energies Article
An Improved Current Control Strategy for a Grid-Connected Inverter under Distorted Grid Conditions Ngoc Bao Lai and Kyeong-Hwa Kim * Department of Electrical and Information Engineering, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul 139-743, Korea;
[email protected] * Correspondence:
[email protected]; Tel.: +82-2-970-6406; Fax: +82-2-978-2754 Academic Editor: Shuhui Li Received: 13 November 2015; Accepted: 7 March 2016; Published: 12 March 2016
Abstract: This paper presents an improved current control strategy for a three-phase grid-connected inverter under distorted grid conditions. The main challenge associated with the grid-connected inverter in distributed generation (DG) systems is to maintain the harmonic contents in output current below the specified values even when the grid is subject to uncertain disturbances such as harmonic distortion. To overcome such a challenge, an improved current control scheme is proposed for a grid-connected inverter, in which the fundamental and harmonic currents are independently controlled by a proportional-integral (PI) decoupling controller and a predictive basis controller, respectively. The controller design approach is based on the model decomposition method, where the measured inverter currents and grid voltages are divided into the fundamental and harmonic components by means of moving average filters (MAFs). Moreover, to detect the angular displacement and angular frequency with better accuracy, even in the presence of the grid disturbance, the MAF is also introduced to implement an enhanced phase-lock loop (PLL) structure. Theoretical analyses as well as comparative simulation results demonstrate that the proposed control scheme can effectively compensate the uncertainties caused by the grid voltages with fast transient response. To validate the feasibility of the proposed scheme, the whole control algorithms are implemented on 2 kVA three-phase grid-connected inverter system using 32-bit floating-point DSP TMS320F28335. As a result, the proposed scheme is an attractive way to control a grid-connected inverter under adverse grid conditions. Keywords: current control; distorted grid conditions; DSP TMS320F28335; grid-connected inverter; model decomposition; moving average filter
1. Introduction Three-phase grid-connected inverters have been widely employed in various applications, including renewable power generation and regenerative energy systems. This is due to the recent development trend constructing the electrical grid in terms of distributed generation (DG) systems, in which grid-connected inverters are connected in parallel with each other to form a microgrid [1,2]. The essential functionality of microgrids is to have the ability to operate either in grid-connected or autonomous mode in case of the absence of the main grid. Another requirement is to handle effectively the exchange of active and reactive power between the microgrid and main grid [3,4]. In order to fulfill the aforementioned criteria, the control strategy of a microgrid is generally designed based on three levels of hierarchical structure to provide smartness and flexibility to microgrid, which includes the primary control, the secondary control, and the tertiary control [5]. To follow the development trend of the microgrid, the grid-connected inverter should be able to not only provide stable operation
Energies 2016, 9, 190; doi:10.3390/en9030190
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but also improve the system performance even during the presence of abnormal grid conditions. In general, the current control loop, which belongs to the primary control, is responsible for the quality of the exchanging power. According to the recently published utility interface standard regarding DG systems [6,7], the harmonic contents in the injected current need to meet certain current-distortion levels in order to guarantee the power quality as well as fulfill interconnection requirements. Consequently, the current control loop should be designed to ensure the effective operation of the grid-connected inverter under any operating conditions of grid. The PI controller has been widely used as current controller in variety of inverter applications because of its simplicity and stability. The design and implementation of this controller are quite straightforward in continuous as well as in discrete-time domain [8]. Furthermore, low computational burden of this control algorithm makes it easier to implement the whole control system with only one digital signal controller. However, despite these advantages, the PI controllers