Advanced Active Front-end Rectifier Control for Grid Emulator ...

This paper was presented at the 14th Wind Integration Workshop and published in the workshop’s proceedings

Advanced Active Front-end Rectifier Control for Grid Emulator Application Ander Gonz´alez, Yves Mollet, Thomas Geury, Ram´on L´opez-Erauskin and Johan Gyselinck Bio Electro and Mechanical Systems department ´ Ecole Polytechnique de Bruxelles Universit´e Libre de Bruxelles Brussels, Belgium Email: [email protected]

Abstract—The grid-emulator is a laboratory platform that reproduces grid voltages under various normal or abnormal conditions. It is designed to perform test to both loads and generators. In this paper the grid connection of a grid emulator is described. The connection to the grid is done by means of an LC filter connected to the lab transformer, resulting thus in a LCL type filter. The system control is described and tested for different grid inductance values. The evolution of the important parameters is tracked with the variation of the grid inductance showing how the variation of this affects the control and could lead to an unbalanced system.

L2

Ig

L1

Grid

Grid side VSC C

I. I NTRODUCTION With the increasing penetration of renewable energies in the low voltage (LV) network, some problems arise from the fact that the electrical network was designed for unidirectional downstream distribution of energy. This challenges the companies installing renewable generation in households, such as photovoltaic panels, due to repeated generation stops or power quality issues under certain unfavorable conditions. To adapt the existing installations rather than purchasing new equipment, the inverters must be tested in order to analyze their behavior and design new strategies to increase the penetration of renewable energy sources. Grid-emulator examples found in literature include different approaches and topologies in order to emulate the behavior of the utility grid in laboratory for equipment testing purpose. These are different following the tests to perform and the needs of each laboratory. A usual case is the study of device behavior during grid faults. In [1] hardware test-bed is presented which has a modular approach using reprogrammable three-phase inverters in charge of simulating different load and generator types, while in [2] a similar approach is reported using parallel connected converters simulating again loads and generators, including characteristic inertia of electromechanical generators in the control. The development of a back-to-back converter based grid-simulator controlling impedance, voltage, harmonics and frequency at the ac interconnection of several distributed generation units is presented in [3]. Biligiri et al. presented a preliminary approach to build a grid simulator for testing wave energy converters. The simulator is built using 3 level neutral point clamped converters attached to a transformer allowing to test equipment of power rising up to 100kW [4]. In [5], [6] an inverter based grid-emulator, in which the neutral point is connected to the midpoint of the DC-bus, is presented. This topology requires split DC-bus capacitors. To overcome this problem, that can lead to increased volume

Emulator side VSC

DUT

Fig. 1. Description of the grid-emulator

and cost due to the need of higher DC-bus capacitance, in [7], [8] the authors present a converter with neutral point connection using a fourth half-bridge, thus allowing to control the neutral point voltage and avoiding DC-bus voltage unbalance. This control of the neutral point voltage allows for generating unbalanced grid conditions. II. S YSTEM DESCRIPTION Since unbalanced grid conditions are going to be tested, and the direct connection of the neutral point to the midpoint of the DC-bus requires compensation of DC-voltage unbalance in the control, a four=phase voltage-source converter (VSC), referred to as emulator-side was selected. This includes an output LC output filter in order to reduce the generation of high-order voltage harmonics due to PWM modulation. This is part of a back-to-back converter comprising two VSCs as shown in figure 1. The control of the emulator-side of the grid-emulator allows to generate grid-like voltages (3-phase plus neutral), including or not flicker, grid sags, over- and under-voltage, frequency change, and harmonics. Thanks to this, singleand three-phase inverters can be tested and their behavior can be studied under normal and abnormal grid conditions. The system is a four-quadrant converter designed for testing up to 20kW equipment (both load and generation), with voltage limits of 400V± 10%. This translated to the DC-bus using a PWM modulation, is a requirement of a minimum DC-voltage equal to 588-719V if no over-modulation is wanted. With no voltage sag, the least DC-voltage demanding condition is undervoltage testing, requiring down to

This paper was presented at the 14th Wind Integration Workshop and published in the workshop’s proceedings

Kp =

L1 + L2 3Ts

(1)

Ti =

L1 + L2 R1 + R2

(2)

VDC ref

X

 1  K p 1   sT i  

-

-1

Id ref

Measured VDC

Fig. 2. DC-voltage control loop

DC side power 4500 4000 3500 Active Power [W]

