A Multi-Functional Distributed Generation Control

A Multi-Functional Distributed Generation Control Scheme for Improving the Grid Power Quality Ali, Zunaib; Christofides, Nicholas; Hadjidemetriou, Lenos; Kyriakides, Elias Published in: IET Power Electronics

Digital Object Identifier DOI: Publication date: xxxx

Citation for published version (APA): xxx

General rights The authors and/or other copyright owners retain copyright and moral rights for the publications made accessible in the public portal and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights.  

Personal use of this material is permitted. Permission from the copyright owner of the published version of this document must be obtained (e.g., IEEE) for all other uses, in current or future media, including distribution of the material or use for any profit-making activity or for advertising/promotional purposes, creating new collective works, or reuse of any copyrighted component of this work in other works. You may freely distribute the URL/DOI identifying the publication in the public portal.

Policy to take down free access If you believe that this document breaches copyright please contact us at [email protected] providing details, and we will remove access to the work immediately and investigate your claim.

1

A Multi-Functional Distributed Generation Control Scheme for Improving the Grid Power Quality Zunaib Ali 1*, Nicholas Christofides 1, Lenos Hadjidemetriou 2, and Elias Kyriakides 2 1

Department of Electrical Engineering, Frederick University, Nicosia, Cyprus Department of Electrical and Computer Engineering, KIOS Research and Innovation Center of Excellence, University of Cyprus, Nicosia, Cyprus Corresponding author: *[email protected] 2

Abstract: The large-scale integration of renewable energy sources require routine planning. Renewable sources are expected to be a key element of future power systems. With many challenges ahead, thinking out of the box is necessary in order to equip the power system with additional advanced functionalities and capabilities to combat the anticipated challenges. The associated equipment of distributed generation can be seen as a grid asset upgrade because of the increased number of elements connected to the grid, such as grid side converters (GSC) of photovoltaics and battery storage systems. It therefore makes sense to think of ways to diversify the role of distributed renewables in a way that benefits the grid, consumers, and prosumers in terms of power quality. In parallel with the diversified role of distributed renewables, this approach can be also thought of as a systematic process of developing, operating, maintaining and upgrading the grid. The work proposes an advanced, multi-function GSC control technique for improving the distribution grid power quality by enabling the injection of asymmetric, DC and harmonic currents in case it is needed. Injecting for example such currents locally through the GSC of a residential photovoltaic system can compensate undesired characteristics of the prosumer loads in order to allow the flow of symmetric and high quality currents between the prosumer and the distribution grid (irrespective of the load conditions). The proposed control technique consists of a Phase-Locked Loop (PLL) necessary for synchronization purposes and advanced PQ and current controllers necessary for injecting the reference currents. Experiments and simulation results are presented to validate the performance of proposed control technique. 1. Introduction The road towards smart grids, smart metering, microgrids and storage necessitates smarter grid-connected renewable energy sources. Diversifying the role of distributed renewables is therefore acquiring momentum and new ideas of how to better utilize Renewable Energy Sources (RES) are continuously emerging. It is well appreciated that RES can support and improve the power quality of the grid. The contribution of distributed generation systems towards abnormal grid events (such as unbalanced faults, asymmetric loading conditions, harmonics and DC offset, voltage sags and phase unbalance) and the need for a proper interaction with smart grids and micro-grids, are research areas related to RES diversification. This can be accomplished by utilizing the flexibility of the Grid Side Converter (GSC), which is the main component for the integration of rooftop PV systems. Thus, the installation of additional power electronic components such as shunt, series and series-parallel (unified power quality conditioner) active power filters [1-6] can become unnecessary resulting in lower installation costs to distribution network operators when dealing with such abnormal grid conditions. The necessary power electronics required for the mitigation of abnormal grid conditions are already present in the GSC of a PV system and can be utilized by providing it with advanced functionalities through flexible control algorithms. The possibility for example of a GSC to deliver asymmetric and non-linear currents will present many benefits to the distribution network operators. The fact that the generated power from residential RES is not consumed directly at all the times, gives way to investigate the

compensation of connected load currents using residential RES and their associated advanced GSC current and PQ controllers. The control technique proposed in this paper improves the power quality of the distribution grid by injecting asymmetric, harmonic and DC currents. Passive residential or commercial consumers in the electrical network become active when rooftop PV systems are installed. Such consumers are referred to as prosumers [7]. The term “prosumer” refers to consumers who in addition to consuming power are also capable of delivering any excess power back to the grid. The GSC is the key component of PV systems responsible for delivering the produced PV power to the grid in a controlled manner [8, 9] (Fig. 1). The GSC is usually a three-phase inverter for systems over 4 kW rated power. As most of the commercial and/or residential threephase prosumers/consumers consist of mainly single-phase loads, the total power consumption is always unbalanced by the nature of the loads. Furthermore, with more power electronic loads installed (due to the increased penetration of renewables and non-linear loads), the currents suffer by the presence of harmonic and DC components and thus, the power quality of the grid can be jeopardized. In addition, higher distribution network losses, reduced power factor, increased grid loading and reduced capacity, negative effects on the operation of speed drives and electrical machines (such as torque oscillations and overheating) are examples of other negative consequences to distribution network operators [10]. To improve the power quality by utilizing the presence of the GSC of a RES system, various approaches have been proposed in the literature, but with certain restrictions and limitations. In [11, 12], a PV system with a single phase GSC

2

PCC

Power Grid

vabc

Prosumer s Load (iLoad)

i abc

LC Filter Lf Rf

AC

v abcGSC

L grid Cf PLL

 Pref / VDC Qref / Vgrid

n

DC GSC

Energy Extracted from Solar/Wind

PLL

PQ Controller with FRT capability

i ref

Current Controller

v*GSC

PWM Modulation

Fig. 1: Schematic and control diagram of grid-connected RES system.

is employed to mitigate the harmonic currents generated by nonlinear loads. The ability to balance a prosumer load, however, is not supported by this configuration. A method involving the injection of both positive and negative sequence currents is proposed in [10] for mitigating the voltage asymmetries of the distribution network. Although this method does not involve the measurement of three-phase prosumer’s load currents, information about the grid impedance at the Point of Common Coupling (PCC) is required for its implementation. The grid impedance information is not always available. An interesting method is presented in [13] for a GSC, where a modified deadbeat current controller and Delayed Signal Cancellation (DSC) scheme is employed to compensate the asymmetric and selected harmonic load currents. The DSC scheme is used for generating the required current references and subsequently the deadbeat controller enables the accurate injection of these currents. The disadvantage of the deadbeat controller is that the bandwidth of the overall current controller is limited and it is also affected by system uncertainties. A flexible control scheme for mitigating load asymmetries is presented in [14], but it does not allow the compensation of harmonics and DC offset caused by the nonlinear loads. For generating the reference currents in accordance with the prosumer load currents, alternative methods based on physical component analysis and conservative power theory are discussed in [15] and [16], respectively. These methods, however, present slow dynamic response and are very complex for real time implementation in digital signal processors. A technique proposed in [17] allows the compensation of asymmetric and nonlinear load currents but cannot compensate for loads that require DC current components at the AC side. A PV system employing a Z-sourced inverter as a GSC is discussed in [18] for improving the grid power quality. However, presents high input ripple due to the large number of passive elements and requires a complex algorithm for control purposes. In addition, the method for reference current generation discussed in [18] requires more filters (hence slow dynamic response) complicating further the control method. To mitigate the prosumer load harmonics a method based on voltage control is discussed in [19]. It does not employ a current tracking loop, which can be dangerous for the safety of the GSC due to uncontrolled over currents. This paper proposes an advanced control technique for improving the grid power quality. This is accomplished by injecting asymmetric, harmonic, and DC currents via the GSC in order to compensate the non-linear and asymmetric