have the limitations that they are unable to cope with sinusoidal reference signals and periodic disturbances [9]. Although the sinusoidal tracking problem can be completely solved by implementing the controller in the synchronously rotating reference frame, poor disturbance rejection capability makes the PI type controller unsuitable for current control strategy of a grid-connected inverter in the presence of the distorted grid voltages. For the purpose of eradicating the harmonics from inverter currents, several control approaches have been proposed, which is categorized as selective and non-selective methods [10]. Proportional resonant (PR) controller is widely used as selective harmonic compensation scheme [11]. This controller is often implemented in the stationary reference frame and the resonant term is added to the main controller to suppress the harmonic component in the specific order. However, since this method requires separate resonant terms to compensate each harmonic component, this approach is usually considered to alleviate only a few harmful low order harmonics. When the numbers of resonant terms increase, the control structure becomes complicated or even impractical. Other approaches to eliminate the harmonics from inverter current use nonlinear control techniques such as the sliding mode control (SMC) [12], predictive control [13], or repetitive control [14]. These control strategies are often referred as non-selective method since the controllers work in wide range of frequency, in contrast to the selective method that only regulates the harmonics in some specified orders. By using such nonlinear controllers, the distorted level of inverter current can be mitigated even under the distorted grid voltages. However, the design task of a robust controller based on above techniques usually makes the system structure complicated because of the remaining problems related to those techniques such as the chattering problem in SMC, parameter sensitive in predictive control, slow dynamic response in repetitive control and so on. Furthermore, the practical complexity of nonlinear controller may degrade the performance of the controlled system. As another approach, a neural-network-based waveform processing and filtering scheme has been reported to reshape voltage or current waveforms [15]. However, this algorithm generally requires lots of computations to be processed in real time, which increases the computational burden of main controller. Moreover, offline training is often required in this method. Recently, a sliding mode harmonic compensation strategy based on the system model decomposition has been reported to reduce the harmful effects caused by the nonlinear controller [16]. In this work, the system model is first divided into two using the fundamental and harmonic components. Using two decomposed models, the controllers are separately designed, that is, the controller for the fundamental term by the conventional decoupling controller and the harmonic suppression controller by SMC. To decompose the grid voltages and inverter currents into the fundamental and harmonic components, the fourth-order band pass filters (BPFs) have been employed in the harmonic extractors. As reported in [16], even though the steady-state current responses can be quite improved with reduced chattering by adopting the decomposed model, the inverter system exhibits a slow transient response due to the sluggish dynamic characteristics of the BPF. Moreover, the slow response of the BPF may even cause the instability problem during transient duration.
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In addition to current controller, the phase lock loop (PLL) also influences on the inverter currents under the distorted grid voltages. Indeed, the conventional synchronous reference frame phase lock loop (SRF-PLL) algorithm integrated with a PI controller to determine the angular displacement of grid voltage is unable to cope with high frequency disturbances due to the limitation of the PI controller. Consequently, the high frequency uncertainty caused by the distorted grid voltages has a profound effect on the determination of the angular displacement of grid voltages. The effects of distorted grid on PLL can be alleviated by reducing the PLL bandwidth. However, this results in slow dynamic response in PLL, which means that the PLL cannot track the angular displacement of grid voltages rapidly. Recent studies have proved the effectiveness of the moving average filter basis PLL (MAF-PLL) under the distorted grid voltages [17,18]. The main concept of the MAF-PLL is to use the