PPM-Based Development-and-Control Strategy of Fault Tolerant Inverter-Fed Multiphase Electromechanical AC Systems

Transcription

1 PPM-Based Development-and-Control Strategy of Fault Tolerant Inverter-Fed Multiphase Electromechanical AC Systems A.V. Brazhnikov*, E.S. Brazhnikova*, and I.R. Belozerov* * Siberian Federal University, multypha@mail.ru, P.O. Box 16142, Krasnoyarsk, , (Russia) Abstract--New principles of design and control strategy for creation of fault tolerant inverter-fed electromechanical systems (such as inverter-fed AC motor drives, molten metals electromagnetic stirring systems, etc.) have worked out by the authors of this paper. This strategy is based on the use of the phase-pole method (PPM) of control of an inverter and electromechanical energy transformer (EMET; for example, an induction motor). The application of worked out principles allows to develop the above mentioned type electromechanical systems having high reliability (strictly speaking, post-fault vitality) and less EMET mass-andoverall dimensions than existing ones. Index Terms--AC systems, fault tolerance, reliability, variable speed drives. I. INTRODUCTION At present ensuring of post-fault vitality (i.e. fault tolerance) for the inverter-fed electromechanical systems (such as inverter-fed AC motor drives, molten metals electromagnetic stirring systems, etc.) is the most important and prospective line in the field of these systems reliability rise [10, 12]. New principles of development and post-fault control strategy for the above mentioned type electromechanical systems have worked out by the authors of this paper. This strategy is based on the use of the phase-pole method of these systems control in abnormal (i.e. postfault) situations and has some advantage over existing analogous strategies. II. KEY ELEMENTS OF PPM-BASED DEVELOPMENT-AND- CONTROL STRATEGY OF FAULT TOLERANT MULTIPHASE INVERTER-FED ELECTROMECHANICAL AC SYSTEMS A. The use of phase-pole control method The increase of the phase number m more than four allows not only to improve a number of technical-andeconomic characteristics of the inverter-fed linear and non-linear induction motors [16], but also to open the way for the design of the electrical drives having radically new properties and possibilities. It is conditioned by the possibility for the use of some nontraditional motor control methods in the induction drive system which appears when m 5 [11]. These nontraditional control methods cannot in principle be used This work was supported in part by the Ministry of Education and Science of the Russian Federation under Grant П232. when the inverter-fed linear motor phase number is equal to three or four. The greater control potentials of the multiphase inverter-fed induction drives are explained by the following. If m is equal to three or four, the drive system has two variables of operating influence on the electromagnetic processes occurring in the system the phase voltage magnitude, and its frequency. In the case, when m>4, one more variable of operating influence may be added to the above mentioned ones the magnitude of the phase shift (i.e. electrical angle) between the nearest (in time) phase voltages of a multiphase inverter. The change of this shift can be obtained by mere corresponding application of the corresponding software, namely, by the corresponding change in the inverter transistors control algorithm (i.e. by the change of the moment in which the corresponding transistors are switched on and switched off) without application of any additional electronic or mechanical switchers, or some complicated motor winding sets. The possibility of above mentioned phase shift change results in the extension of the set of the motor control methods by adding to this set a number of non-traditional ones which may be used in the multiphase drive systems. In particular, the phase-pole control method (PPM) is one of the above-mentioned non-traditional ones. It was developed by the authors of this paper for the use in the field of both linear and non-linear inverter-fed multiphase (i.e. having the phase number m 5) induction motor drives. The use of phase-pole control method described in [7, 13-16, 18, 20, 21] is the main key element of the worked out by the authors of this paper development-and-control strategy of fault tolerant inverter-fed electromechanical AC systems. The essence of the control according to PPM is that in this case the electrical angles α between the voltages (or currents) of the nearest phases of inverter are increased by a factor of H (in comparison with any traditional control method) without any change of the inverter voltage (or current) amplitude and frequency, i.e. in this case α H =H α T, where H is some whole number, α T is the value α when some traditional control method is used, α T =2π/m, m is the phase number of an inverter-fed electromechanical AC system, and α H is the value α when PPM is used. The essence of PPM can be clearly illustrated by the vector diagrams of inverter phase voltages for the case of 1

