series magnetic circuit and a hybrid excitation claw-pole alternator are investigated, respectively. Their rotors are composed of permanent magnetic parts producing electricity and electrical excitation parts regulating voltage, and they are installed coaxially. By adjusting the exciting current, the air gap magnetic flux can be changed to realize the purpose of voltage stabilizing. However, these structures will cause defects in the resultant assembly process and high maintenance costs, aggravating the burden of the rotor, and reducing power density. In this paper, a novel hybrid excitation bearingless permanent magnet generator (HEBPMG), in which the bearingless technology is utilized to realize the radial suspension and a set of excitation windings is added on the stator to compensate the synthesis of the magnetic field, is proposed. The structure of the HEBPMG and the operating principle are analyzed in Section 2. The voltage equations and the accurate mathematic model of suspension force are derived in Section 3. What is more, the correctness of the model is verified by finite element analysis (FEA). In terms of the instability suspension force and power voltage under variable loads, a compensation control strategy based on flux-linkage observation is proposed in Section 4. In Section 5, the corresponding digital control experiment platform is constructed. The simulation and experiment results verify the validity of the theoretical analysis and the effectiveness of the control system. 2. The Operation Principle and Structure of the HEBPMG 2.1. The Motor Structure and Windings Distributions of the HEBPMG The radial profile sketch of the HEBPMG is shown in Figure 1. The HEBPMG adopts 36 stator slots, and there are three sets of windings dividing into two layers in the stator slot. Bottom layer windings are the generation windings, which are the distributed windings with three slots per pole and per phase form adopted. In a counter-clockwise direction, the winding phase sequence arrangement is A1+, B1−, C1+, A1−, B1+, C1−, A2+, B2−, C2+, A2−, B2+, C2−. For this arrangement, when the generation winding current is induced, the 2-pole-pair air gap magnetic field can be generated, which is equal to the pole number of the permanent magnet air gap magnetic field. In the upper layer windings, symbol X1+, Y1−, Z1+, X1−, Y1+, Z1−, X2+, Y2−, Z2+, X2−, Y2+, Z2− and a+, b−, c+, a−, b+, c− represent the exciting windings and the suspension force windings, respectively. Specifically, exciting windings X+ are arranged in the upper layer of the first slot among the three slots where the generation windings A+ are arranged in the bottom layer, and suspension force windings a+ are arranged in the upper layer of the second and the third slots. Generation windings B− are arranged in the bottom layer of the next three slots, in which the exciting windings Y− are arranged in the upper layer of the first slot, and the suspension force windings a+ are placed in the upper layer of other two slots. The exciting windings a+ slot here together with the above two a+ slots form an intact exciting windings a+. Taking three stator slots as an example, one exciting winding and two suspension force windings are arranged alternatively. By means of this winding structure, 1-pole-pair suspension force winding air gap field and 2-pole-pair generation winding air gap field can be generated to satisfy the principle of suspension for the HEBPMG [9]. The pole pairs of exciting winding air gap field is the same as that of the generator winding air gap field to realize the compensation and weakening effect for the resultant magnetic field.
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Figure 1. 1. The The structure and windings distributions of the the hybrid hybrid excitation excitation bearingless bearingless permanent permanent Figure structure and windings distributions of magnet generator (HEBPMG). magnet generator (HEBPMG).
2.2. The Suspension Principle of the HEBPMG 2.2. The Suspension Principle of the HEBPMG In the HEBPMG, the given current signal of the suspension force windings is adjusted by real‐ In the HEBPMG, the given current signal of the suspension force windings is adjusted by real-time time detecting the rotor radial displacement signal based on position sensor to realize self‐aligning detecting the rotor radial displacement signal based on position sensor to realize self-aligning control. control. The suspension principle of is HEBPMG shown in Figure 2. Taking A‐phase generation The suspension principle of HEBPMG shown inis Figure 2. Taking A-phase generation windings and windings and a‐phase suspension force windings as an example, the 2‐pole‐pair generator windings a-phase suspension force windings as an example, the 2-pole-pair generator windings Nga and the Nga and the 1‐pole‐pair suspension force windings N 1-pole-pair suspension force windings Nsa are woundsa are wound around the stator slots. When the around the stator slots. When the suspension suspension force windings are not energized, the air gap resultant magnetic field ϕ , consisting of force windings are not energized, the air gap resultant magnetic field ϕm , consisting mof the induced the induced generation winding magnetic field and permanent magnet magnetic field, are spatially generation winding magnetic field and permanent magnet magnetic field, are spatially symmetric symmetric distributions. Then, according to Maxwell’s stress tensor, the radial suspension force F m is distributions. Then, according to Maxwell’s stress tensor, the radial suspension force Fm is zero. zero. The 1‐pole‐pair air gap flux ϕ α is generated when current is injected into the suspension force The 1-pole-pair air gap flux ϕα is generated when current is injected into the suspension force windings. windings. As a result, the flux density is increased in the left and decreased in the right. Then the As a result, the flux density is increased in the left and decreased in the right. Then the radial suspension radial suspension force, namely Maxwell resultant force, F m is obtained which points to the negative force, namely Maxwell resultant force, Fm is obtained which points to the negative direction in the direction in the x‐axis. A radial suspension force toward the positive direction of the x‐axis can be x-axis. A radial suspension force toward the positive direction of the x-axis can be acquired with aacquired with a reverse current. Similarly, the radial suspension force in the y‐axis can be obtained reverse current. Similarly, the radial suspension force in the y-axis can be obtained by providing by providing corresponding in the other is aimed realize the corresponding current in thecurrent other windings. In windings. summary, In it summary, is aimed toit realize theto rotor stable rotor stable suspension on radial displacement and the winding suspension force winding control. current suspension based on radialbased displacement and the suspension force current closed-loop closed‐loop control.
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Figure 2. The suspension principle of HEBPMG. Figure 2. The suspension principle of HEBPMG. Figure 2. The suspension principle of HEBPMG.
2.3. The Power Generation Principle of the HEBPMG 2.3. The Power Generation Principle of the HEBPMG 2.3. The Power Generation Principle of the HEBPMG Compared with the traditional PMSG, HEBPMG has the same principle of power generation. Compared with the traditional PMSG, HEBPMG has the same principle of power generation. Compared with the traditional PMSG, HEBPMG has the same principle of power generation. Under driving of the prime motor, three phase induced currents can be generated by cutting magnetic Under driving of the prime motor, three phase induced currents can be generated by cutting magnetic Under driving of the prime motor, three phase induced currents can be generated by cutting magnetic induction lines permanent magnet rotation 3 shows the external circuit induction ofof thethe permanent magnet rotation field. field. FigureFigure 3 shows external of HEBPMG. induction lines lines of the permanent magnet rotation field. Figure 3 the shows the circuit external circuit of of HEBPMG. The current flows into the load, generating voltage at both ends of the load. Where The currentThe flows into the load, generating at both endsat ofboth the ends load. of Where C represents HEBPMG. current flows into the load, voltage generating voltage the load. Where C C represents capacitive load, Z represents resistance‐inductance load, V represents breaker. capacitive load, Z represents resistance-inductance load, V represents breaker. represents capacitive load, Z represents resistance‐inductance load, V represents breaker. U Udd 22
U Udd 22
U Udd 22
U Udd 22
Figure 3. The external circuit of HEBPMG. Figure 3. The external circuit of HEBPMG. Figure 3. The external circuit of HEBPMG.
