Wound Rotor Machine With Single-Phase Stator and ... - IEEE Xplore

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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 30, NO. 2, JUNE 2015

Wound Rotor Machine With Single-Phase Stator and Three-Phase Rotor Windings Controlled by Isolated Three-Phase Inverter Kahyun Lee, Student Member, IEEE, Yongsu Han, Student Member, IEEE, and Jung-Ik Ha, Senior Member, IEEE

Abstract—This paper proposes a single-phase grid-connected wound rotor machine that has the single-phase stator and threephase rotor windings. The machine has no auxiliary winding or capacitor unlike conventional single-phase machines. Nevertheless, it can operate in all four quadrants of the torque–speed plane with a three-phase inverter. For adjustable speed drives, an isolated three-phase inverter is applied to the rotor windings while the stator winding is directly connected to a single-phase source. The grid filter and rectifier of the conventional system are eliminated and the rotor-side slip rings can be also removed by the inverter integration. So the overall structure of the proposed drive system is simple and cost effective. In this paper, the proposed machine is modeled into a modified d–q model considering the absence of qaxis stator coil. Its characteristics are analyzed and vector control methods of the grid power factor, dc-link voltage, and speed are proposed. For more efficient control, the optimal rotor current set is calculated from the minimum copper loss condition. The system has wider operating areas than other single-phase drive systems. The feasibility of the proposed system is verified by experiments. Index Terms—Modeling, minimum copper loss (MCL), singlephase grid, vector control, wound rotor machine.

I. INTRODUCTION NERGY shortage has become one of the major concerns over the world. There has been an enormous increase in electric energy consumption due to population growth and industrial development. As electric machines produce virtually all electricity and consume a major part of that, the demand for energy-efficient electric machine technology has steadily increased [1]–[8]. Generally, the electric machine drives are more efficient when powered by three-phase power than single-phase power. The three-phase utility power, however, is typically available only in high-capacity industrial and commercial areas due to its high installation cost. Therefore, most of motor applications in domestic and light industrial fields still utilize singlephase power, and in rural regions, the single-phase supply has been the only option for their basic needs [9]–[15]. In single-phase applications, single-phase induction motor (SPIM) with an auxiliary winding and split-phase capacitor has

E

Manuscript received April 22, 2014; revised August 19, 2014 and January 13, 2015; accepted January 16, 2015. Date of publication February 16, 2015; date of current version May 15, 2015. This work was supported in part by the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science, ICT, and Future Planning (MSIP) under Grant 2009-0083495, and in part by the Brain Korea 21 Plus Project, 2014. Paper no. TEC-00265-2014. The authors are with the Department of Electrical and Computer Engineering, Seoul National University 599 Gwanak-ro, Gwanak-gu, Seoul, 151-744, Korea (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEC.2015.2394807

Fig. 1. Single-phase drive system of an SPIM with two-phase full-bridge inverters.

been widely used due to its cost-effectiveness. Although the machine mostly operates at fixed speed so far, variable-speed drives have been preferred in recent decades as a response to constant concerns for an energy crisis. The variable-speed drive has many advantages over the fixed-speed one, such as improved efficiency and power quality, higher power density, and wider stability margin. Thus, variable-speed drive systems for SPIMs have been developed in various ways [15]–[25]. Replacing a fixed split-phase capacitor by an adjustable ac capacitor is discussed in [16]. The main disadvantage of this topology is a quite limited operating range. Hence, multileg inverters are applied to supply the stator windings [17]–[25]. In [18]–[20], a two-leg inverter along with a full-bridge rectifier is used. In this case, the motor utilizes only half the rectified input voltage and it is crucial to keep the voltage across the dc-link voltage capacitors balanced. Although the three-phase inverterdriven systems proposed in [21]–[24] eliminate the need for a divided dc bus and reduce the total harmonic distortion (THD), they still suffer from low modulation index. To solve this problem, a drive system using two H-bridge inverters was introduced in [25]. In this system, an H-bridge inverter is used to supply each winding as shown in Fig. 1, and the torque and speed can be precisely controlled by separate control of two winding voltages. Also, it is possible to implement the field-oriented control (FOC) as in three-phase machines. This topology is superior to others in speed range, performance, and power factor. However, the overall system becomes bulky and expensive since too many semiconductor devices, eight switches and four diodes, are used. The inverter-driven SPIM systems require additional devices such as the rectifier and grid filter for coupling ac grid to dc voltage level and improving power factor of grid. These elements increase the costs and lower the energy efficiency. Also, only the motoring operation is possible due to the unidirectional rectifier and operating range is limited by the dc-link voltage limits.

0885-8969 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

LEE et al.: WOUND ROTOR MACHINE WITH SINGLE-PHASE STATOR AND THREE-PHASE ROTOR WINDINGS CONTROLLED BY ISOLATED

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Fig. 2. Single-phase drive system of a three-phase wound-rotor machine with a three-phase inverter: SEF-SDFWM. Fig. 4.