2 normal (i.e. without-fault) operation conditions of a 6- phase inverter-fed electromechanical AC system (see Fig. 1). U 6 U 1 T U 2 U 5 U3 U 1, U 4 H U 3,U 6 U 2, U 5 p m p m const, (2) e e where m is real value of the phase number of the inverter multiphase AC electromechanical system (m 3; minimal value of m is m m = 3), m e is equivalent (observed) value of the electromechanical system phase number, p is real value of the number of the EMET poles pairs, and p e is equivalent (observed) value of the number of the EMET poles pairs (p e = p H). The values of parameter p e for m [6; 30], which can be achieved when PPM is used, are given in Table I for the case when p =1. U 4 (a) (b) TABLE I. VALUES OF THE PARAMETER FOR GIVEN VALUES m AND p 1 p e Fig phase system of the inverter output voltages: (a) H=1, (b) H=2. H is the major parameter of PPM that characterizes the type of this control method (the value H =1 corresponds to any traditional control method, and the value H >1 corresponds to PPM; when PPM is used, minimal value of H m =2). The range of the parameter H (including its maximal value), which can be achieved in the given electromechanical AC system, depends on the phase number of the system and on a motor stator winding type. The change of the parameter H results in the change of the filtering properties of the inverter multiphase AC electromechanical system. In particular, the numbers of the harmonics, which take part in the creation of the magnetic field in the air gap of the corresponding type electromagnetic energy transformer (EMET), are described by the following equation: n H c b m, (1) p where c is the number of the phase voltage (or current) harmonic (i.e. the number of the time harmonic), n are the numbers of the harmonics of the functions which describe a space distribution of the mutual inductances between motor phase windings (i.e. the numbers of the space harmonic), p is the number of the EMET poles pairs, and the coefficient b 0, (1, 2,3,...). In the case, when the inverter-fed electromechanical AC system is an electric drive, EMET is an electric motor; in the case, when it is a molten metals electromagnetic stirring systems, EMET is a stator, etc. The magnetic fields created in a motor air gap by the harmonics, numbers of which does not satisfy equation (1), cancel each other. During PPM application process, when the parameter H changes, the filtering properties of the electromechanical AC system changes, and the effect adequate to the synchronous change of EMET phase number and number of EMET poles appears PPM being used, the following equation is fulfilled: m p e When PPM is used, the maximal torque M m of EMET are described by the formula M m. H H M m. T, (3) where M m.t is the maximal value of EMET torque when the traditional control method is used (i.e. when H =1), M m.h is the same parameter when PPM is used (i.e. when H >1). Thus in the case when PPM is used the considerable increase of the maximal and starting torques of EMET can be provided. This effect may be obtained in all the range of EMET magnetic field speed regulation, but in this case the frequency and amplitude of inverter output voltage must be increased by a factor the value of which depends on the parameter H value. Because of this the transition from the traditional control method (when H =1) to PPM (when H > 1) in an abnormal situation (after stator winding open-circuiting or shorting) allows to keep the required value of EMET torque. B. The increase of inverter and EMET phase numbers It is profitable to use PPM (in a complex with the increase of inverter voltage frequency by a factor of H) for the development of the multiphase inverter-fed electromechanical AC system having: 2

