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Excitation procedure for brushless wound‐rotor synchronous starter generator with seamless transitions

2019; Institution of Engineering and Technology; Volume: 12; Issue: 11 Linguagem: Inglês

10.1049/iet-pel.2019.0058

1755-4543

Adel Deriszadeh, Orkun Karabaşoğlu, Salih Barış Öztürk,

Sensorless Control of Electric Motors

IET Power ElectronicsVolume 12, Issue 11 p. 2873-2883 Research ArticleFree Access Excitation procedure for brushless wound-rotor synchronous starter generator with seamless transitions Adel Deriszadeh, Corresponding Author Adel Deriszadeh adel.deriszadeh@polito.it Dipartimento Energia, Politecnico di Torino, Torino, 10129 ItalySearch for more papers by this authorOrkun Karabasoglu, Orkun Karabasoglu Department of Industrial Engineering, Yasar University, No: 37-39, Bornova, Izmir, TurkeySearch for more papers by this authorSalih Baris Ozturk, Salih Baris Ozturk Department of Electrical and Electronics Engineering, Istanbul Okan University, Istanbul, 34959 TurkeySearch for more papers by this author Adel Deriszadeh, Corresponding Author Adel Deriszadeh adel.deriszadeh@polito.it Dipartimento Energia, Politecnico di Torino, Torino, 10129 ItalySearch for more papers by this authorOrkun Karabasoglu, Orkun Karabasoglu Department of Industrial Engineering, Yasar University, No: 37-39, Bornova, Izmir, TurkeySearch for more papers by this authorSalih Baris Ozturk, Salih Baris Ozturk Department of Electrical and Electronics Engineering, Istanbul Okan University, Istanbul, 34959 TurkeySearch for more papers by this author First published: 15 August 2019 https://doi.org/10.1049/iet-pel.2019.0058Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract An analytical model of excitation system of brushless wound-rotor synchronous starter generator for aircraft applications is developed and presented in this study. During engine start-up process, the starter generator operates as a motor to start the aircraft turbine and to assist it up to the self-sustaining speed. On the basis of rotation speed of the starter generator in the engine start-up process, there are three excitation modes for the exciter and two transient modes for the field current of the main generator (MG). In this study, for each excitation mode, the relationship between the excitation current (field current of the exciter) and the field current of MG is investigated by taking into account the influence of power electronic parts. This study also proposes a control method for the generator field current in all excitation modes which can detect optimum operating points for transition between excitation modes. Furthermore, a seamless transient control strategy is proposed for the transient modes of the generator field current. Simulation and experimental results are provided to demonstrate the feasibility of the proposed solution. Nomenclature Iexc, fexc excitation current and excitation frequency, ωexc = 2·π·fexc Mrs_exc mutual inductance between field and armature ωr rotation angular speed ϑ0 initial electrical rotor position va, vb, vc induced voltages on exciter armature windings ia, ib, ic armature phase currents Rr armature resistance Sa, Sb, Sc switching functions of rotating rectifier vdc DC output voltage of rotating rectifier without the commutation voltage drop If field current of main generator Rcom resistance which represents the commutation voltage drop Rf, Lf MG field winding resistance and inductance s exciter slip, s = (ωexc−ωr)/ωexc Von forward voltage of rectifier diodes Lc commutation inductance ωr_acdc rotor speed for AC–DC excitation switching 1 Introduction Since safety is a crucial requirement for the aircraft power system, brushless electric machines are the preferred candidates for integrated starter generator application due to their advantages of high safety level and low maintenance requirement [1, 2]. Among the brushless electric machines, the wound-rotor synchronous machine with brushless excitation system is a popular solution due to its higher reliability with respect to permanent magnet (PM) machines since its field flux can be controlled [3]. Typically, the brushless wound-rotor synchronous starter generator (WRSSG) consists of a brushless excitation system and the main generator (MG). The brushless excitation system consists of three-phase PM pre-exciter (PE), the main exciter (ME) and a rotating rectifier, as shown in Fig. 1 [4]. Fig. 1Open in figure viewerPowerPoint Three-stage brushless synchronous starter generator for aircraft The PE supplies the field winding/s of the ME through a power electronic converter. The voltages induced in the three-phase rotor windings of the ME are rectified by a rotating diode bridge rectifier and applied to the field winding of the MG, providing the MG field current If. On the