Exciting magnetic field ϕ e will be changed by injecting the current in the exciting windings Nex Exciting magnetic field ϕ Exciting magnetic field ϕee will be changed by injecting the current in the exciting windings N will be changed by injecting the current in the exciting windings Nexex to realize the magnetic‐field compensation. As shown in Figure 4a, when the load is increased, air to realize the magnetic‐field compensation. As shown in Figure 4a, when the load is increased, air to realize the magnetic-field compensation. As shown in Figure 4a, when the load is increased, air gap resultant magnetic field is weakening. To maintain stable operation, a strengthened excitation gap resultant magnetic field is weakening. To maintain stable operation, a strengthened excitation gap resultant magnetic field is weakening. To maintain stable operation, a strengthened excitation magnetic field must be provided. At this time, the direction of the exciting winding magnetic field is magnetic field must be provided. At this time, the direction of the exciting winding magnetic field is magnetic field must be provided. At this time, the direction of the exciting winding magnetic field is in in accordance with that of the air gap resultant magnetic field. On the when the load in accordance air gap resultant magnetic field. On the contrary, contrary, load is is accordance withwith that that of theof airthe gap resultant magnetic field. On the contrary, when the when load isthe decreased, decreased, an excitation magnetic field in the opposite direction will weaken the resultant magnetic field. decreased, an excitation magnetic field in the opposite direction will weaken the resultant magnetic field. an excitation magnetic field in the opposite direction will weaken the resultant magnetic field. Thus, Thus, the quality of the power generation will be improved by adding the excitation magnetic field. Thus, the quality of the power generation will be improved by adding the excitation magnetic field. the quality of the power generation will be improved by adding the excitation magnetic field.
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(a)
(b)
Figure 4. The excitation principle of HEBPMG. (a) The synthesis of magnetic field is compensated by Figure 4. The excitation principle of HEBPMG. (a) The synthesis of magnetic field is compensated by excitation magnetic field; (b) The synthesis of magnetic field impaired by excitation magnetic field. excitation magnetic field; (b) The synthesis of magnetic field impaired by excitation magnetic field.
3. Mathematical Model of HEBPMG 3. Mathematical Model of HEBPMG 3.1. Mathematical Model of Inducted Voltage 3.1. Mathematical Model of Inducted Voltage The equations of the flux linkage in the HEBPMG can be expressed as The equations of the flux linkage in the HEBPMG can be expressed as
L i M i M i M i
a b ac c afd fd pma ψa = − Laaaaiaa − Mab ab ib − Mac ic − Mafd ifd + ψpma ifd i +pmbψ bb iibb bfdbfd ψb=b −MMbabaiaia− LLbb −MMbcbcicic−MM fd pmb ψ = − M i − M i − L i − M i + ψ M i M i L i M i ca cb bb ca aa cb ccccc c cfdcfd fd fd pmc pmc c c ψfd =− M i − M i − M i − L + ψpmfd a c fda fdb b fdc = M i M i M i L ffd i ifd
fd
fda a
fdb b
fdc c
ffd fd
(1) (1)
pmfd
where Laaaa, L ,L Mab ba=, M Mbc , Mbc = Mcb , cc are self-induction of three phase generation windings.ab = M ba = M where L bbbb , L, ccL are self‐induction of three phase generation windings. M cb, Mca = Macca are mutual inductance of three phase generation windings. M = Mac are mutual inductance of three phase generation windings. Mfda fdb = = M Mafdbfd ,M fdb = Mbfd M fda = Mafd, M are mutual are mutual inductance between the generation windings and the excitation windings. Furthermore, inductance between the generation windings and the excitation windings. Furthermore, ψpma, ψpmb, , ψpmb , ψpmc are flux linkage generated by three generation windings and ψpmfd is the excitation pma ψψpmc are flux linkage generated by three generation windings and ψ pmfd is the excitation winding winding flux linkage. flux linkage. The equivalent equivalent circuit circuit of of the the HEBPMG HEBPMG is is shown shown in in (Figure (Figure 5), 5), and and voltage voltage equation equation can can be be The expressed as expressed as . . . us = dψs /dt + Rs I (2) u dψ d t R I (2) s s s . where us = [ua ub uc ufd ]T is voltage matrix in which ua , ub , uc are the generation windings voltage where b uc u fd]Tis is voltage matrix in which u a, ub, uc are the generation windings voltage at at bothu˙ s = [u endsa u and ufd the excitation windings voltage. I˙ = [ia ib ic ifd ]T is current matrix in both ends and u fd is the excitation windings voltage. İ = [i b ic iifd]T is current matrix in which i a, ib, ic which ia , ib , ic are the current of the generation windingsa iand fd is the excitation windings current. are the current of the generation windings and i fd is the excitation windings current. R s = [−r −r −r −r ] Rs = [−r −r −r −rfd ] is the resistance matrix in which r is the generation windings resistance and fd rfd T is the resistance matrix in which r is the generation windings resistance and r fd is the excitation is the excitation windings resistance. ψs = [ψa ψb ψc ψfd ] is flux linkage matrix in which ψa , ψb , ψc windings resistance. ψ ˙ s = [ψ a ψb ψc ψand fd]T is linkage windings, matrix in respectively. which ψa, ψb, ψc and ψfd are the and ψfd are the generation windings theflux excitation generation windings and the excitation windings, respectively.
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p a
ifd
p b p c ua ia
ub ib
r uc ic R
ufd
rfd p a
L (a)
(b)
Figure 5. The equivalent circuit of HEBPMG (a) The equivalent circuit of power generation; (b) The Figure 5. The equivalent circuit of HEBPMG (a) The equivalent circuit of power generation; (b) The equivalent circuit of excitation. equivalent circuit of excitation.