MAF as an ideal low pass filter (LPF) to remove the sinusoidal components in the synchronous reference frame before the measured grid voltages are processed in PLL algorithm. The main objective of this paper is to present a robust current control scheme for a three-phase grid-connected inverter under abnormal grid conditions like the distorted grid. The proposed control strategy is based on the system model decomposition, in which the fundamental and harmonic current controllers are designed separately. Whereas the synchronous PI decoupling controller is employed to control the fundamental current component, a predictive basis compensator is introduced to suppress the harmonic components in inverter currents. For this purpose, the harmonic contents are extracted by means of the MAFs. Furthermore, an MAF-PLL is employed to improve the detecting performance of the conventional SRF-PLL. Also, a simple modification method to improve the transient current response is presented by changing the q-axis and d-axis harmonic currents only during the transient period of the MAF. As a result, the proposed control scheme can effectively control a grid-connected inverter during steady-state as well as transient periods even under the distorted grid voltages. This paper is organized as follows: Section 2 presents the mathematical system model as well as the decomposition method. Section 3 describes the proposed control scheme composed of the PI decoupling controller, MAF-based harmonic extractor, MAF-PLL, and the predictive basis harmonic compensator. Simulation results are presented in Section 4. Afterwards, the experimental results are provided in Section 5. Finally, the conclusions are given in Section 6. 2. Modeling of a Grid-Connected Inverter Figure 1 shows a whole configuration of three-phase grid-connected inverter with an L filter. The analyses for current controller in inverter with an L filter are still valid for the case with LCL filter as long as the control bandwidth is kept below resonant frequency of LCL filter [19]. Considering the filter inductance of L and the filter resistance of R, the voltage equations of a grid-connected inverter are expressed in the synchronous reference frame as follows: vq “ Riq ` L
diq ` ωLid ` eq dt
(1)
vd “ Rid ` L
did ´ ωLiq ` ed dt
(2)
where iq and id are the q-axis and d-axis inverter currents, respectively; eq and ed are the q-axis and d-axis grid voltages, respectively; vq and vd are the q-axis and d-axis inverter output voltages, respectively; and ω is the grid angular frequency.
𝑣𝑑 = 𝑅𝑖𝑑 + 𝐿
𝑑𝑖𝑑 − ω𝐿𝑖𝑞 + 𝑒𝑑 𝑑𝑡
(2)
where 𝑖𝑞 and 𝑖𝑑 are the q-axis and d-axis inverter currents, respectively; 𝑒𝑞 and 𝑒𝑑 are the q-axis and d-axis grid voltages, respectively; 𝑣𝑞 and 𝑣𝑑 are the q-axis and d-axis inverter output voltages, Energies 2016, 9, 190 4 of 23 respectively; and 𝜔 is the grid angular frequency.
Figure 1. Block diagram of three-phase grid-connected inverter. Figure 1. Block diagram of three-phase grid-connected inverter.
When phase voltages and currents include harmonic components, the transformed variables into the synchronous reference frame are not in pure direct current (DC)-quantity. Instead, they contain the harmonic components as well as DC-quantity. To apply the decomposition method, the voltage and current variables can be expressed with DC-quantity and sinusoidal harmonic terms as follows: vqd “ Vqd ` vqdh
(3)
iqd “ Iqd ` iqdh
(4)
eqd “ Eqd ` eqdh
(5)
where the capital letter V, I, and E denote the inverter voltages, inverter currents, and grid voltages having DC-quantity, respectively, the subscript “qd” denotes the variables on the q-axis and d-axis in the synchronous reference frame, the subscripts “h” denotes harmonic quantities. The decomposed models for the voltage equations of a grid-connected inverter are derived by substituting Equations (3), (4), and (5) into Equations (1) and (2) as follows: ´ ¯ ´ ¯ dpIq ` iqh q Vq ` vqh “ R Iq ` iqh ` L ` ωL pId ` idh q ` Eq ` eqh dt
(6)
´ ¯ dpId ` idh q ´ ωL Iq ` iqh ` pEd ` edh q dt
(7)
Vd ` vdh “ R pId ` idh q ` L
Voltage equations in Equations (6) and (7) can be rewritten with respect to the DC-quantities and harmonic components as follows: dIqs ` ωLId ` Eq dt
(8)
dId ´ ωLIq ` Ed dt
(9)
vqh “ Riqh ` L
diqh ` ωLidh ` eqh dt
(10)
vdh “ Ridh ` L
didh ´ ωLiqh ` edh dt
(11)
Vq “ RIq ` L
Vd “ RId ` L
For convenience, Equations (8) and (9) are referred to the fundamental voltage equations because they are obtained through the Park’s transformation of phase variables in the fundamental components. Similarly, Equations (10) and (11) are referred to the harmonic voltage equations.
