A NEURAL NETWORK-BASED SVPWM CONTROLLER FOR A TWO-LEVEL VOLTAGE-FED INVERTER INDUCTION MOTOR DRIVE

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1 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: A NEUAL NETWOK-BASED SVPWM CONTOLLE FO A TWO-LEVEL VOLTAGE-FED INVETE INDUCTION MOTO DIVE AHMED A. HASSAN, SAMI DEGHEDIE, MOHAMED EL HABOUK,, Department of Electrical Engineering, Faculty of Engineering, Alexandria University ahmed_hassan6@hotmail.com, deghedie@gmail.com, eepgmme@yahoo.co.uk ABSTACT In this paper, a detailed description of a neural network-based implementation of the SVPWM algorithm for two-level voltage source inverters is proposed using a modular approach which facilitates the expansion of the scheme to higher levels SVM, each step in the SVPWM algorithm is achieved using a simple feedforward artificial neural network that consists of one or more layers. Simulation results are provided by employing the proposed scheme inside a closed loop V/Hz drive system. Keywords: Space Vector Modulation (SVM), Artificial Neural Networks (ANNs), Two-Level Inverter. INTODUCTION The main objective of inverters is to produce an AC output waveform from a DC power supply where the amplitude, phase, and frequency of the voltage should always be controllable which is a requirement for many applications such as adjustable speed drives (ASDs), uninterruptible power supplies (UPS), active filters, etc [] Modulation techniques are responsible for controlling the amount of time and the sequence used to switch the power switches on and off. The modulation techniques most used are the sinusoidal pulse-width modulation (SPWM), space-vector modulation (SVM) and the selective harmonic elimination pulse-width modulation (SHEPWM) []. The square-wave or six-step operation mode of the inverter is simple to implement and characterized by low switching losses because there are only six switching per cycle of the fundamental frequency. Unfortunately, the lower order harmonics will cause large distortions of the current wave unless filtered by a bulky low-pass filter [].. Inverter Topology and Space Vectors The two-level three-phase (VSI) is shown in figure. Valid switch states for the two-level threephase VSI are shown in table, States - 6 produce non-zero ac output voltages while states 0 & 7 produce zero ac line voltages. In this case, the ac line currents freewheel through either the upper or lower components []. The selection of the states in order to generate the given waveform is done by the modulating technique that should ensure the use of only the valid states []. A 0 denotes that the lower switch is conducting while a denotes that the upper switch is conducting in the respective leg V dc S D S D S 5 D 5 S 4 D 4 S 6 D 6 S D B A N C. FUNDAMENTALS OF SVM Space-vector pulse-width modulation has recently grown as a very popular PWM method for voltagefed converter AC drives []. SVM is based on the representation of the three phase quantities as vectors in a two-dimensional α-β plane [4].. Figure : Two Level Inverter Topology

2 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: Table : Valid Switch States for Two-Level Inverter State ON Switches Space Vector 0 S, S4, S6 V 0 (000) S, S, S6 V (00) S, S, S V (0) S, S, S4 V (00) 4 S, S4, S5 V 4 (0) 5 S4, S5, S6 V 5 (00) 6 S, S5, S6 V 6 (0) 7 S, S, S5 V 7 (). otating Space Vector and SVM Theory [] If the three-phase sinusoidal and balanced voltages with peak value V m are given by: V b = V sin θ (9) Where V a and V b are the components of V aligned in the directions of V & V respectively. V 4 eference Vector Trajectory V β Vb θ eference Vector Limit V α v a = V m cos(θ) () Va V v b = V m cos θ π () 4 6 v c = V m cos θ + π () V 5 5 V 6 The space vector in complex notation is given by: V = v a + v b e jπ + v c e jπ (4) Substituting equations (), () and () into equation (4) and simplifying, we get: V = V m e jθ = V m e jωt (5) Figure : eference Vector Trajectory and Space Vectors. ANN-BASED TWO-LEVEL SVM Figure shows the general block diagram for generating the gate pulses for two-level SVM. Each block is responsible for achieving certain task which is described in the following sections. This indicates that the vector V rotates in circular orbit with angular velocity ω, where the direction of rotation depends on the phase sequence of the voltages. The vector magnitude is given by: V = V m = v α + v β (6) θ Time Base Vector Sector LA Trig Sec Boundary Vectors Generator V a V b At any instant, the vector angle θ w.r.t the α-axis is given by θ = tan v β v α (7) If the reference vector V lies in sector as shown in figure, the PWM output is generated by resolving V using the adjacent vectors V & V on a part-time basis to satisfy the average output demand. V a = V sin π θ (8) V T s Switching Time Calculator Figure : Block Diagram of Two-Level SVM Generator. Time Base The purpose of the block diagram shown in figure 4 is to generate different timing signals as follows: The sampling frequency is integrated to produce a ramp function, when the ramp reaches its peak T a T b Gate Pulses Generator