loads of the prosumer (residential grid-connected PV system). Injecting such currents locally through the GSC allows the flow of symmetric and high quality currents between the prosumer and the distribution grid. Hence, the power quality of the power grid is improved. The proposed control technique consists of a Phase-Locked Loop (PLL) necessary for synchronization purposes, an advanced PQ controller (proposed in this work) consisting of a sequence analyzer to split the load current into various sequences and orders, and to generate the reference currents for the advanced current controller (proposed in this paper). The proposed advanced control technique requires an efficient current controller that accurately injects the necessary high quality currents with less oscillations/overshoots, fast dynamic response and above all with less computational complexity. Furthermore, the current controller should provide the ability of on-purpose injecting asymmetric and distorted currents when needed. So far, in the literature, many current controllers dealing with various power system issues have been addressed. None of them however combines the advanced features nor have the performance and functions of the proposed current controller. The following paragraphs elaborate the state of the art research work on current controllers and demonstrate the contribution of the proposed controller. The conventional Synchronous Reference Frame (SRF) current controller [20, 21] enables the injection of fundamental positive sequence currents by employing two Proportional-Integral (PI) controllers in positive rotating reference frame (SRF+1). The major shortcoming of SRF+1 current controller is that it cannot perform accurately in the presence of unbalanced grid faults and also it cannot inject negative sequence currents. The reason for the inaccurate performance is the existence of double frequency (2𝜔) oscillations on the transformed SRF+1 voltage/current vectors [22]. The inaccurate response of the SRF+1 controller under unbalanced faults is mitigated by the dual SRF (DSRF) current controller [23, 24]. The DSRF controller employs two SRF frames: one rotating with a positive (+𝜔) and the other with a negative (−𝜔) synchronous speed. It also employs notch filters. The response with the filters, however, is less accurate and it also affects the dynamic response of the controller. Consequently, an Enhanced Dual SRF (EDSRF) current controller is proposed in [25] which offers improved accuracy and enhanced dynamic response. Consequently, it accurately alleviates the effect of double frequency oscillations and enables the simultaneous injection of fundamental positive and negative sequence currents. The

3

controller, however, is not immune to DC offset in the grid voltage and it does not allow the on-purpose injection of harmonic and DC currents. In addition, the EDSRF controller does not allow the use of feedforward terms, ultimately leading to undesired PI control effort [26, 27]. The SRF based current controller proposed in [26] allows the accurate injection of only positive or negative sequence currents. Simultaneous injection is, however, not supported. The current controllers discussed in [14, 27] are capable of injecting the fundamental positive and negative sequence, but cannot compensate for the DC offset in the grid voltage. Furthermore, the injected currents suffer from small oscillations in the event of faults or changes in the reference current. The Type D and Extended Type D (ETD) current controllers presented in [17] allow the simultaneous injection of negative sequence and harmonic currents with lower complexity, but do not work accurately in the presence of DC offsets in the grid voltage. Furthermore, the ETD controller does not allow the on-purpose injection of DC current. The equivalent of the SRF-PI controller in stationary reference frame is the Proportional Resonant (PR) controller without cross-coupling and feedforward terms [28, 29]. It does not require an extra frame for unbalance compensation nor for the injection of negative sequence currents [29]. In [30, 31], resonant controllers are nested inside the SRF+1 current controller for enabling accurate injection of positive sequence currents in the presence of grid voltage harmonics and faults. Such controllers do not perform accurately under unbalanced grid faults and they cannot inject negative sequence currents. Some current controllers for the injection of positive sequence currents are discussed in [32-34] where PI and PR controllers are combined to achieve better performance. In general, PR controllers do not allow the use of necessary feedforward terms and result in unnecessary higher control effort [26, 35]. The tuning procedure of the PR controller is also complicated as it results in a higher order closed-loop transfer function. A self-synchronized current controller is proposed in [36] where SRF+1 and complex integrals are combined to compensate for unbalanced faults and enable the injection of only positive sequence currents. The controller, however, works for unity power factor only; that is, it cannot inject reactive power. A current controller based on complex integral is discussed in [37] for positive sequence injection, but does not allow the injection of other current sequences. A moving average filter (MAF) based controller is presented in [38] for compensating the grid voltage harmonics and enabling the injection of positive sequence currents only. The use of a MAF results in slower dynamic response of the injected currents [22, 39, 40]. It is worth mentioning that none of the current controllers discussed above allow the on-purpose injection of DC and harmonic currents. As discussed in the beginning, this diversified functionality is necessary in order to supply the non-linear and non-symmetric current demand of loads thereby improving the grid power quality. Furthermore, the controllers discussed above are not immune to DC offset in the grid voltage, which is a major drawback because the presence of DC offset in the grid voltage may result in DC current injection from GSC to the grid [40, 41]. However, according to IEC61727, the DC current injection to the grid must be less than 1% of the rated output current of the RES. The advanced Multi-Function Current Controller (MFCC) proposed in this paper can work under unbalanced faults and

DC offsets in the grid voltage. At the same time, it allows the flexible operation of renewable energy systems by enabling the on-purpose injection for the cases of non-linear (unbalanced, DC, and harmonic) load currents in situ through the GSC of PV systems. Thus, the proposed current controller provides advanced functionalities, has lower complexity (hence requires less computational resources), and can significantly improve the grid power quality when necessary. The advanced MFCC current controller is discussed and analyzed in Section 2. Section 3 describes the frequency response of the proposed MFCC current controller. The advanced PQ controller is discussed in Section 4. Simulation and experimental results validating the performance of the proposed controller are presented in Section 5. 2. Design of Proposed Multi-Functional Current Controller (MFCC) The presence of unbalanced (−), DC offset (0) and harmonic (h) currents that may appear because of the distorted grid voltage or caused by the loads, result in undesired double, fundamental and (1−h) frequency oscillations on the transformed dq-frame voltage/current vectors. Existing current controllers do not compensate these oscillations and as a result, they do not accurately operate in the presence of these grid current components. The novel Multi-Function Current Controller (MFCC) proposed, effectively mitigates these oscillations and is able to inject the positive sequence (+), negative sequence (−), DC (0) and harmonic (h) current components in order to compensate undesired effects such as asymmetric, DC, and harmonic current components of the prosumer’s load. If the off-nominal grid voltage conditions are not compensated, the injected GSC current will contain unbalanced, DC and harmonic components. This, in essence, violates grid regulations and degrades the power quality of the grid. The significance of the MFCC current controller can be expressed in two ways. a)

Accurate injection of required currents in the presence of unbalance and DC offset in the grid voltage. In the event that the grid voltage (𝐯𝑎𝑏𝑐 ) is unbalanced, DC shifted and harmonically-distorted, if the GSC generates 𝐺𝑆𝐶 ), the resulting balanced three-phase voltage (𝐯𝑎𝑏𝑐 current will be asymmetric with DC offset, as shown in (1) and can be realized from Fig. 1. However, using the proposed MFCC, the generated GSC voltage is modified in accordance to these grid disturbances. Consequently a balanced three-phase current will be generated from the GSC. 𝐢𝑎𝑏𝑐 =

𝐺𝑆𝐶 𝐯𝑎𝑏𝑐 − 𝐯𝑎𝑏𝑐 𝑅𝑓 + 𝑗𝜔𝐿𝑓

(1)

where, 𝜔 is the nominal grid frequency and Rf and Lf are the series resistive and inductive parameters of the LC filter. b) In addition to compensating grid voltage abnormalities, MFCC is capable of injecting asymmetric, DC and harmonic currents on-purpose, if for example instructed by the distribution network operator and depending on the extent and severity of the asymmetric and non-linear

