Autonomous reactive power support for smart photovoltaic inverter based on real-time grid-impedance measurements of a weak grid

Electric Power Systems Research 182 (2020) 106207

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Autonomous reactive power support for smart photovoltaic inverter based on real-time grid-impedance measurements of a weak grid

T

Henrik Aleniusa,*, Roni Luhtalab, Tuomas Messoa, Tomi Roinilaa a b

Faculty of Information Technology and Communication Sciences, Tampere University, Finland Faculty of Engineering and Natural Sciences, Tampere University, Finland

ARTICLE INFO

ABSTRACT

Keywords: Power electronics Photovoltaic systems Power conditioning Reactive power control Power flow optimization

A large share of renewable energy production is connected to a weak grid with significant grid impedance. The transmission impedance causes unintended flow of reactive power to grid, coupling the grid reactive power to the active power fed from the inverter. The reactive power causes transmission losses, strains the grid with reactive power requirements, and can even compromise system stability. Requirements on reactive power support were recently imposed on new photovoltaic inverters, which are often implemented with proportional power factor control or droop control for local voltage regulation. The present work proposes a method for realtime compensation of the unintended reactive power, which decouples the reactive power from the active power of a photovoltaic inverter. Based on real-time measurement of the grid impedance, the unintended reactive power is estimated and autonomously compensated in the inverter. The method removes the fluctuating reactive power component, while still permitting unrestricted manual control of the reactive power. Unlike conventional methods, the proposed method requires no prior knowledge on grid impedance values or delicate tuning. The method outperforms conventional power factor control even when the conventional method is tuned optimally with known grid inductance. The method is validated with simulations and experiments on three-phase photovoltaic inverter connected to a weak grid.

1. Introduction The share of renewable electricity production has increased rapidly over the last decade, as the related technologies have advanced [1]. The most prominent renewable methods are solar and wind power, which are mostly connected to the grid through power electronics. Large-scale plants are usually located in remote areas due to space constraints, which means the transmission lengths to consumption centers are often long [38,29]. Consequently, the impedance of the transmission line becomes significant imposing challenges on the performance of gridconnected converters. The inverter for renewable production is synchronized to a local point of connection (PoC), where the measurements are taken for control feedback. The current fed to the PoC causes an unintended flow of reactive power when flowing through the reactive grid impedance of the transmission line. The active power from an inverter operating at unity power factor (PF) appears as both active and reactive power on the grid side. Thus, in a weak grid the active power of a PV inverter becomes coupled with reactive power seen by the grid. Unintended reactive power increases transmission losses, reduces the maximum

⁎

transmission capacity, compromises system stability, and strains the grid with excessive reactive power requirements [31,30,21,38,36]. The rise of inverter-based distributed generation has provoked new requirements for the grid connection of the devices, which also consider the reactive power capabilities [11,18]. The reactive power balance of the power system has been traditionally managed by synchronous generators, capacitor banks [17], and recently with FACTS devices [24,12,3]. Optimization of reactive power management has been widely discussed, as the topic is vital for reliable and efficient operation of the power system [8,25,36,9,33,42]. Several studies have shown the localized reactive power compensation to be an effective and favorable method [21,31,33,39,5]. The reactive power of an inverter is controllable to a great extent, providing a flexible method for reactive power compensation with no need for additional investments. Consequently, reactive power control has become integrated operation in most new PV systems, usually controlled by a system operator, a droop control, or power factor control [8,25,9,39,42]. The objective of reactive power control is usually either voltage regulation, reactive power optimization, or a tradeoff between the two [33]. Both voltage regulation and reactive power flow optimization cannot be

Corresponding author. E-mail address: [email protected] (H. Alenius).

https://doi.org/10.1016/j.epsr.2020.106207 Received 5 September 2019; Received in revised form 12 December 2019; Accepted 8 January 2020 Available online 24 January 2020 0378-7796/ © 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Fig. 1. Simplified grid connection of a remote PV plant.