Fig. 3. Two structures of the proposed system. (a) Slip-ring type. (b) Integrated-rotor type.

Thus, a different single-phase drive system using a wound-rotor machine, named single external feeding of single-phase doubly fed wound rotor machine (SEF-SDFWM), has been recently proposed [26]. The system applies a three-phase wound rotor machine to the single-phase source as shown in Fig. 2, and the machine can be regarded as a wound-rotor-type SPIM whose auxiliary winding is short-circuited. Unlike in the SPIM drive system in Fig. 1, an inverter is applied to the rotor side and there is no power circuit in the stator side. This topology simplifies the drive circuits to a 6-switch inverter and dc link and extends operating range by raising the dc link voltage beyond the values reached by conventional rectifier systems. However, only twothirds of the amplitude of the grid voltage can be utilized due to the short-circuited stator windings. This paper proposes a novel wound rotor machine called single-phase stator and three-phase wound rotor machine (SSTWRM) and its drive system as an alternative of the conventional single-phase powered drive systems. SSTWRM has the singlephase stator winding and three-phase rotor windings as shown in Fig. 3. The absence of the auxiliary winding is the main difference of the proposed machine with the conventional SPIM. As shown in Fig. 3(a), an isolated three-phase inverter is applied to the rotor windings and the single-phase stator winding is directly connected to the grid. In this configuration, the rotorside inverter can be integrated on the rotor shaft as shown in Fig. 3(b) since it is electrically isolated from the grid. Then, slip rings and brushes are eliminated. Without any auxiliary winding or capacitor, SSTWRM operates in all four quadrants

Equivalent circuit of the proposed machine.

of the torque–speed plane with only six switches. In addition, the system has higher torque capability than the conventional SPIM and SEF-SDFWM systems. Thus, it has merits of broad operating range and simple structure. The proposed system can also perform unity power factor (UPF) control without any additional device at the same time while regulating the dc-link voltage and average torque. Therefore, this system is suitable for the applications such as small wind turbines and variablespeed home appliances including heating, ventilation, and air conditioning (HVAC), and washing machines because of its regenerative capability, wide operating range, compact structure, and excellent controllability. In this paper, SSTWRM is modeled into the modified d–q model and its characteristics are analyzed. Also, a vector control method for regulating the grid power factor, dc-link voltage, and torque is proposed. For higher efficiency, the optimal set of the rotor currents for the minimum copper loss (MCL) is calculated and applied in the vector control. The feasibility of the proposed SSTWRM system is validated by experiments. II. SYSTEM CONFIGURATION AND MODELING A. Modeling of SSTWRM To analyze the dynamic characteristics of SPIMs, the d–q equivalent circuits have been used [19]. SSTWRM in Fig. 3 is different from SPIM because the stator has no auxiliary winding in the q-axis and the rotor is not squirrel-cage but wound-rotor type. Thus, the q-axis stator current is zero but the rotor voltages and the power are no longer zero. Considering those differences, the d–q model of the proposed machine is constructed in a stationary reference frame (SRF) as shown in Fig. 4. Unlike the general model in [19], the q-axis stator circuit is removed and the rotor-side terminals are not short-circuited in Fig. 4. Here, the stator and rotor voltages are determined as follows: dλsds (1) dt dλs s s Vdr = Rr Idr + dr + ωr λsq r (2) dt dλsq r − ωr λsdr (3) Vqsr = Rr Iqsr + dt where the superscript “s” denotes the SRF; the subscripts “s” and “r” mean the stator and the rotor, respectively; λ denotes the magnetic flux; Rs and Rr are the stator and the rotor resistances, respectively; Lls and Llr are the stator and rotor leakage s s = Rs Ids + Vds

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inductances; Lm is the mutual inductance; and ωr is the electrical frequency of the rotor speed. The d–q rotor voltage equations are represented in terms of the rotor currents and stator fluxes as follows: L2m d s s s + σLr Idr + Lr ωr Iqsr Vdr = Rr + Rs 2 Idr Ls dt +

Lm s Rs Lm s V − λds Ls ds L2s

(4)

d s Lm s s I − Lr ωr σIdr − ωr λ (5) dt q r Ls ds where σ is defined as Ls Lr − L2m /Ls Lr . Although the stator and rotor windings are evenly distributed in SSTWRM, the d–q rotor voltage equations are unbalanced since there is no q-axis stator current. While the d-axis fluxes are induced by the d-axis stator and rotor currents, the q-axis fluxes are generated by the q-axis rotor current alone. Accordingly, the d–q impedances from the rotor side are asymmetric as in (4) and (5), which is addressed in the vector control. Also, considering that the amount of the torque produced by an electric machine is proportional to the cross product of the stator and rotor currents, the proposed machine can generate the torque using the d-axis stator and q-axis rotor currents. The winding set of SSTWRM consisting of single-phase stator and three-phase rotor windings has the minimum number of windings for the constant torque generation. The three-phase rotor windings are essential to continuously flow the q-axis rotor current in SRF regardless of the rotor position. This structure is also founded in a dc-excited synchronous machine, which has the three-phase stator and single-phase rotor windings. Compared to the case of SSTWRM, the stator and rotor are switched in the configurations, the rotor has saliency due to the asymmetric structure, and the source applied to the single-phase winding is changed from ac to dc source. Vqsr = Rr Iqsr + Lr