3.2. Mathematical Model of Radial Suspension Force 3.2. Mathematical Model of Radial Suspension Force According to the electromagnetic field theory of the HEBSG, the resultant air gap magnetic field According to the electromagnetic field theory of the HEBSG, the resultant air gap magnetic field is generated by the generation windings, the permanent magnet, the suspension force windings and is generated by the generation windings, the permanent magnet, the suspension force windings and the exciting windings. The pole‐pairs of the generation winding magnetic field, the permanent the exciting windings. The pole-pairs of the generation winding magnetic field, the permanent magnet magnet and the exciting windings are identical, which can be represented as pG, and the magnetic and the exciting windings are identical, which can be represented as pG , and the magnetic field of the field of the suspension force windings is pB‐pole‐pair. Above all, there are only two types of magnetic suspension force windings is pB -pole-pair. Above all, there are only two types of magnetic motive motive force (MMF) in the air gap for the HEBPMG. The fundamental component of MMF can be force (MMF) in the air gap for the HEBPMG. The fundamental component of MMF can be expressed as expressed as f G (ϕ, ft) φ,= f 1 f(ϕ, t) + f f (ϕ, t) + f 3 (ϕ, t) t G 1 φ, t ff φ, t f3 φ, t = F1m cos(ωt − pG ϕ − µ1 ) (3) F1m cos(ωt pG φ μ1 ) + Ffm cos(ωt − pG ϕ − µf ) (3) cos(ωt p φ μ ) F + Ffm 3m cos(ωt −G pG ϕ f− θ1 ) F3m cos(ωt pG φ θ1 ) f 2 (ϕ, t) = F2m cos(ωt − pB ϕ − λ1 ) (4) f 2 φ, t F2m cos(ωt pBφ λ1 ) (4) where, F1m , Ffm , F2m , F3m are the fundamental component amplitude of the air-gap MMF produced by the generation windings, the permanent magnet, the suspension force windings and the exciting where, F 1m, Ffm, F2m, F3m are the fundamental component amplitude of the air‐gap MMF produced by windings, respectively. Meanwhile µ1 , µf ,magnet, λ1 , θ1 arethe thesuspension initial phase angles of corresponding MMF the generation windings, the permanent force windings and the exciting fundamental wave, respectively. ϕ is the space angle. ω is the electric angular frequency of the windings, respectively. Meanwhile μ 1, μf, λ1, θ1 are the initial phase angles of corresponding MMF generation windings current and the suspension windings current. fundamental wave, respectively. ϕ is the space force angle. ω is the electric angular frequency of the According to the theory of Electrical Machinery, the value of F1m , Ffm , F2m , F3m is generation windings current and the suspension force windings current. √ √ According to the theory of Electrical Machinery, the value of F 1m, Ffm, F2m, F3m is F = 3 4 2 N1 I1 kd1 F = 3 4 2 N2 I2 kd2 2m 1m 2 π √2 pG 2 π √2 pB (5) kd1 3 43 4 2 2NN 23 IN 3 34 4 2 N 3 k2d3I 2 kd2 Gd1 1 I11Ik F = F = 3m fm F F 2 π 2 p 2 π 2 p 1m 2m G G 2 2 2 2 pG pB (5) where, kd1 , kd2 and kd3 correspond wave 3 to 4 the 2 Nfundamental 3 4 windings 2 N 3 I 3 kd3 factors of the generation 1 I G kd1 F3m windings, the suspension force windings N1 , N2 and N3 are Ffm 2 2and the pG excitation windings, 2 2 prespectively, G the turn numbers in series of each phase of the generation windings, the suspension force windings where, d1, kd2 and kd3 correspond to the windings factors of the generation and the kexcitation windings respectively. I1 fundamental is the inducedwave current in the generation windings, I2 and windings, the suspension force windings and the excitation windings, respectively, N 1 , N 2 and N 3 are I3 are the current injected respectively into the suspension windings and the excitation windings. the turn numbers in series of each phase of the generation windings, the suspension force windings and the excitation windings respectively. I1 is the induced current in the generation windings, I2 and I3 are the current injected respectively into the suspension windings and the excitation windings. IG
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represents the synthesis of current including the generation windings induced current, the excitation windings induced current and the equivalent current of permanent magnet. IG represents the synthesis of current including the generation windings induced current, the excitation Because the relative permeability of the stator core and the rotor core is much larger than that of windings induced current and the equivalent current of permanent magnet. air, the magnetic resistance of stator core and rotor core can be neglected. The air gap flux density Because the relative permeability of the stator core and the rotor core is much larger than that of can be obtained as air, the magnetic resistance of stator core and rotor core can be neglected. The air gap flux density can B φ, t B φ, t B φ, t be obtained as (6) μFt) + B (ϕ, t) μF B (ϕ, t) = B (ϕ, cos(ωt pφ μ) µFcos(ωt pφ λ) (6) µF = δ cos δ (ωt − pϕ − µ) + δ δ cos(ωt − pϕ − λ) δ = δ0 as the rotor is non‐eccentricity. Considering the rotor eccentricity, the distribution of the δ = δ 0 as the rotor is non-eccentricity. Considering the rotor eccentricity, the distribution of the air gap length is unbalance as shown in Figure 6. The air gap length in any direction0 − is air gap length is unbalance as shown in Figure 6. The air gap length in any direction is δ(ϕ) = δ δ(ϕ) = δ0 − se). ·cos(ϕ − ϕs ). ecos(ϕ − ϕ
Figure 6. The definition of rotor eccentricity. Figure 6. The definition of rotor eccentricity.
According to the Maxwell tensor method, the radial suspension force per unit area along an According to the Maxwell tensor method, the radial suspension force per unit area along an electric angle ϕ on the rotor surface can be expressed as electric angle ϕ on the rotor surface can be expressed as
B 2 (φ, t ) B 2 (φ, t ) dF (φ) B2 (ϕ, t) ds B2 (ϕ, t) (lrdφ) 2μ 0 ds = 2μ 0 (lrdϕ) dF (ϕ) =
(7) (7)
2µ0 2µ0 where, l is the effective iron core length of HEBPMG, r is the rotor radius. For the HEBPMG (pG = 2, where, l is the effective iron core length of HEBPMG, r is the rotor radius. For the HEBPMG pB = 1), it is computed by the integral for Formula (7) with ϕ from 0 to 2π, and can be simplified as (pG = 2, pB = 1), it is computed by the integral for Formula (7) with ϕ from 0 to 2π, and can be F km IG I2 cos(μ λ1 ) simplified as x 2 F x = k m IG I2 cos λy21 ) y √(xµ − kn 2IG2 [ x x2 +y2 cos(2ωt 2λ1 arctan y)] + kn I [ x + 2 · cos(2ωt − 2λ1 − arctanx x )] (8) F k GI I sin(μ2 λ ) F = k I I sin ( µ − λ1 1 ) y m G 2 y m 2 G √ x22+y2 2 +kn IG2 2[y + x2 y· cos(2ωt − 2λ1 + arctanyyx )]
Among them, km =
kn IG [ y
9 µ0 lrN1 N2 kd1 kd2 , kn 2 πδ20
2
cos(2ωt 2λ1 arctan )] x
2 2 9 µ0 lrN1 kd1 2 4 πδ0 2 2
= 9 μ 0lrN1 kd1 9 μ 0lrN1 N2 kd1kd2 Among them, km , kn 2 4 δ02 2 δ0 3.3. FEA Analysis of HEBSG According to the structural model and working principle of the HEBPMG, the finite elements 3.3. FEA Analysis of HEBSG model is built utilizing ANSYS software for dynamic electromagnetic performance simulation. The According to the structural model and working principle of the HEBPMG, the finite elements structural parameters of the prototype are optimized through the analysis of parameterized, as shown model is built utilizing ANSYS software for dynamic electromagnetic performance simulation. The in Table 1. The flux density cloud map and the distribution of magnetic field lines of HEBPMG are structural parameters of the prototype are optimized through the analysis of parameterized, as shown in Figure 7. shown in Table 1. The flux density cloud map and the distribution of magnetic field lines of HEBPMG are shown in Figure 7.
