HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 92 5. CURRENT CONTROL TECHNIQUES IN HIGHPERFORMANCE AC DRIVES 5.1. REVIEW OF CURRENT CONTROL METHODS As both vector controlled induction machines and vector controlled SPMSM require current controlled PWM inverter, then it is possible to discuss current control methods independently of the type of the drive. In other words, all the current control techniques described further on are applicable in both induction motor and SPMSM vector controlled drives. Current controlled PWM inverter is the most frequent choice in highperformance AC drives as decoupled flux and torque control by instantaneous stator current space vector amplitude and position control is achieved relatively easily. All the current control techniques essentially belong to one of the two major groups. The first group encompasses all the current control methods that operate in the stationary reference frame while the second group includes current control techniques with current controllers operating in the rotational frame of reference. If the current control of an induction machine is performed in rotational reference frame, decoupling of stator voltage equations substitutes local current feedback loops in stationary reference frame, which suppress influence of stator voltage equations. Current control in stationary reference frame is usually implemented in an analogue fashion. The two most common alternatives are hysteresis current controllers and ramp-comparison controllers. Both of these have essentially already been implicitly looked at. In particular, the experimental results related to the performance of a rotor flux oriented induction machine (Section 3.4.) are obtained on a drive that utilises ramp comparison current controllers. Hence the current wave-forms of Figs. 3.16-3.18 apply to this method of current control. On the other hand, the experimental results presented in Section 4.6. for a vector controlled SPMSM machine apply to a drive that is equipped with hysteresis current controllers (Figs. 4.13-4.16). Approaches with three independent phase current controllers and two dependent current controllers in α β , stationary frame of reference are possible. The most pronounced shortcoming of the hysteresis current control is the variable inverter switching frequency over a period of output voltage. Current control by ramp-comparison controllers overcomes this problem. Here current error serves as modulating signal which is compared to the triangular carrier wave. Deviation of amplitude and phase of phase currents with respect to commanded values unfortunately takes place and some compensation has to be introduced, the common choice being a PI compensator. Another difficulty arises from a possibility that multiple crossing of the carrier may occur if the frequency of the current error becomes greater then the carrier frequency. This can be overcome by adding hysteresis to the controller. The advantage of the ramp-comparison current control with respect to hysteresis current control is fixed and constant inverter switching frequency (see current spectrum shown in Fig. 3.16, that contains only those current harmonics that have a frequency situated around multiples of the inverter switching frequency). Current control in stationary reference frame requires that current controllers process alternating signals, that can be of a large frequency range. Furthermore, controller characteristics in steady-state depend on the operating frequency and machine impedance. These shortcomings can be partially but not completely eliminated by different modifications of the basic current control principles. At low operating speeds the induced rotational electromotive force in the machine is small and current control enables very good tracking between reference and actual currents, with respect to both amplitude and phase. However at higher speeds, due to limited voltage capability of the inverter and finite inverter switching frequency, tracking worsens and an error is met in both amplitude and phase of actual currents compared to reference currents. This feature becomes very pronounced in the field weakening region where the inverter operates very close to the voltage limit. The problem may be HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 93 solved by removing the current controllers from stationary reference frame into the rotational reference frame. The outputs of the current controllers then become voltage references in rotational reference frame. If the inverter switching frequency is high enough, decoupling circuit for stator dynamics is usually omitted and the machine is still treated as being current fed. In the field weakening region the machine is usually fed with square-wave voltages and here the concept of current feeding has to be abandoned. Decoupling circuit is included in the control system and the machine is treated as being fed from a voltage source. The same concept of voltage feeding has to be applied in the base speed range as well if the switching frequency of the inverter is low, this being the case with thyristor inverters utilised in conjunction with vector controlled high power induction motors. As already discussed in Chapter 4, current control in rotational reference frame is well suited to fully digital realisation. The main advantage of this method of current control is that current controllers (most frequently of PI type) process DC signals. As the current control is performed