4

connected loads. Consequently, these currents will not be drawn from the grid, but will be locally supplied by the GSC. Therefore, the grid power quality will be improved. It is worth mentioning that these currents are provided without introducing the fundamental, double, or any other frequency oscillations on the other rotating vectors. Before the new current controller is proposed and further elaborated, the analysis of grid currents under abnormal grid/load conditions is provided. The three-phase injected current (𝐢𝑎𝑏𝑐 ) by a GSC under abnormal grid conditions consists of various current components, that is the positive (𝐢+1 ), the negative (𝐢−1 ), the DC (𝐢0 ), and the harmonic (𝐢ℎ ) components of the current: 𝐢𝑎𝑏𝑐 = 𝐢+1 + 𝐢−1 + 𝐢0 + 𝐢ℎ

(2)

where, h represents the harmonic order and holds any integer value other than +1, -1 and 0, such as -5, +7, -11…. The presence of the extra components such as, −1, 0 and h are due to the abnormal grid voltage conditions or due to the nonlinear connected loads. Since the control of the GSC is designed in the SRF dq-frame, the behavior of the corresponding currents in the SRF domain must be discussed. The three-phase current 𝐢𝑎𝑏𝑐 is transformed to the corresponding SRF frame using (3) and the overall current in the dq-frame is given by (4). 𝑛 𝐢𝑛𝑑𝑞 = [T𝑑𝑞 ] ([𝑇 ⏟𝛼𝛽 ]𝐢𝑎𝑏𝑐 )

(3)

𝐢𝛼𝛽 0 +1 −1 ℎ 𝐢𝑑𝑞 = T𝑑𝑞 (𝐢𝛼𝛽 ) + T𝑑𝑞 (𝐢𝛼𝛽 ) + T𝑑𝑞 (𝐢𝛼𝛽 ) + T𝑑𝑞 (𝐢𝛼𝛽 )

(4)

where, 1 1 − 2 2 2 [𝑇𝛼𝛽 ] = 3 √3 √3 [0 2 − 2 ] cos(𝑛𝜃) sin(𝑛𝜃) 𝑛 [T𝑑𝑞 ]=[ ] −sin(𝑛𝜃) cos(𝑛𝜃) 1

−

(5)

(6)

The transformation angle 𝜃 is obtained using a phaselocked loop. This transformation in (3) with 𝑛 = 1, under normal grid conditions, results in a positive sequence nonoscillating terms only, that is 𝐢+1 𝑑𝑞 . However, under abnormal grid conditions, the non-oscillating terms of positive SRF+1 𝐢+1 𝑑𝑞 is accompanied by undesired double, fundamental and (1−hth) frequency oscillations because of the unbalance sequence (𝑚 = −1), DC offset (𝑚 = 0), and harmonic component (𝑚 = ℎ), respectively. Likewise, if the transformation is carried out with 𝑛 = −1, 0 𝑜𝑟 ℎ, coupling oscillations are observed because of the remaining sequences present in the current. About the presence of DC offset in the measured current, it is important to mention that if all the three-phases of grid voltage have identical DC offset (which may arise from the power supply or the active components of the sensors), then according to (5) it will not appear in the resulting currents 𝐢𝛼 and 𝐢𝛽 , and hence oscillations do not originate in dq-frame for such a case. For instance, if the three-phase current has a DC component of [𝑖𝑑𝑎 𝑖𝑑𝑏 𝑖𝑑𝑐 ]𝑇 , the d-component of current will be superimposed by 2⁄3 (𝑖𝑑𝑎 cos(𝑛𝜃) + 𝑖𝑑𝑏 cos(𝑛𝜃 − 120°) + 𝑖𝑑𝑐 cos(𝑛𝜃 +

240°)) and is zero if 𝑖𝑑𝑎 = 𝑖𝑑𝑏 = 𝑖𝑑𝑐 . Consequently, fundamental frequency oscillation will be caused only if all the three phases of current have unequal DC value, (i.e. unbalanced DC current caused by unbalanced DC offset). Equation (7) describes the oscillations in the dq-frame that appear on current vectors because of the coupling effect between these vectors rotating at different angular speeds. cos(𝜃𝑛 ) 𝑛−𝑚 cos(𝜃𝑚 ) 𝐢𝑛𝑑𝑞 = 𝐼 𝑛 [ ] + ∑ {𝐼 𝑚 [T𝑑𝑞 ][ ]} sin(𝜃𝑚 ) ⏟ sin(𝜃𝑛 ) ⏟ 𝐷𝐶 𝑇𝑒𝑟𝑚

𝑚≠𝑛

(7)

𝑂𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛 𝑇𝑒𝑟𝑚

The problem that arises while designing the GSC controller in the SRF frame is the generation of undesired oscillations when a three-phase current signal containing more than one frequency is transformed with a specific speed. The fast and accurate elimination of these oscillations is the key for accurate control in SRF using a simple proportional integral controller. The MFCC current controller employs a mathematical-based algorithm for cancelling the oscillations in order to eliminate the undesired effect of DC offset and other components. Considering that the measured current contains positive (+1), negative (−1), DC (0) and harmonic (ℎ) components, the measured current in αβ-frame can be expressed as, −1 0 ℎ 𝐢𝛼𝛽 = 𝐢+1 𝛼𝛽 + 𝐢𝛼𝛽 + 𝐢𝛼𝛽 + 𝐢𝛼𝛽

(8)

As mentioned earlier, when dealing in the dq-frame, the presence of more than one frequency component give rise to undesired oscillations when transformed with a specific speed. Therefore, the main objective is to obtain oscillation +1∗ −1∗ free positive (𝐢𝑑𝑞 ), negative (𝐢𝑑𝑞 ), DC (𝐢0∗ 𝑑𝑞 ), and harmonic ℎ∗ (𝐢𝑑𝑞 ) components of current in the dq-reference frame. These current vectors are obtained by analyzing and designing a novel mathematical-based decoupling network in the αβframe. Each of the unknown current components +1 (𝐢+1 𝛼𝛽 ), −1 0 ℎ −1 (𝐢𝛼𝛽 ), DC (𝐢𝛼𝛽 ) and h (𝐢𝛼𝛽 ) are separated out of the actual known measured current 𝐢𝛼𝛽 and this results in oscillation −1∗ 0∗ ℎ∗ free estimated vectors 𝐢+1∗ 𝛼𝛽 , 𝐢𝛼𝛽 , 𝐢𝛼𝛽 , and 𝐢𝛼𝛽 . The reason for selecting the αβ-frame is that it results in lower complexity as compared to designing such algorithms in the dq-rotating reference frame. Thus, the αβ-version of current vectors (𝐢+1 𝛼𝛽 , −1 0 ℎ 𝐢𝛼𝛽 , 𝐢𝛼𝛽 and 𝐢𝛼𝛽 ) are obtained first and are then transformed to the corresponding dq-frame by a simple transformation; consequently, they are sent to the PI controller for necessary action. Equation (8) can be used multiple times to obtain each of the component separately, as shown in (9). 𝐢+1 𝛼𝛽 𝐢−1 𝛼𝛽 𝐢0𝛼𝛽 ℎ

[𝐢𝛼𝛽 ]

𝐢𝛼𝛽 𝐢𝛼𝛽 = − 𝐢𝛼𝛽 [𝐢𝛼𝛽 ]

−1 𝐢𝛼𝛽 + 𝐢0𝛼𝛽 + 𝐢ℎ𝛼𝛽 +1 𝐢𝛼𝛽 + 𝐢0𝛼𝛽 + 𝐢ℎ𝛼𝛽 +1 ℎ 𝐢𝛼𝛽 + 𝐢−1 𝛼𝛽 + 𝐢𝛼𝛽

(9)

+1 −1 0 [𝐢𝛼𝛽 + 𝐢𝛼𝛽 + 𝐢𝛼𝛽 ]

The unknown current vectors 𝐢𝑛𝛼𝛽 (where, 𝑛 = +1, −1, 0, ℎ) on the left side of (9) are replaced with estimated current vectors 𝐢𝑛∗ 𝛼𝛽 in (10), whereas, the unknown current vectors 𝐢𝑚 on the right side of (9) are replaced with 𝛼𝛽 the filtered estimated vectors 𝐢𝑛′ 𝛼𝛽 in (10). The filtered estimated vectors are used on the right hand side because it is necessary for subtraction purposes to filter out the vectors. It