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(a)
(b)
Figure 7. The finite element model of HEBPMG (a) Flux density cloud map; (b) The distribution of Figure 7. The finite element model of HEBPMG (a) Flux density cloud map; (b) The distribution of magnetic field lines. magnetic field lines. Table 1. Structural parameters of the prototype. Table 1. Structural parameters of the prototype.
Symbol Quantity Value Symbol Quantity Value Q Stator slot counts 36 Stator slot counts 36 DS1 Q Outer diameter of stator 180 mm Outer diameter of stator 180110 mm mm DS2D S1 Inner diameter of stator DS2 Inner diameter of stator 110 mm Dr1D Outer diameter of rotor Outer diameter of rotor 98 98 mm mm r1 Dr2D r2 Inner diameter of rotor Inner diameter of rotor 30 30 mm mm Radial length of air-gap 1 mm Lg Lg Radial length of air‐gap 1 mm l Axial length of rotor 50 mm l Axial length of rotor 50 mm P Rated power 2.2 kW P Rated power 2.2 kW Stator slot full rate 0.75 I Stator slot full rate Suspension force winding current 5A0.75 I Φ Suspension force winding current 5A Windings wire diameter 0.71 mm Material of stator and rotor D32_50 Ф Windings wire diameter 0.71 mm Material of permanent magnet rotor NFeB35 Material of stator and rotor D32_50 Magnetization of permanent magnet rotor parallel magnetization h Material of permanent magnet rotor NFeB35 Auxiliary bearing thickness 0.7 mm a PM Magnetization of permanent magnet rotor parallel magnetization Pole-pair of generation windings 2 Pole-pair of suspension windings 1 ha PB Auxiliary bearing thickness 0.7 mm Pole-pair of excitation windings 2 2 PM PE Pole‐pair of generation windings Turns in series of each phase of generation windings 40 N PB N1 Pole‐pair of suspension windings 1 Turns in series of each phase of suspension windings 60 2 PE N3 Pole‐pair of excitation windings 2 Turns in series of each phase of excitation windings 40 N 1 J Turns in series of each phase of generation windings 40 The rotational inertia 0.00059 kg ·m2 N 2 Turns in series of each phase of suspension windings 60 N 3 Turns in series of each phase of excitation windings The PWM rectifier circuit shown as Figure 3 is connected to the generation40 windings of the 2 J The PWM rectifier system The rotational inertia 0.00059 kg∙m HEBPMG. can not only realize the adjustment of DC side voltage, but also enhance the power factor of the generator on the AC side, and reduce the harmonic of the The PWM rectifier circuit shown as Figure 3 is connected to the generation windings of the generator current. Moreover, the flux linkage of the generation windings varies with the change of HEBPMG. The PWM rectifier system can not only realize the adjustment of DC side voltage, but also rotor position angle, which can generate back electromotive force (back-EMF). Then the induction enhance the power factor of the generator on the AC side, and reduce the harmonic of the generator current is generated and the voltage is formed on the load when the winding forms a return circuit, as current. Moreover, the flux linkage of the generation windings varies with the change of rotor shown in Figure 8. position angle, which can generate back electromotive force (back‐EMF). Then the induction current is generated and the voltage is formed on the load when the winding forms a return circuit, as shown in Figure 8.
120 100
10
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40
0
Capacitive load branch current Resistance load branch current
20 -5 0
20
40
Trunk current Load voltage 60
20 160 0 100140
80
15
120 Figure 8. The load current and voltage of Pulse Width Modulation (PWM) rectifier circuit. 100
10 The mathematical model derived in the second section can be validated by using the parameters 80 in Table 1. The correctness of the model can be verified without rotor eccentricity in Figure 9. The radial suspension force on the permanent magnet rotor increases linearly with the increase of the 5 60 suspension force windings current. However, on the other side, the increased speed of the suspension 40 force value becomes slow and nonlinear due to saturation magnetic fields. 0 According to the results of the simulation, the angle between the vectors of the suspension force 20 and the x‐axis is 128° without rotor eccentricity. The rotor position angle is set to −52° which is the 0 -5 of the suspension force. Therefore, the unilateral magnetic opposite direction force and the 0 60 80 the suspension 100 controllable suspension force 20are in the 40opposite direction. When force current amplitude is small, the unilateral magnetic force plays the leading role in the radial suspension force. Figure 8. The load current and voltage of Pulse Width Modulation (PWM) rectifier circuit. Figure 8. The load current and voltage Pulse Width Modulation (PWM) rectifier circuit. However, the controllable suspension force ofgradually increases with the increase of current, and there will be a point when the controllable suspension force is equal to the unilateral magnetic force. The mathematical model derived in the second section can be validated by using the parameters Then, after the balance point, the controllable suspension force continues to increase until it occupies The mathematical model derived in the second section can be validated by using the parameters in Table 1. The correctness of the model can be verified without rotor eccentricity in Figure 9. The the main part, the composition radial suspension force tends to be linear growth. Also, when current in Table 1. The correctness of the model can be verified without rotor eccentricity in Figure 9. The radial suspension force on the permanent magnet rotor increases linearly with the increase of the reaches a certain degree, there will be the trend of magnetic saturation. In general, conclusions can radial suspension force on the permanent magnet rotor increases linearly with the increase of the suspension force windings current. However, on the other side, the increased speed of the suspension be drawn from the dynamic analysis of the simulation waveform and the established mathematical suspension force windings current. However, on the other side, the increased speed of the suspension force value becomes slow and nonlinear due to saturation magnetic fields. model is accurate. force value becomes slow and nonlinear due to saturation magnetic fields. According to the results of the simulation, the angle between the vectors of the suspension force and the x‐axis is 128° without rotor eccentricity. The rotor position angle is set to −52° which is the 350 FEA without rotor eccentricity opposite direction of the suspension force. Therefore, the unilateral magnetic force and the controllable suspension force are in the opposite direction. 300 Model calculation without rotor eccentricity When the suspension force current amplitude is small, the unilateral magnetic force plays the leading role in the radial suspension force. FEA with rotor eccentricity 250 However, the controllable suspension force gradually increases with the increase of current, and Model calculation with rotor eccentricity there will be a point when the controllable suspension force is equal to the unilateral magnetic force. 200 Then, after the balance point, the controllable suspension force continues to increase until it occupies the main part, the composition radial suspension force tends to be linear growth. Also, when current 150 reaches a certain degree, there will be the trend of magnetic saturation. In general, conclusions can be drawn from the dynamic analysis of the simulation waveform and the established mathematical 100 model is accurate.