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3. Proposed Control Scheme The issue on power quality of DG systems is one of most common interconnection requirements for grid-connected inverter basis generation systems, which is being presented in all standards. According to the published standards [6,7], the grid injected current should not have the total harmonic distortion (THD) greater than 5% in most of operating conditions. Although recently developed current controllers for grid-connected inverters including linear and non-linear schemes can fulfill the THD Energies 2016, 9, 190 5 of 21 requirement in normal grid condition, the THD of inverter output current may exceed the limit during distorted grid voltages. The main purpose of the proposed control scheme is not only to fulfill the grid voltage accurately. Similarly, the transformed currents into the synchronous frame are processed interface requirements but also to minimize the harmonic contents in grid injected currents. with the MAF to obtain DC-quantity. These voltages and currents in DC-quantity are subtracted from Figure 2 shows the control block diagram of the proposed control scheme in which the three-phase 𝑒𝑞𝑑 and 𝑖𝑞𝑑 to extract the harmonic components of 𝑒𝑞𝑑ℎ and 𝑖𝑞𝑑ℎ . The current controller is formed inverter is connected to the grid through L filter. The overall system mainly consists of a three-phase by combining a synchronous PI decoupling controller and a predictive controller, where the PI inverter, a current controller, a predictive basis harmonic compensator, and MAFs, which are used decoupling controller is employed to regulate the inverter currents to follow their references and for system model decomposition as well as performance improvement in PLL. The grid voltages referred as a main controller. and inverter currents are measured and then transferred into the variables on the synchronous From the inverter voltage equations in Equations (1) and (2), the reference voltages are obtained reference frame using the Park’s transformation. The transformed grid voltages into the synchronous from the PI decoupling controller as follows: frame are first processed with the MAF to obtain pure DC-quantity without the harmonic distortion, 𝑘𝑖 the∗angular displacement in grid voltage accurately. ∗ determine and then, used in PLL algorithm𝑉to ) ∙ (𝑖𝑞 − 𝑖𝑞 ) + 𝜔𝐿𝐼𝑑 + 𝐸𝑞 (12) 𝑞 = (𝑘𝑝 + 𝑠 Similarly, the transformed currents into the synchronous frame are processed with the MAF to obtain 𝑘𝑖 DC-quantity. These voltages and currents in DC-quantity are subtracted from eqd and iqd to extract the 𝑉𝑑∗ = (𝑘𝑝 + ) ∙ (𝑖𝑑∗ − 𝑖𝑑 ) − 𝜔𝐿𝐼𝑞 + 𝐸𝑑 (13) 𝑠 harmonic components of eqdh and iqdh . The current controller is formed by combining a synchronous PI decoupling controller a predictive controller, where and, the PI𝑘decoupling controller is employed to where the symbol “*” and denotes the reference quantity 𝑝 and 𝑘𝑖 are the proportional and regulate the inverter currents to follow their references and referred as a main controller. integral gains of the PI controller, respectively.
Figure Figure2.2. Block Blockdiagram diagramof ofthe theproposed proposedcontrol controlscheme. scheme.