achieved simultaneously, as the objectives are partially in conflict. In this work, the reactive power support functions are discussed in the context of reactive power flow optimization, and voltage regulation objective is not considered. The multi-objective optimization of reactive power is beyond the scope of this paper. Several studies have discussed the use of PV inverters for reactive power compensation [20,33], and the behavior has been analyzed in simulations [34,35,22,40,23]. Although reactive power control has been extensively discussed in previous works, feasible and precise method for complete decoupling of unintended reactive power from active power has not been presented. The majority of research has focused on local voltage regulation in distributed systems with high share of photovoltaic generation [14], while the issues related to fluctuating unintended reactive power have been discussed less. Power factor control (PFC) is the standard approach for reactive power management in utility-scale PV plants, in which the reactive power injection is proportional to active power feed. This is also known as a Q–P droop control. In order to obtain the optimal power factor, the grid inductance must be known [14]. Recent studies have provided methods for online identification of the grid impedance [28,2], which can be used to calculate adequate power factor set point. However, the conventional PFC does not consider the effect of changing operating point accurately. The reactive power injection from the inverter affects the PoC voltage level changing the Q/Prelation, which the PFC assumed to be constant. In addition, the unintended reactive power is quadratic to the active power making the coupling nonlinear. Consequently, the conventional PFC achieves accurate decoupling only when the inverter operates at nominal power level. However, in photovoltaic systems, the active power fluctuates drastically along with the irradiance conditions and the majority of time the system operates outside nominal power level. This leads to suboptimal reactive power compensation when a conventional PFC method is utilized. Therefore, the previous methods for reactive power flow optimization achieve only partial decoupling between reactive and active powers, and additionally, require accurate information on the grid inductance. The present work proposes a novel method for accurate and autonomous compensation of unintended reactive power flow resulting from the transmission line reactance. A continuous real-time grid impedance measurement is used for estimating the transmission inductance [16]. Based on the inductance estimate and output measurements, an internal control algorithm estimates and compensates the unintended reactive power. This decouples the active power of PV from

the resulting reactive power seen by grid. The reactive power can still be freely controlled in the inverter, but is now set to zero at the gridside by default. In addition, a comparison to conventional PFC shows more accurate reactive power compensation, even when the PFC is tuned based on known grid inductance. The proposed method offers two significant improvements over conventional methods; the real-time impedance estimation removes the need for precise prior knowledge on grid parameters, and the scheme achieves complete decoupling of reactive power from the fluctuating active power of the PV inverter in the complete power range. The proposed method is verified first by simulations and then experimentally in a power hardware-in-the-loop setup in varying conditions. The remainder of the paper is organized as follows. Section 2 discusses the origin of unintended reactive power in a weak grid and presents the conventional power factor control method. Section 3 shows the methods and implementation for real-time grid-impedance measurement and autonomous reactive power compensation. In Section 4, the method is applied in a MATLAB/Simulink – simulation for a utilityscale PV inverter. Section 5 shows experimental results with threephase hardware prototype down scaled to kW power range. The operation of the proposed adaptive reactive power compensation is tested in different grid and irradiance conditions, and in transient scenarios. Finally, Section 6 concludes the main findings of this work. 2. Reactive power control for transmission optimization in PV inverters 2.1. Grid connection of distributed generation Fig. 1 presents the grid connection of a typical distributed generation (DG) unit. DG is often located in remote areas and the grid connection consists mainly of inductive transmission lines and transformers [13]. The inductive transmission line consumes reactive power as the current flows through. If the inverter is operated at unity power factor, pure active power is fed to the PoC of the inverter (output PoC). However, at the grid side (grid PoC) the PF is decreased as the reactive power is drawn from the grid. Fig. 2 illustrates the voltage and current phasors of the system when the unity power factor is set to either (a) output PoC or (b) grid PoC. When the inverter is set to unity PF, the output current is in phase with the output voltage. On the grid side, however, the voltage and current are in phase shift of θ, so the grid-side PF is reduced to cosθ, which Fig. 2. Phasor diagrams when power factor is set to unity at (a) output PoC or (b) grid PoC.

2

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corresponds to reactive power of the transmission line. The phase difference can be directly compensated by setting the angle of the inverter output current to match the angle of the grid voltage. This compensates the unintended reactive power and defaults the grid-side PF to unity. 2.2. Coupling of reactive and active power in weak grids The unintended reactive power flow depends on the grid current and grid impedance, which is greater in weaker grids. Weak grid refers to grid part with high impedance, where the current at PoC has significant impact on the local voltages. A short-circuit ratio (SCR) is commonly used to define the stiffness of the grid, given as

SCR = Vn2/(Sn Zg ),

Fig. 4. Block diagram of conventional proportional PFC implementation.

control (PFC), where the cosϕ of the inverter is set to other than unity. PFC provides flexible method to regulate the reactive power output of the converter by associating reactive power input to active power level. Some standards require the power factor to be controllable, e.g. from 0. 95cap to 0. 95ind [18]. If the grid impedance can be obtained from the system parameters or by measurements, the desired power factor can be calculated from the approximated unintended reactive power at unity power factor operation (cf. Fig. 2a)