50 350 0 300 0
FEA without rotor eccentricity
1 2 3 without 4 rotor5eccentricity 6 Model calculation
7
8
9
10
FEA with rotor eccentricity
250 Figure 9. The relationship between radial levitation force and levitation force winding current amplitude. Figure 9. The relationship between with radial Model calculation rotorlevitation eccentricity force and levitation force winding current amplitude. 200
According to150 the results of the simulation, the angle between the vectors of the suspension force and the x-axis is 128◦ without rotor eccentricity. The rotor position angle is set to −52◦ which is the opposite direction100 of the suspension force. Therefore, the unilateral magnetic force and the controllable suspension force are in the opposite direction. When the suspension force current amplitude is small, 50 the unilateral magnetic force plays the leading role in the radial suspension force. However, the controllable suspension force gradually increases with the increase of current, and there will be a 0 point when the controllable suspension force is4 equal5 to the 0 1 2 3 6 unilateral 7 8magnetic 9 force. 10 Then, after the
Figure 9. The relationship between radial levitation force and levitation force winding current amplitude.
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balance point, the controllable suspension force continues to increase until it occupies the main part, the composition radial suspension force tends to be linear growth. Also, when current reaches a certain degree, there will be the trend of magnetic saturation. In general, conclusions can be drawn from the dynamic analysis of the simulation waveform and the established mathematical model is accurate. 4. Control System of the HEBPMG Based on Flux Observation In fact, the generator normally operates under the variable load condition, which causes instability of the suspension force and generating voltage. The air gap magnetic field used to generate power is determined by the permanent magnet, the generation windings and the excitation windings. Therefore, the generating performance can be improved by adjusting the amplitude of the excitation current for compensating the variable air-gap magnetic field. What is more, the stability of suspension force can be obtained by observing and adjusting the magnetic field generated by the suspension force windings. In consequence, flux-linkage observation is the key to controlling the suspension force and the generated voltage [10,11]. The flux-linkage of the generation windings, the excitation windings and the synthesis air gap flux-linkage can be observed with the following equations. R ψs1α = (u1α − R1 i1α )dt R ψs1β = (u1β − R1 i1β )dt q ψ = ψs1β 2 + ψs1α 2 s1 µ = arctan(ψ /ψ ) 1
s1β
s1α
R ψs3α = (u3α − R3 i3α )dt R ψs3β = (u3β − R3 i3β )dt q ψ = ψs3β 2 + ψs3α 2 s3 θ = arctan(ψ /ψ ) 1
s3β
ς = arctan(ψs1β + ψs3β /ψs1α +ψs3α ) ψm1α = ψs1α + ψs3α − L1l i1α − L3l i3α ψm1β = ψs1β + ψs3β − L1l i1β − L3l i3β q ψm1 = ψs1β 2 + ψs1α 2 µ = arctan(ψ m1α /ψm1β )
(9)
s3α
(10)
(11)
where ψs1 , µ1 are the flux-linkage amplitude and phase of generation windings. ψs3 and θ1 are the flux-linkage amplitude and phase of excitation windings. ζ is the resultant flux-linkage phase of the generation windings and the excitation windings. ψm1 , µ are the amplitude and phase of the resultant flux-linkage, L1l and L3l are the leakage inductance of the generation windings and the excitation windings. The flux-linkage observation to the suspension force windings is as follows: ψs2 , λ1 are the flux-linkage amplitude and phase of the suspension force windings. R ψs2α = (u2α − Rs i2α )dt R ψs2β = (u2β − Rs i2β )dt q | ψ | = ψs2α 2 + ψs2β 2 s2 λ = arctan(ψ /ψ ) s2β s2α
(12)
When HEBPMG is operating stably, the rotor eccentricity is small enough to be neglected. The simplified equations of suspension force are as follows (
Fα = km IG I2 cos(µ − λ1 ) Fβ = km IG I2 sin(µ − λ1 )
(13)
While substituting ψm1 = IG LM , ψs2 = I2 LB into the equations, the expression of suspension force on the current can be converted into an expression on the flux-linkage. The self-inductance of the excitation windings and the suspension force windings can be expressed as
α w m1 s2 1 F k ψ ψ sin(μ λ β w m1 s2 1) where k w
(15)
72kd1kd2 . π μ 0 lrN1 N 2 3
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Based on the strategy of the flux‐linkage observation, the performance of suspension force and the generating voltage can be compensated under the variable load condition. Its control system block 2 2 diagram is shown in Figure 10. Firstly, the induced current i 1a and i1b in the generation windings and 2 1 LB = µ0 πlrN LM = µ0 πlrN , and then 4δ 4δ the excitation current i3a and i3b in excitation windings are acquired by the flux‐linkage observer to ( 4δ 4δ calculate the resultant flux‐linkage ψ Fα = kms13 ψ and its phase ξ. After comparing the resultant flux‐linkage m1 ψs2 µ πlrN 2 µ πlrN 2 cos(µ − λ1 ) 2 1 0 0 (14) with the given reference flux‐linkage and by the space vector pulse width 4δ modulated 4δ Fβ = km ψm1 ψs2 being 2 2 sin(µ − λ1 ) µ πlrN µ πlrN 2 1 0 0 modulation (SVM) module, the switching signals for the voltage source inverter of the excitation windings is obtained. Therefore, the magnetic field can be controlled in closed loop. Substituting the value of km , the estimation value of suspension force based on flux-linkage Part of the force is controlled by radial displacement and suspension force double closed loop observation can be derived ( control system. Firstly, the current iF2aα and 2b of suspension force windings are collected. The = kwiψ m1 ψs2 cos(µ − λ1 ) (15) suspension force windings flux linkage ψ Fβ s2= and its phase λ kw ψm1 ψs2 sin(1µ is observed by suspension force windings − λ1 ) flux‐linkage observer. At the same time, the amplitude ψm1 and its phase μ of resultant flux‐linkage d1 k d2 where kw = π372k . are observed online by the generation and excitation windings flux‐linkage observer. The suspension µ0 lrN1 N2 Based onβthe strategy of the flux-linkage observation, the performance of suspension force and force F α and F can be calculated with these two sets of signals by the suspension force estimating the generating voltage can be compensated under the variable load condition. Its control system block module. Then, the errors between rotor position command values x*, y* and the detection values x, y diagram is shown in Figure 10. Firstly, the induced current i1a and i1b in the generation windings and which are observed from the displacement sensor are derived. Thus, the suspension force command the excitation current i3a and i3b in excitation windings are acquired by the flux-linkage s2α observer to values F α* and F β* can be produced by the PID controller. The flux‐linkage increment ∆ψ , ∆ψs2β of calculate the resultant flux-linkage and its from phasethe ξ. After thecalculated resultant flux-linkage the suspension force windings can ψ be errors comparing between the values and s13derived with the given reference flux-linkage and being modulated by the space vector pulse width modulation command values of the suspension force. Finally, the switching signals to voltage source inverter of (SVM) module, switching for thefrom voltage sourcemodule. inverterIn ofconclusion, the excitation is suspension force the windings can signals be obtained the SVM the windings suspension obtained. Therefore, the magnetic field can be controlled in closed loop. force can be controlled.
