International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering
MenuISSN ONLINE(2278-8875) PRINT (2320-3765)
ISSN ONLINE(2278-8875) PRINT (2320-3765)
K. Reddy Swathi1, P. Anjappa2 and V.Ramesh3
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This paper describes a combination of direct torque control (DTC) and space vector modulation (SVM) for an adjustable speed sensor less induction motor (IM) drive. In this paper we introduced a new strategy i.e., the induction motor drives fed by a four switch inverter emulate the operation of the conventional six switch operation. Therefore, a suitable combination of the four unbalanced voltage vectors intrinsically generated by the FSTPI, leading to the synthesis of the six balanced voltage vectors of the SSTPI. Simulation results have revealed that, the proposed DTC strategy with SVM modulation, FSTPI-fed IM drives exhibit interesting performance
Keywords |
| Direct torque control (DTC), Space vector modulation (SVM), SSTPI, FSTPI-fed IM drives. |
INTRODUCTION |
| Direct torque control (DTC) is a high-dynamic and high performance control technique for induction motor drives which has been developed in the last two decades as possible alternative to DC servo drives. In direct torque controlled adjustable speed drives, the motor flux and the electromagnetic torque are the reference quantities which are directly controlled by the applied inverter voltage vector.[1] The main advantages of DTC are: fast torque and flux responses, no need for speed or position sensors and no requirements for coordinate transformation. In fact, it only needs to know the stator resistance and terminal quantities (v and i) in order to perform the stator flux and torque estimations. Therefore, the DTC schemes have attracted many researchers to study and investigate for a long time. |
| DTC has also some disadvantages: the difficulty to control the torque and the flux at very low speed, the higher current and torque ripple which imply higher machine losses and noise, the inherent variable switching frequency and the lack of direct current control. Recently, an attempt to discard the previously described disadvantages has been proposed in where a DTC scheme using a 16-sector vector selection table has been implemented. Nevertheless, it has been noted that the drive. Performance remains relatively low due to the increase of the CPU time which is linked to the complexity of the involved vector selection table. In order to achieve a constant switching frequency and to decrease the torque ripple, many DTC schemes based on SVM, using the FSTPI as a VSI, dedicated to control induction and permanent-magnet synchronous motors have been reported in the literature.[2] These strategies offer high performance in terms of torque ripple reduction allied to the control of the inverter switching losses. However, these performances are compromised by the complexity of their implementation schemes. |
| This type of packaging can minimize the stray inductance and the size of the power devices. Yaskawa Company has implemented a commercial matrix converter and has shown it has many advantages[3]. For example, it requires small mounting place because the braking resistance or regeneration converter is unnecessary. It has less total current harmonic distortion and higher power factor at the input side when compared with the rectifier/dc link/ inverter. Moreover, it has longer life because no capacitor is used. The cost of matrix converters will be reduced and will compete with the traditional VSI. As a result, one can predict that the applications of matrix converters will become more and more popular in the near future. |
| The DTC using a multi-level inverter can produce more sets of space vectors to control torque and flux of a motor and gain smoother electromagnetic torque of the motor. However, the multi-level inverters need more power switch elements and cause more cost and complication to the whole system.By combining the advantages of matrix converters with the advantages of DTC schemes, it is possible to achieve fast torque and flux responses in a wide speed range. But the main drawback of the conventional DTC will make more serious electromagnetic torque ripple. As a result, the drive system fed by the matrix converter doesn’t need any additional power switch elements and can attain the same performance as the multi-level inverter.[5] According to the properties of a matrix converter, there are three different voltage vectors on each space vector location. By suitably selecting the space vector, the current deviations and the torque ripple of the motor can be effectively reduced. This paper proposes to select the most appropriate voltage vector with respect to the error of the torque[4]. The standard look-up table for direct torque control by matrix converters is improved in order to include the small, medium and large voltage vectors of Matrix Converters. With the new look-up table and new hysteresis comparator with seven levels output the system will differentiate between small, medium and large torque errors and consequently reduce the electromagnetic torque ripple and output current THD. Simulation results demonstrate the effectiveness of the proposed scheme. |