MG side, the stator windings are supplied by a three-phase inverter. During aircraft engine start-up process, the PE cannot be used to supply the ME field winding through the dc–dc converter (Fig. 1). In this case, the dc–dc converter is fed through a DC bus supplied by a battery bank or the auxiliary power unit [5]. Therefore, in starting operation of the WRSSG, only ME contributes in the brushless excitation system. At standstill, because relative speed between field (stator) and armature (rotor) windings of ME is zero, DC excitation of the ME's field winding fails to induce voltages in rotor windings of ME. Therefore, at standstill, AC excitation is required. Also, at low speeds since the coupling between field and armature windings of ME is not strong enough, still AC excitation is needed. At high speeds, the relative speed creates a firm coupling between stator and rotor windings of ME and the excitation can be switched from AC to DC. The optimum speed at which AC excitation can be switched to DC excitation is one of the ambiguous issues with single-phase exciters which is addressed in this paper. The power converter for ME supply can be a simple bridge dc–dc converter that can easily provide both AC and DC excitations for the ME during starting and generation modes. Therefore, the single-phase exciter is fully compatible with the existing aircraft generator control units (GCU) since the power converter used for ME excitation during engine start-up process can be easily performed by the same GCU that controls the starter generator during generator mode. However, the single-phase ME needs a particular attention in case of AC excitation since it produces a pulsating magnetic field. To produce a rotating magnetic field, polyphase ME stator windings have been proposed in [6-13]. These solutions have better performance with AC excitation, but they need more complicated power converters. Moreover, the transition from AC excitation to DC excitation is performed with relays and additional wiring to rearrange connectivity of ME's field windings, so the system reliability is reduced. For these reasons, the single-phase ME solution is preferable for the industry with respect to the polyphase solutions in terms of compatibility, size, simplicity and safety. In addition, it must be emphasised that the starting time with AC excitation is very small when compared with the generation and starting time with normal DC excitation, so the use of polyphase ME windings is not justified only for a very small part of the starting. This highlights the importance of research on investigating proper excitation control for the single-phase exciter in line with its industrial application. Few researchers have addressed the excitation control of the single-phase exciter and most studies have been carried out on excitation control of WRSSG with polyphase exciters which produce a rotating field flux with easier analytical presentation. These papers dealing with the starting of WRSSG with single-phase ME presented solutions based on intensive experimental tests to find the relationship between field current of ME (the ME excitation current) and the MG field current. In [14], a linear relationship between excitation current Iexc and MG field current If was obtained for a WRSSG by experimental tests. An exponential function was proposed in [15] representing relationship between the excitation frequency and speed. Although the proposed function can be used to find the instant of the AC–DC excitation transition, since the relationship between the required excitation frequency and speed obtained from experimental data using curve fitting, it works only for the machine used for the test, and therefore it is not a generic solution. To the best of the authors' knowledge, an analytical study to get the relationship between the ME excitation current and the MG field current with AC and DC ME excitation has not been addressed in the literature. Another problem in motoring operation of WRSSG is that knowing the value of the MG field current if is essential for torque control of WRSSG. However, in brushless WRSSG, MG field winding is not accessible, and its current is not measurable. One solution is to estimate the MG field current using model of the brushless excitation system (including model of exciter stator, exciter rotor, rotating rectifier and MG field winding). Since these models are very non-linear, the model-based approach can be accurate and is sensitive to machine parameters. In [10], an estimation method was proposed for MG field current estimation. This method was used in [11] to develop a control system for WRSSG at start-up process. As an alternative solution, in [16], a two-phase ME was proposed which produces a rotating field when AC excitation is required. In this topology, the MG field