x
Fα
x y y
Fα Fβ
U DC
ψs2α
Fβ
1
Δψs2β
i2a i2b
ψs2
ψ m1
ψs13
i1a
U DC
U DC
i1b
i3a
I dc
i3b
ψ*s Figure 10. The compensation control block diagram of the flux‐linkage observation. Figure 10. The compensation control block diagram of the flux-linkage observation.
Part of the force is controlled by radial displacement and suspension force double closed loop control system. Firstly, the current i2a and i2b of suspension force windings are collected. The suspension force windings flux linkage ψs2 and its phase λ1 is observed by suspension force windings flux-linkage observer. At the same time, the amplitude ψm1 and its phase µ of resultant flux-linkage are observed online by the generation and excitation windings flux-linkage observer. The suspension force Fα and Fβ can be calculated with these two sets of signals by the suspension force estimating module. Then, the errors between rotor position command values x*, y* and the detection values x, y which are observed from the displacement sensor are derived. Thus, the suspension force command values Fα * and Fβ * can be produced by the PID controller. The flux-linkage increment ∆ψs2α , ∆ψs2β of the suspension force windings can be derived from the errors between the calculated values and command values of the suspension force. Finally, the switching signals to voltage source inverter of
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suspension force windings can be obtained from the SVM module. In conclusion, the suspension force can be controlled. 5. Simulation and Experiment Energies 2016, 9, 673
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5.1. Simulation and Analysis
5. Simulation and Experiment According to the flux-linkage observation and compensation system of flux linkage in Figure 10, the simulation module of HEBPMG controller system is built and experimented in the 5.1. Simulation and Analysis MATLAB/Simulink environment. Parameters of experiment are shown in Table 1, where the time of According to the flux‐linkage observation and compensation system of flux linkage in Figure 10, simulation is set to 0.2 s and the eccentricity of rotor is (−0.6 mm, 0.8 mm). the simulation module of HEBPMG controller system is built and experimented in the Simulation of stepping up from zero voltage experiment, which means progress of voltage rising MATLAB/Simulink environment. Parameters of experiment are shown in Table 1, where the time of from zero voltage to steady state, is shown in Figure 11. As depicted in Figure 11a,b, the original simulation is set to 0.2 s and the eccentricity of rotor is (−0.6 mm, 0.8 mm). Simulation of stepping up from zero voltage experiment, which means progress of voltage rising position of rotor is (−0.6 mm, 0.8 mm). When controller of radial suspension force is activated, rotor is from zero voltage to steady state, is shown in Figure 11. As depicted in Figure 11a,b, the original set to balance location quickly after 8 ms. Maximal displacement in x-axis is 0.12 mm while in y-axis is position of rotor is (−0.6 mm, 0.8 mm). When controller of radial suspension force is activated, rotor 0.2 mm, which is accepted in eccentricity with accuracy control scheme and compensation circuits. is set to balance location quickly after 8 ms. Maximal displacement in x‐axis is 0.12 mm while in y‐ When stepping up from zero voltage of the synchronous generator, the automatic voltage regulator axis is 0.2 mm, which is accepted in eccentricity with accuracy control scheme and compensation should circuits. When stepping up from zero voltage of the synchronous generator, the automatic voltage guarantee that the terminal voltage overshoot should not exceed 15% of the rated voltage, the time of regulator should guarantee that the terminal voltage overshoot should not exceed 15% of the rated adjustment should not more than 10 s, the frequency of voltage fluctuation should not be more voltage, the time of adjustment should not more than 10 s, the frequency of voltage fluctuation should than three times. The overshoot of voltage is 8.18% and the steady adjustment rate of voltage is 0.45% not be more than three times. The overshoot of voltage is 8.18% and the steady adjustment rate of in Figure 11c, which satisfy the basic requirements of the control system [12]. After applying load, the voltage is 0.45% in Figure 11c, which satisfy the basic requirements of the control system [12]. After output voltage returns to a steady state after 15 ms due to the modulation of excitation current. As can applying load, the output voltage returns to a steady state after 15 ms due to the modulation of be seen excitation current. As can be seen in Figure 11d, the capacitance, inductance and other energy‐storage in Figure 11d, the capacitance, inductance and other energy-storage elements of the load are in the charging state the beginning ofcharging load work, three-phase induction currents turn into steady elements of at the load are in the state then at the beginning of load work, then three‐phase induction currents turn into steady state after 10 ms. The winding current is obtained by rectifying state after 10 ms. The winding current is obtained by rectifying action of the external circuit shown in action of the external circuit shown in Figure 3. At 0 ms, closing the breaker V1 and opening V2, the Figure 3. At 0 ms, closing the breaker V1 and opening V2, the generator operates under normal load generator operates under normal load conditions and the external circuit has a certain filtering effect conditions and the external circuit has a certain filtering effect at that time. It can be seen in Figure 11e at that time. It can be seen in Figure 11e that five harmonics and seven harmonics are generated by that fivethe methods of harmonic analysis under the condition of rated load, so it is good sinusoidal and THD harmonics and seven harmonics are generated by the methods of harmonic analysis under 1 the condition of rated load, so it is good sinusoidal and THD1 = 4.59%. = 4.59%.
(a)
(b)
(c)
(d)
Figure 11. Cont.