B. Proposed Drive System The adjustable-speed drive system of SSTWRM is proposed in this paper, aimed at efficient energy conversion. As shown in Fig. 3(a), a stator winding is directly connected to singlephase grid without any power circuit such as grid filter, rectifier, or inverter. The rotor windings are connected to a three-phase inverter for vector control. In this configuration, the machine can operate both in motoring and generating modes with only six semiconductor devices, which is half the devices required by the SPIM system in Fig. 1. By removing the rectifier and input filter, the system saves energy conversion costs and losses. Also, in the proposed system, the rotor-side inverter and dc link are isolated from grid and power consumed in the inverter such as control board drive power and switching losses is provided from the stator-side grid. Thus, any external power is not needed while the inverter controls rotor power and dc-link voltage considering the power needed in itself. This isolated inverter-and-dc-link set can be integrated on the rotor shaft as depicted in Fig. 3(b). Then, the circuits, including the inverter, dc link, and control board, rotate with the rotor shaft and the slip rings and brushes in the rotor side are no longer needed. In this

Fig. 5.

Power flow between the stator and the rotor.

case, the control signal can be transferred to the rotating inverter either by high-frequency signal injection through the stator or wireless signal transmission with additional devices. C. Rotor Current Variables for Vector Control Fig. 5 shows the power flow in the proposed system. As aforementioned, since there is no q-axis stator current in the SSTWRM, only the cross product of the d-axis stator and q-axis rotor currents contributes to generate the torque as depicted in Fig. 5 with the red bidirectional arrow. Also, the black arrow in the figure shows the d-axis power flow. While the torque is regulated by the q-axis rotor current to the reference value, the q-axis rotor power varies with the operating conditions. This rotor power variation indirectly affects the stator power since the stator-side grid is the only power source in the proposed drive system. In other words, the variation of the q-axis rotor power by the torque control influences both the stator and rotor powers. Therefore, the system should regulate both of them during the torque control in order to meet the grid code and balanced energy condition in the isolated inverter. As described in Fig. 5, these power properties can be controlled through the regulation of the d-axis power flow of the black arrow. In the proposed system, torque and power are determined by the rotor current, which is regulated by the rotor-side inverter. Their relationship can be easily analyzed in SRF due to zero q-axis stator current in that frame. Although the voltages and currents oscillate at grid frequency in SRF, their fundamental components can be represented with dc variables and grid angle with an assumption that the harmonics are negligible. Where the single-phase grid voltage is defined as (6), d- and q-axis rotor currents are represented as in (7) and (8) s = Vgrid = −Egrid sin (θgrid ) Vds

(6)

s Idr

= Idr c cos (θgrid ) + Idr s sin (θgrid )

(7)

Iqsr = Iq r c cos (θgrid ) + Iq r s sin (θgrid )

(8)

where Egrid is the amplitude and θgrid is the angle of the grid voltage, the subscript “c” and “s” mean the cosine and sine components, respectively. Idr c and Iq r c are cosine components of the d- and q-axis rotor currents, which lead grid voltage by 90°. Also, Idr s and Iq r s are sine components that are in phase with grid voltage. The proposed system controls torque and power using the four rotor current variables, Idr c , Idr s , Iq r c , and Iq r s , which are dc components in SRF.


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III. OPERATION PRINCIPLES There are three control requirements in the proposed system: grid power factor, torque, and dc-link voltage. They are represented as functions of the rotor currents and stator fluxes. Here, the stator flux can be divided by the grid angle into the cosine and sine components, which are denoted by λdsc and λdss , as in (7) and (8). Also, since the voltage drop by the stator resistance is negligible compared to the other terms in (1), the cosine and sine components of the d-axis stator flux roughly have the fixed values as follows: λdsc ≈ Egrid /ωg

λdss ≈ 0

(9)

where ωg is the grid frequency. With the approximation of (9), the stator flux is the constant value. Thus, the torque and both side powers can be represented in terms of the rotor currents. In this section, characteristics of the torque, rotor power, and stator power are mathematically analyzed and operating areas of the SSTWRM system are compared with the conventional systems.

Fig. 6.