current is measured directly through off-line tests at standstill. Therefore, MG field current at standstill and for a specific excitation is known. Keeping this known MG field current constant during entire start-up process, the MG field current will be known throughout the motoring operation of the WRSSG. In [16], the constant keeping of the MG field current was performed by an excitation frequency control which keeps the relative speed between the rotating field flux and armature windings of ME constant. Therefore, induced voltages in ME's armature windings and consequently output voltage and current (if) of the rotating rectifier are constant. Now, knowing the value of if, torque control can be carried out by controlling the MG stator currents. The same idea of keeping a known MG field current during starting process is adopted in this paper for the single-phase exciter by analytically modelling the pulsating field flux of ME during entire engine start-up process of WRSSG. A universal excitation control strategy based on analytical study of ME during engine start-up process is proposed in this paper. Moreover, the proposed strategy presents a seamless transition between AC and DC excitations and detects the optimal speed at which the transition should be performed. Unlike the presented method in [11], in the proposed excitation control non-linear effects of the rotating rectifier are taken into account. This leads to increased accuracy in excitation and transition control. This paper is organised as follows. Three starting excitation modes are defined and modelled analytically in Sections 2–4. The influence of the exciter rotor inductance and resistance on the MG field current is described in Section 5. Then, two possible transition conditions of the MG field current are analysed in Section 6 using the revolving field theory. An excitation current control is proposed in Section 7 to obtain quasi-constant MG field current during the starting, with seamless transitions between different excitation modes. Moreover, the proposed procedure specifies an optimum speed when the AC excitation should be switched to DC excitation. Simulation and experimental verifications are reported in Sections 8 and 9, respectively. 2 ME operation at starting There are two ambiguous issues with starting of WRSSG during its starting operation as follows: What is the value of MG field current under a given excitation? In practise, for a given WRSSG, MG field current at standstill is measured by experimental tests using open rotor measurement. Knowing the MG field current is essential for optimal control of the machine in starting mode. In this paper, as a solution an excitation control strategy is proposed which keeps the known MG field current constant during entire starting process. This is performed by keeping the rotating rectifier output voltage constant. At which speed AC excitation should be switched to DC excitation? As mentioned before, when WRSSG is at standstill, since there is no relative speed between the field and rotor windings of the ME, AC excitation is required. The AC excitation at standstill will be called hereinafter the first excitation mode. When the machine starts rotating, the ME excitation remains AC up to a certain rotor speed ωr_acdc, at which the excitation should be switched to DC. AC excitation when the machine is rotating, and the rotation speed is below ωr_acdc is called the second excitation mode. The third excitation mode starts when the rotor speed exceeds ωr_acdc and the ME excitation is DC. In this paper, switching functions of the rotating rectifier in all excitation modes are calculated in Section 4. By knowing the switching function of the rotating rectifier, it is possible to calculate the rotating rectifier output voltage during entire starting process. The proposed excitation control uses the MG field current at standstill If1 which had been measured through off-line tests as the reference value for the next two excitation modes (If2 for the second excitation mode and If3 for the third excitation mode). Thus, the AC excitation current amplitude in the second excitation mode Iexc2 is controlled to keep the If2 equal to If1. Meanwhile, the required DC excitation Iexc3 to provide If3 equal to If1 is calculated. Once the required DC excitation Iexc3 becomes equal to amplitude of Iexc2, the excitation switches from AC to DC. In this case, transitions of the MG field current between different excitation modes are smooth and its known value is kept constant. 