(1)

where Vn is the nominal voltage, and Sn the nominal apparent power, which typically in DG systems is chosen to be the nominal power of the inverter. Usually, the inverter has equal (or approximately equal) power rating than the grid-connecting transformer, which is another approach to choose the nominal power. The exact values for SCR in weak grid vary, but a grid with SCR below 5 can be considered weak, and very high-impedance grids with SCR below 2.5 are known as ultraweak grid [39,37,4]. Fig. 3 visualizes the impact of SCR at the output PoC on the reactive power consumption, PF at the grid PoC, and maximum active power capacity on the transmission line. The SCR at remote DG plants is typically very low, so the unintended reactive power flow becomes significant. Varying irradiance conditions cause fluctuations in active power of a PV generator, which results in variance of reactive power consumption of the transmission line. Thus, the active and reactive power become coupled in a weak grid, which can result in unpredicted fluctuations in reactive power. The flow of reactive power increases the total current in a transmission line, which increases transmission losses. In addition, this can limit the maximum active power of the line and even compromise the system stability in the large-signal sense, if the angle difference in the inverter output current and grid PoC increases excessively [6]. The loss of stability occurs when the reactive power flow changes the power angle so that equilibrium point no longer exists, which is analogous stability issues of synchronous generators when the grid synchronization is lost [10]. In order to consider the fluctuating nature of active power illustratively, a concept of equivalent shortcircuit ratio (eSCR) is applied in this work. The eSCR describes the ratio of short-circuit power to instantaneous power of the inverter (instead of the nominal power). Thus, an inverter operating at 50% of nominal power in grid with SCR of 2 corresponds to operation at eSCR of 4.

cos

= cos atan

Q line P

cos atan

3Io2 Xg 3Io Vo

cos atan

Sn Zg ( 3 Vo )2

= cos atan

1 SCR

(2) when the resistive component is negligible, where Io and Vo are phase current and voltage, and 3 Vo = Vn . Fig. 4 shows a straightforward PFC block diagram utilizing proportional Q/P-ratio for reactive power regulation, where gain K is given as

K=

tan(acos(PF))

(3)

where PF is the desired power factor for the inverter output power. 3. Proposed method for autonomous compensation Fig. 5 shows a flowchart of the proposed method for compensation of unintended reactive power flow. The grid inductance is estimated from a continuous real-time grid-impedance measurement. The inductance value is then used to calculate the resulting reactive power, which is compensated by setting the output current angle accordingly. Although the underlying methods have been widely discussed, the realtime impedance estimation has not been previously applied for unintended reactive power compensation. 3.1. Real-time grid-impedance measurements

2.3. Power factor control of inverter

Recent studies have presented online methods, which can analyze the grid impedance in real time. In the methods, the grid impedance was measured by the inverter itself: the inverter produces a broadband injection on top of the normal output current, measures the resulting responses in the grid voltage, and applies Fourier analysis to extract the

Utility-scale PV inverters rarely operate at unity power factor due to reactive power requirements [11]. A widely applied method for reactive power control in current-controlled inverters is power factor

Fig. 3. Impact of SCR on grid side power factor (blue) and on reactive power flow (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 3

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corresponding frequency components in both the voltage and current. The grid impedance is then determined by the ratio between the perturbed voltage and current,

Z( ) =

U( ) I( )

(4)

where Z(ω) is the frequency-dependent grid impedance and U(ω) and I (ω) are the Fourier transformed voltages and currents. Maximum-length binary sequence (MLBS) is widely used for online measurements of grid-connected devices [26,19]. The MLBS is a periodic binary sequence, so the measurements can be averaged over multiple cycles, and the MLBS provides the lowest possible peak-factor [7]. These features allow relatively low injection amplitude, while still providing sufficient signal-to-noise ratio. Low injection amplitude is desirable in continuous measurements for minimizing the output current distortion [15]. The MLBS is periodic over the sequence length of N = 2n − 1 and can be generated using n-stage shift register and XORfeedback from specific stages. The frequency resolution of the MLBS is defined as fres = fgen/N, where fgen is the generation frequency. Thus, the measurement time for one sequence cycle is Tmeas = N/fgen [27]. In this work, the perturbation sequence is injected from the inverter side and constructed in the MLBS-generation block inside the inverter control system. The sequence is generated continuously and injected on top of the d-component current reference. In the setup, a 127-bit-long MLBS was generated at 4 kHz, so the frequency resolution was approximately 31.5 Hz. The perturbed grid currents and voltages are measured using the output sensors inside the LC-filter, from which the grid impedance is extracted using Fourier analysis. The obtained grid impedance is the equivalent impedance of the complete power grid as seen from the PoC. When approximating the grid impedance to consist only of resistive and inductive components below 450 Hz, the imaginary part represents the grid inductance. Thus, the grid inductance can be estimated from

Lg = Fig. 5. Flowchart of proposed compensation method.

|imag[Zg ( )]|

=

|imag[Rg + jXg ( )]|

=

|jXg ( )|

=

Xg ( )

(5)

where frequency (ω/(2π)) is less than 450 Hz, and Rg denotes the resistance of the grid [16].