Rotor-side circuit.

is zero in SRF. From (10), it is rewritten in terms of the rotor currents 3P 3 P Lm s s s Lm Iqsr Ids = I (Lm Idr − λsds ) . (15) Te = − 22 2 2 Ls q r As the currents are divided into the cosine and sine components, there are three types of torques 3 P Lm Te,avg = Iq r c (Lm Idr c − λdsc ) 4 2 Ls + Iq r s (Lm Idr s − λdss ) (16)

A. Power and Power Factor in Grid In the proposed system, the grid power is equal to the stator power, so the grid power factor depends on the ratio between the stator active and reactive powers. The d-axis stator current can be represented with the grid angle as follows: λdsc − Lm Idr c s Ids = cos (θgrid ) Ls λdss − Lm Idr s (10) + sin (θgrid ) . Ls From (10), the stator active and reactive powers, Ps and Qs , are obtained as λdss − Lm Idr s 3 Ps = − Egrid (11) cos2 (θgrid ) 2 Ls λdsc − Lm Idr c 3 Qs = − Egrid cos (θgrid ) sin (θgrid ) . (12) 2 Ls As shown in (11) and (12), the stator active and reactive powers are determined by Idr s and Idr c , respectively. It corresponds to the stator power control through the d-axis power flow. Thus, while the active power depends on the operating condition, the power factor of grid is regulated by manipulating the reactive power that becomes zero under the following condition: Idr c =

λdsc Egrid ≈ ≡ Idr c,PF . Lm Lm ωg

(13)

Here, Idr c,PF means the d-axis current magnitude required for UPF. B. Torque Characteristics The torque of SSTWRM is determined by the cross product of the stator and rotor currents s s∗ 3P Lm Im Idq (14) Te = s Idq r . 22 . As aforementioned, the torque is determined by the d-axis stator and q-axis rotor currents since the q-axis stator current

Te,ripple,c =

Te,ripple,s =

3 P Lm Iq r c (Lm Idr c − λdsc ) 4 2 Ls − Iq r s (Lm Idr s − λdss )

(17)

3 P Lm Iq r s (Lm Idr c − λdsc ) 4 2 Ls + Iq r c (Lm Idr s − λdss )

(18)

where Te,avg is the average torque and Te,ripple,c and Te,ripple,s are cosine and sine components of the ripple torque oscillating at twice the grid frequency. Due to the direct connection between the stator winding and single-phase source, the proposed drive system has torque pulsations. The amplitude of the ripple torque depends on the d–q rotor currents as follows: 3 P Lm 2 Iq r c + Iq2r s Te,ripple,am p = 4 2 Ls

(Lm Idr c − λdsc )2 + (Lm Idr s − λdss )2 . (19) Such torque variations cause the speed ripple, though, have no effect on the average speed. The average torque can be precisely controlled by the q-axis rotor current variables Iq r c and Iq r s , while the d-axis rotor currents are used for the power regulation. Therefore, the system is suitable for the applications where there is no need to precisely control the rotor position. For example, the system is great for small wind turbines utilizing single-phase generators and variable-speed home appliances like HVAC and washing machines. In these applications, effects of the torque ripple can be smoothed by rotational inertia since the machine is coupled with relatively large inertia [3]. C. Rotor Power and DC-Link Voltage In the proposed system, the isolated inverter is connected to the rotor windings as shown in Fig. 6, where Pr is the power supplied from the inverter to the rotor side, Ploss,inv is the power consumed in the inverter, and Vdc and Idc denote the voltage and

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current of the dc-link capacitor. The dc-link voltage needs to be controlled to the desired level for the system stability. Since the dc link is electrically isolated from any external power source, its voltage level depends on the rotor power and the power needed in the inverter, including control board drive power and switching losses. As a result, the relationship between the power flow and dc-link voltage is as follows: dVdc (20) dt where Cdc is the capacitance of dc link. From (20), the dc link keeps a fixed voltage level, where the rotor power as much as the losses in the inverter is supplied from the rotor side. In SSTWRM, the rotor power is determined by the rotor voltages and currents 3 s s Vdr Idr + Vqsr Iqsr . (21) Pr = 2 As in the torque, there are three types of the rotor power 3 Pr,avg = Vdr c Idr c + Vdr s Idr s 4 (22) + Vq r c Iq r c + Vq r s Iq r s − Pr − Ploss,inv = Vdc Idc = Vdc Cdc

Pr,ripple,c =

Pr,ripple,s =

3 Vdr c Idr c − Vdr s Idr s 4 + Vq r c Iq r c − Vq r s Iq r s

(23)

3 Vdr c Idr s + Vdr s Idr c 4 + Vq r c Iq r s + Vq r s Iq r c

(24)

where Pr,avg denotes the average rotor power and Pr,ripple,c and Pr,ripple,s are the cosine and sine components of the ripple power oscillating at twice the grid frequency. Although the ripple power causes the voltage ripple in the dc link, the energy of the rotor-side inverter is balanced if the required average rotor power is supplied. From the d–q rotor voltage equations in (4) and (5), the average rotor power can be rewritten in terms of the rotor currents and stator fluxes

3 Rs L2m 2 2 Idr c + Idr Rr + Pr,avg ≈ s 2 4 Ls Rs Lm Egrid Idr c + Rr Iq2r c + Iq2r s − 2 Ls ωg L2m ωr Egrid + Iq r c Idr c − Ls Lm ωg 2 Lm ωr Lm + Idr s Iq r s − Egrid . Ls Ls

(25)

Under the unity power factor condition in (13), the aforementioned equation is simplified as follows: 2 Lm ωr 3 Lm Iq r s − Egrid Pr,avg = Pr,cl + Idr s (26) 4 Ls Ls where the current squared terms in (25) are related to the copper loss and classified as Pr,cl in this paper. Except for Pr,cl , other

Fig. 7.