3 Analytical model of the single-phase brushless exciter The analytical model uses the revolving field theory to analytically describe the pulsating field which is produced by the ME single-phase field winding. This pulsating field can be decomposed into two imaginary rotating fields which are rotating in opposite directions with amplitude equal to half of the real stationary field magnitude. The field that rotates in the same direction of the rotor is called forward rotating field (λFW), whereas the field that rotates in the opposite direction of the rotor is called backward rotating field (λBW). The induced three-phase voltages on armature windings are (1) (2) (3)The above equations explicitly demonstrate the revolving field theory; the first term on the right-hand side of equal sign denotes an armature voltage component induced by the backward rotating flux, whereas the second term represents a voltage component induced by the forward rotating flux. 4 Starting excitation modes 4.1 AC excitation at standstill When the machine is at standstill, the rotor position is ϑ0, ωr is equal to zero while the slip is unity. As a result, the induced phase voltages can be rewritten as follows: (4) (5) (6)From (4)–(6), it is concluded that two of the phase voltages have same phase, whereas the third phase has 180° phase shift. Since armature windings feed a rotating diode rectifier bridge, only two phases which have phase shift to each other and have largest amplitudes contribute in voltage rectification. The third phase just carries current during phase commutations which lead to three-phase short circuit. This phenomenon will be investigated in detail in Section 5.1. In this paper, to understand the relation between input voltages of the rotating rectifier and its output voltage which governs field current of MG, switching functions of the rotating rectifier in all excitation modes are calculated. Switching function method is described in detail in [17]. Using the switching functions, the output of the rectifier is obtained as (7)The switching functions (Sa, Sb and Sc) can be defined as the input voltages divided by their amplitude. The switching function vector of the rotating rectifier in the first excitation mode, with the armature resistance neglected, is calculated as follows: (8)where the coefficient (4/π) is calculated from the Fourier series calculation of the switching functions [17]. Δa, Δb and Δc depend on the initial rotor position (ϑ0) and are expressed in Table 1. Substituting (8) into (7), the rotating rectifier output voltage in the first excitation mode can be calculated. Its mean value over one electrical period [] is (9) Table 1. Δa, Δb and Δc functions in the first excitation mode Initial rotor position Δa Δb Δc 1 −1 0 1 −1 0 0 −1 1 0 −1 1 −1 0 1 −1 0 1 −1 1 0 −1 1 0 0 1 −1 0 1 −1 1 0 −1 1 0 −1 Equation (9) indicates that the rotating rectifier output voltage at standstill depends on the initial rotor position, excitation current amplitude Iexc and frequency ωexc. 4.2 AC excitation at low speed When the machine starts rotating up to the rotor speed ωr_acdc, the excitation remains AC. During this interval, the induced phase voltages on armature windings are the same as (1)–(3). As the rotation speed increases, the frequency of voltage component induced by backward imaginary field increases, whereas the frequency of voltage component induced by forward field decreases. Hence, the sum of two voltage components is like a beat signal which voltage component induced by backward field is its carrying signal and another voltage component induced by forward field is a modulating signal (for detailed demonstrations see the Appendix). The switching functions of the rotating rectifier in this mode are (10)where the coefficient [] is calculated from the Fourier series calculation of the switching functions [17]. Substituting (10) into (7) and calculating the mean value, the simplified average value of the rectifier DC output voltage, in the second excitation mode, can be written as (11)where E is an incomplete elliptic integral of the second kind [18]. In this paper, the maximum slip for AC excitation is considered as zero. Hence, s(2 − s) changes from 1 to 0, it is possible to replace the elliptic integral with an approximated function. By curve fitting, an approximated function for E[π, s(2 − s)] can be written as (12)where x = s(2 − s). Equation (11) demonstrates that below ωr_acdc, the DC output voltage variation depends on Iexc, ωexc and the E[π, s(2 − s)]. 4.3 DC excitation at high speed The third excitation mode starts when the excitation changes from AC to DC. In this case, the induced voltages in the armature windings are (13) (14) (15)The switching function vector of the rectifier in this mode is (16)Using (16) in (7) and calculating its mean value, the mean rectifier output voltage, in the third excitation mode, becomes (17)As results from (17), the DC output voltage during the third excitation mode is proportional with the DC excitation current and the rotor speed. 