3 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: value, the Trig signal is generated and the integrator is reset to indicate the start of a new sampling period. The sampling period Ts is generated from the sampling frequency. Where, Ts = F s (0) The ramp r directly generated from integrating Fs is multiplied by the sampling period Ts to generate the ramp function with amplitude equal to Ts (figure 5). T s times in sector for all the other sectors without the need to develop separate equations for each sector, figure 7 outlines this concept. Θ Boundary Angles Compare Local Angle Calculator Sec LA Figure 6 Block Diagram for Determining Sec & LA F s r V θ eset Trig Figure 4: Time Base Generation LA V T s Figure 5: amp Generation. Vector Sector The purpose of this block is to determine the location of the reference vector at the start of the sampling period. Figure 6 represents a simplified block diagram for implementing this function. r Figure 7 eference Vector Local Angle (LA) Table shows the relation between LA and θ in different sectors Table : elation Between θ, LA and Sec θ Sec LA 0 o < θ < 60 o LA = θ 60 o < θ < 0 o LA = θ - 60 o 0 o < θ < 80 o LA = θ - 0 o -80 o < θ < -0 o 4 LA = θ + 80 o -0 o < θ < -60 o 5 LA = θ + 0 o - 60 o < θ < 0 o 6 LA = θ + 60 o Figure 8 shows the ANN used to generate Sec & LA. Where, Θ eference vector angle, measured from α- axis Sec Sector number in which the reference vector Lies at the time of sampling LA eference vector Local Angle (measured from The beginning of the sector) The purpose of generating a local angle is to reflect the equations used to calculate the switching

4 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: θ w st Hidden Layer nd Hidden Layer N N N Figure 8: Vector Sector ANN used to determine eference Vector Sector Sec and Local Angle Inside Each Sector LA.. st Hidden layer: The purpose of this layer is to indicate (at the sampling instant) that the reference vector angle θ is greater than which of the angles that represent the beginning of each sector. Each neuron in the st layer will fire when the reference vector angle θ is greater than or equal to the starting angle of the respective sector. Table shows the firing conditions for neurons of the st layer, where, N x is the neuron number and O x is the output of the respective neuron, the superscript denotes the layer number (this convention is followed in all neural networks described throughout this paper). The weight, input and output matrices are defined as follows: w w w w W.0944 w w =.46 = w 4 w 4.46 w 5 w w 6 w w 7 w 7 P = θ o w 7 o 7 N 7 N N N N Sec Sec Sec LA=o Sec 4 Sec 5 Sec 6 hardlim(θ + 0) o hardlim(θ.047) o hardlim(θ.0944) o O = hardlim(θ.46) = o 4 hardlim(θ +.46) o 5 hardlim(θ ) o 6 hardlim( θ +.047) o 7 Where w ij denotes the weight connecting the i th neuron to the j th input Table : Firing Conditions for Neurons of the st Layer for the Vector Sector ANN N x O x = if N θ 0 N θ.047 N θ.0944 θ.46 θ.46 θ.0944 N 7 θ nd Hidden layer: This layer indicates that the reference vector angle θ is less than which of the angles that represent the end of each sector and to use this information along with the information presented from the st layer to determine the boundary angles of the sector in which the reference vector lies. The weight, input and output matrices are defined as follows: W = O O O O 5 O 6 O 7 P = O O O 4 O 6 O 7 O hardlim(o O ) hardlim(o O ) sec sed O hardlim(o = O 4 ) sec hardlim(o 5 O 6 ) = sec = Sec 4 hardlim(o 6 O 7 ) sec 5 hardlim(o 7 O sec ) 6 4