Operating areas in the proposed system.

terms in (26) are proportional to Idr s . Thus, the proposed system controls the dc-link voltage by adjusting Idr s . D. Operating Areas When the proposed drive system controls the grid power factor, torque, and dc-link voltage, the operating areas are restricted due to the rotor current limit concerning the thermal issue. The rated rotor current condition is as follows: 2 2 2 2 Idr c + Idr s + Iq r c + Iq r s 2 ≤ Ir,rated (27) RM S 2 where Ir,rated RM S denotes the root-mean-square (RMS) value of the rated rotor current. Considering the current limit, the possible operating areas of the system are drawn in Fig. 7. In the figure, the solid lines show the torque capability of the proposed system according to the normalized speed ωN . The area between the solid lines represents the operating areas in motoring and generating modes. Differently with the conventional SPIM, which has no auxiliary winding, the machine can generate the starting torque by controlling the q-axis rotor current. Also, the area between the dashed lines is the operating region where the power factor of the grid is larger than 0.95. In the low-speed range, the torque capability is significantly reduced under the above power factor condition. In (16), the term in the first parenthesis (Lm Idr c − λdsc ) becomes zero and the term in the second parenthesis (Lm Idr s − λdss ) is also very small due to low average rotor power at low speed. Though, the operating areas can be extended by a capacitor in parallel with the stator winding. As the reactive power flows through the capacitor, the grid power factor is improved without the d-axis current regulation. The required capacitance for unity power factor is determined as follows:

CPF =

3 λdsc − Lm Idr c 3 Egrid − Lm ωg Idr c ≈ . 2 Ls Egrid ωg 2 Ls Egrid ωg2

(28)

For the comparison with the conventional system, the torque capability curves of the vector-controlled three-phase squirrelcage induction machine (SCIM) and SEF-SDFWM are presented with that of the proposed system in Fig. 8. Here, the machine parameters and the grid conditions in Table I are applied to the three cases. In the case of the SCIM, the dc-link


Fig. 8. Torque capability curves of vector-controlled three-phase squirrelcage induction machine (green), SEF-SDFWM (red), and the proposed system (blue).

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Fig. 9. The values of rotor currents Id r s , Iq r c , and Iq r s and the corresponding average copper loss at the synchronous speed where the torque is 2 N·m and the average rotor power is zero. (a) Id r c is zero. (b) Id r c is equal to Id r c , P F .

A. Condition of MCL TABLE I MACHINE PARAMETERS AND GRID CONDITIONS Rated power

1 kW

Rated speed

1720 r/min

Stator resistance (R s ) Rotor resistance (R r ) Stator inductance (L s ) Rotor inductance (L r ) Mutual inductance (L m )

0.6 Ω 0.7 Ω 54 mH 56 mH 49 mH

Rated torque Rated current Number of Poles Grid voltage Grid frequency

5.5 N·m 9 Arms 4 110 Vrms 60 Hz

voltage of the inverter applied to the stator side is fixed to the magnitude of the single-phase grid. In Fig. 8, the blue, green, and red lines are the torque capability curves of the SSTWRM, SCIM, and SEF-SDFWM systems, respectively. The proposed system has lower capability than the SCIM system in the lowspeed range because of the absence of the q-axis winding. On the other hand, the proposed system has higher capability in the high-speed range where |ωN | > 1 since the system can boost the dc-link voltage by the rotor-side inverter. Considering that the back electromotive force becomes increasingly dominant as the rotating speed rises, the proposed system is more suitable to generate the torque in the high-speed range due to higher dc-link voltage. Also, the drive system of the SCIM requires the additional switches between the grid and the dc link of the stator side inverter for the bidirectional operation. Furthermore, the proposed system has wider operating areas in overall range compared to the SEF-SDFWM. The reason is that the d-axis stator voltage in the SEF-SDFWM is reduced to two-thirds of the grid voltage due to the connection method between the stator windings and grid while the d-axis voltage in the proposed system is equal to the grid voltage. Therefore, the effective flux for generating the torque is higher in the proposed system. IV. VECTOR CONTROL METHODS FOR MCL In order to improve the energy efficiency, the vector control method for the MCL is proposed. Although the losses in the machine are mainly composed of the iron loss and copper loss, this paper focuses on only the copper loss as in [1] since the iron loss is difficult to set an accurate loss model.