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(e) Figure 11. The performance of generator and harmonic analysis under normal operation. (a) Rotor
Figure 11. The performance of generator and harmonic analysis under normal operation. (a) Rotor floating waveform in x axis; (b) Rotor floating waveform in y axis; (c) The output voltage effective value; floating(d) The generation winding induced current; (e) Winding current harmonic under the rated load. waveform in x axis; (b) Rotor floating waveform in y axis; (c) The output voltage effective value; (d) The generation winding induced current;(e) (e) Winding current harmonic under the rated load. For ensuring good static and dynamic performance of the HEBPMG system, the operation Figure 11. The performance of generator and harmonic analysis under normal operation. (a) Rotor parameters of the motor must follow the command values quickly and accurately in the processes of floating waveform in x axis; (b) Rotor floating waveform in y axis; (c) The output voltage effective value; For ensuring good static and dynamic performance of the HEBPMG system, the operation load connection and disconnection. The external circuit is shown in Figure 3. At 0 ms, closing the (d) The generation winding induced current; (e) Winding current harmonic under the rated load. parameters of the motor must follow the command values quickly and accurately in the processes breaker V1 and opening V2, the generator operates under normal load conditions. At 70 ms, opening of load V1 connection and disconnection. The external circuit shown in Figure 3. the Atand 0 ms, and ensuring remaining V2 as it was, generator operates under load shedding conditions the closing For good static and the dynamic performance of isthe HEBPMG system, operation filtering function of the external circuit is weakened. It can be seen in Figure 12c that many five times the breaker V1 and opening V2, the generator operates under normal load conditions. At 70 ms, parameters of the motor must follow the command values quickly and accurately in the processes of harmonic and seven harmonics are generated by the methods of harmonic analysis under load opening V1 and remaining V2 as it was, the generator operates under load shedding conditions load connection and disconnection. The external circuit is shown in Figure 3. At 0 ms, closing the and shedding conditions, so there is poor sinusoidal and THD2 = 11%. At 140 ms, opening V2, the the filtering function of the external circuit is weakened. It can be seen in Figure 12c that many five breaker V1 and opening V2, the generator operates under normal load conditions. At 70 ms, opening generator operates under overload conditions. The resistance‐inductance load is added in the initial and remaining V2 as it was, the generator operates load of shedding conditions the load timesV1 harmonic and seven harmonics are generated by theunder methods harmonic analysisand under external circuit in order to enhance the filtering function. The winding current shows hardly any filtering function of the external circuit is weakened. It can be seen in Figure 12c that many five times shedding conditions, so there pooroverload sinusoidal and THD = 11%. Atperformance 140 ms, opening V2, the generator harmonics in Figure 12d isunder conditions, so 2sinusoidal is improved and harmonic and seven harmonics are The generated by the methods of harmonic analysis operates under overload conditions. resistance-inductance load is added in theunder initialload external THD 3 = 1.38%. Figure 12 shows the results of anti‐interference experiment of the HEBPMG control shedding conditions, so there is poor sinusoidal and THDeffective value is shown in Figure 12a, 2 = 11%. At 140 ms, opening V2, the system based on flux‐linkage observation. The output voltage circuit in order to enhance the filtering function. The winding current shows hardly any harmonics generator operates under overload conditions. The resistance‐inductance load is added in the initial and the generation winding induced current is shown in Figure 12b. When the system instantly cuts in Figure 12d under overload conditions, so sinusoidal performance is improved and THD3 = 1.38%. external circuit in order to enhance the filtering function. The winding current shows hardly any off load, the synthesized magnetic field of the generator is weakened but voltage increases quickly, Figure 12 shows results of anti-interference experiment of the performance HEBPMG control system based harmonics in the Figure 12d under overload conditions, so sinusoidal is improved and three‐phase induction currents decrease immediately and then tend to quickly become steady. The on flux-linkage observation. The output voltage effective value is shown in Figure 12a, and the THD 3 = 1.38%. Figure 12 shows the results of anti‐interference experiment of the HEBPMG control maximal overshoot of load disturbance is 30 V. It can be seen that the overshoot of the load generation winding induced current is shown in Figure 12b. When the system instantly cuts off load, system based on flux‐linkage observation. The output voltage effective value is shown in Figure 12a, disturbance is about 13.6% of the rating value and the time of adjustment is 0.02 s. These results meet the synthesized magnetic field of the generator is weakened but voltage increases quickly, three-phase the related theory [12]. When the load is applied instantly, the variation of the parameters is quite the and the generation winding induced current is shown in Figure 12b. When the system instantly cuts contrary. Figure 12e indicates the whole variation progress of suspension force in x‐ and y‐axis along off load, the synthesized magnetic field of the generator is weakened but voltage increases quickly, induction currents decrease immediately and then tend to quickly become steady. The maximal with the variable load. The compensation strategy of flux‐linkage observation allows the HEBPMG three‐phase induction currents decrease immediately and then tend to quickly become steady. The overshoot of load disturbance is 30 V. It can be seen that the overshoot of the load disturbance is about to quickly respond to commands, and the dynamic performance is improved. maximal overshoot of load disturbance is 30 V. It can be seen that the overshoot of the load
13.6% of the rating value and the time of adjustment is 0.02 s. These results meet the related theory [12]. disturbance is about 13.6% of the rating value and the time of adjustment is 0.02 s. These results meet When the load is applied instantly, the variation of the parameters is quite the contrary. Figure 12e the related theory [12]. When the load is applied instantly, the variation of the parameters is quite the indicates the whole variation progress of suspension force in x- and y-axis along with the variable contrary. Figure 12e indicates the whole variation progress of suspension force in x‐ and y‐axis along load. with the variable load. The compensation strategy of flux‐linkage observation allows the HEBPMG The compensation strategy of flux-linkage observation allows the HEBPMG to quickly respond to commands, and the dynamic performance is improved. to quickly respond to commands, and the dynamic performance is improved.
(a)
(a) Figure 12. Cont.
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(b)
(c)
(d)
(e)
Figure 12. The performance of the generator and harmonic analysis during load disturbance. (a) The
Figure 12. The performance of the generator and harmonic analysis during load disturbance. (a) The output voltage effective value; (b) The generation winding induced current; (c) Winding current output voltage effective value; (b) The generation winding induced current; (c) Winding current harmonic under load shedding condition; (d) Winding current harmonic under overload condition; harmonic under load shedding condition; (d) Winding current harmonic under overload condition; (e) The suspension force in the process of operation. (e) The suspension force in the process of operation.
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5.2. Experiment Result and Analysis 5.2. Experiment Result and Analysis Based on flux-linkage observation, a 2.2 kW HEBPMG prototype is tested in Figure 13, and the Based on flux‐linkage observation, a 2.2 kW HEBPMG prototype is tested in Figure 13, and the experimental results will be compared with simulation results. Parameters of the HEBPMG are listed experimental results will be compared with simulation results. Parameters of the HEBPMG are listed in Table 1. According to the control system block diagram in Figure 10, TMS320F2812 DSP is used as in Table 1. According to the control system block diagram in Figure 10, TMS320F2812 DSP is used as the digital controller of the experimental platform to realize the compensation control of magnetic the digital controller of the experimental platform to realize the compensation control of magnetic field and suspension force. Intelligent power module (IPM) in the power board adopts Mitsubishi field and suspension force. Intelligent power module (IPM) in the power board adopts Mitsubishi PS21265 to drive these three circuit boards, which has a bootstrap circuit and protecting function. PS21265 to drive these three circuit boards, which has a bootstrap circuit and protecting function. An An auxiliary bearing is installed, and length between auxiliary bearing and shaftis isδ1δ 1= =300 300μm. µm. auxiliary bearing is installed, and the the length between auxiliary bearing and shaft Voltage regulators are adopted to supply voltage for suspension force windings, excitation windings Voltage regulators are adopted to supply voltage for suspension force windings, excitation windings of HEBPMG driving prime motor. VB 6.0 software is utilized for on-line adjustment of parameters of HEBPMG and and driving prime motor. VB 6.0 software is utilized for on‐line adjustment of in the experiment. parameters in the experiment.
