Modelling and control of a cycloconverter with ... - IEEE Xplore

382

Modelling and Control of a Cycloconverter with Permanent Magnet Generator € Polinder I . t P.PJ. van den Bosch t

N.H.M. Hofmeester LJJ. OMqa

t Delft Univemity of Techdogy, The Netherlands t-

University ofT-,

The Nethalsad.

Abatraet: A 5puLe

current cycloeonverteris d (U tkquency changer for a hi& hrquency permaaent masnet #or. A v m c y , hiehgpd gasturbinem the power mngs of 260 k W to 870 kW,drivea the p n a u ~ c o u r v e r t eunit. r This system is intended for w in totd enngysystermr orhybrid systems in &des andhigh speedveads. The cydoanvateris dwigmed for three-phase 833 HE to 60 Ha applications. A new vector-controllike digitd coptml n t r a k g y and a special discrete Fourier fUter (DFT), intended for use with a one-phasc version of the cyclocmverter,

described. Both M implemented in a rrmt.i-pf.0digital controllerwd for feedback contml andpuLbpstterngenantion.Simulationd t n and "meritsofalaboaatayone-phasc d o n of the converter and a dummy-genaator,u;ler thin digitd control strategg and DET,M given. M

Keywords: cydoconvcrter,pennsnmt “gn&pmntor, frequency changer, h t c Fou~iex form, digitd feedback contml, vector control, power conves8ion,VSCF.

INTRODUCTION

A high-speed gasturbine (k75.000 rpm) exhibits a lowvolume, high4iciency performance in generating locally mechanical power. A classical solution for producing 50 & electrical power use8 a high-ratio gearbox and AC synchronous generator. Another approach u t i k a cydoconverter to transform the high frequencies to 50 & [l], [6]. In [2] such a new conversion system is described with 500 k W electrical power delivered at a utility grid. In this paper, a model is described and a new control strategy is proposed for a one-phase output cycloconverter. To achieve tidl advantage of the new conversion system’s dynamics, the power converter’s output must be controllable within a few grid periods. Therefore, conventional control strategies bascd on rms measurements are insufficient. The power fador at the converter’s input side is not actively controlled, but improvementscan be made as is d d b e d in [5]. A controller for the on+ phase cycloconverta is proposed and implemented in a digital si&nal processor DSP.The proposed control strategy is simplified and will improve in the full three-phase output c y h n v e r t e r . Although the objective is a full threc-phase 500 k W system, test results of a one-phase 50 k W laboratory version me shown. This system does not include the high-speed gasturbinagenerator set, but a lZpole synchronous generator. A preliminary permanent magnet generator design shows that a 506 k W generator with a speed of 25000 r p m is the utmost possible resulting in a low-ratio (1:3) gearbox between the gasturbine and the generator (fig. 1). This generator is connected to a utility grid by an 833 Ha to 50 Hs noncirculating current cycloconvcrter, controlled by a new vector-control like algorithm implemented in a digital signal processor [4]. In conveutional energy conversion systems (without a power converter) a mechanical gearbox is used to 4 u s t the power sourcc axis speed to the generator axis speed. Since the generator is connected directly to the grid, its axis speed is fully The generator-mwertu system is a development pmject of Delft University of Technology in cooperation with Eindhoven University of Technology. This project is spomred by NOVEM (Netherlands Asency for Energy and the Environment). The gturbine is a development of OPRA B.V. in Hengelo, the Nethw landS.

Q 1993 The European Power Electronics Association

ddamined by the grid frequency. The converted power is adjusted by the power source. This requires careful power source design where the nominal speed, nominal power, and most efficient power conversion coincide. If variations in the grid or in the power tiow occur,torque pulsation in the mechanical system result which cause m+chanical stress and axis windup. The rigid axis and gearbox become a spring with a high spring constant. The torque pulsations causes the mechaaical system to oadllate around the nominal speed and cause a distorted current delivered to the grid and mechanical streas.

-

................,. ............. ._. ............ ..................................

____.

;.e ..............!!!!..%.5.,*e..?.e ....1

Fig. 1: Higlbfrequency converaion syatem for coup[ing a BMt u A n e t o a utility grid.