Fig. 6. Measured grid impedance at a given time instant (red), analytical impedance (black), and chosen measurement frequencies for inductance estimation (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 4

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Table 1 Frequencies for grid inductance estimation and the closest harmonic frequency (in 60 Hz system). Estimation frequency #, mfres

Frequency (Hz) Closest harmonic (Hz)

8

9

10

11

12

13

252 240

284 300

315 300

347 360

378 360

409 420

Fig. 6 shows the grid impedance measurement at a given time instant. The grid inductance value is calculated from six frequencies given in Table 1 and then averaged. The currents of fundamental frequency and integer harmonics may deteriorate the measurement accuracy. The estimation frequencies can be chosen to minimize the distortions in estimation by avoiding integer harmonics and using appropriate frequency range. The acquired inductance estimation refreshes every measurement (every 31.75 ms), is continuously averaged over five periods, and finally low-pass filtered with 3.1 Hz cut-off frequency.

Fig. 7. Phasor diagram for reactive power compensated inverter with an LCfilter.

through an LC-filter. The implementation will be used for simulations and power hardware-in-the-loop experiments. The reactive power compensation (shown with red) is implemented based on (11) by applying measured vod , igd, and igq and estimated grid inductance Lg*. The filter capacitive reactance is a known parameter by the filter design. The control block produces a compensation term for output current qcomponent, which compensates the reactive power of the transmission line and filter based on (11), and thus defaults the power factor to unity at the grid PoC. The introduced method does not interfere with the operation of normal control schemes of the inverter, and the reactive power can still be controlled in parallel with the proposed autonomous compensator.

3.2. Compensation of unintended reactive power The unintended reactive power can be compensated by shifting the output current angle of the inverter to match the grid PoC voltage angle. The transmission line with reactance Xg consumes reactive power Qg, and a capacitive filter with reactance Xc produces reactive power Qc. The total reactive power loss Qtot is given by

Qtot = Qg + Qc = 3Io2 Xg

3

Vo2 , Xc

(6)

where Vo and Io are output phase voltage and current. The reactive power equation for dq-domain values is

Qtot = 3

Qtot

p iod

3

2

2

p ioq

+

Xg

3

3

p vod

3

2

1 , Xc

2 vod

3 2 2 = (iod + ioq ) Xg 2

3 , 2 Xc

4. MATLAB/Simulink – simulations in MW-scale (7)

The method presented was verified with simulations in MATLAB/ Simulink. A simulation model for a 1 MW grid-connected inverter with an LC-filter was built, where the converter-side inductor of the filter is included in the control dynamics of the converter. Table 3 in Appendix B presents the setup parameters.

(8)

p

where superscript denotes power-invariant variable and voq is set to zero by the inverter synchronization. Thus, the inverter can be controlled to compensate the reactive power of the transmission line by setting Qo = Qtot. Based on instantaneous power theory, the reactive power of the inverter is given by

Qo =

p p vod ioq

4.1. Compensation with varying grid inductances The proposed method autonomously compensates the unintended reactive power flow caused by the transmission line, which is verified in simulations for different grid strengths. Fig. 9 shows the reactive and active powers on the grid side for different SCR values of the inductive grid, when the compensation method is turned on at t = 0.8 s. After enabling the compensation, the reactive power settles to zero after fast transient. Table 2 presents the corresponding grid SCRs, reactive powers, power factors, and compensation q-current references in steady state operation. The unintended grid-side reactive power is accurately compensated, with residual reactive power flow less than 1%. The real-time estimation of the grid inductance makes the compensation method adaptive as the reactive power control adapts to the grid impedance, which may improve performance in changing grid conditions. In addition, knowledge on grid parameters and parameter changes is no longer required. Fig. 10 demonstrates the proposed scheme in changing grid conditions;

(9)

The voltage is fixed to output PoC voltage, but the current q-component can be freely controlled. The reactive power balance is achieved when p p vod ioq =

3 2 2 (iod + ioq ) Xg 2

2 3 vod 2 Xc

(10) p the ioq

In order to compensate the reactive power, reference must be set according to (10). The inverter is controlled in the amplitude-invariant dq-domain, so the power-invariant variables are transformed to corresponding amplitude invariants and the compensation current reference is given as