in rotational reference frame, measured currents have to be transformed from stationary to rotational reference frame. When current control in rotational reference frame is applied, different PWM methods may be utilised for creation of the desired voltages at machine terminals. For example, sinusoidal PWM may be selected or voltage space vector modulation may be chosen. As a separate sub-group predictive methods of stator current space vector control may be identified. One method, for example, calculates the required voltage space vector in such a way that the current vector error is kept within prescribed boundaries at all times. State of the inverter does not change as long as it is predicted that the current vector error will remain within defined boundaries. This approach enables minimisation of the inverter switching frequency. The required voltage space vector is created by means of voltage space vector modulation technique, utilising the two neighbouring voltage vectors and the zero voltage vector. It should be noted that all the predictive methods significantly complicate the overall control system as numerous additional calculation are required. With respect to SPMSM drives, current control is again performed either in stationary or in field- oriented reference frame. Fully digital versions of SPMSM drive usually employ current control in field co-ordinates. The application of current controllers that operate in the stationary reference frame is once more common in analogue and hybrid digital-analogue realisations, although fully digital realisations are available as well. It should be noted that the control system structure is significantly simpler in a SPMSM drive, compared to induction motor drive. Thus it is easier to achieve fully digital control of a SPMSM drive. Current control of SPMSM drives in stationary reference frame is again performed by the aid of hysteresis controllers or ramp-comparison current controllers. The variety of complex hysteresis modulation methods for VSI current control exist, however the most frequently used one is the classic hysteresis method. The hysteresis window defines inverter switching frequency, which is, as already stated, not constant over a period of output voltage. It is possible to overcome this shortcoming by the aid of ramp-comparison controller application. In this case switching frequency is constant and determined with the triangular carrier wave frequency. Both schemes can be implemented with either two or three current controllers. If the current control of' a SPMSM drive is performed in rotational reference frame, voltage space vector modulation is the most frequent choice. If the inverter switching frequency and sampling rate are sufficiently high, decoupling circuit is sometimes simplified or omitted. The usual choice for current controllers in field-oriented reference frame is standard PI structure, although more complex predictive techniques exist for SPMSM drives as well. In what follows the most important current control techniques will be described. A SPMSM drive will be considered as an example in all the cases, due to a considerably simpler control system structure. Both current control in stationary reference frame and current control in rotational reference frame are elaborated. The encompassed current control methods are hysteresis control and ramp comparison control in stationary reference frame, and control in field co-ordinates with PI current controllers and with phase voltage generation by means of voltage space vector modulation and by means of ramp comparison method. In the latter case, the need for decoupling circuit application is addressed as well. HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 94 5.2. CURRENT CONTROL METHODS 5.2.1. Current control in stationary reference frame - hysteresis controllers The structure of the SPMSM drive with hysteresis current control in the stationary reference frame is depicted in Fig. 5.1. Either three independent controllers in three phase a,b,c reference frame can be applied (as shown in Fig. 5.1), or the control can be performed by the aid of two controllers in stationary two phase α,β reference frame. Comparative study of these two possibilities shows that there are no differences in dynamic response of the drive. The idea of hysteresis current control is in essence very simple and well suited for analogue realisation. It has already been introduced in conjunction with a separately excited DC motor drive in Chapter 1 (Fig. 1.3). The principle remains the same when hysteresis current control is applied for an AC drive. However, the reference currents (rather than a current) are now AC. Phase current references are in any steady-state sine functions. Actual currents are allowed to deviate from their reference values for a fixed value termed as hysteresis band. The discrepancy between actual and reference currents will vary in time and will be either positive or negative. The values of the hysteresis band are the same for both positive and negative variation. The state of the appropriate leg of the inverter bridge changes once when the difference between actual and reference current exceeds hysteresis band. For example, suppose that the upper switch in phase a leg is closed, while the lower switch is open. This state will be preserved as long as the current error in phase a is within hysteresis band. However, when the actual current in phase a becomes greater than the reference value plus hysteresis