3 the greater time of operating to total failure than the analogous 3-phase systems; the less EMET mass-and-overall dimensions than the EMET of the fault-tolerant multiphase (i.e. having m>4) inverter-fed electromechanical AC systems that PPM is not used in. The necessity of the PPM use causes some requirements to the inverter and EMET designs. In particular, they must have the phase number m (m m H m =6), where m m is the minimal value of m required for obtaining possibility of the PPM use, m m =3, H m is the minimal value of H required for obtaining possibility of the PPM use, H m =2. Nowadays a number of research and design works are devoted to development of 3- and multiphase fault tolerant electromechanical AC systems [1, 2, 4-10]. Taken alone, the increase of the phase number more than five (without any changes in the system of inverter phase voltages) does not ensure any essential increase of the inverter-fed AC electromechanical system reliability (contrary to some erroneous contentions [3]). The increase of the system phase number more than five allows to increase the inverter-fed AC electromechanical system reliability only in the two following cases (i.e. when the following development and post-fault control strategies are used): Strategy 1. If in post-fault situations the output power of a multiphase (i.e. having m>4) inverter per phase can be increased by the factor N P (without the application of PPM in post-fault situations) by the corresponding increase in phase voltages and currents, where N P m/m N =m/(m m F ), m N is the number of the intact phases of an inverter (or an EMET), m N =m m F, m F is the number of the damaged phases of an inverter (or an EMET). Every concrete drive system in every concrete situation (i.e. at the concrete EMET load) can operate only till the moment that some maximal number m F.max of phases will be damaged to. The increase of the time of the AC electromechanical system operating to failure may be determined by the coefficient K T.O : KT. O TO ( m, mf.max ) TO. 3 m mn NP 1 3 3, m N (4) P where T O (m, m F.max ) is the time of the m-phase inverterfed AC electromechanical system operating till the moment that m F.max phases will be damaged to, T O.3 is the time of the 3-phase drive system operating to total failure. Below such development and post-fault control strategy is termed The base development and post-fault control strategy (BPFS). It is necessary to use the inverter and EMET windings wires, EMET magnetic circuits, and inverter power gate elements (for example, transistors), which are designed with a reserve of the corresponding voltages, currents and magnetic induction magnitudes, for obtaining this strategy application possibility in the given inverter-fed AC electromechanical system [10]. It is obviously that the application of this strategy is accompanied by the increase of mass-and-overall dimensions and manufacturing cost of the inverter-fed AC electromechanical systems. This increase degree is approximately described by the coefficient N P. Because of this the use of the first strategy is profitable only if m F m/2, i.e. if N P 2. If m F >m/2, the cold redundancy (i.e. the use of reserve motor, for example) is more profitable than the application of BPFS. Strategy 2. If the PPM-based strategy of development of the fault-tolerant inverter-fed AC electromechanical system is used for the increase of time to total failure (i.e. for the increase of reliability) of the system. One of the key elements of this strategy is the use of peculiar inverter control algorithms for the decrease of the motor torque (linear force) oscillation magnitude in abnormal (i.e. post-fault) situations [17]. If PPM-based strategy is used, the increase of the time of the AC electromechanical system operating to failure may be determined according to formula (4). Thus the increase of the system phase number more than five is necessary for ensuring the possibility of PPM application. C. The use of peculiar EMET designs Besides, the necessity of the PPM use causes the application of the peculiar versions of EMET designs [13, 15, 16, 19]. The design of multiphase induction motor of rotating type worked out according to one of the above mentioned version is shown in section in Fig. 2. This motor has toroidal-type stator winding set and E-shaped rotor enveloping the motor stator both on the outside and on the inside. The motor stator has two rows of slots: the first row is located on the inner surface of the stator core (the inner stator slots), and the second row is located on the outer surface of it (the outer stator slots). Every stator phase winding drops in radial direction in two slots in one inner slot and in one outer slot. Exterior view of the 24-phase induction motor stator, which is developing according to the drawing shown in Fig. 2, is shown in Fig. 3. D. The use of peculiar inverter control algorithms In the last-named element of the worked out by the authors of this paper PPM-based development-andcontrol strategy of fault tolerant inverter-fed electromechanical AC systems there is the use of some peculiar control algorithms for transistors of the inverter, which is a part of the above mentioned system, for obtaining required evenness of the AC motor rotor rotation in abnormal situations after stator winding opencircuiting or shorting. The synthesis of these control algorithms is achieved according to the corresponding method presented in [17]. According to this method the space trajectories of the resulting vector F of the switching functions of the inverter phases are chosen as the subjects of analysis and design action. This choice is explained by the following fact: the character of the motion (in time) of the vector F is analogous to the character of the AC motor torque. 3