* = ioq

2 2 (iod + ioq ) Xg

vod

+

vod . Xc

(11)

With an LC-filter at inverter output and current feedbacks from inverter-side, the grid current is ig = io − ic, where ic denotes the capacitor current of the filter. Fig. 7 shows the currents and voltages for the inverter with an LC filter when ig is set to match vg , and the reactive power is compensated (grid PoC PF set to unity). Fig. 8 presents the implementation of the presented methods to the control system of a three-phase PV inverter with grid connection

1. at 2.0 s: grid impedance doubles (SCR → 3), 2. at 4.0 s: grid impedance further increases (SCR → 2), 3. at 6.0 s: issues are cleared (SCR → 6). The figure shows known and estimated grid inductance and gridside powers with and without compensation. The grid inductance 5

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Fig. 8. Block diagram of inverter control system with adaptive compensation method.

grid-side powers when the input power of the PV system is linearly increased, which in turn decreases the equivalent SCR (eSCR) of the grid. The DC power is increased from 900 to 2100 kW with total grid inductance of 170 μH, resulting in eSCR decrease from 2.8 to 1.2. The grid is chosen to be very weak for demonstrating the stability enhancement with the proposed method. Without compensation, the grid-side reactive power increases very rapidly, destabilizing the system at t = 6.9 s. This corresponds to DC power of 1500 kW and eSCR of 1.8. Before the stability is lost without compensation, the unintended reactive power flow is extremely high, which would require immediate balancing actions. The compensation regulates the grid reactive power to zero through the power ramp, and the system stability is retained although the grid conditions become very challenging. In addition, the reactive power is decoupled from the active power, so no changes are seen in the reactive power on the gridside.

Fig. 9. Grid side powers when compensation is enabled at 0.8 s with different grid SCRs (weakest grid in case 1). Table 2 Steady-state values for grid side reactive powers, power factors, and compensation current references. Case #

6 5 4 3 2 1

SCR

10 6 4 3 2.5 2

Uncompensated

4.3. Decoupling reactive power from fluctuating irradiance

Compensated

Qgrid (kVAr)

PFgrid

iq* (A)

Qgrid (kVAr)

−65 −123 −200 −289 −375 −568

0.997 0.991 0.975 0.950 0.920 0.837

−110 −231 −379 −517 −617 −755

−0.36 −0.58 0.05 −0.28 −2.60 −6.32

Shading from clouds can change the irradiance conditions rapidly, causing varying input power for the system. In addition, partial shading from cloud edges can temporarily increase the local irradiance power above normal maximum through cloud enhancement [41]. Fig. 12 presents measured irradiance data from a rooftop PV plant (1st of August 2011), where multiple cloud enhancement peaks occur above normal maximum of 1050 W/m2. The plant and measurement setup is presented in [32]. In order to test the method in realistic conditions, a 180 s sample of measured irradiance data is used, which contains high cloud enhancement peaks (measured between 12:28:03 and 12:31:03). Fig. 13 shows the irradiance, active power, and reactive power during the test. The highest irradiance value corresponds to 1380 W/m2, and causes a momentary peak in power production, which decreases the eSCR of grid connection from 2.5 to 1.8. Without compensation the reactive power varies dramatically up to −80% of nominal active power, and at the third cloud enhancement peak (at 128 s) the excessive unintended reactive power destabilizes the system. The proposed method compensates the grid-side reactive power to zero, meaning that the reactive power becomes decoupled from the active power. Thus, the stability is maintained with the increased transmission capacity. As the power input varies in the range of tens of seconds, fixed or manually controlled reactive power compensation would be inefficient. In order to validate the performance increase and enhanced reactive power compensation capabilities, the proposed method is compared to conventional proportional PFC (cf. Fig. 4), which has been optimally

estimation accurately produces correct inductance value with settling time less than 1 s, verifying the robustness of estimation method. Without the scheme, the inverter operates at unity power factor by default and reactive power drawn from the grid increases based on the grid inductance. During the lowest SCR of the grid, 600 kVAr of unintended reactive power is drawn from the grid without compensation (60% of active power feed). The compensation method regulates gridside reactive power back to zero within 0.5 s from transient, validating the autonomous compensation method. 4.2. Increase in transmission capacity The flow of reactive power in the transmission line increases the total current and Joule losses in the line. In addition, a large proportion of unintended reactive power may destabilize the inverter in very weak grids. Consequently, the unintended reactive power imposes limitations to maximum active power feed from the PV inverter. Fig. 11 shows the 6

