AC-DC-AC Converter with Induction Machine-modeling and Implementation on Floating Point DSP as a Cost Effective Interface for Renewable Energy Applications M. Jasinski, G. Wrona and M. P. Kazmierkowski Warsaw University of Technology, Institute of Control & Industrial Electronics, ul. Koszykowa 75, 00-662 Warszawa, E-mail Poland, tel. (48) 22 628 06 65. fax (48) 625 66 33, e-mail:
[email protected],
[email protected],
[email protected]. Abstract- The paper presents advanced vector control system for ACDC-AC converter operating as grid interface for renewable energy systems. The control method is based on Direct Torque Control with Space Vector Modulation (DTC-SVM) for Machine Side Converter (MSC) and Direct Power Control with Space Vector Modulation (DPCSVM) for Line Side Converter (LSC). The whole control and protection system has been implemented on cost effective floating point DSP microcontroller TMS320F28335. Simulation and experimental results which illustrate steady state and dynamic properties of the developed system obtained from the 3kW laboratory model are given.
The Up voltage is controllable and depends on switching signals pattern and DC-link voltage level. Thanks to control magnitude and phase of the Up voltage, the line current can be controlled by changing the voltage drop on the input choke - Ui . Therefore, inductances between grid and AC side of the LSC are indispensable. They create a current source and provide boost feature of the LSC. Through controlling the converter AC side voltage in its phase and amplitude, Up the phase and amplitude of the line current vector IL is controlled indirectly.
INTRODUCTION Recently, in control of power electronic converters new and more complex algorithms require more and more computing power. Also, advances in power semiconductor technology allows to use higher switching frequency. This leads to requirement of high-speed Digital Signal Processors (DSP). One of them is floating point microcontroller TMS320F28335 from Texas Instrument. This system combines sophisticated peripherals which are typical for microcontrollers and high computing power characteristic for DSPs. The main advantage of this DSP controller is ability to operate on floating point numbers without having to use additional libraries [5]. In this paper Direct Torque Control (DTC) for machine side converter and Direct Power Control (DPC) for line side converter are presented. Instead of hysteresis controllers used in the conventional schemes [8] in this work linear PI controllers with Space Vector Modulators (SVM) are implemented [9]. This eliminates the fundamental drawback of hysteresis controllers, a variable switching frequency, and also facilitate their implementations on digital platform. The Direct Power and Torque Control with Space Vector Modulation (DPTC-SVM) algorithm is characterized by simple structure, limited number of transformation, and good operation properties in transient and steady states. In the past works [7,10,12], the DPTC-SVM control algorithm has been implemented on fixed-point DSP/RISC. In this paper we present implementation of this algorithm on floating point microcontroller TMS320F28335.
Fig. 1. Line side converter (LSC) topology: a) three phase system; b) single phase equivalent
RI L
IL
RI L
IL
978-1-4244-6391-6/10/$26.00 ©2010 IEEE
RI L
IL
j ω LI L
j ω LI L
OPERATION OF LINE SIDE CONVERTER – LSC LSC can be described in different coordinate system. Basic scheme of the LSC with AC input choke and output DC side capacitor is shown in Fig. 1a, while Fig. 1b shows it’s single-phase representation. Where, UL is a line voltage space vector, IL is a line current space vector, UP is the LSC input voltage space vector, and Ui is a space vector of voltage drop on the input (AC grid side) choke L and it resistance R.
j ω LI L
j ω LI L
RI L
IL
Fig. 2. Phasor diagrams of LSC: a,b) non unity power factor operation; c,d) unity power factor operation
Further, in Fig. 2 are shown both motoring and regenerating phasor diagrams of LSC. From this figure can be seen that the magnitude of Up is higher during regeneration than in rectifying mode. With assumption of a stiff line power (i.e., UL is a pure
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voltage source with zero internal impedance) terminal voltage of LSC Up can differ up to about 3% between motoring and regenerating modes [10].