588V for 400V-10% phase-to-phase voltage, while the most demanding is the over-voltage condition requiring up to 719V. Besides, if voltage sags are included during the test, one or more phase-to-neutral voltages may require a higher DC-voltage. The DC-voltage has to be kept at least at the double of the highest phase-to-neutral voltage. Therefore in order to avoid unnecessary losses in the converter, a variable test-dependent DC-voltage will be used with the purpose of keeping it as low as possible depending on the test to be performed. The input of the converter, referred to as grid-side, is a grid-tied three-phase VSC. This it is connected to a transformer through an LC filter, and has the task of keeping the DC-voltage of the converter bus at admissible levels while tests are performed. This means that it has to charge the DC-bus capacitors during start-up, and push or pull the input power to the grid in order to keep the DC-voltage under rated conditions during operation with generators and loads respectively. The DC-bus charging before operation is done using precharge resistors and the free-wheeling diodes included in the three half-bridges of the grid-side converter. After the required time to charge the DC-bus is elapsed, the grid-side converter control is started. To keep the DC-voltage under rated conditions the dynamics of the active front-end (AFE) have to be faster than those of the device under test. As the system is intended to test the performance of PV inverters at this moment, in order to identify the required power output dynamics, some tests have been done to two available PV inverters from different manufacturers determining a power change rate of about 1kW/s in both cases. The power has been measured at the PV panel connection during the start-up of the PV inverter from zero power to MPP, and resulting power change rates are shown in table I. The power change rates, as the one presented in figure 3, have been approximated using straight lines. Neglecting the PV inverter and grid emulator losses, this straight line represents the maximum rate of change of power that the grid emulator has to exchange with the grid. The grid synchronization is made by means of a phaselocked loop (PLL). The grid current is controlled in a synchronous rotating dq frame, where the d axis is aligned with the phase-to-neutral voltage of the first phase. This way the DC bus voltage can be controlled by means of d-axis current reference, while the q-axis current reference is kept to zero, in order to achieve unity power factor. The currentloop PI controllers are tuned neglecting the filter capacitance, resulting thus an L type filter, with an equivalent inductance equal to the sum of all inductances. This assumption is valid because the capacitor will strongly attenuate the switching harmonics while they barely change the filter response at low frequencies as the one of the grid. The proportional gain and integration time are calculated following the technical optimum [9] firstly:

3000 2500 2000 1500 1000 500 0 78

80

82 84 Time [s]

86

88

Fig. 3. Example of inverter DC power input showing power change rate

TABLE I T ESTED PV INVERTERS : APPROXIMATED MAXIMUM POWER CHANGE RATE

Inverter

Type

dP/dt [kW/s]

A B

5kVA / 3-phase 3kW / single-phase

1.02 0.97

where Ts is the micro-controller sampling time, L1 and R1 are the converter inductance and resistance respectively, and L2 and R2 are the equivalent grid side inductance and resistance respectively. Then the gains are adapted to reach the desired response time and overshoot. Since the grid inductance L2 and resistance R2 are unknown, this method is used as stating point estimating their values. The control structure for current loops is shown in figure 4. The DC-voltage PI controller is tuned in order to achieve a much slower response compared to the current controllers, allowing for decoupled loops for DC-bus voltage and current control while being still 1.5 times faster than the output dynamics of the tested inverters. The DC-voltage control structure is presented in figure 2. The output of the PI controller is multiplied by the DC-voltage reference in order to make the control react faster to changes in DC-voltage reference while keeping the rejection to voltage oscillation. Energy contained into a capacitor is proportional to the square of its voltage, this strategy allows to better adapt the control to the non-linearity of the DC-voltage. The current and voltage sensors are placed at the transformer terminals, to measure the three-phase grid voltage and current. Using this setup, the stability is increased [10] at the expense of a reduction of converter safety since the current supplied by the converter is not directly measured.

This paper was presented at the 14th Wind Integration Workshop and published in the workshop’s proceedings ig sRd C + 1 = 3 2 v s CL1 L2 + s C (Rd L1 + Rd L2 + R1 L2 + R2 L1 ) + s (L1 + L2 + CRd R1 R2 ) + R1 + R2

-

-

1 sL2

Ig

Rd

Iref

-

 1  K p 1    sTi 

-

CONVERTER 1 1.5Ts s  1

-

1 sL1

-

1 sC

Ucap

-

Icap

1 sC

Vi

1 sL1

Vi ref

-

Vg

LCL FILTER

CONTROL Ucap

1 1.5Ts s  1

Icap

CONVERTER Vi

 1  K p 1    sTi 

Vi ref

Iref

Vg

LCL FILTER

CONTROL

(4)

-

1 sL2

Ig

Rd

Fig. 4. Block diagram of the system with passive damping

Fig. 5. Block diagram of the system with virtual resistor active damping

III. F ILTER

When using damping resistors for attenuating the resonant behavior of the LCL filter, a resistance value close to the third of the capacitor impedance at resonance frequency ωres is recommended [15]:

Considering the grid and transformer inductances, the resulting filter is of the LCL type. These filters present a resonant frequency (at which inductors and capacitors have the same impedance), that has to be damped at that frequency for the sake of system stability. This resonant frequency is calculated as follows: r L1 + L2 1 (3) fres = 2π L1 L2 C The different ways of damping the resonant behavior of the filter can be divided into two main groups: (i) passive and (ii) active damping techniques. Passive techniques rely on including damping resistors, while active damping techniques modifying the control structure of the converter. In general, since no passive elements are included, the active damping techniques present higher efficiency, and flexibility [11], [12]. On the other hand, active damping techniques may require additional sensors. A. Passive damping Passive damping techniques consist in including resistors in some parts of the filter in order to damp the resonant behavior. These can be placed in parallel with the inductors, or in parallel or series with the filter capacitors. These can also be found together with other inductors or capacitors, added in different configurations [13]. Using passive damping does not require any change in control scheme nor installation of new sensors in the circuit [9]. In the grid-emulator a passive damping technique relying on resistors connected in series with the 3-phase star-connected filter capacitors is adopted to connect the converter to the grid. This method ensures stability for every working condition without increasing the complexity of the controller loops. On the other hand, special attention has to be paid to the losses and the forced cooling that may be required [14]. This method changes the filter transfer function that yields (4), where C is the filter capacitor, and Rd is the resistance of the damping resistors. A block diagram is shown in figure 4 in which the dq decoupling terms, grid voltage feed-forward, and parasitic resistances of the inductors are not included for ease of understanding.

Rd =

1 3ωres C

(5)

In this case the adopted value for Rd is 4Ω. This may increase the losses in the filter due to the relatively high value of damping resistance compared to the result of equation (5), but since the grid-side inductance is unknown it is preferable to work with an overdamped system. B. Active damping Active damping techniques consist in changing the control structure so as to damp the resonant behavior of the filter. This can be done in three ways: through either including a state-variable feedback, filtered current control, or pole-zero cancellation [16]. Among digital filters included in current control for active damping, lead filters and notch filters can be found. The lead compensator can increase the phase margin of the system but this is limited by the spacing of its zero and pole. Notch filters tuned at resonant frequency will also damp the resonant behavior of the LCL filter [17]. State variable feedback consists in including a filter capacitor voltage [18] or current [19] feedback loop in the control. This method is very similar to the one adopted, and results in the same transfer function as in (4), but without the zero introduced by the damping resistors. This allows keeping the original roll-off rate of 40dB/dec of the filter while the real damping resistors reduce this rate to 20dB/dec as a result of the introduced zero [17]. This method is also known as virtual resistor. A block diagram of the system using virtual resistor damping technique is shown in figure 5. IV. S YSTEM RESPONSE VS . IMPEDANCE VARIATION Once the current controllers are tuned and the different parts are selected, system response can be analyzed for grid parameter variations. The values of the considered used parts are summarized in Table II. Since the grid impedance is unknown a large variation of the inductance can occur,

This paper was presented at the 14th Wind Integration Workshop and published in the workshop’s proceedings

Bode Diagram

Root Locus

8000

40

6000

20

4000

0

−1

Imaginary Axis (seconds )

Magnitude (dB)

60

−20

Phase (deg)

0 −90 −180

−360

−2

−6000 0

10

0 −2000 −4000

0.1mH 1mH 4mH

−270

2000

2

10

10

−8000 −3.5

Frequency (Hz)

−3

−2.5

−2

−1.5

−1

−0.5

−1

Fig. 6. Open-loop frequency response of the system for different grid inductances

0 4

Real Axis (seconds )

x 10

Fig. 7. Root-locus of closed-loop system for Lg = 0.1mH Root Locus

8000

specially when connected to weak grids [20]. The open-loop transfer function of the system is the following:

6000

KGdelay GF ilter OL = 1 + KGdelay GF ilter

−1

2000 0 −2000 −4000 −6000 −8000 −3.5

−3

−2.5

−2

−1.5

−1

−0.5

Real Axis (seconds−1)

4

Fig. 8. Root-locus of closed-loop system for Lg = 1mH Root Locus

8000 6000 4000 2000 0 −2000 −4000

(7)

−6000 −8000 −3.5

−3

−2.5

−2

−1.5

−1

−0.5

Real Axis (seconds−1)

TABLE II F ILTER COMPONENT VALUES

Grid pulsation Converter inductance Converter resistance Grid side resistance Filter capacitor Damping resistance

0 4

x 10

Fig. 9. Root-locus of closed-loop system for Lg = 4mH

Symbol

Value

ωg L1 R1 R2 C Rd

100π rad/s 2 mH 12.9 mΩ 1.5ωg Lg 30 µF 4Ω

As can be seen in table III, the resonance frequency of the filter is always between 10 times the grid frequency, and the half of the switching frequency; this is recommended for avoiding resonance problems in both upper and lower harmonic spectrum limits [21].