5

is worth mentioning that 𝑛 refers to the current vector that is under consideration and 𝑚 denotes all the other contained sequences in the current vector 𝐢𝛼𝛽 . For example, if positive sequence extraction is required, 𝑛 must be equal to +1, where as 𝑚 contains all the other values except +1 (i.e. -1, 0, h). Thus, (9) can be re-written as: +1∗ 𝐢𝛼𝛽 −1∗ 𝐢𝛼𝛽 𝐢0∗ 𝛼𝛽 ℎ∗ 𝐢 [ 𝛼𝛽 ]

0′ ℎ′ 𝐢−1′ 𝛼𝛽 + 𝐢𝛼𝛽 + 𝐢𝛼𝛽 0′ ℎ′ 𝐢+1′ 𝛼𝛽 + 𝐢𝛼𝛽 + 𝐢𝛼𝛽 +1′ −1′ 𝐢𝛼𝛽 + 𝐢𝛼𝛽 + 𝐢ℎ′ 𝛼𝛽 +1′ −1′ 0′ 𝐢 + 𝐢 + 𝐢 [ 𝛼𝛽 𝛼𝛽 𝛼𝛽 ]

𝐢𝛼𝛽 𝐢𝛼𝛽 = − 𝐢𝛼𝛽 [𝐢𝛼𝛽 ]

P-Module

i

i

T  1 dq

   i 1*





1' dq

The filtered estimated current vectors in (11) are the dq-versions of the vectors in αβ and are obtained by passing the error vectors ∆𝐢𝑚 𝑑𝑞 through a first-order Low Pass Filter (LPF) ([𝐹(𝑠)]) and subtracting it from the reference current 𝐢𝑚𝑟 𝑑𝑞 , as described in (12) and shown in Fig. 2. The user provides the reference current as a control input, whereas the error vectors ∆𝐢𝑚 𝑑𝑞 is described by (13).

s s  f



T  1 dq

i

0'

1* dq



id1*

id1r

1'

i

i



 

1' 0'

T  1 dq

1* i

i



1' dq



T 

i

h'

1* dq

i i i



1*  iq



iq1r

s

s s  f



id1*

DC-Module

i





T  0*

i

1' 1' h '

i

0 dq



0' dq

Tdq0 

i

0* dq

i i i



h-Module h'

i

i



 

1' 1' i i i 0'

T  h dq

h*

i

i

Tdq h 

PI

s



h' dq

s s  f



0* d

i

0*  iq

s s  f s s  f



idh*

id1r id1 



PI

i



s s  f

1* v

 vq1



iq1r



PI



PI





PI





vd0

Tdq0  0* v



vq0

iq0

idh



PI

 iqh r

1* v

iq1



idh r

T  1 dq

 vq1

id0r id0

iq0r

vd1



h L

h*  iq

T  1 dq



h L

h* dq



iq1

L

1*  iq



vd1



L

s  f

i

PI

L

1 dq

0'

id1



s  f

N-Module

(11) 𝐢𝑚′ 𝑑𝑞

L



h' 1' i i i

−𝑚 𝑚′ 𝐢𝑚′ 𝛼𝛽 = [𝑇𝑑𝑞 ]𝐢𝑑𝑞

(10)

1'

i

The filtered oscillation-free estimated current vectors (𝐢𝑚′ ) necessary for the subtraction purposes are obtained by 𝛼𝛽 using the transformation given in (11).

PI i

h q



vdh

 Tdq h     

h* v

vqh

Fig. 2: Proposed Multi-Function Current Controller (MFCC) block diagram for P, N, DC and h modules.

6

𝑚𝑟 𝑚 𝐢𝑚′ 𝑑𝑞 = [𝐢𝑑𝑞 − [𝐹(𝑠)] ∆𝐢𝑑𝑞 ]

(12)

𝑚𝑟 𝑚∗ ∆𝐢𝑚 𝑑𝑞 = (𝐢𝑑𝑞 − 𝐢𝑑𝑞 )

(13)

[𝐼] and [𝐼] = [1 0], and 𝐢𝑚∗ 𝑑𝑞 is the 0 1 desired oscillation-free positive current component in the dqframe. The appropriate value of the cut-off frequency 𝜔𝑓 plays an important role in the accurate estimation of oscillation-free 𝐢𝑛∗ 𝑑𝑞 currents. The further investigation shows that the selection of 𝜔𝑓 is a trade-off between accuracy and dynamic response. The value of 𝜔𝑓 = 𝜔⁄√2 is the appropriate value for LPF of positive sequence (+1), negative sequence (-1) and harmonic (h) module, whereas the ideal 𝜔𝑓 for the DC part of current controller is 𝜔𝑓 = 𝜔⁄4.5, with 𝜔 as the fundamental frequency. The lower cut-off frequency of the DC module makes sense because in the transformed 𝑑𝑞 0 frame, the positive sequence and negative sequence (which are the most dominant components) appear as fundamental frequency (+𝜔 or – 𝜔) oscillations on the transformed vectors. The value of 𝜔 is usually small (for instance, 𝜔 = 2𝜋50); consequently, a smaller cutoff frequency is required to cope with these low frequency oscillations. In a similar way, where 𝜔𝑓 = 𝜔⁄√2 is used to filter the 2𝜔 and (1−h)ω oscillations, 𝜔𝑓 = 𝜔⁄4.5 is an appropriate selection for the mitigation of 𝜔 frequency oscillations. Thus, by substituting (12) and (13) in (11), where, 𝐹(𝑠) =

𝜔𝑓

𝑠+𝜔𝑓

−𝑚 𝑚𝑟 𝑚𝑟 𝑚∗ 𝐢𝑚′ 𝛼𝛽 = [𝑇𝑑𝑞 ][𝐢𝑑𝑞 − [𝐹(𝑠)] (𝐢𝑑𝑞 − 𝐢𝑑𝑞 )] −𝑚 𝑚𝑟 𝑚𝑟 𝑚∗ ⇔ 𝐢𝑚′ 𝛼𝛽 = [𝑇𝑑𝑞 ][𝐢𝑑𝑞 − [𝐹(𝑠)]𝐢𝑑𝑞 + [𝐹(𝑠)]𝐢𝑑𝑞 ]

(14)

Equation (14) can further be modified by the 𝑚 𝑚∗ transformation, 𝐢𝑚∗ 𝑑𝑞 = [𝑇𝑑𝑞 ]𝐢𝛼𝛽 and rewritten as: −𝑚 𝑚 𝑚∗ 𝐢𝑚′ 𝛼𝛽 = [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]𝐢𝛼𝛽

(15)

𝑚𝑟 where, it is valid that the 𝐢𝑚𝑟 𝑑𝑞 = [𝐹(𝑠)]𝐢𝑑𝑞 under steady state conditions (since the filtered reference value is always be equal to the unfiltered). Now, as the 𝐢𝑚′ 𝛼𝛽 is obtained, (10) can be modified into (see (16)) by the multiple use of (15). Thus, (see (16)) results in oscillation-free positive, negative and DC components of current in the stationary αβ-frame. It is worth mentioning that in (see (16)) the estimated current vectors (𝐢𝑛∗ 𝛼𝛽 ) on both sides of equation are the same. These are subsequently used to remove the undesired contained current components in order to result in oscillation free DC terms for the desired nth current component. The generic form of the (see (16)) for obtaining oscillation-free current vectors is given in (17). −𝑚 𝑚 𝑚∗ 𝐢𝑛∗ 𝛼𝛽 = 𝐢𝛼𝛽 − ∑ [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]𝐢𝛼𝛽 ⏟ 𝑚≠𝑛