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Fig. 10. Estimated grid inductance and reference (above) and grid-side powers during grid fault, which changes grid impedance.

impedance. The proposed autonomous method outperforms the conventional PFC even when it is tuned optimally, and the performance enhancement is alleviated when the grid impedance is unknown or varying. 4.4. Manual reactive power control during autonomous operation Most of the new PV inverters are capable of reactive power support. The proposed autonomous compensation method defaults the grid-side reactive power to zero, but does not interfere with external reactive power control. Thus, reactive power can still be freely controlled in parallel with the proposed method, but the unintended reactive power resulting from the inverter itself is automatically mitigated. Fig. 15 demonstrates the grid-side powers during fluctuating irradiance conditions (measured 60 s sample between 10:46:08 and 10:47:08) when additional requests for reactive power input are made (grid SCR = 2.5). At first, the inverter is controlled to produce 200 kVAr for reactive power support. As the DC power decreases along with the irradiance, the reactive power balance changes and the reactive power reference is changed first to 120 kVAr, and then to 0 kVAr. Finally, a reference of −150 kVAr is given to the inverter at 50 s. Without decoupling method, the irradiance fluctuation translates directly to grid-side reactive powers. With the decoupling, the unintended share of reactive power is fully compensated and the external reactive power requests are fully met on the grid-side. The reactive power management is drastically simplified, as the reactive power resulting from the PV system itself is automatically balanced.

Fig. 11. Active and reactive powers with increasing PV input power with and without compensation (line and dashed line, respectively).

Fig. 12. Measured daily irradiance on 1st of August 2011.

tuned based on known grid inductance. Fig. 14 shows the grid-side reactive powers in the fluctuating irradiance scenario for both the proposed adaptive compensation and PFC. While the PFC provides significant improvement over the uncompensated system, the fluctuating reactive power component persists and is only reduced in magnitude (ranging from −100 to 100 kVAr). With the proposed method, the fluctuating component is completely removed. Additionally, the optimal PFC tuning can be achieved only when the grid inductance is known, and the method does not account for changes in grid

5. Experiments 5.1. Power hardware-in-the-loop setup The effectiveness of the introduced method for compensation of unintended reactive power is verified with power hardware-in-the-loop experiments. Fig. 16 presents a schematic of the experimental setup and a photograph of the setup is shown in Appendix A (Fig. 23). The setup consists of a PV emulator (Spitzenberger&Spies PVS 7000), an inverter

7

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Fig. 13. Irradiance, active power, and reactive power during cloud enhancement peaks.

5.2. Enabling the autonomous compensation in weak grid First, the operation is demonstrated by enabling the compensation and measuring the grid-side reactive powers when the inverter is connected to a weak grid (SCR = 3.2, Lg = 12.9 mH). The method compensates the reactive power consumption of the transmission line, which sets the grid-side power factor to unity. Fig. 17 presents the phase A current and voltage at grid side measured with oscilloscope when the compensation output is enabled (dashed red line). Before the compensation, a significant phase difference is visible in the grid-side waveforms resulting in unintended reactive power flow and decreased PF. The compensation quickly shifts the current phase to match the voltage phase (by producing adequate reactive power), which results in pure active power on the grid side. Enabling the compensation adjusts the current within one fundamental period.

Fig. 14. Reactive powers during fluctuating irradiance for conventional PFC (black) and proposed autonomous compensation (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

5.3. Adaptation to changing grid conditions

(MyWay Plus MWINV-9R144), an LC output filter, and a grid emulator (Spitzenberger&Spies PAS 15000). The PV emulator provides the DC power for the inverter and is manually set to maximum-power point. The inverter is controlled with a dSPACE real-time simulator, which also defines the voltage references for the grid emulator. The interconnection between the inverter and the grid emulator is realized with an LC-filter, an isolation transformer, and an additional external inductors acting as transmission line inductance. Step-wise transients are produced to grid inductance by changing the state of the switch S. The initial parameters of the test setups are given in Table 3 in Appendix B.