Step Response

1 0.8 Amplitude

Parameter

0 x 10

−1

Where GC = Kp + Ksi is, the controller transfer function, Gdelay = 1.5T1s s+1 the first-order approximation of the total delay introduced by the computation time and modulation in the converter, and Gf ilter the filter transfer function shown in equation (4), relating the converter voltage to the resulting grid current. The studied range comprises L2 grid inductances from 100µH to 4mH. In table III the filter resonance frequency value is shown for different grid inductances while keeping the other values constant but changing R2 accordingly. In figure 6 the open-loop system response for L2 equal to 0.1, 1, and 4mH is shown including stability margins. Figures 7 to 9 show the root locus of the open loop system Gdelay GF ilter for the same grid inductance variation, where a K gain is applied and the loop is closed using unity feedback. The result shown in figures is the pole and zero location and the evolution of their location with the change of K of the open-loop transfer function excluding the controller:

Imaginary Axis (seconds )

(6)

Imaginary Axis (seconds )

4000

Gol = GC Gdelay GF ilter

0.6 0.4 0.1mH 1mH 4mH

0.2 0 0

0.005

0.01

0.015

Time (seconds)

Fig. 10. Step response of closed-loop system for different grid inductances

This paper was presented at the 14th Wind Integration Workshop and published in the workshop’s proceedings TABLE III R ESONANCE FREQUENCY AS FUNCTION OF GRID INCLUDING DAMPING RESISTANCE ACCORDING TO (5)

0.1 0.5 1 2 3 4

fres [Hz]

Rd Ω

2978 1453 1125 919 839 796

1.78 1.22 1.57 1.92 2.11 2.22

10 5 Iabc [A]

Lg [mH]

15

0 −5 −10 −15 0.02

0.025

0.03

0.035

0.04 Time [s]

0.045

0.05

0.055

0.06

0.03

0.035

0.04 Time [s]

0.045

0.05

0.055

0.06

80 Rd=3 Rd=4

70

vR =4

I

d

15

Iq

50 10

40 Idq [A]

Grid current THD [%]

d

vRd=5

60

30

5

20 0

10 0

−5

0

0.2

0.4

0.6 0.8 1 1.2 1.4 Grid−side inductance [mH]

1.6

1.8

2

Fig. 11. Grid current THD for different grid inductances using passive damping (Rd) and virtual resistor damping (vRd) for a 15A current reference

0.02

Fig. 12. Grid currents during reference step from 0 to 15A-peak

Simulation Reference

10

5

0 1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5 6 Time [s]

7

8

9

10

4000

2000

DC−bus voltage [V]

Active power input [W]

d−axis current [A]

V. S IMULATION The described system was simulated using Matlab Simulink. Simulations where performed for different grid inductances with current controller values of Kp = 4.2 and Ti = 0.15 using damping resistor values of 3 and 4 Ω and virtual resistor method gains of 4 and 5. In figure 11 the total harmonic distortion of the grid current is shown for 15A-peak reference. The grid-current waveforms for a reference change from 0 to 15A-peak are shown in figure 12. This is simulated using a grid-inductance of 1.2mH and damping resistors of 4Ω. The whole system has been simulated using an averaged model of the system (neglecting the converter switching dynamics). A measured DC power curve has been used as power input coming from the PV inverter under test. This can be considered as regular operating conditions. In figure 13 the d-axis current and its reference, the active power input from the inverter under test, and the DC-voltage are shown. The simulation corresponds to the start-up of the inverter under test followed by a sudden disconnection after 8.5 seconds.

0.025

0

720 700 680

Fig. 13. Simulation of a regular operation of the grid-emulator

use section* for acknowledgement

VI. C ONCLUSION The grid connection by means of an LCL filter of a gridemulator is presented. The components of the filter must be carefully selected in order to place the resonant frequency of the filter far enough from both controller bandwidth and modulating frequency. It is important to keep this condition for grid impedance variations. Besides, the filter response must be damped so as to avoid exciting the resonant behavior that otherwise may provoke large undesired currents and may destroy the device.

ACKNOWLEDGMENT This work was supported by the Belgian Walloon region under the project BATWAL. R EFERENCES [1] L. Yang, Y. Ma, J. Wang, J. Wang, X. Zhang, L. M. Tolbert, F. Wang, and K. Tomsovic, “Development of Converter Based Reconfigurable Power Grid Emulator,” pp. 3990–3997, 2014.

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