The high-frequency energy conversion system studied in [Z]replama the mechanical gearbox by an electrical gearbox (power converter) with a fast controllable transmis sion ratio. Thia electrical gearbox decouples the grid frequency and the mechanical system’s speed and allows a high-speed generator to be applied. High-speed gcner* tors allow reduction of the mechanical construction and an improved conversion dficiency. Another advantage is mechanicalgearbox reduction (or elimination)which suffers f “ high mechanical strand needs expensive maintenance. The power converter allows torque pulaa tions to be damped actively and reduca the stress in the mechanical system. Furthermore, the power source can be operated at variable speed, enabling optimal efficiency operation. Actually, the decoupling of grid frequencyand speed creates an extra energy buffer. The energy in the rotating mechanical inertia (23.8 MJ)can be varied and controlled actively. The power converter also allows 8ctive control of the quality of the power (current) delivered to the utility grid. A compact energy generation unit pc sults with improved efficiency compared to a conventional conversion system.

383

CONTROLLER A vector controller for the grid current &(t)based on a discrete Fourier t d o r m a t i o n (DET) of the sampled data is described. Although this controller is designed for the onaphase cycloconverter, it can easily be extended to the three-phase converter. The three-phase situation simplifiar the control algorithm since a Parktransformation replaces the DFT. In contrast with rms control algorithms, the vector controller needs a DSP for the calculations involved. S i n c e the PM generator is Still under design, nimulatiom and meaaunments of a 50 kW/soO Ha teat system are shown.

Hardnue Since this paper only describes a oncphase output cydcrconverter connected to a high-frequency generator, the system in fig. 2 results. The cyclocmvater reduces to two anti-pmdel connected controlledd e r bridges for both positive and negative output current.

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One phase of a grid and a cyclmuerter fed Sy o gmcmtor.

With the thyristor firing angle a(*)the average converter output voltage can be modulated. Suppose the c0"Utsr tion interval is much d e r than the conduction interval of each switch and the fuing angle incresses from aero to 70'. Fig. 3 showa the converter output voltage and the generator line voltages. In code the generator frequency fi is much higher than fa, the following relation holds:

where u3(t) is 4he average converter output voltage and (2) makes the converter a controllable voltage aoum with the 6ring angle as control input. In fig. 3 the calculated u3(t) is shown for the situation that fi>fa. During a conduction interval the converter output is always around the calculated u3(t).

6 1 is the generator voltage amplitude.

is not 5ero since the converter output voltage is never a smooth (sinusoidal) signal. A current ripple of frequency Sfi and an amplitude invasely proportional to the inductor's sise La results. The combination of power converter and inductor givesthe convasion aystem a current munx character towards the grid controlled via the inductor voltage by ~ ( tvia ) 4 t ) . In this 001lvert~ the generator has a frequency of fi=!c83s Hs=flSfa. a(t) can only resort effectsix times per generator period IC sulting in a discretatime controlled system. The actual firing of the conductor depends on a(t)and results in a varying time delay from the natural commutation moment. Both reanons mate the cycloconverkr difficult to control as a current source since La is small and any d c viation from the ideal us(t), will r c d t in a rapid increase or deaease of the grid current.

The Low Level Controller (LLC) in fig. 2 is a digital arcuit sampling ~ ( from t ) the High L e d Controller (HLC) at evcry natural commutation moment and generating trigger pulsa for the firing circuits. In this paper the generator is modelled as three voltage murcea in saiea with commutation inductan- L1 and the grid is modelled as a f50 Hs voltage source. In [SI the inkraction of the converter and the generator is studied. The HLC will be described next.