5 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: Which means that neuron will fire and outputs a if O O which is possible if and only if O = AND O = 0 Therefore, neuron will fire and output a if and only if angle θ is greater than 0 o but not greater Than 60 o, i.e., the reference vector lies in sector The firing conditions for the other neurons can be obtained in a similar manner The results are summarized in table.4. Table 4 Firing Conditions for Neurons Of the nd Layer For the Vector Sector ANN N x O x = if N O = AND O = 0 N O = AND O = 0 N O = AND O 4 = 0 O 5 = AND O 6 = 0 O 6 = AND O 7 = 0 O 7 = AND O = 0.. Output layer This layer determines the local angle LA The weight, input and output matrices are defined as follows: W = [ ] P = [θ O O O O 4 O 5 O 6 ] t O = [purelin(θ.047o.0944o +.46O O O 6 )] only one neuron from the nd layer will present a at its output while all other five neurons will present a 0, indicating the presence of the reference vector in one of six sectors, therefore, all the terms in the expression for O will cancel except the first term (θ) and only one of the other six terms, consequently, the expression for O will always reduce to: O = LA = θ + C Where, C is a constant whose possible values are chosen to be multiples of.047 rad (60 o ) that needs to be subtracted from or added to "θ" to produce LA (refer to table & figure 7) All results are summarized in table 5 Table 5 esults of Output Layer for the Vector Sector ANN, Indicating the Expression used to Calculate LA in Different Sectors O O O O 4 O 5 O 6 Sec O (LA) θ θ θ θ θ θ Switching Time Calculator This block computes the three time intervals during which the reference vector is sampled to two boundary vectors (V V 6 ) and one zero-vector (V 0, V 7 ). The Trig signal triggers the block to start computing the switching times according to the following equations: T a = V T V s sin π LA () dc T b = V V dc T s sin(la) () = T s T a T b () Where, T a Interval of first boundary vector (V a ) T b Interval of second boundary vector (V b ) To Interval of zero-vector ( V 0, V 7 ) The non-linear part of equations () & () which is the sin function can be computed using an ANN as shown in figure 9 instead of using look-up tables which requires large memory space. θ Sin θ Figure 9: ANN Sine Wave Generator 5