band, the upper switch will be opened and the lower switch will be closed. Thus the actual current will be forced to reduce and fall once more within the hysteresis band. As the actual current change in time is function of the drive dynamics and operating state, the instants of inverter semiconductor switching cannot be predicted and will vary. Furthermore the switching frequency of the inverter varies and is not constant even over one cycle of the output frequency. The principle of hysteresis current control is illustrated in Fig. 5.2, where the inverter leg voltage is shown as well. One clearly observes in Fig. 5.2 how the switching frequency of the inverter varies from one cycle of operation to the other cycle. Periods of inverter switching are denoted as T1, T2, T3 and T4 and one easily observes that T1 is the largest out of the four, while T4 is the smallest. In the system shown in Fig. 5.1 only speed controller is present, whose output becomes q-axis current command. Stator d-axis current reference is set to zero. Note that Fig. 5.1 is essentially identical to Fig. 4.8 and that the only difference is the detailed representation of the hysteresis current controller in the lower part of the figure. 5.2.2. Current control in stationary reference frame - ramp comparison control If the ramp comparison current control technique is applied, configuration of a SPMSM drive corresponds to the one shown in Fig. 5.3. Current error is formed in stationary reference frame and passed through PI current controllers. The outputs of the current controllers are phase voltage references which are compared to the triangular carrier wave of the fixed frequency. As the triangular carrier wave is of fixed frequency, while frequency of the current error varies, the ratio of these two frequencies is not an integer and so-called asynchronous PWM of output voltages results in this way. Asynchronous PWM in general leads to generation of unwanted subharmonics in the output voltage wave-form. However if the triangular carrier wave frequency is high enough this effect can be neglected as it will not have any serious impact on the drive behaviour. In general three carrier waves are needed, one per phase. However if the triangular carrier frequency is high enough, one carrier wave may be utilised for all the three phases as is done here. HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 95 Diode bridge DC link PWM SPM rectifier inverter SM hysteresis i a i b i c position current control sensor ω*Pi qs *i αs *i a * − Iexp2i b * − − (jθ)3i c * − ω i ds *=0 i βs * sin / θ cos d/dt Comparator with hysteresis Upper switch i a * ∆i a IGBT drivers − i a Lower switch Fig. 5.1 - Hysteresis current control of a SPMSM drive. h = hysteresis band i a i a * i a *+h t i a *-h v An V DC t T1 T2 T3 T4 Fig. 5.2 - Principle of hysteresis current control: currents and a leg voltage. HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 96 It should be noted that the structures of the two drives shown in Figs. 5.1 and 5.3 are identical and that the only difference is in the method of current control applied. In other words, only the local current control loops used to control the inverter differ (lower portions of Figs. 5.1 and 5.3). Generation of the inverter leg voltages using ramp comparison control is illustrated in Fig. 5.4. Diode bridge DC link PWM SPM rectifier inverter SM Ramp comparison i a i b i c position current control sensor ω *Pi qs *i α s *i a * − Iexp2i b * − − (jθ)3i c * − ω i ds *=0 i β s * sin / θ cos d/dt i a *PIv a * controller P Power − i a stage i b *PIv b *ofthe controller W − i b i c *PIv c *PWM controller M VSI − i c Triangular carrier wave Fig. 5.3 - Ramp comparison current control of a SPMSM drive. 5.2.3. Current control in field co-ordinates with voltage space vector modulation The SPMSM drive with current control in field co-ordinates is shown in Fig. 5.5. Current controllers are of the PI structure. Block PWM denotes voltage space vector modulator. On the basis of the reference voltage space vector, actual voltage space vector is generated by the aid of two adjacent HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 97 available voltage vectors and zero voltage vectors. The principle of voltage space vector modulation has already been discussed extensively in Section 2.4.2. Triangular carrier wave (fixed frequency and amplitude) Reference signal (variable frequency and amplitude) time v An time Fig. 5.4 - Current control using ramp comparison method with a triangular carrier wave. ω * i=0 ds - - - contr. contr. qs * v qs * i ds e φ ω j SPMSM θ = φ i v i i i a b cc b a φ = θ r i i a b P W M ** * * * Speed contr. i i s* s qs v i ds qs dsr s r v v v n v e r t e r i r e θ-j 2 3 v ** ** v qs ds e e d q r Fig. 5.5 - SPMSM drive with current control in field co-ordinates and phase voltage generation by means of voltage space vector modulation. As explained in Section 2.4.2., voltage source inverter is capable of delivering six different non-zero discrete voltage vectors and two zero voltage space vectors to the machine. However reference voltage vector is continuously travelling in time and in steady state it forms a circle in the complex plane. As the inverter cannot provide such a voltage vector to the machine, actual reference vector is approximated by two adjacent non-zero voltage vectors and by zero voltage vectors in such a way that the applied average voltage vector value equals reference voltage vector during the inverter