Rotating coordinatoll Suppose the system is in ~tationatyopemtion connected to an ideal grid, rarulting in sinusoidal voltages and currents. The signala can be depiaed as vectors in a 50 Ha phasor plane as shown in fig. 4b. In the phasor plane, a phasor (signal) is characterisedby three values: the cornmon p h e , the relative phase, and the amplitude. S ince the system is in stationary operation, all sinusoidal signals have the same kquency ( w ) , rcfleded by the common phase (ut). This is the base frequency for the p b 801 diagram. The relative phase shift between signals is refleaed by the relative angles in a phasor diagram. Usually, one of the signala is positioned on the rcal-axis, the other signals are rotated ova an angle qual to their relative phase shift in the timedomain. The amplitude of the phaaors can be the amplitude or the rms value of the time domain signals. Note that all characteh tics of phasors are DCvalues and that they cannot be measured instantancoualy. They are defined for periodic sign& and need at least one period to be measured.

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Fig.

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4: 0 ) Relotions between mrdinate .ystems d&g"

and b) phcuor an K-coordinates w e d for contmller.

t + [a1

Fig. 3: Converter output voltage and the genemtor line uoltages.

The oncphase converter output terminal is connected to the utility grid by a small inductor La. Even if a(t)is modulated such that us(t)=ua(t), the inductor voltage

The aim of the vector conholler, is to bring the system into stationary operation, where the p h r relations of fig. 4b hold and h(t)is sinusoidal. The setpoints involved with thi controller, are the amplitude and phase angle of q t ) .

The current can be controlled via the inductor voltage uL(t) by varying the converter output voltage us(t). The static relations of the phasor plane given by (3) M elucidated in fig. 6. I, = ~ . ~ / 1 - I k u m + p + # WL?

(8) is the basis for the phasor plane where the time vary-

ing components (cosine and sine) arc unity on the phaaor plane's orthogonal axis. Usually, ua(t) is not a y n b niaui with the Cosine term in the DFT and the nsulting phase p,. will have an arbitrary value in the Rframe in fig. 4a. The same holds for the current &(t). Since the p h r diagram is used for control purposes, a standard area of operation must be ddined for tuning the conTo do this, a new coordinate frame troller para". K (q,d) is introduced with its real axis in the dinction of the grid voltage phasor, M elucidated in fig. 4. In thii frame an areacan be defined for dmhiblecurrent phasor positions, and compondingly, the inductor voltage phasor UL. The controller must keep phaaors in positions relative to the grid voltage phaaor M is dictated by the setpoint of the controller. Usually, this setpoint can be translated into a wmplez pmucr phosor S depicted in the phaaor plane. The complex power S is ddined by (9). Note that the S is independent of the phase angle v,, and thus in the same direction in the phasor plane K. S = U.I'

LO

a)

w

30

11, +

OO

b)

10

w

30

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Fig. 5: a) Phase angle (p and b) nnr value I2 of the grid current in steady state as function of phase angle of the converter voltage u3(t).

+

In the vector wntroller this phasor diagram is used for controlling grid current ia(t). A Discrete Fourier T h w formation (DFT) is used to create the phssor diagram shown in fig. 4b. The DFT is used for calculating the amplitude and the phase of a signal relative to a discrete cosine signal with amplitude one and phase 5ero. The accuracy of the calculations depends on the number of samples N. used per period we selected N.=40. Therefore, the HLC samples the grid voltage and current at a frequency f,=50N.=2 kH5. Frequencies up to the Nyquist frequency (1 kH5) can be reconstructed errorless by the DFT if the signals to be sampled contain no higher frequenciesthan the Nyquist frequency. Apropriate antialiasiig filters are assumed. The vector controller uses just the 50 H5 component and only this component is calculated by the implemented DFT ( f , = 2 kHz) with:

= P+jQ

(9)

Translating the phaaor into the K-frame is done by rotating all vectors in the phasor plane (Rframe) with an angle -y*. The DFT returns information about 60 HB signala only, however, if the grid frequency is dii€aing from 50 Ha, there w i l l be a negligible small ripple on the amplitudes returned by the DFT. The phases returned by the DFT will not be constant and will decrease when the grid frequency is smaller than 50 Hs (and increase for fa250 Hz). This will result in rotating phasors in the phasor plane R (=SO HB) and can cause problrms when a controller is based on this phaaor plane. However, in the K-frame the rotation is ruled out and the controller can function undisturbed. In this frame, all and amplitudes an constant and a controller can be tuned for a certain range of positions of phasor l a , From the amplitude and phasc information about the grid voltage and current the average active power P; and reactive power Qa delivered to the grid can be calculated. Note that Pa resp. Qa an proportional to the q- resp. &component of the inductor voltage UL. Thus, in steady state o p eration the active and reactive power can be controlled separately by influencing the inductor voltage's orthogcnal components.