5 Effects of front-end inductance on rectifier output voltage The AC-side front-end inductances (hereafter is called commutation inductance) lead to a finite commutation interval when the output current of rectifier switches between the rectifier legs. During the commutation interval, two or more diodes are carrying current which makes a line-to-line short circuit between armature phases [19]. On the basis of the commutation duration, there are three operation modes for a rectifier which are described in detail in [20]. The commutation influence on the output voltage is a voltage drop that is usually modelled by a virtual resistance Rcom. This resistance will be obtained in the next section for the different excitation modes. 5.1 Commutation voltage drop in the first excitation mode In the first excitation mode, the supply voltages of the rotating rectifier are two phases with 180° phase shift. Fig. 2a shows the interval, in which the positive current is transferring from phase b to phase a and voltage of phase a is higher than phase b. Therefore, the current commutation of phase a is faster than of phase b and the phase c carries the difference between phase a current and phase b current. Fig. 2Open in figure viewerPowerPoint Commutation interval waveform in the first excitation mode and its equivalent circuits (a) Current commutation interval, (b) First mode, (c) Second mode During commutation, there are two distinct modes (Fig. 2). In the first mode, always more than three diodes are on. Fig. 2b shows the equivalent circuit of this mode. Applying Kirchhoff voltage law (KVL) in the indicated loops yields (18) (19)Applying KCL at point O yields (20)Substituting (20) into (19) (21)Substituting (21) into (18), the time interval needed by the phase a current to reach If is (22)In (22), vab and vbc can be calculated from (4)–(6). For the first commutation mode, dia = 2If and dib = ib1−If, where ib1 is the current of phase b at the end of the first commutation mode. Substituting (22) into (21), at the end of the first mode, the phase b current is (23)Rewriting (18) yields (24)Multiplying both sides of (24) by dt·ωexc and integrating for 180° interval yields (25)The left-hand side of (25) is the voltage drop during this mode that is lost every 180°. This voltage drop can be modelled by a resistor at the rectifier output (26)When the phase a current gets its final value (If), the second mode starts. Fig. 2c shows the equivalent circuit of the second mode. During this mode, only three diodes are conducting. Applying KVL in the indicated loop yields (27)Left-hand side of (27) is the voltage drop due to commutation in the second mode. Multiplying both sides of (27) and integrating for 180° interval yield (28) (29)Finally, the total voltage drop due to commutation for the first excitation phase can be represented by the sum of resistances from (26) and (29) as (30)At initial positions of 0° and 180°, where Vb and Vc are equal, only first commutation mode happens. Applying KCL at point O yields (31)Substituting (31) into (18) yields (32)Calculating average value of (32) for 180° as in (25), Rcom is obtained as (33) 5.2 Commutation voltage drop in the second and third excitation modes In the case of a three-phase system with 120° phase shift between phases (such as in the third excitation mode), in each electrical period of the input voltages, six commutations occur. For each commutation, fLc represents the resistance to model the commutation voltage drop. In the Appendix, it is demonstrated that in the second excitation mode, during each period of the dominant voltage component, almost six commutations happen. Therefore, with a good approximation, the frequency of the dominant voltage component (carrying component) can be considered in calculation of Rcom. Thus, Rcom for the second and third excitation modes is (34)where f for the second excitation mode equals fexc + ωr/(2·π) and for the third excitation mode it is ωr/(2·π). 5.3 Commutation inductance As mentioned before, during the commutation interval, line-to-line short circuit occurs. Hence, the commutation inductance is not a steady-state machine inductance. In this paper, the average value of d and q axes sub-transient inductances is chosen as Lc [21]. 5.4 Effect of the armature resistance When the armature phases are in conduction interval (when there is no commutation between the armature phases), two phases carry the rectifier output current If. In this case, the voltage drop due to the armature resistance is 2Rr·If. This is the voltage drop of each line voltage. From (4)–(6), it should be noted that in the first excitation mode, when ϑ0 is 0° and 180°, amplitude of va is twice the amplitudes of vb and vc. Thus, ib and ic are equal. The amplitudes of ib and ic is half of the amplitude of ia. In this case, voltage drop of each line voltage is . During commutation intervals, one phase carries If and the commutating phases carry less than If. Therefore, voltage drop of the line voltage is less than 2Rr·If. In this paper, this phenomenon is neglected, and the voltage drop due to the armature resistance is considered constant. 