U rK = Rr I rK +
dΨ rK + j ( Ω K − pb Ω m ) Ψ rK , dt
(4)
Flux-currents equations:
LSC MODEL IN STATIONARY αβ COORDINATES
Ψ SK = LS I SK + LM I rK ,
(5)
In some studies is useful to present the LSC model in two axis coordinates. Equations, after transformation into stationary αβ coordinates, can be described using the complex space vector notation as: dI (1) L L + RI L = U L − U dcS1 dt
Ψ rK = Lr I rK + LM I SK ,
(6)
(2)
dU 3 C dc = Re ⎡⎣I LS1* ⎤⎦ − I load dt 2
MACHINE SIDE CONVERTER (MSC) Basic control methods of MSC-fed IM (see Fig. 3. and Fig. 4.) require a space vector based IM mathematical model, therefore short description can be found in next Subsection.
And motion equation: d Ωm 1 ⎡ mS ⎤ Im ( Ψ*SK I SK ) − M L ⎥ = ⎢ pb 2 dt J⎣ ⎦
CONTROL SCHEME The block diagram of control scheme for AC-DC-AC converter interfacing grid with induction machine (IM) is shown in Fig. 5. It consist of two parts: IM side converter control and grid side converter control. 1. Direct Torque Control with Space Vector Modulator - DTC-SVM The outputs of the PI flux and torque controllers can be interpreted as the xy stator voltage components Usx, Usy in the stator flux oriented coordinates giving the block scheme of Fig. 5. (right side). The control strategy relies on a simplified description of the stator voltage components, expressed in stator-flux-oriented coordinates as:
dΨs dΨs ≈ dt dt U sy = Rs isq + ω m Ψ s = k s M e + ωm Ψ s U sx = Rs isd +
Fig. 3. Machine Side Converter (MSC) with induction machine (IM) equivalent circuit: a) three phase system; b) single phase equivalent circuit.
jLSσ I S E
Ψ
jLSσ I S
E Ψ
Is
Us
RSr I S
Is
Fig. 4. Phasor diagrams of MSC-fed induction machine IM
IM MATHEMATICAL MODEL IN ROTATING COORDINATES WITH ARBITRARY ANGULAR SPEED The model of the IM in natural ABC coordinates is complicated. Therefore, in order to reduce the set of equations from 12 to 4, the complex space vectors are used. Moreover, based on transformation into a common rotating coordinate system with arbitrary angular speed ΩK and referring rotor quantities to the stator circuit, a following set of equations can be written [8]: Voltage equations: dΨ SK (3) U SK = RS I SK + + j Ω K Ψ SK , dt
(8) (9)
where ks = Rs /Ψs and ωs is the angular speed of the stator flux vector. The above equations show that the component Usx has influence only on the change of stator flux magnitude, and the component Usy - if the term ωsΨs is decoupled – can be used for torque adjustment. Therefore, after coordinate transformation dq/αβ into the stationary frame, the command values Usα, Usβ are delivered to Space Vector Modulation (SVM) block. Torque and flux are calculated with the following equations:
Lm Ψ r β + σ Ls isβ Lr m M e = pb s (Ψ sα isβ - Ψ sβ isα ) 2
Ψ sβ =
RSr I S Us
(7)
(10) (11)
L2m (12) Lr Ls The rotor flux Ψr is estimated based on equations (13) and in the dq rotating coordinate system: d Ψr (13) Tr + Ψ r = Lmis dt where: T = Lr is the rotor time constant. r Rr where:
2.
σ = 1-
Direct Power Control with Space Vector Modulator DPC-SVM The DPC-SVM (left side in the Fig. 5) has similar structure to the DTC-SVM scheme. Torque and flux estimator is replaced by the active and reactive power estimator. The power estimation is based on a Virtual Flux (VF) concept, which improved the quality of estimated signals in terms of noise immunity.