(4)

(5)

which yields the relative phase y,, and amplitude ir:

In general, any signal u(t) of one frequency (d) can be written as a linear combination of a cosine and a sine function: u(t) =

U,,

cas(wt)

+ U.i,

sin(&)

(8)

Summary: h m samples of the grid voltage ua(t) and current i a ( t ) phasors Ua and Za can be calculated at any sample moment by the DFT. The vector controller is responsible for creating the required phasors U3 and ULin the K-frame. The phasors can be translated from the Kframe bade into time signals at evay sample moment n and used as reference signals for a current tracking controller. (11) shows, for example, the inductor voltage UL, where y , , ~is the inductor voltage phase angle relative to the p a x i s in the If-frame.

385

Algorithm The vector eontmlkr applied controllers in the rotating phasor plane (K-frame) of iig. 4b. All nccwsary signals from the SJnkm and setpoints arc sampled and translated into the K-plane. The controllera outputs arc translated from the phasor plane back to the time domain and a p plied to the power converter. This results in a current phasor l a position relative to the grid voltage phasor Ua. The controllcm bringa the current phasor to this position by adjusting the inductor voltage phasor U,, or quilently, the converter output voltage phasor US.

which is sinusoidalin steady state. If the m n t deviates from the sinusoidal shape, us(t) is adjusted such that the powera deliveredto the grid arc correct (P.=Q.=ieO), regardless of the shape of h(t).The controlla just u8es information returned by the DFT about the 50 Ha components of grid current and voltage neglecting informs tion about DC or higher harmonics components. Higher harmonic currents are filtered out by the DFT in the controller and arc not compensated for.

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ai

For sinusoidal signal (9) is complementedwith (12) and (13). (12) makes it useful to express the converter setpoints into the average active m p . reactive power (P. resp. 9.) delivered to the grid, resulting in setpoint p sitions of the phasors Ia and UL (and thus U~=U~+UL). Using the DFT the phasors h and Ua arc determined and the average powas Pa and Qa, delivered to the grid are calculated with (12). Comparing actual values and setpoints gives an error signal for adjusting the inductor voltage phasor U,. This is elucidated in fig. 6 where the HLC is divided into two blocks. The schedule shows the DFT of ia(t) and M(t) and the invcm~DFT of U3. The DFT samples at f.=2 lcH& which is slower than the LLC sample rate dictated by the natural commutation points fa%3.6kHa (test system). All calculations in block 1 are done at this frequency f.. Usually, the inversc DFT would be done at the same f r c quency, however, this transformation (11) just needs the 'common phase' m / N , which is determined by the relative sample number n in the DFT expressing the phase angle of the cosine signal used in the DFT. f. discretisee this phase angle into f,/50 values between aero and 360°. However, if a high frequent clock ( f 2 0 MHa) on the DSP board is restarted at the sample moment where n=O,the relative phase angle can be calculated more accurate at any moment and signala from the phasor plane can also be translated into the time domain at fa. Since the LLC requires a signal a(t)which is compensated for the time delay between the sample moment of a(t)and the actual fuing, the HLC must have a block synchronised with the LLC (block 2 in fig. 6) at fa Hs resulting in a dead-time compensated a(t).The inverse DFT on U3 can be shifted from block 1 (f.) to block 2 resulting in more accurate signala ~ ( tand ) a(t). The HLC controller needs the value of inductor La. However, inductor values are usually hard to determine accurately. The PEcontroller adapts to variations in the system in order to deliver the correct active and reactive power to the grid. To make the feed forward dfective, some 'best' a priori knowledge about inductor value La is sufficient. Note that the inductor value used in the HLC block does not adjust itself, only the PI-controller output changes. Fig. 7a shows a step response in the current rms value from 20 A to 40 A rme simulated for the laboratory test system. The phase angle between u,(t) and i,(t) is cp=-26O and P=O in block 2. Note that this controller makes a signal a ( t )resulting in a converter output u3(t)

t

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am

o

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t

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0.1

[SI

4 t -+ [SI b) t [SI Fig. 7: Vector controller: step msponae in current m vdue fnnn 90 A to 40 A. a) P=O (standard) b) P=O.5 (..tended) in block 1. -+