The decoupled vectors (17) can be transformed back to obtain corresponding oscillation-free estimated current vectors 𝐢𝑛∗ 𝑑𝑞 in the dq-frame, given by (18) and are subsequently provided to the corresponding PI controllers based decoupled SRF control structure, in order to generate the desired voltage reference signals for the GSC. The result in (18) is the core to develop the proposed multi-function current controller and is referred to as novel mathematicalbased decoupling of currents. The multiple use of (18) results in the proposed MFCC. The structure of the proposed MFCC current controller for positive (𝑛 = 1), negative (𝑛 = −1), DC (𝑛 = 0), and harmonic (𝑛 = ℎ) current injection is shown in Fig. 2. 𝑛 −𝑚 𝑚 𝑚∗ 𝐢𝑛∗ 𝑑𝑞 = [𝑇𝑑𝑞 ] (𝐢𝛼𝛽 − ∑ [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]𝐢𝛼𝛽 ) ⏟ 𝑚≠𝑛

Thus, the proposed MFCC controller developed based on (18) has the ability to perform accurately in the presence of unbalanced faults and DC offset. Furthermore, it has the capability to inject on-purpose asymmetric, DC, and nonlinear harmonic currents if required by the connected nearby loads. 3. Frequency Domain Analysis of Proposed MFCC Current Controller The frequency domain transfer function of proposed MFCC is obtained for each sub-module, that is, positive (Pmodule), negative (N-module), DC-module, and harmonic (h-module) by the multiple use of (17). For simplicity, only one harmonic component is included in the analysis and h is set equal to −5. Thus, for 𝑛 = +1, −1, 0 and −5 the corresponding transfer function for each sub-module is presented in (19), (20), (21) and (22) respectively. The reason for selecting the αβ-frame is to clearly analyze the response of the proposed mathematical-based decoupling MFCC for each frequency component, that is, +f (positive sequence component), 0 (DC component), −f (negative sequence component), −5f (negative sequence 5th harmonic component), with f being 50 Hz. +1∗ 𝐢𝛼𝛽

𝐢𝛼𝛽 −1∗ 𝐢𝛼𝛽

𝐢𝛼𝛽 𝐢0∗ 𝛼𝛽 𝐢𝛼𝛽

(17)

−5∗ 𝐢𝛼𝛽

𝐢𝑚′ 𝛼𝛽

𝐢+1∗ 𝛼𝛽

[0] 𝐢𝛼𝛽 −1∗ −1 +1 𝐢 ] [𝐢𝛼𝛽 ] = [ 𝛼𝛽 ] − [[𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 0∗ −1 +1 𝐢 𝛼𝛽 𝐢𝛼𝛽 ⏟[𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]

(18)

𝐢𝑛∗ 𝛼𝛽

𝐢𝛼𝛽 +1 −1 [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]

[0]

=

1 − [𝑇𝐹𝑇−1 + 𝑇𝐹𝑇0 + 𝑇𝐹𝑇−5 ] 1 − [𝑇𝐹𝑇−1 + 𝑇𝐹𝑇0 + 𝑇𝐹𝑇−5 ]𝑇𝐹𝑇+1

(19)

=

1 − [𝑇𝐹𝑇+1 + 𝑇𝐹𝑇0 + 𝑇𝐹𝑇−5 ] 1 − [𝑇𝐹𝑇+1 + 𝑇𝐹𝑇0 + 𝑇𝐹𝑇−5 ]𝑇𝐹𝑇−1

(20)

=

1 − [𝑇𝐹𝑇+1 + 𝑇𝐹𝑇−1 + 𝑇𝐹𝑇−5 ] 1 − [𝑇𝐹𝑇+1 + 𝑇𝐹𝑇−1 + 𝑇𝐹𝑇−5 ]𝑇𝐹𝑇0

(21)

=

1 − [𝑇𝐹𝑇+1 + 𝑇𝐹𝑇−1 + 𝑇𝐹𝑇0 ] 1 − [𝑇𝐹𝑇+1 + 𝑇𝐹𝑇−1 + 𝑇𝐹𝑇0 ]𝑇𝐹𝑇−5

(22)

0 0 [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]

+1∗ 𝐢𝛼𝛽

−1∗ 0 0 [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]] [𝐢𝛼𝛽 ]

+1 −1 [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]

[0]

(16)

𝐢0∗ 𝛼𝛽

𝑈𝑛𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑠

7

where, −𝑘 𝑘 𝑇𝐹𝑇𝑘 = [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]

cos(𝑛𝜃) 𝑛 [T𝑑𝑞 ]=[ −sin(𝑛𝜃)

(23)

and 𝑘 is the corresponding current sequence (+1, 0, −1 or −5). The complex frequency-domain transfer function for 𝑇𝐹𝑇𝑘 can be defined by a lengthy mathematical analysis and is achieved by representing the Park’s transformation given by (6) to the corresponding Euler formula as in (24).

1 (𝑒 𝑗𝑛𝜃 + 𝑒 −𝑗𝑛𝜃 ) = [ 𝑗𝑛𝜃 2 𝑗(𝑒 − 𝑒 −𝑗𝑛𝜃 )

𝑛 [T𝑑𝑞 ]

0 db

1* i i

1* i ai

0 db

0 db

0 db

0o

0o

0o

sin(𝑛𝜃) ]⇔ cos(𝑛𝜃) −𝑗(𝑒 𝑗𝑛𝜃 − 𝑒 −𝑗𝑛𝜃 ) (𝑒 𝑗𝑛𝜃 + 𝑒 −𝑗𝑛𝜃 )

(24) ]

5* i

0* i i

i

0o

(a)

GSC Controller

i

Negative sequence, DC and harmonic component Spliter

Load abc

1,0,h) i(dq1,0,h)r  i(dq-L

Q*1 ReactiveProfile

Positive P*1 Sequence PQ MPPT Controller

 , v dq1,1,0,h

i dq

1,0,h  r

v abc g

v

Advanced PQ Controller

abc g Synchrnonization

(PLL)

v dq1,1,0,h

MFCC Current Controller



i abc PV

i dq1r

v*GSC

v

abc g

i

abc PV

VDC

PWM Modulation

LC Filter

Lf Rf Cf M

PV

+

i

b

DC-Link

PCC

Three-phase Grid Side Converter (GSC) Load i abc

I DC

a

c

g abc

-

Power Grid

Prosumer (b) Fig. 3: (a) Bode diagram of proposed MFCC current controller, (b) Grid-connected prosumer and advanced control technique (proposed advanced PQ and MFCC current controller).