The proposed method utilizes real-time information on the grid conditions and adapts to changing grid conditions, which drastically improves performance during abrupt changes in grid impedance. Fig. 18 shows the measured grid inductance and grid-side reactive powers when the grid inductance abruptly doubles from 4.9 to 9.9 mH (e.g. a parallel transmission line is disconnected). If the inverter is operated at unity PF, the reactive power drawn from the grid increases significantly. The autonomous decoupling method detects the increased grid inductance, and regulates the reactive power compensation 8

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Fig. 15. Fluctuating irradiance and grid-side reactive power with changing reactive power reference for the inverter (dashed black).

accordingly. Within seconds, the reactive power flow returns close to zero. The settling time results from the averaging and filtering of the inductance estimate. An inverter with conventional PFC cannot respond to grid changes, and the tuning would remain unchanged.

mitigate reactive power fluctuations by decoupling grid-side reactive power from active power feed of PV system. The method is tested with measured 180 s irradiance data as input power, which contains the same cloud enhancement peaks as in simulations (Fig. 13). The grid inductance was chosen to 12.9 mH, corresponding to a weak grid with 3.2 SCR. Fig. 20 shows the active and reactive powers on the grid-side, with and without decoupling method, and Fig. 21 shows the phase A current envelope taken from oscilloscope. Without decoupling method, clear correlation between reactive and active power is shown, which makes the reactive power management on system level difficult. The proposed method keeps the grid-side reactive power set to zero by default, providing accurate decoupling of reactive power. Consequently, irradiance fluctuations no longer translate to reactive power status of the system. Fig. 22 compares the reactive powers of the proposed method and conventional PFC optimized to match the known grid inductance, cosϕ = 0.956. Adopting PFC shows significant improvement over the uncompensated system, but the system still has significant coupling in the reactive powers. The proposed method achieves substantially better decoupling, although a slight overcompensation occurs at the highest peaks. However, the PFC usually does not have information on the precise grid inductance, which further deteriorates the performance of the PFC. With the proposed method, the grid inductance is continuously estimated, which mitigates this shortage.

5.4. Transmission capacity during power increase In order to illustrate the improved transmission capacity, the DC input power of the PV system is ramped up from nominal 2.7 to 5.1 kW. The total grid inductance is 12.9 mH, so the eSCR is effectively reduced from 3.2 to 1.7. Fig. 19 shows the grid-side powers during the ramp. Inverter at unity power factor draws increasing amount of reactive power from the grid-side during the ramp up. At t = 37.4 s, the reactive power has increased to 3 kVAr (73% of active power), which destabilizes the system and the setup trips. With the proposed method, the reactive power remains regulated to zero and the system stability is preserved. In addition, the reactive power flow without compensation increases transmission losses, which is seen as decreased active power flow (−6% when the protection triggers). 5.5. Decoupling reactive power from irradiance The power input of PV generator depends on irradiance conditions, and may fluctuate rapidly. The aim of the proposed method is to

Fig. 16. Block diagram of the experimental setup. 9

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Fig. 17. Oscilloscope waveforms of phase A current and voltage when the compensation output is enabled (dashed red line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 18. Inductance estimate and grid-side reactive powers, with abrupt increase in grid inductance at t = 4.0 s.

active power production. The improved reactive power support mitigates the issues in reactive power managements resulting from varying power flows in systems with large-scale photovoltaic plants. This work presents the proof-of-concept for the autonomous and adaptive control, and further work is still required for optimal and robust operation. In the simulations, the method operated as expected with high precision and robustness while still having fast response time to changes in the grid. However, the experimental setup imposed practical constraints on the accuracy of the method, which resulted in slight inaccuracies in the compensation are slower adaptation response due to increased averaging of the measurements. The minor errors can be assumed to result from inaccuracies in measurements (probe calibrations), component tolerances, and system non-linearities; the experimental inverter has very high switching deadtime of 4 μs (3.2% of switching cycle) and the used isolation transformer is known to cause inaccuracies to measurements. The inaccuracies cause cumulative error on the output, which appears as slight overcompensation in this setup. However, even with

Fig. 19. Grid-side powers when the input power is ramped up.

5.6. Discussion The experiments validate the concept of the proposed autonomous reactive power compensation, which decouples the reactive power from 10

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Fig. 20. Grid-side powers and compensation current with 180 s of measured irradiance data.

Fig. 21. Oscilloscope phase A current envelope during the fluctuating irradiance conditions.

all the said inaccuracies and non-idealities, a reactive power decoupling ranging from 80% to 97% is measured from the grid side and the method is shown to outperform conventional power factor control. The inaccuracies would deteriorate the performance of other reactive power support schemes as well. At this point, the method is limited to systems where the grid-connection of the inverter is through mainly inductive transmission line. The further validation of the proposed method (and autonomous reactive power support in general) is required for more complex systems with meshed network and multiple parallel devices. For parallel devices, a master-slave configuration could be adopted, where a master inverter is responsible for the impedance measurements and shares the inductance estimate to slave inverters. However, these issues remain as a future topic and are not included in this work.