In thethe discrete-time domain, the reference voltages Equations (12) and voltages (13) can are be expressed From inverter voltage equations in Equations (1) in and (2), the reference obtained at each sampling instant k as follows: from the PI decoupling controller as follows: 𝑉𝑞∗ (𝑘)
ˆ ˙ ´𝑘 ¯ k i = 𝑘V 𝑇𝑠 +d ` ω𝐿𝐼 𝑝 q∙˚𝑖𝑞,𝑒𝑟𝑟 𝑞,𝑒𝑟𝑟 i˚q 𝑖´ iq (𝑖) ` ∙ωLI Eq𝑑 (𝑘) + 𝐸𝑞 (𝑘) “ (𝑘) k p `+ 𝑘𝑖 ∙ ∑ s 𝑖=0 ˆ
𝑉𝑑∗ (𝑘)
=
˙
k ˚ “ (𝑘) k p `+ 𝑘i𝑖 𝑘𝑝V∙d 𝑖𝑑,𝑒𝑟𝑟 s
(14) (12)
𝑘
`˚ ˘ id 𝑖´ id (𝑖) ´ ωLI Ed𝑞 (𝑘) + 𝐸𝑑 (𝑘) ∙∑ ∙ 𝑇𝑠 − ω𝐿𝐼 q` 𝑑,𝑒𝑟𝑟
(13) (15)
𝑖=0
where the symbol “*” denotes the reference quantity and, k p and k i are the proportional and integral where 𝑖𝑞,𝑒𝑟𝑟 = 𝑖𝑞∗ − 𝑖𝑞 , 𝑖𝑑,𝑒𝑟𝑟 = 𝑖𝑑∗ − 𝑖𝑑 , and Ts is the sampling period. gains of the PI controller, respectively.
3.1. MAF and MAF-PLL An MAF is employed as ideal LPF in the proposed control scheme, where the window length is chosen as one period of the fundamental grid voltage to retain the generality. However, the window length can be set to half of fundamental period in the case of the filtered variables are in the synchronous reference frame since the majority of the uncertainties in three-phase voltages are odd harmonics that become even harmonics in the synchronous reference frame.
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In the discrete-time domain, the reference voltages in Equations (12) and (13) can be expressed at each sampling instant k as follows: Vq˚ pkq “ k p iq,err pkq ` k i
k ÿ
iq,err piq Ts ` ωLId pkq ` Eq pkq
(14)
id,err piq Ts ´ ωLIq pkq ` Ed pkq
(15)
i “0
Vd˚ pkq “ k p id,err pkq ` k i
k ÿ i “0
where iq,err “ i˚q ´ iq , id,err “ i˚d ´ id , and Ts is the sampling period. 3.1. MAF and MAF-PLL An MAF is employed as ideal LPF in the proposed control scheme, where the window length is chosen as one period of the fundamental grid voltage to retain the generality. However, the window length can be set to half of fundamental period in the case of the filtered variables are in the synchronous reference frame since the majority of the uncertainties in three-phase voltages are odd harmonics that become even harmonics in the synchronous reference frame. The input–output relationship of the MAF can be described in continuous-time domain by 1 xout ptq “ Tw
żt t´Tw
xin pτq dτ
(16)
where Tw is the window length, xout ptq is the output signal, and xin pτq is the input signal. The continuous-time transfer function of the MAF can be obtained from Equation (16) as G MAF psq “
xout psq 1 ´ e´Tw s “ xin psq Tw s
(17)
The transfer function in Equation (17) shows that the MAF only requires a time equal to its window length to reach the steady state. For a digital implementation, the transfer function of the MAF can be discretized from Equation (17) as G MAF pzq “
1 1 ´ z´ N N 1 ´ z ´1
(18)
where Tw = NTs with N equal to the number of samples in one window length (N must be an integer). From Equation (18), it can be observed that the MAF provides an effective solution in view of the computational burden as compared with the BPF. Moreover, since the MAF only requires one period of fundamental grid voltage for the filter output to converge, the dynamic response of the MAF-based harmonic extractor is much faster than that of the BPF-based harmonic extractor, which requires almost six periods of fundamental grid voltage to reach steady-state condition [16]. In practical implementation, the mismatch between the designed window length Tw and the value of NTs makes errors in amplitude and phase angle. This problem can be solved by using several proved techniques such as rounding of Tw /Ts to the nearest integer, weighted mean value approach [20], and linear interpolation [21]. In order to secure the calculating capability of main controller while retaining the errors within an acceptable value [17], the rounding scheme that adjusts Tw /Ts to the nearest integer is used in this paper. Thus, the number of samples in one window length N can be obtained as follows: ˆ ˙ Tw (19) N “ round Ts where “round” denotes the round function which returns the nearest integral value.