With P=O, damping of DCcomponents is left to the conversion system itself and, fortunately, is caused by commutation of switches (without power loss) and by (parasitic) resistance in the main circuit. According to [3], commutation causes a voltage drop of the converter output voltage being a linear function of the converter output current (in case of DC output voltage and current). If commutation is modelled in the phasor plane, an actual output voltage phasor U3 results, which is the calculated phasor of U, minus the commutation phasor U-,,,. Fig. 8a shows the rotating phasor plane K with commutation modelled. The dashed phasors are controlled by the HLC in the standard vector controller to result in the actual solid phasors. d

d

Fig. 8: Vector conhllers: a) standad b) extended vith COUpled inner loop c) coupled inner loop and wrongly eatimated Lq d) extended with &coupled inner loop.

The standard vector controller is now extended with an

386

extra control loop synchronised with the LLC. The control loop is implemented in HLC block 2 with P#O and compares the actual value of &(t) with the calculated one, resulting in a instantancow correction of the value u3(t)and a(t).The &point of this "nt tracking l00p (or inner loop) is calculated from the inductor voltage components in block 1 of the HLC using (13) and resulb ing in the phasor diagram of fig. 8b. The inner loop usen a P-controller. At any moment a positive (negative) error i. = d t ) - & ( t ) results in an in(d-) of u3(t). This control loop reduces higher harmonics in the current since they can be regarded as deviations from the sinusoidal reference signal *t) and result in higher harmonics on u3(t) thereby reducing the higher harmonica in the inductor volhgc u ~ ( t ) .However, the dead time between the measurement of &(t) and the accompanying u ~ ( t )c, a d by the digital fuing circuits and the converter topology, makc it impossible to avoid higher harmonica in the inductor voltage. The inner loop gives the converter system good damping characteristics. 7b shows a step response in the current rms value from 20 A to 40 A r m a simulated for the laboratory teat system. The converter output voltage u4t) is not necessarily sinusoidal. Note the fast damping of D C components in the current. The inductor voltage and current are coupled by (13) in the controller and the inner loop brings the calculated phasor 12, to 12 in tig. 8b. This results in a calculated inductox voltage and US. both coinciding with the actual values. Therefore, the inner loop must compensate for the commutation voltage gap between the calculated value and the actual value. The calculated phasor U3. is corrected upon by the inner loop. This correction is done in the time domain. If inductor La is diffuent from the estimated value, the actual required inductor voltage (and Us) changes, however, the signals in block 1 remain unchanged, and the inner loop must compensate the relative large errors betcalculated reference values and actual required valuca (fig. 8c). The admiiible deviation between the actual and the e+ timated inductor value posts constraints for the proportional controller and requires a proportional gain that is high enough. To see the &ect of the inner loop on the inductor voltage, a simulation is carried out where the system is in steady state and the inner loop is switched off (P=O). The inductor voltage is adjusted in order to meet the setpoints. Block 1 of the HLC starts com-

pensating commutation and wrong inductor estimates. Fig. 9a shows the inner loop disconnection simulation where the estimated inductor value is halve the actual value ( L a d 0 mH). The extended vector controller b e comes the standard vector controller and the controlled phasors in fig. 8c m m in the directions of fig. Sa.

Fig.

Fig. 9: Disconnection of inner loop in steady state d wrongly estimated b. Inductor voltage and current are a) orthogonal b) &coupled.

