18th INTERNATIONAL SYMPOSIUM on POWER ELECTRONICS - Ee 2015

NOVI SAD, SERBIA, October 28th - 30th, 2015

Abstract: In order to fully utilize distributed power generation systems (DPGS) and other systems based on inverters, control design engineers ought to follow procedures that will supply them with controllers’ parameters the usage of which will result in converter working inside of the demanded control boundaries. This paper presents one procedure for controllers’ parameters tuning that ensures the above-mentioned behaviour. Also, beside simple and straightforward software setting up, a procedure of how converter hardware can be set up and operated is proposed. Thus this paper can be used as a source of initial sofware and hardware framework or as a kind of a ’know-how’ for power electronics engineers that are just starting their research in the area of DPGS.Key Words: Grid-tie inverter/Voltage loop/Current loop/PI tuning/DPGS/VAR Compensator.

1. INTRODUCTION

Applications in which inverter is a focal point can be roughly devided in three categories. The first is one in which inverter acts as a bridge between renewable energy sources and existing grid. These applications are generally referred to as distributed power generation systems. The second group is comprised of motor drive applicarions in which inverter acts as a bridge between existing grid or other source of energy, and motor drive. The last group includes other applications that do not belong to previous two (var compensators etc.)[1]. Although these applications are quite different, system models are similar if not the same and thus controller synthesis proposed here can be extended and applied to most of the above-mentioned applications[2]. Hardware is also similar, and thus hardware setup proposed here can be used as a starting point in many inverter applications.

Traditional control structures in grid-tie inverter based applications comprise of outer voltage loop and of inner current loop[3]. Voltage loop controlls DC-link voltage, and thus, indirectly the power flow. Inner current loop controls the current flow and secures inverter from reaching undesired working points. This paper focuses on voltage loop controller parameters determination (current loop parameters being determined following the well-known Dahlin’s algorithm[4]). As it will be shown, through both simulation and experimental results, following proposed algorithm fast aperiodic

response is obtained. This response ensures that no ringing in power flow is observed.

On the other hand, in this paper conventional grid connected inverter topology, that is DPGS, is taken into account [5]. Hardware schematics is shown in Fig 1. It should be noted that no DC-link side rectifier is used. DC-link is rather charged via inverter itself, or specifically via freewheeling diodes. This way, experimental setup is simplified, without losing any functionalities met in inverter with separate rectifier. In order to properly charge DC-link on startup pre-charge resistors and an appurtenant contactor are used.

Fig 1. Power stage schematics.

2. INVERTER MODEL AND OPERATION PRINCIPLES

Inverter model in synchronously rotating reference frame is given by equations (1) and (2)[6].

τ el

d id

dt=−r∗id+x∗iq+udC−udG (1)

τ el

d iq

dt=−r∗iq−x∗id+uqC−uqG (2)

Considering Fig 2. which depicts simplified model of grid connected inverter based on above equations (resistance is omitted for simplicity), one can obtain diagrams (Fig 3.) that represent different power flow situations. Also, equations (3) and (4) that express active and reactive power being transferred should be taken into account[7]. Positive current flow direction is chosen to be from inverter into the grid.

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GRID CONNECTED INVERTER DC-LINK CHARGE ANALYSIS

Ivan Todorović, Stevan Grabić, Zoran Ivanović, Vlado Porobić, Evgenije Adžić

University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia

Fig 2. Simplified model of grid-tie inverter.

pG=−udG id(3)

qG=udGiq(4)

Top left picture in Fig 3. shows the situation when reactive energy is being transferred from inverter to the grid. The top middle picture shows case when active energy is absorbed by inverter. The top right picture shows cumulative case. The bottom pictures depict a similar process, with the difference that here active power is also being produced, not absorbed, by the inverter. Similar diagrams could be obtained for the situation where reactive power is being absorbed by inverter. In Fig 3. index c indicates converter, index g indicates grid and x indicates voltage drop over inductance.

These diagrams in conjunction with equations (3) and (4) thus imply that in order to produce or absorb active or reactive energy inverter should produce voltage with such amplitude and phase angle that big enough current starts to flow. On the other hand, how much active energy should be exchanged depends on DC-link voltage deviation from reference value. Reactive power flow is manually set up, although it can be controlled by some superordinate logic.

Fig 3. Current and power flow diagrams.

3. CONTROL ALGORITHM AND PARAMETERS CALCULATION

3.1. Current loop

Current loop in case of grid-tie inverter can be approximated with loop depicted in Fig 4.

Fig 4. Simplified current loop.

Current loop PI parameters can be calculated using Dahlin’s algorithm. Using this algorithm aperiodic response to a step change in current reference is obtained.

K pidq= 1−e− λT i

K∗(eT i

Ts−1) (5)

K iidq

=eT i

T s−1.(6)

3.2. Voltage loop

Considering that by direct control of DC-link voltage one would obtain nonlinear loop, indirect control of voltage is realized. Actually, energy transferred through DC-link is controlled and only as a result of this physical quantity being controlled DC-link is kept constant [8].

Fig 5. Simplified voltage loop.

Transfer function of voltage loop is given by equation (7).