6 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: The network is trained using MATLAB Toolbox Neural Fitting Tool (nftool).4 Boundary Vectors Generator The Trig signal initiates the operation of the block to evaluate the two non-zero components of the reference vector "V a " and "V b " at the start of the sampling period, the input to this block is Sec (sector no.) and the outputs are V a V b Component of the reference vector aligned With the start of sector Component of the reference vector aligned With the end of sector Figure 0 shows the neural network used to produce the boundary vectors. The weight, input and output matrices are defined as follows: W = The elements of the input matrix, denotes the active sector (this is exactly the output matrix of the nd hidden layer from the Vector Sector ANN). The weight matrix elements are chosen such that the space vectors elements are aligned vertically in the first six columns (each column contains the two vectors that are the boundaries of the six sectors), i.e., the boundary vectors of sector (00 & 0) are aligned in columnwhile the boundary vectors of sector (0 & 00) are aligned in column and so on.(refer to table and figure for boundary vectors in each sector). The weight of the bias is chosen so that, the elements of the column which corresponds to the active sector will be available at the output. For example, if the reference vector lies in sector 5, then: P = [ ] t hardlim(0 0.5) hardlim( 0.5) hardlim(0 0.5) hardlim( 0.5) 0 0 O = hardlim( + 0.5) = hardlim(.5) = hardlim( + 0.5) hardlim(.5) hardlim(0 0.5) hardlim( 0.5) 0 hardlim( + 0.5) hardlim(.5) P = Sec = sec sed sec sec 4 sec 5 sec 6 O = hardlim[wp] N N V a i.e., vectors 00 & 0 will be available at the output, which are the boundary vectors for sector 5..5 Gate Pulses Generator This block is divided into two sub-blocks.5. Vector selector Generates VS (Vector Select) signal which indicates the vector that should be present at the output in the correct instant by comparing the ramp signal with different time instants to produce the symmetric sequence modulation technique as shown in figure, the neural network which implements this function is shown in figure Sec N V b Figure 0: ANN for producing the Boundary Vectors 6

7 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: T s 4 + T a + T b 4 + T a + T b 4 + T a + T b 4 + T a + T b 4 + T a 4 Selected Vector V 0 V a V b V 7 V b V a V Phase a Phase b represents points in time at which the output vector should be changed. The weight, input and output matrices for the st hidden layer are defined as follows: W = P = T a T b hardlim( 0.5T 0 ) hardlim( T a ) O hardlim( 0.5T = 0 0.5T a 0.5T b ) hardlim( 0.75T 0 0.5T a 0.5T b ) hardlim( T a T b ) hardlim( 0.75 T a T b ) Phase c 4 T a T b T b T a 4 For example, N, will fire when 0.5, N, will fire when T a and so on. All results are summarized in table 6. Figure : Generation of VS Command during Complete Sampling Period in Sector T s Table 6: Firing Conditions for Neurons of the st Hidden Layer for the Vector Selector ANN N x O x = if N N 0.5 N T a N N N T a + 0.5T b T a + 0.5T b N N VS T a + T b T a + T b T a T b Figure : ANN for Producing the VS Command.5.. st hidden layer: This layer triggers the change of the output vector Each neuron in the first layer (N x ) will fire when increases above the horizontal lines, which N.5.. nd hidden layer This layer produces a code that represents the correct VS command. The weight, input and output matrices for the nd hidden layer are defined as follows: W 0 0 =

8 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: O O O P = O 4 O 5 O 6 hardlim( O + O 6 + ) O hardlim(o = O + O 5 O 6 ) hardlim(o O + O 4 O 5 ) hardlim(o O 4 ) N, will fire (indicating that V 0 should be present at the output) when, O + O This is possible when O = 0 AND O 6 = 0, i.e., < 0.5 AND < T a + T b (interval in figure ) O O = AND O 6 =, i.e., > 0.5 AND > T a + T b (interval 7 in figure ) N, will also fire if O = 0 AND O 6 = but this case is not applicable because this means that < 0.5 AND > T a + T b which is not possible. Possible input combinations and the corresponding outputs for N are summarized in table 7. Table 7: Input Combinations of N for the Vector Selector ANN O O 6 O Interval N/A 0 0 N/A 7 Similarly, N will fire (indicating that V a should be present at the output) when, O O + O 5 O 6 0 N, will fire (indicating that V b should be present at the output) when, O O + O 4 O 5 0, will fire (indicating that V 7 should be present at the output) when, O O Output layer: This layer implements a bit-wise NOT function on the output of the nd hidden layer to produce the VS vector Where, VS = [VS VS VS VS 4 ] t The output of the Vector Selector ANN for Two- Level SVM is summarized in table 8 Table 8: Output of the Vector Selector ANN VS O O O O 4 Interval Selected Vector 0, 7 V 0 0, 6 V a 0, 5 V b 0 4 V 7.5. Vector decoder Ensures that the appropriate vector is present at the output in the correct instant so that the inverter switches are switched ON or OFF according to the selected modulation scheme. The output vector V out can assume one of four values (V a, V b, V 0 or V 7 ) at different instants in the sampling period T s The neural network used to implement this function is shown in figure..5.. st Hidden layer: The purpose of this layer is to select one of the 4 vectors (V 0, V a, V b and V 7 ) and pass it to the next layer. The selected vector depends on the value of the VS vector. This layer contains neurons divided into 4 groups of neurons each ( neurons for each one of the 4 input vectors), each neuron in this layer represents a ANN switch port, where the neurons of each group is enabled/disabled by a 0/from the respective bit in the VS vector, as shown in table nd Hidden layer This layer contains neurons, the input to each neuron is similar elements in the 4 vectors so that each neuron passes one element of the selected vector to the output layer. The output of this layer represents the states of the upper inverter switches. The weight, input and output matrices for this layer are defined as follows: 8