Since there are four rotor current variables and three control conditions, one variable can be used to minimize the copper loss while the grid power factor, torque, and dc-link voltage are simultaneously controlled. The black, blue, and green lines in Fig. 9 show the values of rotor currents Idr s , Iq r c , and Iq r s and the corresponding average copper loss in the stator and rotor coils Pcl,avg at the synchronous speed where kPF means the ratio of Idr c to Idr c,PF , the torque is fixed to 2 N·m, and the average rotor power is zero for the dc-link voltage regulation. As mentioned in Section III-C, the losses in the inverter can cause the variation at the dc-link voltage but they are small enough to be ignored. Hence, the effect of Ploss,inv in (20) is not considered in the dc-link voltage regulation. As shown in Fig. 9, there are many solutions of rotor currents satisfying a certain operating condition. The black dashed line shows the rotor currents where the total copper loss is the maximum under the rated current condition. Also, the red dashed line represents the currents where the copper loss is the minimum. In Fig. 9(a) and (b), where Idr c is set to zero and Idr c,PF , respectively, variations of Idr s are quite small while the magnitudes of Iq r c and Iq r s are changed from 0 A to around 10 A. Therefore, the MCL condition mainly depends on the q-axis rotor current variables Iq r c and Iq r s . The average of total copper loss Pcl,avg in Fig. 9 is calculated 2 Egrid 3 3L2m 2 Pcl,avg ≈ Rs − Idr c + Idr s 4 2L2s Lm ωg 2 2 2 2 + Rr Idr + I + I + I . (29) c dr s qrc qrs In (29), the stator current of (10) is substituted, and the stator flux is approximated into (9). The average copper loss has the minimum value where its derivative is zero 2 3Lm dIdr s dIq r s 3 dPcl,avg = R + R Idr s s r 2 dIq r c 2 2Ls dIq r s dIq r c dIq r s + Rr Iq r c + Rr Iq r s = 0. (30) dIq r c In (30), the derivative of Idr c becomes zero since the variable is independently controlled for the power factor regulation.

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Fig. 11.

Block diagram of the proposed speed controller.

Fig. 10. Constant average torque curves of the proposed system in q-axis rotor currents plane.

Also, the derivative of Idr s is relatively small in all operating ranges. dIdr s Rs ωr (Egrid − Lm ωg Idr c ) = (31) dIq r s Ls ω 2 (Lm ωr Iq r s − Egrid ) 1. g Thus, the variation of Idr s is negligible and the stator current, which is a function of the d-axis rotor current, also barely changes. As a result, the MCL condition in (30) is simplified as in (31). From (31), it is deduced that the loss is minimized when the amplitude of the q-axis rotor current is the minimum Iq r c

dIq r c 1 d + Iq r s = (I 2 + Iq2r s ) = 0. dIq r c 2 dIq r c q r c

(32)

3P Lm 1 + Rq2 8 Ls

|Iq r c (Lm Idr c − λdsc )| .

The reference of the q-axis rotor current is determined by the average torque equation of (16) for the average torque control. Also, the condition of (32) is additionally considered for minimizing the loss. In Fig. 10, the blue lines are constant average torque curves in the q-axis rotor currents plane, where the average rotor power is zero and the rotating speed is equal to the grid frequency. According to the condition of (32), the MCL operation is achieved at the closest point to the origin of the current plane. The MCL points according to various values of kPF are marked as the red points. The q-axis rotor current variables Iq r c and Iq r s vary with kPF since their relationship at the MCL point depends on the d-axis rotor current as follows: Rq (Idr c , Idr s ) =

Iq r s Lm Idr s − λdss = Iq r c Lm Idr c − λdsc

(33)

where Rq is the ratio of Iq r s to Iq r c . With the MCL condition in (33), the optimal q-axis rotor currents are determined by Cq Te,avg , 1 + Rq2

Iq r s =

Rq Cq Te,avg 1 + Rq2

(34)

where the constant Cq is defined as follows: Cq =

Under this condition, the amplitude of the ripple torque of (19) is the same as the magnitude of the average torque Te,ripple,am p = |Te,avg | =

B. Torque Control

Iq r c =

Fig. 12. Zero average rotor power curves of the proposed system in d-axis rotor currents plane: (a) at the rated rotating speed; and (b) at various speeds.

8Ls . 3P Lm (Lm Idr c − λdsc )

(35)

(36)

That means that the peak-to-peak ripple torque is twice of the average torque and the resultant torque oscillates between zero and the peak torque point. Fig. 11 shows the block diagram of the proposed speed controller where the superscript “∗ ” means the reference value. A proportional–integral (PI) controller is applied to minimize the difference between the measured speed, and its reference by adjusting the torque. Here, a notch filter, where the stop frequency is twice the grid frequency, is applied to eliminate the ripple component. The references of the q-axis rotor currents are obtained from (34). Then, they are limited by the rated rotor current considering the d-axis rotor current for the power factor and dc-link voltage control as the energy balance in the rotor side is prior to the torque control. C. DC-Link Voltage Control As mentioned earlier, the dc link in the rotor-side inverter maintains the desired voltage level where the average rotor power is zero, with an assumption that the inverter losses are negligible. The blue lines of Fig. 12 show the trajectories of zero average rotor power on the d-axis rotor currents plane at various operating conditions. In Fig. 12(a), the upper side of the curve is negative average rotor power region where the dc-link voltage increases. On the other hand, the lower side is positive average


Fig. 13.