8

Then, by combining (24) with the Laplace frequencyshifting property (𝑒 𝑎𝑡 = 𝐹(𝑠 − 𝑎)) and by considering the geometry of αβ-domain, 𝑣𝛽 = −𝑗𝑣𝛽 , the first-order complex frequency domain transfer function of 𝑇𝐹𝑇𝑘 is given by (25). 𝜔𝑓𝑘 −𝑘 𝑘 𝑇𝐹𝑇𝑘 = [𝑇𝑑𝑞 ][𝐹(𝑠)][𝑇𝑑𝑞 ]= (25) 𝑠 + (𝜔𝑓𝑘 − 𝑗𝑘𝜔) where 𝜔𝑓𝑘 is the cut-off frequency for the low pass filter of the respective sequence. Using the transfer functions in (19), (20), (21) and (22), a bode diagram is presented in Fig. 3 (a). In all the four +1∗ cases, it can be seen that the components of interest i.e., 𝐢𝛼𝛽 −1∗ 0∗ −5∗ or 𝐢𝛼𝛽 or 𝐢𝛼𝛽 or 𝐢𝛼𝛽 , propagate with unity gain and zero phase shift through the respective sub module, while the remaining three components are blocked by providing negative gain and phase shift. This implies that the multiple use of (18) as shown in Fig. 3 (a), allows the desired current component to pass through to the corresponding PI controller, while at the same time it blocks the others. This justifies the fast and accurate operation of the proposed MFCC current controller. The simultaneous injection of positive sequence, negative sequence, DC, and harmonic currents is enabled without being affected from coupled oscillations. 4. Design of Proposed Advanced PQ Controller (APQC) The proposed current controller of Section 3 must be accompanied by an advanced PQ controller for mitigating the asymmetries and DC currents required by the connected loads, thereby enhancing the power quality of the grid. An advanced PQ controller (APQC) is proposed in this Section for generating the current reference in order to deliver the required active/reactive power to the grid and in addition, for delivering the asymmetric and DC currents required by the connected prosumer loads, as an auxiliary function. The proposed APQC consists of two parts, that is, the conventional and the advanced, as shown in Fig. 3 (b). The conventional part is responsible for generating the current references 𝐢∗+1 𝑑𝑞 to the P-module for enabling the injection of desired active and reactive power from the RES to the grid. The advanced part is necessary to generate the references for the N-module, DC-module and h-module by analyzing the load current (𝐢𝛼𝛽‑𝐿 ) and splitting it into the required sequences. The load current is split into positive sequence +1 −1 (𝐢𝑑𝑞‑𝐿 ), negative sequence (𝐢𝑑𝑞‑𝐿 ), DC (𝐢0𝑑𝑞‑𝐿 ) and harmonic ℎ component (𝐢𝑑𝑞‑𝐿 ) by the multiple use of (26) for 𝑥 = +1, −1, 0 and ℎ, where 𝑦 denotes all the contained sequences other than the selected 𝑥. The estimated negative sequence, DC and harmonic component of load currents are directly used as the reference currents for the GSC of the RES, that is, 0𝑟 0 ℎ𝑟 ℎ −1 𝐢−1𝑟 𝑑𝑞 = 𝐢𝑑𝑞‑𝐿 , 𝐢𝑑𝑞 = 𝐢𝑑𝑞‑𝐿 and 𝐢𝑑𝑞 = 𝐢𝑑𝑞‑𝐿 . (𝑥)

−𝑦

𝑦

𝑦′

𝑥 𝐢𝑑𝑞‑𝐿 = [𝑇𝑑𝑞 ] [𝐢𝛼𝛽‑𝐿 − ∑[𝑇𝑑𝑞 ]𝐹(𝑠)[𝑇𝑑𝑞 ]𝐢𝛼𝛽‑𝐿 ]

(26)

𝑦≠𝑥

The APQC is also well-equipped with fault ride through capabilities so that the GSC should not disconnect in the event of severe asymmetries, DC-shifted, and harmonic load conditions resulting in over-currents. Consequently, under such events, the positive sequence is maintained

according to the desired P and Q reference, whereas the negative sequence, DC, and harmonic current injection is limited not to violate the converter’s maximum current limits 𝐢𝑚𝑎𝑥 . The maximum magnitude for N, DC, and h modules reference currents is calculated according to (27) and consequently, the magnitude of injected negative, DC and harmonic currents must stay below the limits, |𝐢−1𝑟 𝑑𝑞 | < 0𝑟 𝐷𝐶 ℎ𝑟 ℎ 𝐢𝑁 , |𝐢 | < 𝐢 and |𝐢 | < 𝐢 . However, 𝑑𝑞_𝑚𝑎𝑥 𝑑𝑞 𝑑𝑞_𝑚𝑎𝑥 𝑑𝑞 𝑑𝑞_𝑚𝑎𝑥 under intense asymmetric, DC and harmonic conditions, if ℎ𝑟 −1𝑟 |𝐢𝑑𝑞 |, |𝐢0𝑟 𝑑𝑞 | and |𝐢𝑑𝑞 | exceed the assigned allowable limit, the −1𝑟 𝑁 reference currents must be limited by 𝐢𝑑𝑞 ⁄𝐢𝑑𝑞_𝑚𝑎𝑥 , 0𝑟 𝐷𝐶 ℎ𝑟 ℎ 𝐢𝑑𝑞 ⁄𝐢𝑑𝑞_𝑚𝑎𝑥 and 𝐢𝑑𝑞 ⁄𝐢𝑑𝑞_𝑚𝑎𝑥 , respectively. Therefore, the safe operation of the GSC within safety limits is ensured. −1𝑟 𝐢𝑁 𝑑𝑞_𝑚𝑎𝑥 = |𝐢𝑑𝑞 | 0𝑟 𝐢𝐷𝐶 𝑑𝑞_𝑚𝑎𝑥 = |𝐢𝑑𝑞 |

𝐢ℎ𝑑𝑞_𝑚𝑎𝑥

𝑚𝑎𝑥

𝑚𝑎𝑥

=

|𝐢ℎ𝑟 𝑑𝑞 |𝑚𝑎𝑥

= 𝐢𝑚𝑎𝑥 − |𝐢+1𝑟 𝑑𝑞 |

−1𝑟 = 𝐢𝑚𝑎𝑥 − |𝐢+1𝑟 𝑑𝑞 | − |𝐢𝑑𝑞 |

=𝐢

𝑚𝑎𝑥

−

|𝐢+1𝑟 𝑑𝑞 |

−

|𝐢−1𝑟 𝑑𝑞 |

−

(27) |𝐢0𝑟 𝑑𝑞 |

The proposed APQC allows an accurate compensation of asymmetric, DC, and harmonic currents by injecting the required load current. These currents are locally generated by an existing GSC of installed PV systems. Consequently, the grid current becomes symmetric and free of DC and harmonic components. It is worth mentioning that the accurate injection of generated reference currents is achieved using the proposed MFCC current controller. The proposed APQC together with MFCC enhance the power quality of the grid without compromising the injection of the desired active power and without risking the GSC integrity. 5. Results and Discussion The proposed current controller and advanced control technique is validated through simulations and experiments. The proposed MFCC and APQC proves to be beneficial towards improving the grid power quality. 5.1. Simulation Results A model of 5 kVA three-phase grid-connected GSC is developed in MATLAB SimPowerSystem/Simulink toolbox, as per the schematic shown in Fig. 2. The three-phase voltage at the PCC is 230 V and the fundamental frequency is 50 Hz. 5.1.1 Validation of Proposed MFCC Current Controller: The first test is carried out to analyze the performance and observe the transient behavior of the proposed MFCC for the mitigation of DC offset in the grid voltage. Initially, the grid voltage is balanced at 50 Hz and later on, an unbalanced DC offset occurs in the grid voltage. With zero initial value, at 0.4 s the references for the positive sequence of current, i.e., 𝑖𝑑+1𝑟 and 𝑖𝑞+1𝑟 are subjected to a step change of 4 A and 2 A, respectively. Similarly, the negative sequence is injected at 0.5 s. The references for negative sequence 𝑖𝑑−1𝑟 and 𝑖𝑞−1𝑟 are changed from zero to 2 A and 1.5 A respectively. At 0.6 s, the DC offset with values of -2%, 1% and 2% is superimposed on all the three phases of the grid voltage. The result is presented in Fig. 4 (a). The DC module is activated and deactivated to show what happens if the DC offset is not mitigated. It is clear from Fig. 4 (a) that when a DC offset occurs at 0.6 s with the DC-module deactivated, nondecaying fundamental frequency (50 Hz) oscillations are