Fig. 22. Comparison of reactive powers on the grid side when utilizing PFC (blue) or adaptive compensation method. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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6. Conclusion

conventional proportional power factor control (Q/P-droop), even in systems where the grid parameters are known by system design. The performance of the proposed method is validated in simulations and kW-scale experiments, where the tests show improved reactive power control, mitigation of reactive power fluctuations, and improved transmission capacity.

Utility-scale photovoltaic systems are often connected to weak grids with inductive transmission lines. Power generation flowing through the transmission line causes unintended flow of reactive power to the grid side, as the transmission reactance consumes reactive power. Thus, the grid-side reactive power becomes coupled with the active power production of the photovoltaic inverter, which fluctuates along with irradiance conditions. The fluctuating reactive power challenges reactive power management and may cause additional transmission losses or even large-signal stability issues. This paper proposes an autonomous reactive power compensation method, which decouples the reactive power from the active power production preventing unintentional fluctuations in reactive power flow. The method estimates the grid inductance continuously by applying real-time grid-impedance measurements. Based on the obtained inductance value, the reactive power compensation is precise and adapts to different and even changing grid conditions. The proposed method is shown to outperform the

Authors’ contribution Henrik Alenius: conceptualization, methodology, validation, formal analysis, writing – original draft. Roni Luhtala: conceptualization, software. Tuomas Messo: project administration, funding acquisition. Tomi Roinila: supervision, funding acquisition. Conflict of interest None declared.

Appendix A

Fig. 23. Photograph of the experimental setup.

Appendix B

Table 3 Simulation parameters for inverter and grid. Parameter

Simulation

Experimental

Nominal DC power DC voltage Fundamental frequency Grid phase voltage Switching frequency Nominal d-current reference

2.7 kW 414.3 V 60 Hz 120 V 8 kHz 10.6 A

iq*

Nominal q-current reference

1 MW 1500 V 60 Hz 230 V 5 kHz 1.97 kA

CDC Lc Cf Rc Ltf Rtf Lg

DC capacitance Converter side inductance Filter capacitance Damping resistance Transformer inductance Transformer resistance Grid inductance

20 mF 60 μH 400 μF 70 mΩ 30 μH 8 mΩ 0…225 μH

1.5 mF 2.2 mH 10 μF 1.8 Ω 0.9 mH 0.4 Ω 0…12 mH

KP−CC KI−CC

Current controller gain

1.134e−4 0.0214

0.0149 23.442

Pin Vin f0 Vg fsw id*

0A

0A

(continued on next page) 12

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Table 3 (continued) Parameter

Simulation

Experimental

4.294 134.89 0.1679 2.4266

0.0962 1.2092 0.3306 10.593

KP−VC KI−VC KP−PLL KI−PLL

Voltage controller gain

fgen n Iinj

MLBS generation frequency MLBS sequence length MLBS amplitude

4 kHz 127 50 A

8 kHz 127 0.2 A

ωf1 ωf2

Filter pole for measurements

2π8 rad/s 2π3.2 rad/s

2π5 rad/s 2π20 rad/s

ωf3

Filter pole for iqcomp

2π1.6 rad/s

2π20 rad/s

PLL controller gain

Filter pole for Lgest

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Roni Luhtala received his M.Sc. degree in electrical engineering from Tampere University of Technology (TUT), Tampere, Finland, in 2017. Since then, he has worked as a doctoral student with the Faculty of Engineering and Natural Sciences, Tampere University. His main research interests include real-time identifications and adaptive control of grid-connected converters.

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Tuomas Messo received his Ph.D. in electrical engineering from the Tampere University of Technology, Tampere, Finland, in 2014. He is currently with GE Grid Solutions and holds the position of Adjunct Professor at the Tampere University in the field of power electronics, where he also worked as an Assistant Professor between 2016 and 2019. His research interests include grid-connected three-phase power converters for renewable energy applications and microgrids, dynamic modeling, control design, impedancebased interactions in three-phase systems and impedance design of grid-connected inverters.

Tomi Roinila received the M.Sc. (Tech.) and Dr.Tech. degrees in automation and control engineering from Tampere University of Technology (TUT), in Finland, in 2006 and 2010, respectively. He is currently an Academy Research Fellow at TUT. His main research interests include modeling and control of grid-connected power-electronics systems, and modeling of multiconverter systems.

Henrik Alenius received the M.Sc. degree in electrical engineering from Tampere University of Technology, Tampere, Finland, in 2018. Since then, he has worked as a doctoral student with the Faculty of Information Technology and Communication Sciences at Tampere University. His research interests include impedance-based interactions in grid-connected systems and stability analysis of multi-parallel inverters.

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