4 According to the above mentioned method the basic data for the algorithm design is the set of the positions of the vector F for the given phase number m of an electromechanical AC system. The trajectory of the vector F that is close to the ideal trajectory is formed using this set. The type of the ideal trajectory depends on the aim of the algorithm design (minimization of the motor torque oscillations, change in the mechanical characteristics of a motor (if m > 5), etc.). For example, if the aim of the algorithm design is the minimization of the motor torque oscillation amplitudes, the ideal trajectory must have a form of a circle. The formation of the necessary trajectory begins at the choice of the positions of the vector F that have the space angles corresponding to the chosen ideal trajectory. Then it will be necessary to determine the deviation of the amplitudes of the chosen vectors F from the ideal trajectory. This deviation shows the value of the time change in the amplitude of the first harmonic of the inverter phase voltage. This change may be realized by the change of the input circuit voltage of an inverter or by the use of the corresponding pulse modulation of the inverter phase voltage with constant ratio of pulse period-to-pulse duration. Using this design method the set of the multiphase inverters control algorithms has been worked out for a great number of the m values [11]. Fig. 2. The section of multiphase induction motor of rotating type having E-type rotor, where 1 is the stator core (i.e. magnetic circuit), 2 is the rotor core (magnetic circuit), and 3 is a stator phase winding, and 4 is the motor case. Fig. 3. Exterior view of the 24-phase induction motor stator developing according to the drawing shown in Fig. 2. III. PERFORMANCE EVALUATION OF WORKED OUT STRATEGY The above mentioned BPFS was selected as a base version of the corresponding system creation strategy for performance evaluation of the worked out PPM-based development-and-control strategy of fault tolerant inverter-fed multiphase electromechanical AC systems. For performance evaluation of the PPM-based strategy of development of fault tolerant inverter-fed multiphase inverter-fed electromechanical AC systems, which is called PPM-based strategy below, the parameters K I 1/H 0.5 and K U H 0.5 were determined, where the parameter K I shows in what times the EMET phase currents may be increased when the PPM-based strategy is used in comparison with the case when BPFS is used, and the parameter K U shows in what times the EMET phase voltages must be increased when the PPM-based strategy is used in comparison with the case when BPFS is used. The parameters K I and K U were determined for the case when in abnormal (i.e. post-fault) situation the torque created by the EMET stator winding set, and speed of the EMET secondary element (i.e. AC motor rotor or molten metal) should be the same as well as they were in normal (i.e. non-fault) situation. The parameters K I and K U allows to evaluate approximately the change of mass-and-overall dimensions and manufacturing cost of the EMET and inverter when worked out PPM-based strategy is used in comparison with the case when BPFS is used: cost of the EMET may be decreased approximately by a factor of H 0.5 (but no more this value) in passing from BPFS to the PPM-based strategy; 4

5 cost of inverter must be increased approximately by a factor of H 0.5 (but no more this value) in passing from BPFS to the PPM-based strategy. Thus when passing from BPFS to the PPM-based strategy, gain in the EMET mass-and-overall dimensions and its manufacturing cost may be achieved by loss in the inverter corresponding technical-and-economic parameters. For example, if m=6 and BPFS is used, and the system must operate till the moment that m F.max =3 phases will be damaged to, the time T O (m, m F ) is 1.5 greater than the time T O.3 of the 3-phase drive system operating to total failure (i.e. K T.O =1.5). However in this case the mass-andoverall dimensions and manufacturing cost of the whole inverter-fed electromechanical AC system and each of its elements (in particular, motor and inverter) will rise approximately by a factor of N P =2 (in comparison with the 3-phase system). If to pass from BPFS to the PPMbased strategy with H=2, it is possible to decrease massand-overall dimensions and manufacturing cost of the EMET approximately