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\
Fig. 5. Block scheme of DPC-SVM for Line Side AC-DC Converter (LSC) and DTC-SVM for induction Machine Side DC-AC Converter (MSC)
The virtual flux is defined as [9]: Ψ SK
⎡ Ψ Lα ⎤ ⎡ ∫u Lα dt ⎤ ⎥ =⎢ ⎥=⎢ ⎣ Ψ Lβ ⎦ ⎢⎣ ∫u Lβ dt ⎥⎦
(14)
The line voltage is equal: UL = US + UI
(15)
From (7) and (8) follows: Ψ Lα = ∫(u Lα )dt + LiLα
(16)
Ψ Lβ = ∫(u Lβ )dt + Li Lβ
(17)
Active and reactive powers are estimated as: 3 (18) p = ωL (Ψ Lαi Lβ − Ψ Lβi Lα ) 2 3 (19) q = ωL (Ψ Lα iLα + Ψ Lβ iLβ ) 2 The estimated active and reactive power, are compared with commanded values and the instantaneous errors after going through a PI controller define converter voltage in the pq rotating coordinates. After transformation to the stationary coordinates αβ, these signals are delivered to the modulator block SVM, which calculates the switching time of transistors. To meet unit power factor condition, reactive power reference value is set to zero, while the active power is generated by the DC-link voltage PI-controller. MODEL OF THE AC-DC-AC CONVERTER-FED INDUCTION MACHINE WITH ACTIVE POWER FEEDFORWARD (PF) In Fig.1. and Fig.3. is shown simplified diagram of an AC-DC-AC converter which consist of LSC-fed DC-link and MSCfed IM. Note that, the coordinates system for control of the LSC is oriented with VF vector [9] – gives 90O voltage phase shift. Hence, ILxc is set to 0 to meet the unity power factor (UPF) condition. With this assumption the LSC input active power can be calculated as: 3 3 PLSC = ( I LxU px + I LyU py ) = I LyU py (20) 2 2
Under steady states operation ILy =const. and, with assumption that the input choke resistance is R=0, the following equation can be written: 3 (21) PLSC = I LyU Ly 2 From another side the active power consumed/produced by the MSC-fed IM is defined by: PMSC =
3 ( I SxU Sx + I SyU Sy ) 2
(22) Based on VF vector, the LSC input power can be calculated as: 3 3 PLSC = ωL Ψ Lx I Ly − Ψ Ly I Lx = ωL Ψ Lx I Ly (23) 2 2 From the MSC side electromagnetic power of the motor is defined by: m Pe = pb S Ω mΨ Sx I Sy (24) 2 Moreover, it can be assumed (neglecting power losses) that electromagnetic power of the IM is equal to an active power delivered to the motor Pe =PMSC , hence: m PMSC = pb S Ω mΨ Sx I Sy (25) 2 But this is not sufficient assumption because of power losses in the real system, so it should be written: m PMSC = pb S Ω mΨ Sx I Sy + Plosses (26) 2 Further, please consider a situation at stand still Ωm=0 when nominal torque is applied. In such a case the electromagnetic power will be zero but the IM power PMSC will have a significant value. Estimation of this power is quite difficult, because the parameters of the IM and power switches are needed. Hence, for simplicity of the control structure a power estimator based on command stator voltage USc and actual current ISc will be taken into consideration: 3 PMSC = I SxU Sxc + I SyU Syc (27) 2
(
(
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)
)
EQUIVALENT TIME CONSTANT OF POWER RESPONSE The time constant delay of the LSC response TIT is determined. With assumption that power losses of the converters can be neglected, power tracking performance can be expressed by: 1 (28) P (s) = P LSC
1 + sTIT
LSCc
Similarly for the MSC can be written: 1 PMSC ( s ) = PMSCc (29) 1 + sTIF Where, TIF is the equivalent time constant of the MSC step response. Determination of these value can be found in [7]. ENERGY OF THE DC-LINK CAPACITOR The DC-link voltage can be described as: dU dc 1 = ( I dc − I load ) , dt C
So:
U dc =
(30)
1 ( Idc − Iload ) dt, C∫
(31)
Where eUdcf = Udcc −Udcf Therefore Eq. (34) can be rewritten: . (39) PLSCc ( s ) = Pc + PMSCc 2 , From Eqs. (28), (29), the open loop transfer function of the input power (of the LSC) and output power (of the MSC) can be written: GLSCo ( s ) =
PLSC 1 = PLSCc 1 + sTIT
GMSCo ( s ) =
PMSC 1 = PMSCc 1 + sTIF
(41) Such a system can be described by open loop transfer function as: U GAo ( s ) = dc (42) M ec Assuming initial steady state operation, Ωm=Ωmc=const and Udc=Udcc=const. the transfer function of the AC-DC-AC converterfed IM was described. In this case, only the DC-link voltage feedback is used –PF0. Therefore, the model takes a form as shown in Fig. 6. For additional information about power feedforward please refer [7].