| This paper proposes a new DTC strategy dedicated to FSTPI fed IM drives. It is based on the emulation of the SSTPI operation thanks to the synthesis of an appropriate vector selection table, which is addressed by hysteresis controllers. The resulting simplicity of the implementation scheme makes the strategy very attractive in many applications, such as the automotive one. |
DTC OF FSTPI-FED IM DRIVES: BACKGROUND |
| A. DTC Basis: |
| DTC strategies allow a direct control of the motor variables through an appropriate selection of the inverter control signals, in order to fulfill the requirements as whether the stator flux and torque need to be increased, decreased, or maintained. These decisions are achieved according to the output cφ of the flux |
| hysteresis controller, the output cτ of the torque hysteresis controller, and the angular displacement θs of the stator flux vectorΦs in the Clarke (αβ) plane. The dynamic ofΦs is governed by the stator voltage equation expressed in the stationary reference frame, as follows |
| where Vs , Is , and rs are the stator voltage vector, current vector, and resistance, respectively. Neglecting the voltage drop rs Is across the stator resistance, and taking into account that the voltage vector is constant in each sampling period Ts, the variation of the stator flux vector turns to be proportional to the applied voltage vector[6]. Maintaining the stator flux constant, the variation of the electromagnetic torque Tem depends on the direction of the applied voltage vector, such that: |
| where Φsr is the rotor flux vector referred to the stator, δ is the angular shift between the stator and rotor fluxes, Np is the pole pair number, and ls , lr , and M are the stator self-inductance, the rotor self-inductance, and the mutual inductance, respectively. The implementation scheme of the DTC strategy dedicated to a FSTPI-fed IM, shown in Fig. 1, has the same layout as the one of the basic DTC strategy initially proposed in except that |
| 1 The SSTPI inverter is reconfigured to a FSTPI. Such are configuration is carried out by adding to the former three extra TRIACs with three fast acting fuses . |
| 2 The three-level hysteresis controller in the torque loop is substituted by a two-level hysteresis controller. As will be depicted in Section III, this substitution is motivated by the fact that no zero voltage vector is involved in the proposed DTC scheme |
B. Intrinsic Voltage Vectors of the FSTPI |
| The FSTPI topology consists of a two-leg inverter as illustrated in Fig. 1. Two among the three phases of the motor are connected to the FSTPI legs, while the third one is connected to the middle point of the dc-bus voltage[7]. Let us assume that the states of the four insulated-gate bipolar transistors (IGBTs) of the FSTPI are denoted by the binary variables S1 to S4 , where the binary “1” corresponds to an ON state and the binary “0” indicates an OFF state. The IM stator voltages are expressed in terms of the states (S1 and S2) of the upper IGBTs, as follows: |
| The Clarke transform applied to the stator voltages yields: |
| Four combinations of the states of the upper IGBTs are characterized by four active voltage vectors (V1 to V4) in the α β plane, which are given in Table I.Fig. 2 shows the four active voltage vectors represented in the αβ plane. These vectors have unbalanced amplitudes and are shifted by an angle of π2 Indeed, vectors V1 and V3 have |
| an amplitude of Vdc/√6, while vectors V2 and V4 have an amplitude of Vdc/√2. |
C. Limitations of the Basic DTC of a FSTPI-Fed IM |
| The basic DTC of an IM fed by the FSTPI is based on the subdivision of the αβ plane into four sectors [17], limited bythe four active voltage vectors as shown in Fig. 2. The vector selection table corresponding to the basic strategy is presented in Table II.Accounting for the symmetry of the four sectors, the following analysis of the torque and flux variations, will be limited tosector I, considering two cases:1) the initial stator flux vector Φs1 is held by vector V2 ;2) the initial stator flux vector Φs1 is held by vector V3 .Equation (1) could be rewritten as follows: |