6 MG field current transition modes In conventional excitation of WRSSG during the starting process, usually amplitude and frequency of the AC excitation current are kept constant. This method will be called hereafter as the uncontrolled method. In this method, the MG field current will not be constant during the starting. Moreover, the switching between AC excitation and DC excitation is often done at a speed that is chosen experimentally, as in [4, 15]. In this paper, the proposed excitation control method aims to obtain a constant MG field current during starting, by controlling the amplitude of the ME excitation current, while the excitation frequency is constant. Transition modes of the MG field current are: First transition mode: It is the transition between AC excitation at standstill and AC excitation at low speed. Second transition mode: It is the transition between the AC excitation at low speed and DC excitation. 6.1 Assumptions The main assumptions made in designing the proposed excitation control are as follows: Phase displacement between input voltages and currents of the rotating rectifier is imposed by the commutation inductance. As mentioned in Section 5.3, the commutation inductance is a sub-transient inductance of ME rotor windings and its value is small. Therefore, power factor of the rotating rectifier is close to unity and armature reaction of ME has a cross-magnetising effect. In this paper, it is assumed that distorting effect of armature reaction is negligible compensated by the ME field current controller. According to the large inductance of the MG field winding, it is assumed that output current of the rotating rectifier (If) is a smooth DC current. Since mutual inductance between field and armature of ME (Mrs−exc) is used to calculate the required excitation current, saturation effect on the Mrs−exc must be taken into account. In this paper, instead of a constant value, inductance profile of Mrs−exc obtained from the finite element (FE) analysis is used in the proposed excitation control. Resistance of MG field winding during the start-up process is considered constant. Therefore, keeping the rotating rectifier output voltage, field current of the MG remains approximately constant [16]. 6.2 First transition mode The first transition mode occurs when the machine begins to rotate. Since the induced rotor voltages, and therefore the rotating rectifier output voltages are different at standstill and rotation conditions, there is a transition condition for the MG field current. Fig. 3a shows the E[π, (s(2 − s)] versus slip that changes from 1 to −1. From (11) and Fig. 3a, it is concluded that the output voltage of the rotating rectifier increases by increasing the rotation speed when the amplitude and frequency of excitation current are constant. However, as soon as the rotor starts rotating, the output voltage of rotating rectifier may be lower or higher than its standstill value. Fig. 3Open in figure viewerPowerPoint Effective parameters on the first MG field current transition (a) Elliptical integral versus slip, (b) First transient mode condition based on rotor initial position Comparing (9) and (11) for the initial position changing from 0 to 2π, all possible transient conditions for the first transition mode based on initial rotor position are shown in Fig. 3b. Areas with red colour show conditions, where output voltage of the rotating rectifier decreases after rotation and other areas indicate the conditions with output voltage increase. As can be seen in Fig. 3b, in most of conditions, the rotating rectifier output voltage and the MG field current decreases when the machine starts rotating. If1 and If2 are the MG field current in the first and the second excitation modes, and can be written as (35) (36)To keep the MG field current constant (If1 = If2), the amplitude of exciter field current (Iexc) should be changed. The rotating rectifier output voltage is controlled in an open-loop fashion by controlling the ME excitation current amplitude in the proposed method. Using (11), (35) and (36) and knowing value of Vdc1, the excitation current for the second excitation mode is obtained as (37) 6.3 Second transition mode When the machine is in rotating condition, at an optimum speed (slip) which is found by the excitation controller, the AC excitation should switch to DC excitation. The output current of rectifier in the third excitation mode is given as (38)From (17), (35) and (38) and knowing value of Vdc1, to achieve constant MG field current (If3 = If2 = If1), the amplitude of the DC excitation current during the third excitation