+or

The cumnt reference signal for the inner loop is made a feed forward signal by calculating phasor l a . and i d t ) from the power setpoints directly. This control structure change is made by switching C down in fig. 6. The inductor voltage and current phasom are no longer orthogonal allowing the inductor voltage to compensate for commutation and unknown inductor values. Fig. 9b shows the same experiment as iig. 9a but with the decoupled inductor voltage and current phasors. After disconnecting the inner loop the outer loop signals change minimal. Therefore, the inner loop can be tuned for DC and higher harmonics current components without the burden of cormtion for commutation and a wrongly estimated inductor value La. Fig. 10 shows a step response in the current rms value from 20 A to 40 A r m s simulated for the laboratory test system.

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e + I.[ 4 [E31 Fq. 10: Extended vector contruller step response in cumnt rnw value fmnr 40 A t o 40 A. Inductor c u m t and voltage components are decoupled in the phluor plane.

4

and enable the use of an ACsignal-tracking control loop: the inner loop. This control loop shih the actual firing instances of the switches at the latest possible moments using the most up to date available measurements. This loop gives the converter good damping characteristics for frequencies that are not in the controller setpoints. Setpoint changes within a few grid periods % is in the controllers scope. Disturbances aused by bridge switching due to current zero crossings can be corrected if an inner loop is present. The disturbances do not violate the average power rcqnirementa on the current and are not noticed in the phasor plane. Only disturbances with an average dfect are noticed by the DFT and are compensated for, such as commutation and badly estimated (or measured) inductor values.

-+

RESULTS The vector controller has not yet been implemented on the DSP. Instead, tarts of a rms current controller combined with the dead time compensation implemented on the DSP (TMS320C30) are shown. Fig. 11 shows the grid current and its power spectral density. The spectral analysis shows a main component of 50 Hz with amplitude 72 A. Note that a rms current controller does not reduce harmonics caused by harmonics in ua(t). The vector controller does have an algorithm to reduce harmonics in the current. The errors around the zero crossings are not compensated by this controller. im,

I

The measuranenta of signals and translating them into a domain that is easy to control is the main problem in the one-phase output cycloconverter. It poses constraints on the PI-controller actions. Still, the proposed vector controller is expeded to perform satisfactory in practice. The three-phase output cycloeonverter enables a Park tramformation instead of a DFT to transform the signals into a vector domain. This Park transformation has a number of advantages over the DFT: it avoids the time delay of the DFT and also returns information about other frequenaes than 50 Hs. The Park transformation can both simplify the proposed Vector Controller and boost the system performance to the level required for controlling the cycloconverkr as an electronic transmission.

REFERENCES [l] L. Gyugyi and B.R. Pelly, Static Power Bquency Chongers. New York: Wdey, 1976.

[2] N.H.M. Hofmeester, "High-Frequency Cycloconverter Control," Report no: R93.018, DelR University of Technology, Delft, 1993. [3] W.Leonhard, Conhol of Electrid Drives. Berlin: Springer-Verlag, 1990. [4] E.B. Patterson, P.G. Holmes, and D. Morley, "Microprocesaor/ASIC to total ASIC design for cycloconverter drives," Microprocessors ond Mimsystems, Vol. 14,No. 4, pp. 219-226, 1990.

b)

t

-t

[SI

cl

fi.

-+

[Hal

Fag. If: Grid c u m t and power spectral density under DSP m s contml.

CONCLUSIONS The proposed controller for the onephase system uses phasors controlled in a phasor plane rotating at the grid voltagar frequency. In this phasor plane, all relations are static and variables can be handled as slowly varying DC values. This allows the application of PI-controllers. Since the Controllers bring the phasors (or vectors) into =me relative positions determined by power setpoints, the controller is called vector conholler. The digital control strategy allows calculations of AC reference signals

[SI H. Polinder et al., "Cycloconvcrter for High Speed Permanent Magnet Generator Units," to appear in the C o d Rec. 5th European Conference on Power Electronics ond Applicotions, Brighton, 1993. [6]

S. Seong, M. Matsui, and T. Fukao, "Behaviour of a High-Frequency Cycloconverter Operating in Discontinuous C i l a t i n g Mode and a Control Scheme for its Circulating Current," IEE ofJopn, Vol. 110, No. 5, pp. 5666, 1990.