by a factor of H 0.5 = (however in this case the mass-and-overall dimensions and manufacturing cost of the inverter will rise approximately by a factor of 1.4). Ultimately, the change in the mass-and-overall dimensions and manufacturing cost after the phase number increase and application of PPM-based strategy is as follows: cost of the EMET must be increased approximately by a factor of 1.4 (in comparison with the 3-phase system), cost of inverter must be increased approximately by a factor of 2.8 (in comparison with the 3-phase system). For a number of technical systems, in which the system reliability increase and the AC motor mass-andoverall dimensions decrease are very important (for example, oil deep-well pumps), the PPM-based strategy is more preferable than BPFS. In these cases the field of the PPM-based strategy profitable application may be extended up to m F (m H 0.5 )/2. IV. OPTIMAL SYSTEM PARAMETERS In a number of cases (for example, in the field of oil deep-well pumps) it is especially important to obtain at once the electromechanical AC system mass-and-overall dimensions decrease and ensuring of its fault tolerance. The application of PPM allows not only to increase the reliability (strictly speaking, obtaining fault tolerance) of the multiphase inverter-fed electromechanical AC system (in spite of the fact that the number of wires between the inverter and EMET is increased when the phase number m is extended), but also the application of PPM allows to decrease the system mass-and-overall dimensions (when the system is operated in normal (i.e. without-fault) conditions). It should be noted that this two challenges (i.e. the system fault tolerance increase and the decrease of its mass-and-overall dimensions for normal operation conditions) are mutually contradictory: when the system fault tolerance (owing to the use of PPM) increases, the possibility of the decrease (also owing to the use of PPM) of its mass-and-overall dimensions in normal operation conditions is reduced. It is obviously that this opposition of the solutions gives rise to necessity of the existence of some compromise decision. The optimal value H O of PPM parameter H for the given phase number m was found by the authors of this paper. When the equation H=H O is obtained, both the electromechanical AC system mass-and-overall dimensions decrease and its post-fault vitality increase are achieved [14, 16, 20]. The value H O is determined as follows: AH. O if AH. O AH. O 1.0 if AH. O 0.5; H O (5) 0.5; A H. O 2 K A K A 4 K A HM, (6) 2 where [A H.O ] is the integer part of the number A H.O, {A H.O } is the fractional part of the number A H.O, H M is the maximal value of parameter H for the given value of phase number m, H M =[B m ], [B m ] is the integer part of the number B m =m/3. The parameter K A shows, in how many times the decrease in mass-and-overall dimensions of the electromechanical AC system is more important than the increase of its post-fault vitality for the system developer (i.e. the parameter K A establishes the compromise between the above-mentioned mass-and overall dimensions decrease and the electromagnetic AC system post-fault vitality increase). The values of the parameter H O are given in Table II for H M [2; 10] and some set of the parameter K A values. K A TABLE II. VALUES OF THE PARAMETER H O For example, at the previous design stage the developer has chosen value of phase number m=30 (in this case H M =30/3=10). If he has taken an interest in both the EMET mass-and-overall dimensions minimization and its post-fault vitality enlargement to the same extent, he chooses the value K A =1.0. It follows from Table II that in this case the value of the parameter H O =3. H M 5

6 V. CONCLUSIONS The use of worked out PPM-based development-andcontrol strategy has advantages over existing ones (in particular, over BPFS). This strategy allows to develop the multiphase inverter-fed non-traditional controlled AC electromechanical fault tolerant systems having high reliability (strictly speaking, post-fault vitality) and less EMET mass-and-overall dimensions than existing ones (but in this case the inverter mass-and-overall dimensions are more rather than BPFS is used). For a number of technical systems, in which the system reliability increase and the EMET mass-andoverall dimensions decrease are very important (for example, oil deep-well pumps), the worked out PPMbased strategy is more preferable than BPFS. There is the following paradox in the field of the above mentioned systems. On the one hand, the number of wires between the inverter and EMET is increased when the phase number m is extended. It must cause the system reliability decrease. 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