Gsl=K idc T dc 2 z2

z3+z2 ( K1+K2−2 )+ z ( K2+1 )−K1

(7)

Where:

K1=K pdc T dc

2, K2=

K idc T dc

2

(8)

Considering that in denominator there is characteristic equation of the third order and that this equation generally can be factorized as:¿ (9)

equation (10) can be obtained.

z3+z2 (−z1−z2−z3 ) (10)

+z ( z1 z2+ z1 z3+z2 z3 )−z1 z2 z3=0By comparing (7) and (10), equations under (11) are

obtained.z1+ z2+z3=2−K1−K 2

z1 z2+z1 z3+z2 z3=K2+1z1 z2 z3=K1

(11)

After summing above, the terms next expression is obtained.

z1 z2 z3+z1 z2+z1 z3+ z2 z3+ z1+z2+z3=3 (12)

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In order to have aperiodic response of the above-mentioned loop this equation should have real and equal poles.

z p3 +3 zp

2 +3 z p−3=0. (13)

Finally, the next value is obtained:z p=0.587 . (14)

Proportional and integral values of DC-link voltage loop should be set according to (15).

K pudc=

z p3

T dc

2

=0.202T dc

2

,

K iudc=

3 z p2−1

T dc

2

=0.0337T dc

2

.(15)

4. PRE-CHARGING PROCEDURE AND EXPERIMENTAL RESULTS

Depending on application, sometimes rectifier that charges DC-link is mandatory. For example, in case of wind turbines with asynchronous generators, energy is usually transferred to the grid via inverter and not by direct connection of the generator and the grid. In this case, rectifier must be used. Nevertheless, practically all software and hardware functionalities can be tested with significantly simplified hardware shown in Fig 1. (no generator, no rectifier and no concomitant equipment). This way both hardware and software can be explicated and progressively tested.

In order to charge DC-link with an increased time constant, pre-charge resistors are added. When contactor K1 is turned on, current starts to flow from grid, via pre-charge contactors and freewheeling diodes into the DC-link. Thus, DC-link capacitance is being charged to a value of grid line voltage amplitude. After K1 is closed Fig 6. is obtained. This part of the procedure ensures that most of the hardware is properly setup (contactors, IGBTs, sensors etc.).

Fig 6. DC-link voltage- K1 on, K2 off.

Next, contactor K2 should also be closed. This contactor shortens the pre-charge resistors. No significant change should be observed. DC-link voltage, should be changed only for a voltage drop over pre-charge resistors, if DC-link is not completely charged.

Fig 7. DC-link voltage- K1 on, K2 on.

Next, it is advisable to test loops from inside out. That is, current loop should be tested before voltage loop. Here, quadrature current component loop should be tested first. Note that flow of quadrature component should not affect active power flow and thus DC-link voltage. Considering that quadrature and direct current loops are virtually the same, if one behaves as expected the other one should behave in the same manner, and thus after this test direct current response should be observed. Proper response would indicate that both PI controller’s parameters are correctly selected and that the rest of the hardware functions properly. Reference should be set up to be a step change from zero to nominal value (or at first to some small value), and then, after a short while, step change to zero. This is especially important in case of direct current component test, in which case a too long nominal reference would cause DC-link to overcharge or to discharge completely. Quadrature current test is shown in Fig 8.

Fig 8. Quadrature current response.

Once it is concluded that current loops function in a desired way, voltage loop can be tested. Fig 9. shows DC-link voltage response to a ramp change. It can be seen that real value follows reference value and that voltage regulation works properly.

Fig 9. DC-link voltage- regulation on.

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Fig 10. Current components on voltage regulation start.

5. CONCLUTIONS

In order to quickly and effectively establish working and research environment, control engineers must follow some procedures for both hardware and software setting up. Here, one such procedure and its analysis are proposed. How to tune PI controllers in current and voltage loops is explained. Also, what hardware is necessary for initial tests is shown. Both software and hardware settings demand minimal time, effort and equipment. Thus, this paper offers a good starting point for a research in the area of inverter based applications, where engineers can find all the necessary steps needed for its laboratory build-up.

6. REFERENCES

[1] S. Chakraboty, B. Kramer, B. Kroposki, “A review of power electronics interfaces for distributed energy systems toward achieving low cost modular design”, Renewable and sustainable energy review., vol. 13, Issue. 9, pp. 2323–2335, Dec. 2009.

[2] P. R. Remus Teodorescu, Marco Liserre, “Grid converters for photovoltaic and wind power systems”, Ohn Wiley and Sons, and IEEE Press, 2011.

[3] X. Guo, W. Wu, “Improved current regulation of three-phase grid-connected voltage source inverter for distributed generation systems”, IET Renewable power generation, vol. 4, iss.2, pp. 101–115, Sep. 2009.

[4] Zhang Zhi-Gang, Zou Ben-Guo, Bi Zhen-Fu, “Dahlin algorithm design and simulation for time-delay system”, Control and Decision Conference, pp. 5819 - 5822, june 2009.

[5] Bjarte Hoff and Waldemar Sulkowski, “A simple DC-link pre-charging method for three phase voltage source inverters”, IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society, pp. 3364-3367, Oct. 2012.

[6] J. L. Da Silva, R. G. de Oliveira, S. R Silva, B. Rabelo and W. Hofmann, ”A Discussion about a Start-up Procedure of a Doubly-Fed Induction Generator System”, Nordic Workshop on Power and Industrial Electronics, pp. 1-6, June 2008.

[7] Robert Thibault, Kamal Al-Haddad, Louis. A. Dessaint, “Three phase grid connected converter with

an efficient power flow control algorithm: Experimental validation”, IEEE International Symposium on  Industrial Electronics, pp. 1306-1310, July 2006.

[8] Marian P. Kazmierkowski, Marek Jasinski, Grzegorz Wrona, “DSP-Based Control of Grid-Connected Power Converters Operating Under Grid Distortions”, IEEE Transactions on industrial informatics, Vol. 7, N0. 2, pp. 204-211, May 2011.

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