9

observed on the positive and negative sequence currents, resulting in an inaccurate injection. However, after 0.7 s, when the DC-module is activated, the proposed MFCC current controller enables the accurate injection of positive and negative sequence of current by effective mitigation of fundamental frequency oscillations, as verified from Fig. 4 (a). For analyzing the DC offset mitigation, the reference value for on-purpose DC injection is set to zero (as observed under DC offset condition, 𝐢0∗ 𝑑𝑞 reverts to zero when DCmodule is activated). The second case study presents the behavior of the proposed MFCC controller for on-purpose injection of DC current in the presence of DC offset in the grid voltage. The DC current is injected together with the positive and negative sequences of current, as shown in Fig. 4 (b). The positive and negative sequence currents are injected at 0.4 s, whereas before there is no injection. The d and q-axis current references for positive sequence are set to 4 A and 2 A, whereas the negative sequence references are 2 A and 1.5 A, respectively. The d and q-axis DC currents are subjected to a step change of 1.5 A and 2 A, respectively. The fast and accurate response of the proposed current controller to these changes in the reference currents can be observed from Fig. 4 (b). When an unbalanced DC offset (-3%, 1%, 2%) occurs in the grid voltage at 0.6 s, it forces an extra DC current to flow from the converter to the grid. The MFCC current controller tries to inject the opposite of what appeared in the No injection

Positive current injection

Negative current injection

current because of the grid DC offset in order to neutralize its effect. It can be seen that all the three currents are injected with less oscillations and overshoot. The injection of the DC currents is enabled with fast dynamics and without the generation of fundamental frequency components on the other current components, as verified from Fig. 4 (b). This demonstrates the on-purpose DC current injection capability of the proposed current controller together with the positive and negative sequences. Thus, the proposed current controller is more flexible in terms of fulfilling the load demand through GSC of RES relieving in this way the grid from the presence of undesired DC components and thereby improving the grid power quality. As mentioned earlier, MFCC is able to inject the harmonic current in order to be more flexible in terms of fulfilling the harmonic current demand of non-linear loads. The results in Fig. 5 (a) show the simultaneous injection of positive and negative sequences, the DC component, and the 5th harmonic component of current. The d and q axis currents of positive and negative sequences are subjected to a step change of 4 A and 2 A, respectively at 1 s and 1.1 s. The 5 th harmonic d and q axis currents are set to a magnitude of 0.6 A at 1.2 s. Later on, at 1.3 s the d and q axis DC currents change from 0 A to 2 A and 1.5 A, respectively. This clearly shows the simultaneous injection of all the current components with fast and accurate response.

Grid voltage DC offset occurred DC module deactivated

DC module activated

Pos itive and No current injection Negative injection

Phases

Phases

a

b

id

c

(a)

a

b

DC current injection

Grid voltage DC offset occurred and mitigated

id

c

iq

iq (b)

Fig. 4: Simulation results: (a) Effect of DC offset to the injection of positive and negative sequence of current, (b) Injection of positive, negative, and DC currents under grid voltage DC offset condition.

10

No injection

Pos itive current injection

Negative current injection

Harmonic injection

DC current injection

DC-shifted positive sequence current required by load APQC not a ctivate d

Phases

a

b

id

c

iq

a

Phases

b

c

(a) Symmetrical load

(b)

Asymmetric change of 1.1 kW on Another asymmetric change of 2 phase b and c kW on phase b and c

APQC OFF

APQC ac tiva ted

APQC ON

APQC OFF

Asymm etric, DC and harmonic load injecting Operating PV Typesym Ametric Conditions currents

PV operating as per proposed APQC

THD=0.18%

No injection from PV

THD=3.67% PV disconnected

THD=2.65%

THD=0.16%

THD=2.5%

Symmetrical grid currents Distorted currents

Power

Phases

a

b

c

Phases

(c)

a

b

P

Q

c

(d)

Fig. 5: Simulation results for the: (a) Injection of positive, negative, harmonic, and DC currents using MFCC, (b) Validation of advanced control scheme for improving the power quality of the grid under DC-shifted prosumer’s load, (c) Validation of advanced control scheme for the compensation of asymmetric prosumer’s load, (d) Validation of advanced control scheme for the compensation of asymmetric, DC, and harmonic loads.

11

5.1.2 Validation of Proposed Advanced PQ Controller (APQC) using the Proposed MFCC: This Section demonstrates the ability of the proposed MFCC in improving the grid power quality using the advanced control technique discussed above. A load requiring DC-shifted positive sequence currents is connected at the PCC, as shown in Fig. 5 (b). The connected load requires a positive sequence current of 14 𝐴 (peak) in all the three-phases with a DC offset of 𝐢𝑑𝑐−𝑎𝑏𝑐 = [−0.8 𝐴 0.3 𝐴 0.6 𝐴]𝑇 . The positive sequence current injected by the GSC to the grid is determined by the set points of P and Q, that is, 𝑖𝑑+1𝑟 and 𝑖𝑞+1𝑟 and corresponds to threephase 𝑃 = 2000 𝑊 and 𝑄 = 0 𝑉𝐴𝑟. This means that the GSC is restricted to inject positive sequence current maximum up to an active power of 2000 W and the remaining power can be used to improve the power quality. To explain the significance of the proposed APQC, initially the APQC is de-activated and hence the DC current required by the load is drawn from the grid, as shown in Fig. 5 (b). However, at 0.5 s the APQC is activated and the GSC of RES delivers the required amount of DC current thereby balancing the grid current and eliminating the DC offset. The results in Fig. 5 (b) justify the effectiveness of the proposed control scheme for mitigating the undesired DC current requirement of the prosumer’s load. The proposed APQC allows the GSC to deliver real power P (as per 𝐢+1𝑟 𝑑𝑞 ) and at the same time to satisfy the load demand. It is worth mentioning that the proposed APQC is able to provide the asymmetric and harmonic current required by the unbalanced and non-linear prosumer load. A test case study is added in Fig. 5 (c) to demonstrate the asymmetric compensation of the proposed APQC. With initial symmetric load conditions, at 0.5 s phase a and b undergo a step change of 1.1 kW each. The APQC remains deactivated until 0.6 s and during this period the grid current becomes unbalanced. However, at 0.6 s the activation of APQC allows the GSC to inject the unbalanced currents restoring in this way balanced grid conditions. Furthermore, at 0.7 s phase a and b loads undergo a step change of 2 kW each. Despite the fact that the APQC is activated, the grid current cannot become 100% symmetric. This is because the GSC maximum current limit is reached and as mentioned before, when this happens the delivery of asymmetric current will be limited to ensure the safe operation of the GSC. A test case involving compensation of asymmetric, DC, and harmonic load currents in presented in Fig. 5 (d). The current drawn from the grid (iG) is harmonically distorted, DC shifted and asymmetric during 0.25 s to 0.35 s (APQC is deactivated). However, between 0.35 s and 0.45 s (when APQC is activated), the GSC (PV system) generates and supplies the load with asymmetric and harmonic/DC distorted current. It is observed that the grid current iG becomes symmetric (balanced), does not contain a DC component and is free from harmonic distortion. The sudden disconnection of the PV system reverts the grid currents to the initial state as can be seen at 0.45 s. Furthermore, the grid active/reactive power oscillations disappear completely between 0.25 s and 0.35 s, demonstrating the effective contribution of the proposed APQC and MFCC. The clear interaction between the grid and the prosumers, result in improved power quality and demonstrate

that the proposed technique is very effective in improving the power quality of the grid. 5.2. Experimental Results The experimental laboratory setup consisting of a GSC and other peripheral equipment is shown in Fig. 6 (a) and the respective schematic diagram is presented in Fig. 6 (b). The test bed includes a SEMIKRRON Semitech B6U+E1C1F+B6Ci inverter acting as a GSC. The inverter is controlled using a dSPACE DS-1104 with an integrated realtime platform consisting of MATLAB/Simulink and dSPACE Control Desk. The control algorithm is developed in a Personal Computer (PC) using MATLAB and is translated to the dSPACE using MATLAB and dSPACE realtime platform. The GSC is connected to the grid via an LCfilter (Lf = 4.93 mH, Rf = 0.14 Ω, and Cf = 7.8 µH). A California instrument 2253iX three-phase programmable AC source is employed to emulate the grid voltage and an ELEKTRO-AUTOMATIK power supply (EA-PS-9750-20) is used as the DC source to emulate the behavior of the RES. More specifically, the inverter employed in the experimental setup is a three-phase 1.8 𝑘𝑉𝐴 inverter and the voltage at the PCC is equal to 132 V. The corresponding current limit for the 1.8 𝑘𝑉𝐴 inverter is 6.5 𝐴. In addition, a three-phase 5 𝑘𝑉𝐴 wye/delta transformer is connected between the converter and the grid necessary for the grid isolation. For emulating the prosumer loads, a California Instrument 3091LD controllable AC load bank with maximum load of 3 kW is used. The sampling rate for both the simulation and the experimental results is 4 kHz.