Block diagram of the proposed dc-link voltage controller.

rotor power region where the voltage level decreases. When the rotating speed varies, the rotor power curve moves up and down as shown in Fig. 12(b). There are disconnected lines because the machine cannot operate at the given operating conditions as described in Fig. 7. The average rotor power mainly depends on Idr s as in (26) and such relationship is also shown in Fig. 12(b). Hence, the dc-link voltage can be controlled by Idr s while Idr c is used for the power factor control. Fig. 13 shows the block diagram of the dc-link voltage controller. The dc-link voltage is regulated with a PI controller. The input of the controller is the error between the measured dc-link voltage and its reference, and the output is the reference of the dc-link current. Their relationship in s-domain is as follows: kidc ∗ ∗ = sCdc Vdc = (Vdc − Vdc ) kpdc + Idc (37) s

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of Idr s is set to satisfy the required average rotor power. In addition, the speed controller generates the references of Iq r s and Iq r c considering the MCL condition. Then, the references of the d-q rotor currents oscillating at the grid frequency in SRF are obtained from the references of their cosine and sine components as shown in Fig. 15. To control the oscillating currents, proportional–resonant (PR) controller is used. By the PR controller, the differences between the measured rotor currents and the references are converted to the rotor voltage references by the following equation in s-domain: s∗ s s∗ s Vdq r = Idq r − Idq r kpdq cc + kr dq cc 2 s + 2ζr ωg s + ωg2 + Vf f

(41)

where kpdq cc and kr dq cc are the d-q proportional and resonant gains of the controller and Vf f is the feed-forward voltage. To assign the gains, the d-q rotor voltage equations in (4) and (5) are used. Considering the unbalanced impedances, the gains of the d–q current controllers are set as in [27] for the controller to be a first-order low-pass filter by pole–zero cancellation L2 kpd cc = σLr ωcc , kr d cc = Rr + Rs m2 ωcc (42) Ls kpq

cc

= Lr ωcc ,

kr q

cc

= Rr ωcc

(43)

where kpdc and kidc denote the proportional and integral gains of the PI controller, respectively. The relationship between the measured voltage and its reference is as follows:

where ωcc is the bandwidth of the current controller. The rotor voltage references in SRF are converted into the values in rotor reference frame and then applied to the inverter.

Vdc kpdc s + kidc . ∗ = C s2 + k Vdc dc pdc s + kidc

V. EXPERIMENT RESULTS

(38)

The transfer function can be approximated as a second-order low-pass filter and its natural frequency ωn , and the damping ratio ζ of the filter is determined by the required control performance. The gains of PI controller are designed as follows: kpdc = 2Cdc ζωn ,

kidc = Cdc ωn2 .

(39)

From the dc-link current reference generated by the PI controller and measured dc-link voltage, the reference of the average rotor power Pr∗ is calculated, where the notch filter with the stopband of twice the grid frequency is applied as in the speed controller. In (25), the terms unrelated to Idr s are separated by the feed-forward control and subtracted from the average rotor ∗ can be approximated as follows: power reference. Thus, Pr,p 3 Lm ∗ Egrid − Lm ωr Iq r s Idr s = Kdc Idr s (40) Pr,p ≈− 4 Ls where Kdc is the rotor power constant. And the reference of Idr s is limited by the rated rotor current considering Idr c for the power factor control. D. Proposed Vector Control System and Current Control To sum up, the entire block diagram of the proposed control system is shown in Fig. 14. To regulate the power factor of the grid, the reactive stator power is controlled by Idr c . As the dclink voltage depends on the average rotor power, the reference

The experiments are executed with a 1-kW wound rotor induction machine. The a-phase stator winding is directly fed by the single-phase grid, while three-phase rotor windings are connected to a three-phase inverter through slip rings. The photograph of the experiment setup is shown in Fig. 16. A 4.4-kW servomotor is coupled with the SSTWRM as a load machine. Parameters of SSTWRM and the single-phase grid conditions are listed in Table I. Fig. 17 shows the transient responses when the single-phase grid voltage is applied to the machine and the rotating speed is regulated to 1720 r/min. In Fig. 17(a)–(c), the measured results (blue) are compared to the simulated results (red) with the proposed SSTWRM model. The measured and the simulated results closely correspond despite parameter variations in experiments due to magnetic saturation, iron loss, and thermal variation. Thus, the feasibility of the proposed model in Fig. 4 is validated. Fig. 18 shows the control performance of the speed and dclink voltage in step variations of load torque. As shown in Fig. 18(a), the rotating speed and dc-link voltage were controlled to their reference values, 1200 r/min and 300 V. The reference of the average torque for the speed control was larger than the load torque due to the rotational inertia and friction. Fig. 19 shows the performance of dc-link voltage control at rated speed. The reference of the dc-link voltage was changed from 250 V via 300 V to 250 V. When the reference was increased, the reference of Idr s was also increased to the rated

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Fig. 14.