Figure 13. The experimental results based on compensation control strategy of flux‐linkage observation. Figure 13. The experimental results based on compensation control strategy of flux-linkage observation.
Due to the function of gravity, the initial position of rotor is (−0.04 mm, −0.9 mm), then the rotor Due to the function of gravity, the initial position of rotor is (−0.04 mm, −0.9 mm), then the returns to the balance position (0 mm, 0 mm) with the activation of the suspension control system, as rotor returns to the balance position (0 mm, 0 mm) with the activation of the suspension control shown in Figure 14a. In the y‐ direction, the rising time is 1.5 s while the declining time is system, as shown in Figure 14a. In the y- direction, the rising time is 1.5 s while the declining approximately 1 s, maximal eccentricity is 0.3 mm and thus the maximum overshoot is less than time is approximately 1 s, maximal eccentricity is 0.3 mm and thus the maximum overshoot is less 33.3%, which is much smaller than the air gap at the equilibrium point (Lg = 1 mm). In the x‐ direction, than 33.3%, which is much smaller than the air gap at the equilibrium point (Lg = 1 mm). In the the vibration peak‐to‐peak value is approximately 0.12 mm. The deviations of radial displacements x- direction, the vibration peak-to-peak value is approximately 0.12 mm. The deviations of radial are acceptable. The displacement in y‐ direction is larger than that in x‐ direction due to the gravity. displacements are acceptable. The displacement in y- direction is larger than that in x- direction due to Thus, the eccentric displacement track diagrams are nearly‐circular or elliptical, as depicted in Figure the gravity. Thus, the eccentric displacement track diagrams are nearly-circular or elliptical, as depicted 14b. In order to verify the feasibility of the designed HEBPMG and the effectiveness of the proposed in Figure 14b. In order to verify the feasibility of the designed HEBPMG and the effectiveness of the compensation control strategy based on flux‐linkage observation, the generating voltage and the proposed compensation control strategy based on flux-linkage observation, the generating voltage winding current waveform under different load conditions are shown in the following figure. Figure and the winding current waveform under different load conditions are shown in the following figure. 14c is DC voltage in the process of operation. First of all, the generating voltage gradually increases Figure 14c is DC voltage in the process of operation. First of all, the generating voltage gradually from start to operating stably. Then, the fluctuation errors of DC voltage are about 4% under load increases from start to operating stably. Then, the fluctuation errors of DC voltage are about 4% under shedding and overload conditions. The generating voltage restores stability after overshoot, load shedding and overload conditions. The generating voltage restores stability after overshoot, respectively. Meanwhile, the AC current in the process of operation is shown in Figure 14d–f. It can respectively. Meanwhile, the AC current in the process of operation is shown in Figure 14d–f. It can be be seen in in Figure 14d that the AC current will be stabilized about 15 A after reaching stable seen in in Figure 14d that the AC current will be stabilized about 15 A after reaching stable operation. operation. As shown in Figure 14e, winding current amplitude is reduced in 17 s and then recovered to the rated value in a short time through the role of compensation control under load shedding
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As shown in Figure 14e, winding current amplitude is reduced in 17 s and then recovered 16 of 17 to the rated value in a short time through the role of compensation control under load shedding conditions. Subsequently, it can be seen in Figure 14f that the winding current amplitude is raised in 24 s under conditions. Subsequently, it can be seen in Figure 14f that the winding current amplitude is raised in overload conditions. Then, the winding current is recovered to the rated value in a short time based on 24 s under overload conditions. Then, the winding current is recovered to the rated value in a short time flux-linkage observation too. The results above indicate that the proposed compensation and control based on flux‐linkage observation too. The results above indicate that the proposed compensation and strategy has high accuracy, good dynamic response and satisfactory anti-interference ability. control strategy has high accuracy, good dynamic response and satisfactory anti‐interference ability. Energies 2016, 9, 673
(a)
(b)
(c)
(d)
(e)
(f)
Figure 14. The experimental results based on compensation control strategy of flux‐linkage Figure 14. The experimental results based on compensation control strategy of flux-linkage observation. observation. (a) Radial displacement waveforms of x‐ and y‐direction when the start of suspension; (a) Radial displacement waveforms of x- and y-direction when the start of suspension; (b) The (b) The relationships between radical displacement of x‐ and y‐direction for HEBPMG; (c) Generating relationships between radical displacement of x- and y-direction for HEBPMG; (c) Generating voltage voltage of HEBPMG in the process of operation; (d) The winding current waveform under rated load; of HEBPMG in the process of operation; (d) The winding current waveform under rated load; (e) The (e) The winding current waveform load shedding (f) current The winding current winding current waveform under load under shedding conditions; (f)conditions; The winding waveform under waveform under overload conditions. overload conditions.
6. Conclusions In this paper, the motor structure and operation principle of a novel HEBPMG system are analyzed in detail. Then, the mathematic model of induction voltage and suspension force is deduced and tested by FEM software to prove its feasibility. A new compensation and control strategy is presented according to flux‐linkage observation. Finally, both the simulation and experimental
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6. Conclusions In this paper, the motor structure and operation principle of a novel HEBPMG system are analyzed in detail. Then, the mathematic model of induction voltage and suspension force is deduced and tested by FEM software to prove its feasibility. A new compensation and control strategy is presented according to flux-linkage observation. Finally, both the simulation and experimental results prove that the proposed compensation and control strategy has satisfactory performance in adjustment of suspension force, generating voltage and winding current. What is more, the effects on suspension force, voltage and current caused by load variation are weakened. Acknowledgments: This work was sponsored by National Natural Science Foundation of China (51675244), Key Research and Development Program of Jiangsu Province (BE2016150), Jiangsu Province University Achievements in Scientific Research Industrial Production Advancement Project (JHB2012-39), Jiangsu Province “333 Project” Research Projects (2014), Jiangsu Province “Qinglan Project” (2014). Author Contributions: Huangqiu Zhu proposed the control method and performed simulation analysis and assisted in control software compilation test, Yamin Hu carried out the modification of the winding configuration and drafted the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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