9 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: O O V 0 V O 0 O 4 V 0 O V a 5 P V a = O 6 V = a O 7 V b O 8 V b O 9 V b O V 7 0 V 7 O V 7 O W = purelin(v 0 + V a + V b + V 7 ) O = purelin(v 0 + V a + V b + V 7 ) purelin(v 0 + V a + V b + V 7 ).5.. Output layer: This layer implements the NOT function on the output from the nd hidden layer to produce the states of the lower inverter switches. V 0 * ANN Switch Ports the closed loop V/Hz scalar control used in the simulation. The angular velocity, is compared with the reference speed, ω M The speed error signal, ω M, is applied to a slip controller, usually of the PI type, which generates the reference slip speed, ω SL. The slip speed must be limited for stability and overcurrent prevention. The reference synchronous speed ω Syn is obtained by adding ω SL to ω M.The latter signal used to generate the reference values, V and ω [5]. ω M ω M ω M P-I + Limiter ω SL ω Syn V SVM Generator Inverter Figure 4: Closed Loop V/Hz Scalar Control s V a * ANN Switch Ports s s V b * ANN Switch Ports s 4 s 5 V 7 * ANN Switch Ports s 6 Figure 5: otor Speed ω M VS Figure : Vector Decoder ANN 4. SIMULATION ESULTS The two-level ANN SVM generator is employed inside a scalar control drive system to validate its operation. Figure 4 shows the block diagram of 9

10 0 th December 0. Vol. 58 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: EFEENCES: Figure 6: Phase a Stator Current i a [] Muhammad H. ashid, Power Electronics Hand Book, Academic Press, Academic Press Series in Engineering, First Edition, 00, ISBN [] Bimal K. Bose, Modern Power electronic and AC Drives, Prentice Hall, First Edition, 00, ISBN [] Subrata K. Mondal, João O. P. Pinto and Bimal K. Bose, A Neural-Network-Based Space- Vector PWM Controller for a Three-Level Voltage-Fed Inverter Induction Motor Drive, IEEE transactions on Industry Applications, VOL. 8, No., May/June 00 [4] Prasad, V. H., Master of Science In Electrical Engineering, Analysis and Comparison of Space Vector Modulation schemes for Three- Leg and Four-Leg Voltage Source inverters, Virginia Polytechnic Institute and State University, 997 [5] Andrzej M. Trzynadlowski, Control of Induction Motors, Academic Press, First Edition, 000, ISBN Figure 7: Line Voltage v ab Figure 8: Electromagnetic Torque T M 5. CONCLUSION Space vector pulse width modulation (SVPWM) can be implemented using a set of interconnected artificial neural networks, where each network achieves a certain step in the SVPWM algorithm. The proposed SVPWM scheme was employed inside a closed loop v/hz scalar control system and simulated using MATLAB Simulink to verify its operation. 0