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In the grid-connected inverter system, the inverter needs to monitor the angular displacement of the grid voltage in order to synchronize the inverter currents with the grid. Generally, the SRF-PLL, which is based on the Park’s transformation and a low bandwidth PI controller, is commonly employed in three-phase grid-tied inverter systems. Under the distorted grid voltages, however, the angular displacement of grid voltage cannot be tracked exactly due to the inability of the PI controller to reject sinusoidal disturbances. As a result, the detected angular frequency of grid contains high order harmonics, which cause an increase of harmonic contents in inverter currents. As is illustrated in Figure 2, the filtered d-axis voltage is fed directly to the conventional SRF-PLL instead of the measured d-axis voltage. The open loop transfer function of MAF-PLL can be obtained from Equation (17) and the conventional SRF-PLL as k p,pll s ` k i,pll Gol psq “ G MAF psq ˚ (20) s2 where k p,pll and k i,pll are the proportional and integral gains of the PI controller in the conventional SRF-PLL, respectively. By using the first-order Padé approximation [17], Equation (17) may be approximated as 1 (21) G MAF psq « Tw s`1 2 Replacing G MAF psq in Equation (20) by approximated term G MAF psq in Equation (21), the transfer function in Equation (20) becomes
G MAF psq «
´ ¯ 2 k p,pll s ` k i,pll pTw s ` 2q s2
(22)
From Equation (22), the approximated closed-loop transfer function of MAF-PLL can be described as k p,pll k i,pll 2 s`2 Tw Tw Gcl psq « (23) k p,pll k i,pll 2 3 2 s ` s `2 s`2 Tw Tw Tw By using the MAF, which acts as an ideal LPF, to obtain DC-quantity of the d-axis grid voltage, the grid angular displacement can be detected accurately even when the grid voltages are highly distorted. In addition to mathematical analyses, the simulation and experimental results of MAF-PLL will be given in the following sections to demonstrate the performance of the designed filter as well as its effect on inverter currents. 3.2. Predictive Harmonic Compensator The harmonic compensator, which is based on the predictive control, is also illustrated in Figure 2. The high frequency sinusoidal currents and voltages are extracted by means of the MAFs, and then, these values are used to form a predictive basis harmonic compensator. In the discrete-time domain, the harmonic voltage equations in Equations (10) and (11) can be described as vqh pkq “ Riqh pkq `
¯ L ´ iqh pk ` 1q ´ iqh pkq ` ωLidh pkq ` eqh pkq Ts
(24)
vdh pkq “ Ridh pkq `
L pi pk ` 1q ´ idh pkqq ´ ωLiqh pkq ` edh pkq Ts dh
(25)
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In Equations (24) and (25), by replacing the currents at sampling instant pk ` 1) by the reference currents, the predictive control law to suppress the harmonic currents can be expressed as v˚qh pkq “ Riqh pkq `
¯ L ´˚ iqh pkq ´ iqh pkq ` ωLidh pkq ` eqh pkq Ts
(26)
v˚dh pkq “ Ridh pkq `
˘ L `˚ idh pkq ´ idh pkq ´ ωLiqh pkq ` edh pkq Ts
(27)
where i˚qh pkq and i˚dh pkq denote the q-axis and d-axis harmonic reference currents, respectively. These values should be set to zeros in order to eliminate the harmonic components in inverter output current. From Equations (14), (15), (26), and (27) with i˚qh pkq “ i˚dh pkq “ 0, the q-axis and d-axis inverter reference voltages of the proposed control scheme are represented as v˚q pkq “ Vq˚ pkq ` v˚qh pkq
(28)
v˚d pkq “ Vd˚ pkq ` v˚dh pkq
(29)
As a result of using the decomposition model, the predictive basis harmonic compensator only has to deal with the harmonics model. Therefore, the problems associated with the parameters mismatch and time delay in the predictive control are highly reduced. 4. Simulation Results To evaluate the performance of the proposed control scheme, the simulations have been done for three-phase grid-connected inverter using the PSIM software. Figure 3 shows the whole system configuration where the main controller is implemented with the PSIM dynamic link library (DLL) block. EnergiesThe 2016,system 9, 190 parameters are summarized in Table 1. 8 of 21
Figure3.3. The The whole whole system systemconfiguration configurationfor forsimulation. simulation. Figure Table 1. System parameters of grid-connected inverter.