Block diagram of the proposed control system.

Fig. 15.

Block diagram of the proposed current controller.

Fig. 16.

Experiment setup.

rotor current and those of q-axis rotor currents were reduced to zero since the dc-link voltage control is prior to the speed control. As a result, the average rotor power became negative and the dc-link voltage rose to 300 V. Once the dc-link voltage was regulated to its reference, the current references were returned to initial states for the average rotor power and speed control. Also, when the dc-link voltage reference was decreased from 300 to 250 V, the reference of Idr s became negative for the positive rotor power. As shown in Fig. 20, the torque, dc-link voltage, and grid power factor were simultaneously controlled at 1800 r/min with MCL. Fig. 20(c) shows the references of the four rotor current variables. To demonstrate the proposed control system that adjusts the q-axis rotor currents by (34) for the MCL operation, the reference of Idr c was increased in a ramp up to Idr c,PF . As shown in Fig. 20(d), the operating point moved as expected in Fig. 10 and the value of Iq r c became nearly zero at C where unity power factor was achieved. Fig. 21 shows the automatic tracking capability of MCL operating points. The value of Iq r c was manually adjusted, while

Fig. 17. Comparison of transient responses in the SSTWRM system between the measured and simulation results. (a) Stator currents. (b) D-axis rotor currents. (c) Q-axis rotor currents.

Fig. 18. MCL control performance of the speed and dc-link voltage in step variations of load torque. (a) DC-link voltage and rotating speed. (b) Load torque and average torque.


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Fig. 19. DC-link voltage control performance at 1800 r/min, where the reference of the dc-link voltage is changed from 250 V via 300 V to 250 V. (a) DC-link voltage and its reference. (b) References of the rotor currents.

Fig. 21. Rotor current references, MCL criterion values, and current magnitudes at 900 r/min in (a) and 1800 r/min in (b).

rotor currents were minimized. Compared to the worst case, the average of total copper loss decreased by 48.2% at 900 r/min and by 15.6% at 1800 r/min. VI. CONCLUSION

Fig. 20. Control performances of the torque, dc-link voltage, and grid power factor at 1800 r/min. (a) Rotating speed, dc-link voltage, and average torque. (b) Grid voltage and current. (c) References of the rotor currents. (d) References of the q-axis rotor currents.

the average torque and dc-link voltage were controlled to 1 N·m and 300 V. As aforementioned, variations of the d-axis rotor and stator currents were much smaller than that of the q-axis rotor current. In Fig. 21(a) and (b), the MCL operating points were tracked at 900 and 1800 r/min, respectively, and the stator and

This paper proposes a new kind of wound rotor machine for the single-phase grid system. It has the single-phase stator and three-phase rotor windings. Neither an auxiliary winding nor a phase-leading capacitor is required to generate a rotating magnetic field from the single-phase source unlike the conventional single-phase induction machines (SPIMs). For the adjustable speed drive, an electrically isolated three-phase inverter is applied to the rotor windings and the stator winding is directly connected to the single-phase grid. In this paper, the machine is modeled into the modified d-q equivalent circuit where the q-axis stator circuit is removed. With the d-q model, operation principles and operating areas of the proposed system are analyzed. The system has wider operating areas compared to the conventional vector-controlled SCIM due to the boosted dc-link voltage and the SEF-SDFWM thanks to the increased effective flux. In order to improve the efficiency, the condition of the MCL is found and the optimal set of the rotor currents is mathematically obtained. Also, the vector control methods of the grid power factor, dc-link voltage, and torque are proposed. Finally, from the experiments, the modified d-q model and operations of the proposed machine, and its control methods have been validated.

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Kahyun Lee (S’13) was born in Seoul, Korea, in 1990. She received the B.S. degree in electrical engineering in 2013 from Seoul National University, Seoul, where she is currently working toward the Ph.D. degree. Her current research interests include highefficiency control of electric machines, renewable energy system, and power conversion circuits. Ms. Lee is a recipient of the Global Ph.D. Fellowship from the Korean Government.

Yongsu Han (S’12) was born in Korea in 1988. He received the B.S. degree in electrical engineering in 2011 from Seoul National University, Seoul, Korea, where he is currently working toward the Ph.D. degree. His current research interests include electric machine drives and renewable energy conversion system.

Jung-Ik Ha (S’97–M’01–SM’12) was born in Korea in 1971. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1995, 1997, and 2001, respectively. From 2001 to 2002, he was a Researcher in Yaskawa Electric Co., Japan. From 2003 to 2008, he was with Samsung Electronics Co., Korea, as a Senior and Principal Engineer. From 2009 to 2010, he was the Chief Technology Officer at LS Mechapion Co., Korea. Since 2010, he has been with the Department of Electrical and Computer Engineering, Seoul National University, where he is currently an Associate Professor. His current research interests include circuits and control in high efficiency and integrated electric energy conversions for various industrial fields.