switching period. The sampling frequency is synchronised with inverter switching frequency and sampling period is divided into two half-periods. In the first half period two adjacent voltage space vectors and HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 98 appropriate zero vector are applied in sequence. In the second half period the order of adjacent space vectors is reversed and the remaining zero vector is applied. The duration of adjacent and zero voltage vector application is determined on the basis of reference voltage vector magnitude and position, as explained in Section 2.4.2. The speed controller has PI structure. Due to the presence of cross- coupling terms and disturbance term, decoupling circuit is in general needed, as indicated in Fig. 5.5 by additional voltages which are added to the outputs of current controllers. If the inverter switching frequency and sampling rate are high enough, decoupling circuit is often omitted. 5.2.4. Current control in field co-ordinates with ramp comparison controllers The structure of the SPMSM drive remains practically the same as in the previous subsection. The only difference is in the method of phase voltage generation, where now ramp comparison controllers are employed instead of space vector modulator. Phase voltages are generated by means of comparison of phase voltage references with triangular carrier wave, as shown schematically in Fig. 5.6. Due to fixed frequency of the triangular carrier wave, again results asynchronous pulse width modulation. The principle of PWM is identical to the one of Fig. 5.4. The only difference is that the current control is performed in rotating reference frame, so that d-q axis reference voltage are at first obtained. Phase voltage references are created upon execution of the co-ordinate transformation. In contrast to this, in the system of Fig. 5.3 current control is performed in the stationary reference frame and phase voltage references are obtained directly as outputs of the current controllers. qs e φj r v a b c * * * v v P W M V S I triangular carrier wave v qs v * * φ r v a b c v v Fig. 5.6 - Phase voltage generation by ramp comparison method. 5.3. PROBLEMS Q1. A highperformance permanent magnet synchronous motor drive is fed from a current controlled PWM inverter. The inverter input voltage may be regarded as constant and equal to 580 V. (a) Sketch the power circuit of the voltage source inverter and explain its operation assuming 180 degrees conduction mode. Define possible switching states and associate with them corresponding leg voltage values and appropriate voltage space vectors. Calculate all the possible values of the leg- voltage space vector (in a stationary reference frame) and represent them in the complex plane. (b) For the same switching states calculate values of the line-to-line voltages and appropriate values of the stator line-to-line voltage space vector. Represent the stator line-to-line voltage space vector values HIGHPERFORMANCE DRIVES --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 2001 99 in the complex plane and explain the differences when compared to the leg-voltage space vector values. (c) Explain the differences between the two groups of the two most commonly applied current control methods and list the specific current control techniques that belong to each of the two groups. Use appropriate schemes to illustrate individual control techniques. Q2. A sinusoidal permanent magnet synchronous machine (SPMSM) with surface mounted magnets is to be used in a highperformance machine tool drive, for operation in the base speed region only. It is fed from a PWM inverter, whose input DC voltage is constant and equal to 500 V. (a) Sketch the power circuit of the voltage source inverter and explain its operation assuming 180 degrees conduction mode. Define possible switching states and associate with them corresponding leg voltage values and appropriate voltage space vectors. Calculate all the possible values of the leg- voltage space vector (in a stationary reference frame) and represent them in the complex plane. (b) State the mathematical model of an SPMSM in the d-q reference frame firmly attached to the rotor and define all the parameters and variables. Next, define the conditions necessary for realisation of the rotor flux oriented control. (c) Explain the differences between the two groups of the two most commonly applied current control methods and list the specific current control techniques that belong to each of the two groups. (d) Using appropriate diagrams and mathematical expressions, explain the PWM method called ‘voltage space vector modulation’. Q3 . Explain, using appropriate illustrations, the following current control methods: (a) current control in stationary reference frame by means of i) three independent hysteresis current controllers; ii) two dependent hysteresis current controllers; iii) three independent ramp comparison controllers; (b) current control in rotating reference frame in conjunction with i) sinusoidal PWM; ii) voltage space vector modulation. . --------------------------------------------------------------------------------------------------------------------------------------- E Levi, 20 01 92 5. CURRENT CONTROL TECHNIQUES IN HIGH PERFORMANCE AC DRIVES 5 .1. REVIEW OF CURRENT CONTROL METHODS As both. motor and SPMSM vector controlled drives. Current controlled PWM inverter is the most frequent choice in high performance AC drives as decoupled flux and torque