Assuming the initial condition as in steady state, hence, the actual DC-link voltage Udc is equal to commanded DC-link voltage Udcc. Therefore, Eq. (31) can be rewritten: 1 U dc = CU dcc
1 ∫ (U dcc I dc − U dcc Iload ) dt = CU dcc
∫(P
dc
− Pload ) dt ,
U dc
(32) PMSCc P MSCc 2 = 0
1 Pcap dt , CU dcc ∫
(33) If the power losses of the LSC and MSC are neglected (for simplicity), the energy storage variation of the DC-link capacitor will be the integral of the difference between the input power PLSC and the output power PMSC. Therefore, it can be written:
PLSCc = Pcapc + PMSCc ,
(35) Where, Pcapc=Pc denotes power of the DC-link voltage feedback control loop, and PMSCc denotes the instantaneous active power feedforward signal – PF (estimated by different estimators). The command output power can be estimated based on different methods which provide additional time constant [4] : PMSCc 2 ( s ) =
1 sTu + 1
PLSC Pcap 1 1 + sTIT + 1 pCU dcc − PMSC
U dc
Fig. 6. Block diagram of the AC-DC-AC converter-fed IM with DC-link voltage feedback only – PF0
SIMULATION AND EXPERIMENTAL RESULTS 1. Simulation results In this Subsection selected results from Matlab Simulink model are presented. In Fig.7 the regenerating and motoring mode at constant load 5Nm is shown. In Fig.8a, in turn, the active and reactive power, line current and voltage. Fig 8b shows the rotor speed, phase to phase voltage and phase current. a)
b)
1 PMSCc 1 + sT2
(36) Moreover, it should be stressed that the first order filter with time constant TU was used to DC-link voltage feedback which strongly delays the signal Pc: 1 U dcf ( s ) = U dc (37) 1 + sTU This delay is taken into account in DC-link voltage controller design: Pc ( s ) =
+
P + PLSCc
U dcc + U dcf −
1 sTIF + 1
PLSC = Pcap + PMSC ,
(34) From this equation it can be concluded that for proper (accurate) control of the LSC power PLSC the command power should be as follows:
K P _ U (sTI _U + 1) sTI _U
Where, Pdc–Pload=Pcap therefore is obtained: U dc =
(40)
K PU ( sTIU + 1) eU dcf U dcc sTIU
(38)
Fig. 7. Steady states: a) – Line Side Converter (LSC) (from the top: DC link voltage [V], phase current [A], phase voltage [V]); b) – Machine Side Converter (MSC) (from the top: rotor speed [rpm], phase to phase voltage [V], phase current [A]);
The system's dynamic is presented based on the step change of the load from 0 to 50% of the nominal torque. The analysis was carried out for the regenerating mode (see Fig.8).
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3. Brief description of the microcontroller The TMS320F28335 microcontroller is a 32-bit floating point DSP unit belonging to the C2000 Delfino family processors from Texas Instruments. It is made in CMOS technology and can operate at a frequency up to 150 MHz. Bus is based on Harvard architecture. From the standpoint of power electronics the most important module is Pulse Width Modulation (PWM). There are six such modules, where each is composed of two complementary outputs which contain a common 16-bit counter. In every sampling time one of channels in every modules can work under improved resolution (24 bits). In addition, 16 channels analog to digital (ADC) converter with 12 bit resolution. It is characterized by a fast conversion rate of Fig. 8. Transient states, regenerating mode: a) – Line Side Converter (LSC) (from the up to 80 ns at 25-MHz ADC clock [6]. The enhanced quadrature top: Active and reactive power [W, Var], DC link voltage [V], phase voltage [V], encoder pulse (eQEP) module is extremely usefully to get position, phase current [A]); b) – Machine Side Converter (MSC) from the top: electromagnetic torque and flux direction and speed information from a rotating machine. There are [Nm, Wb], rotor speed [rpm], phase to phase voltage [V], phase current [A]); three 32-bit CPU-timers on the device for measuring time [5]. a)
b)
TABLE I MAIN PARAMETERS OF THE LABORATORY SETUP AC machine Phase voltage, current 230V (rms), 6,9A (rms) Nominal toque MN, base speed Ω mN 20 Nm, 1415 rpm Number of pole pairs, moment of inertia 2, 0.0154 kgm2 Stator, rotor winding resistance 1.85 Ω, 1.84 Ω Stator, rotor, mutual inductances 0.17 H, 0.17 H, 0.16 H Input inductance Resistance, inductance of reactors 100mΩ, 10mH VLT FC302 Converters Switching frequency, Nominal Power PN 5kHz, 3kW DC link capacitor 190uF Measurement conditions Phase Line voltage, frequency 120V (rms), 50Hz DC link voltage 400V
2. Laboratory setup Block diagram of laboratory setup is presented in Fig. 9. It consists of two commercial Danfoss Converters VLT FC302 (3 kW) [2]. One of them operates with the IM while the other is connected to the grid. Both converters are coupled through the DC-link. Control signals from the microcontroller are transmitted to the converters through a fiber optic interface, while current and voltage measurements are based on LEM’s transducers.