| where Vi (1≤ i ≤4) is the voltage vector generated by theFSTPI.Fig. 3 shows different phasor diagrams of (5), considering both cases previously cited with four scenarios selected from the vector selection table, for each. One can notice the following remarks which deal with the torque dynamic. |
| 1 The application of voltage vectors V1 or V3 leads to allow torque dynamic if: |
| • Φs1 is close to vector V2 due to the low amplitude of V1 and V3 [see Fig. 3(a1) and (a3)]; |
| • b) Φs1 is close to vectorV3 due to the low angular shift of the flux vector [see Fig. 3(b1) and (b3)]. |
| It is to be noted that the torque command cτ of the control combinations (cφ = −1, cτ = +1) ïÃâ¬Ã corresponding to sector II and (cφ = +1, cτ = +1) corresponding to sector I could not be achieved by the application of vectors V1 and V3 , respectively. |
| 2 The application of voltage vectors V2 or V4 leads to a low torque dynamic if Φs1 is close to vector V2 due to the low angular shift of the flux vector [see Fig. 3(a2)and (a4)]. One can notice One can notice that the control combinations (cφ = +1, cτ = +1) corresponding to sector IV and(cφ = −1, cτ = +1) corresponding to sector I could notbe achieved with the application of voltage vectors V2and V4 , respectively. |
| 3 The application of voltage vectors V2 or V4 leads to ahigh torque dynamic ifΦs1 is located near vectorV3 [seeFig. 3(b2) and (b4)]. Concerning the flux dynamic, one can notice the following.1) High flux variations leading to overshoots or under shoots |
| 4 Outside the flux hysteresis band with :a) the application of voltage vectors V1 or V3 if Φs1is close to vector V3 [see Fig. 3(b1) and (b3)]; |
| • The application of voltage vectors V2 or V4 if Φs1is close to vector V2 [see Fig. 3(a2) and (a4)].2) The flux command cφ is not achieved with the applicationof:a) vector V1 in sector IV corresponding to the control combination (cφ = +1, cτ = −1) as illustrated inFig. 3(a1). |
| • Vector V2 in sector I corresponding to the control combination(cφ = +1, cτ = −1) as illustrated inFig. 3(b2). |
| • Vector V3 in sector I corresponding to the control combination (cφ = +1, cτ = +1) as illustrated inFig. 3(a3). |
| • Vector V4 in sector II corresponding to the control combination (cφ = +1, cτ = +1) as illustrated inFig. 3(b4).From the previous analysis, one can clearly notice that the basic DTC strategy |
| presents different limitations. These could be eradicated considering the introduced DTC strategy which will be developed in the following section. |
PROPOSED DTC STRATEGY |
| A. Approach to Generate Balanced Voltages by the FSTPI |
| The proposed DTC strategy is based on the emulation of SSTPI operation by the FSTPI. This has been achieved through the generation of six balanced voltage vectors using the four intrinsic ones of the FSTPI. The generated vectors have the same amplitude and angular shift as those of the SSTPI[8]. Basically, the active voltage vectors Vk, with 1 ≤ k ≤ 6,yielded by the SSTPI have an amplitude Vk equal to23Vdc,where Vdc is the dc-bus voltage. For the same value of Vdc, the voltage vectors Vi , with 1 ≤ i ≤ 4, generated by the FSTPI, present unbalanced amplitudes Vi , such that: |
| Therefore, a dual application of the voltage vector V1 (respectively,V3 ) of the FSTPI, leads to the generation of the voltage vector V11 (respectively, V33), as shown in Fig. 4. It is to be noted that V11 and V33 are identical to two vectors among the six generated by the SSTPI. Now, let us call Vij the voltage vectors resulting from the sums of successive voltage vectors Vi and Vj , with 1 ≤ i ≤ 4and 1 ≤ j ≤ 4. As far as the angular shift between two successive voltage vectors is equal to π2, the amplitude Vij of vectors Vij can be expressed as follows: |
| One can notice that the voltage vectors Vij have the same amplitude as the ones generated by the SSTPI. Beyond the amplitude, the four generated vectors, namedV12,V23,V34, andV41, as shown in Fig. 4, share the same phases with the four remaining active voltage vectors of the SSTPI. Table III summarizes the Clarke components of the six voltage vectors generated by the FSTPI considering the previously described approach. |