Parameters Rated power Grid voltage Grid frequency DC-link voltage Filter inductance Filter resistance Switching frequency
Symbol PR eg f VDC L R fs
Value 2 180 60 420 7 0.5 10
Units kW V Hz V mH Ω kHz
In addition to ideal grid voltages, the distorted grid voltages are used in order to evaluate the control performance in adverse operating conditions of the grid. For a distorted condition of grid voltage, the 5th and 7th harmonics with 20% of the fundamental component and the 11th and 13th
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Figure 3. The whole system configuration for simulation. Table Table1.1.System Systemparameters parametersofofgrid-connected grid-connectedinverter. inverter.
Parameters Symbol Value Value Symbol Rated power PR 2 Rated power PR 2 eg 180 Grid voltageGrid voltage eg 180 Grid frequency f 60 Grid frequency f 60 DC-link voltage 420 DC-link voltage VDC VDC 420 Filter inductance 77 Filter inductance L L Filter resistance R 0.5 Filter resistance R 0.5 Switching frequency fs 10 Switching frequency fs 10 Parameters
Units Units kW kW V V Hz Hz V V mH mH Ω Ω kHz kHz
In Inaddition additionto toideal idealgrid gridvoltages, voltages,the thedistorted distortedgrid gridvoltages voltagesare areused usedin inorder ordertotoevaluate evaluatethe the control performance in adverse operating conditions of the grid. For a distorted condition of grid control performance in adverse operating conditions of the grid. For a distorted condition of grid voltage, voltage,the the5th 5thand and7th 7thharmonics harmonicswith with20% 20%ofofthe thefundamental fundamentalcomponent componentand andthe the11th 11thand and13th 13th harmonics with 10% of the fundamental component are added to the ideal grid voltages. The resultant harmonics with 10% of the fundamental component are added to the ideal grid voltages. The three-phase grid voltages shownare in Figure THD isthe 31.7%. figure, ea , figure, eb , and 𝑒ec , resultant three-phase gridare voltages shown4,inwhere Figurethe 4, where THDIn is this 31.7%. In this 𝑎 denote three-phase grid voltages. 𝑒 , and 𝑒 denote three-phase grid voltages. 𝑏
𝑐
Figure4.4.Distorted Distortedthree-phase three-phasegrid gridvoltages. voltages. Figure
Figure55shows showsthe theperformance performancecomparison comparisonof ofdynamic dynamicresponses responsesbetween betweenthe theBPF BPFand andMAF MAF Figure under the distorted grid voltages. As a result of harmonic distortion in grid voltages as shown under the distorted grid voltages. As a result of harmonic distortion in grid voltages as shown inin Figure4,4,the theq-axis q-axisand andd-axis d-axisgrid grid voltages 𝑒𝑑the at synchronous the synchronous reference frame contain 𝑞 and Figure voltages e 𝑒and e at reference frame contain the q
d
harmonic components as well as DC-quantity. In Figure 5, eq,BPF and ed,BPF denote the filtered outputs processed with the BPF, respectively. On the other hand, eq,MAF and ed,MAF denote the filtered outputs processed with the MAF, respectively. It is easy to notice that the transient responses of the MAF are nearly five times faster than those of the BPF in extraction of DC-quantity, since the MAF only requires one window length to reach its steady state. Furthermore, by selecting the number of samples N to the nearest integer, the steady-state errors of the MAF can be lower than those of the fourth-order BPF (See the d-axis values).