Both DTC-SVM and DPC-SVM strategies has been implemented on a single microcontroller give DPTC-SVM control. The entire program is executed in one interrupt triggered from PWM interface. The frequency of PWM is set to 5kHz. Measurements of voltages and currents are performed by ADC converter which is synchronized with the PWM signals. In the middle of each interrupts, start conversion process from PWM interface, signals from ADC module, are sampled. Ready-to-use samples are stored in appropriate registers.
Fig. 9. Laboratory setup
The main data and parameters of the laboratory setup are shown in Tab. I.
4. Experimental results Below selected oscillograms of static and dynamic states measured on a laboratory setup are presented. Fig. 10a,b shows the system operation in motoring mode. Waveforms on the left are related to LSC. As can be seen the current and voltage waveforms are in phase which corresponds to Unity Power Factor (UPF) operation. Fig. 10c,d shows the waveforms during operation in regenerating mode. Note, that current is in opposite phase to the line voltage. Moreover, in both figures, the current is nearly sinusoidal shape with low harmonic distortion. Waveforms on the right side (Fig. 10b,d) show the phase current and phase to phase voltage of the induction machine.
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In Fig. 11b the response to step change of the commanded electromagnetic torque from 0 to 75% MN is shown. This illustrates operation of the converter in regenerating mode. It should be pointed that the investigation has been performed with closed DC voltage feedback loop. It can be seen that the DC-link voltage is well stabilized at the expense of an overshoot in phase current. The start up process of the LSC is presented in Fig. 11a. Note that this process runs properly without current overshoot. a)
b)
CONCLUSION In this paper AC-DC-AC converter modeling and vector control using cost effective floating point microcontroller TMS320F28335 is presented. Two advance control methods: Direct Power Control with Space Vector Modulation (DPC-SVM) for Line Side Converter (LSC) and Direct Torque Control with Space Vector Modulation (DTC-SVM) for induction Machine Side Converter (MSC) were implemented on one microcontroller, hence DPTC-SVM operates properly. It was shown that there is enough computation capacity to add some additional code like higher harmonics and/or voltage dips compensation (see Tab. II). Simulation and experimental verification show good accuracy of the model and excellent capability of the floating point microcontroller. ACKNOWLEDGEMENT
c)
Acknowledgement This work has been supported by the NCBiR grant no. Nr N R01 0014 06/2009. And also this work has been supported by the European Union in the framework of European Social Fund through the Warsaw University of Technology Development Programme.
d)
REFERENCES [1]
Fig. 10. Steady states: a), c) – Line side converter (from the top: DC link voltage Udc [100V/div], phase current Ia [5A/div], phase voltage Ua [100V/div]); b), d) – Machine side converter (from the top: phase current Isa [5A/div], phase to phase voltage Uab [200V/div]); a)
b)
Fig. 11. Dynamic states: a) starting up process; b) step change of the electromagnetic torque ( 1-DC link voltage Udc [100V/div], 2-line voltage Ua [100V/div], 3- line current Ia [5A/div], 4-machine current Isa [10A/div] ); TABLE II EXECUTION TIME SELECTED COMPONENTS OF THE ALGORITHM Procedure
Time [μs]
Space Vector Modulator PI controller Measurements Torque and flux estimator Active and reactive power astimator
5.78 2.40 9.44 11.90 9.60
pq axis controllers
12.9
xy axis controllers
14.7
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