| Following the generation of six balanced active voltage vectors(V23, V33, V34, V41, V11, and V12), the αβ plane turns to be subdivided into six symmetric sectors as illustrated in Fig. 4. Moreover, zero voltage vectors can be achieved through the application of two opposite intrinsic ones. The previously described approach represents a great control benefit so far as several DTC strategies implemented in SSTPI fed IM drives could be applied to FSTPI-fed IM ones. |
B. Vector Selection Table of the Proposed DTC Strategy |
| The proposed DTC strategy is inspired from the earlier oneintroduced by Takahashi . For the sake of reduction of the switching frequency as well as the torque ripple, the control combinations (cφ = •}1, cτ = 0) are omitted using a twolevel hysteresis controller in the torque loop[9]. The synthesis of the vector selection table of the proposedDTC strategy is based on the approach described in the previous paragraph. Reaching this advanced step, one can wonder: how the control combinations (cφ = •}1, cτ = •}1) could be |
| Achieved applying the generated balanced voltage vectors? To answer this question, the following approach has been adopted. |
| 1 The application of V1 (respectively, V3 ) during two successive ampling periods 2Ts allows the generation ofV11 (respectively, V33), |
| 2 The application of two consecutive voltage vectors Vi and Vj during two successive sampling periods leads to the generation of Vij .As a result, the equivalent voltage vectors per sampling period s generated by the FSTPI, considering the adopted approach, can be expressed as: |
| where subscript H indicates the half of the corresponding voltage vector. In what follows, the synthesis of the vector selection table will be limited to sector I (−π6≤ θs ≤ π6). In this case and as shown in Fig. 5, the following voltage vectors are applied during a sampling period, according to the corresponding control combinations: |
| In order to emulate the operation of the SSTPI, each control combination (cφ , cτ ) should be maintained during two sampling periods 2Ts , which yields the application of: |
| An illustration of the previously described control scenarios is provided in Fig. 6. An extension of the synthesis to the remaining sectors has led to the vector selection table given in Table IV. The inputs (cφ , cτ , and θs ) of the vector selection table should be maintained during 2Ts which yields the implemented vector selection table provided in Table V. It is to be noted that both intrinsic and compounded voltage vectors are involved in sectors I, III, IV, and VI, while in sectors II and V, only the compounded voltage vectors are applied. Thus, one can expect an increase of the switching frequency in sectors II and V, with respect to the one in the remaining sectors. In this scheme, each node with message searches for possible path nodes to copy its message[10]. Hence, possible path nodes of a node are considered. Using NSS, each node having message selects its path nodes to provide a sufficient level of end-to-end latency while examining its transmission effort. Here, it derives the CSS measure to permit CR-Networks nodes to decide which licensed channels should be used. The aim of CSS is to maximize spectrum utilization with minimum interference to primary system. Assume that there are M licensed channels with different bandwidth values and y denotes the bandwidth of channel c. Each CR-Networks node is also assumed to periodically sense a set of M licensed channels. Mi denotes the set including Ids of licensed channels that are periodically sensed by node i. suppose that channel c is periodically sensed by node i in each slot and channel c is idle during the time interval x called channel idle duration. Here, it use the product of channel bandwidth y and the channel idle duration x, tc = xy, as a metric to examine the channel idleness. Furthermore, failures in the sensing of primary users are assumed to cause the collisions among the transmissions of primary users and CR-Networks nodes. |
SIMULATION REULTS |
CONCLUSION |
| This paper dealt with a new DTC strategy based SVM modulation controller dedicated to FSTPI fed IM drives. The proposed DTC strategy is based on the emulation of the operation of the conventional SSTPI. This approach has been adopted in the design of the vector selection table which is simply addressed by hysteresis controllers, considering a subdivision of the Clarke plane into six sectors. Simulation-based investigations of the IM steady-state features have revealed the high performance of the introduced DTC strategy with FSTPI as compared with the SSTPI. |
References |
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