(a) Prosumer s Load (iLoad) A

DC

PCC

LC Filter Lf =4.93 mH

V

AC DC Power Supply

GSC Semikron

Emulating PV production (EA-PS 9750-20)

(B6U+E1C1F+B6CI)

Rf =0.14 Ω Cf =7.8μF n

V n 2

6

Δ

A

3

2

Control Board

dSPACE DS1104

Y

5 kVA Grid isolation transformer PC: GSC Controller (with MFCC and APQC) developed in MATLAB-RTI and dSPACE control desk

(b) Fig. 6: Experimental test bed: (a) Photo of the experimental setup, (b) Schematic diagram of the experimental setup.

12

Positive sequence sym metrica l c urre nts

Positive sequence sym metrica l c urre nts

Start of negative seque nce injection

ib [2 A/div]

ib [2 A/div]

ic [2 A/div] ia [2 A/div]

Start of negative seque nce injection

ic [2 A/div] ia [2 A/div]

id1r [1 A/div]

iq1r [1 A/div] t [10 ms/div]

t [10 ms/div]

(a) Positive sequence 1 sym metrica l c urre nts d

Positive sequence 1 sym metrica l c urre nts d

Start of DC current

i Injection injection

ib [2 A/div]

ia [2 A/div]

Start of DC current

i Injection injection

ic [2 A/div]

ib [2 A/div]

ia [2 A/div]

id0r [0.4 A/div] t [10 ms/div]

ic [2 A/div]

iq0r [0.4 A/div] t [10 ms/div]

(b) -5th harmonic inje ction started

Positive a nd negative sequence curr ents

ib [2 A/div]

ia [2 A/div] ic [2 A/div]

(c)

iq5r [2 A/div] t [10 ms/div]

Fig. 7: Experimental verification of the proposed MFCC current controller for the injection of (a) negative sequence d and q- axis currents along with positive sequence, (b) DC current injection along with positive sequence, and (c) q-axis −5th harmonic current along with positive and negative sequence current.

The first case study analyses the ability of the MFCC to inject the fundamental positive sequence and unbalanced currents, as shown in Fig. 7 (a). Initially, the positive sequence currents injected, 𝑖𝑑+1𝑟 and 𝑖𝑞+1𝑟 , correspond to 1200 W active and 0 VAr reactive power. The d and q-axis negative sequence currents are subjected to a step change from 0 A to 1 A, Fig. 7 (a). In both cases, the proposed current controller enables the accurate injection of the required currents with fast dynamics. The three-phase injected currents from the GSC are completely symmetrical before the negative sequence injection is enabled, whereas after that, the unbalance in the phase currents reflects the injection of the desired negative sequence currents. The second case study investigates the generation of on-purpose DC current, Fig. 7 (b). The positive sequence current references are similar to the previous case study. After

the initial positive current injection, the d and q-axis reference signals (𝑖𝑑0𝑟 and 𝑖𝑞0𝑟 ) for DC current injection are changed from 0 A to 0.5 A. Initially, the currents are symmetrical with zero DC shift, whereas after the DC current rises to 0.5 A, the three-phase currents are DC shifted to enable the injection of the desired reference DC currents. As mentioned, the occurrence of an unbalanced DC offset causes the flow of the DC current from the GSC towards the grid. The function of MFCC is to inject the opposite DC current of what is already flowing in order to neutralize its effect. The injection of a given arbitrary reference signal (𝐢0𝑟 𝑑𝑞 = 0.5 𝐴) shown in Fig. 7 (b), justifies that the MFCC is able to compensate for the DC offset, by providing the required reverse DC currents. The third case study examines the injection of a harmonic current in addition to positive and negative sequences, Fig. 7 (c). The positive sequence reference

13

5.3. Discussion A detailed THD analysis and the harmonic spectrums for the grid and the PV currents, and the impact of proposed APQC on the grid power quality is presented in this subsection. The THD of the grid current (iG) and the PV current (iPV) is included in Table 1 for different PV operational modes and for various load conditions. The operational modes are the following: 1.

2.

3.

Normal converter operational mode: In this operation mode, the PV system is injecting symmetrical currents according to the conventional operating conditions. The proposed APQC is deactivated. The advanced converter operational mode referred to as the APQC mode: In this mode, the PV system is injecting on-purpose asymmetric, DC and harmonic currents. The proposed APQC is activated. The PV-OFF mode: In this operational mode, the PV system is completely disconnected and the grid supplies all the required load currents including DC and harmonic distorted currents if required. The three load cases investigated are the following:

1.

The first case refers to the loading conditions for the results in Fig. 5 (d), where the load THD is 2.5%.

2.

The second and third load cases are similar to the first case except that the THD of the load in case 2 is 3.8% and in case 3 it is 6.13%.

For all three load cases, as can be seen from Table 1, under normal operation mode the asymmetric and harmonic currents are drawn from the grid increasing in this way the grid current THD. The THD of iPV on the other hand is very low because the proposed APQC is deactivated and PV is injecting only symmetrical currents. When operating the PV converter in the advanced APQC mode, the asymmetric, DC and harmonic currents are delivered locally through the GSC of the PV system and thus, the flow of current from grid is

Table 1: The THD of PV and grid currents for various harmonic load conditions and for different PV operational modes.

3.8%

2.5%

Load THD

6.13%

currents correspond to 1000 W and 0 VAr, whereas the negative sequence reference is set at 𝐢−1𝑟 𝑑𝑞 = [1 0] A. Later on, at the point marked in Fig. 7 (c), the q-axis current of the -5th harmonic is changed from 0 A to 5 A. The three-phase currents are asymmetrical in the start and they become harmonically distorted as well due to the on-purpose injection of harmonic current. The simultaneous injection of positive, negative and harmonic currents validates the fast and accurate response of the proposed MFCC current controller. The experimental results demonstrate the multipurpose functionality of the proposed controller constituting it the most diversified controller allowing, in addition to positive sequence injection, the injection of on-purpose unbalanced, harmonic, and DC currents. The injection of DC, positive and negative sequence currents validates that the proposed controller is able to inject any value of the commanded reference current. Consequently, it can be inferred that based on the specific reference value provided by APQC, the proposed current controller can inject the required currents accurately.

THD (%) i iG

Normal mode 2.65

iPV

0.18

iG

4.25

iPV

0.3

iG

6.4

iPV

0.45

APQC mode

3.67

5.25

8.24

0.16 OP: 2.5 remaining: 1.17 0.25 OP: 3.8 remaining: 1.45 0.37 OP: 6.13 remaining: 2.11

PV-OFF mode 2.5 NA 3.8 NA 6.13 NA

Note: OP: on-purpose, NA: not applicable as PV is disconnected, Normal mode: when APQC not activated and PV injects symmetrical currents, APQC mode: PV injecting as per the proposed APQC, PVOFF mode: PV disconnected

free of harmonics with a THD of only 0.16 %, 0.25 % and 0.37 % respectively for load cases 1, 2 and 3. In the APQC operation mode, the THD of PV current is intentionally increased in order to fulfil the load demand and to improve the grid power quality. Under all the three load cases, after the on-purpose THD is subtracted from the overall THD of PV current, the remaining THD is always less than the allowable limit (THD