of the MAF are nearly five times faster than those of the BPF in extraction of DC-quantity, since the MAF only requires one window length to reach its steady state. Furthermore, by selecting the number of samples N to the nearest integer, the steady-state errors of the MAF can be lower than those of the fourth-order BPF (See the d-axis values). Similarly, Figure 6 shows the comparison of dynamic responses to extracts DC-quantity between the BPF and MAF when the input signals are inverter currents. It is obvious that the transient Energies 2016, 9, 190 response and steady-state error are much more improved by adopting the MAF, which results in the improvement of harmonic extraction.
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Figure 5. Performance comparison of dynamic responses between the band pass filter (BPF) and
Figure 5. Performance comparison of dynamic responses between the band pass filter (BPF) and moving average filter (MAF) when direct current (DC)-quantity of grid voltages is extracted at the moving average filter (MAF) directgrid current (DC)-quantity of(b) grid is extracted at the synchronous frame underwhen the distorted voltages: (a) with BPF; and withvoltages MAF. synchronous frame under the distorted grid voltages: (a) with BPF; and (b) with MAF.
Similarly, Figure 6 shows the comparison of dynamic responses to extracts DC-quantity between the BPF and MAF when the input signals are inverter currents. It is obvious that the transient response and steady-state error are much more improved by adopting the MAF, which results in the improvement of harmonic extraction. Energies 2016, 9, 190 10 of 21
Figure 6. Performance comparison of dynamic responses between the BPF and MAF when
Figure 6. Performance comparison of dynamic responses between the BPF and MAF when DC-quantity DC-quantity of inverter currents is extracted at the synchronous frame under the distorted grid voltages: of inverter(a)currents is and extracted the synchronous frame under the distorted grid voltages: (a) using using BPF; (b) usingatMAF. BPF; and (b) using MAF. As stated earlier, the obtained angular displacement and angular frequency from the conventional SRF-PLL are severely distorted under the distorted grid voltages because of the inability of the PI controller to reject high frequency disturbances. Figure 7 shows the waveforms for the angular frequency 𝜔PLL and angular displacement θ determined by the conventional SRF-PLL. It is easy to notice that the angular frequency fluctuates around the fundamental value 𝜔𝑔𝑟𝑖𝑑 . Also, this fluctuation makes the obtained angular displacement θ distorted as is shown in Figure 7b. On the contrary, Figure 8 shows the simulation results for the MAF-PLL scheme under the distorted grid voltages. It can be clearly observed that the dynamic response of the MAF-PLL is comparable to that achieved by the SRF-PLL. The MAF-PLL, however, provides attractive steady-state response as a
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Figure 6. Performance comparison of dynamic responses between the BPF and MAF when DC-quantity of inverter currents is extracted at the synchronous frame under the distorted grid voltages: stated earlier, angular displacement and angular frequency from the conventional (a) using BPF;the andobtained (b) using MAF.
As SRF-PLL are severely distorted under the distorted grid voltages because of the inability of the PI As stated earlier, the obtained angular displacement and angular frequency from the controller to reject high frequency disturbances. Figure 7 shows the waveforms for the angular conventional SRF-PLL are severely distorted under the distorted grid voltages because of the inability frequency ω and angular displacement θ determined by the conventional SRF-PLL. It is easy to of thePLL PI controller to reject high frequency disturbances. Figure 7 shows the waveforms for the notice that the angular fluctuates around the fundamental value ω grid . Also, this It fluctuation angular frequencyfrequency 𝜔PLL and angular displacement θ determined by the conventional SRF-PLL. is makes the angular displacement θ distorted as the is shown in Figure 7b. the contrary, easy obtained to notice that the angular frequency fluctuates around fundamental value 𝜔 Also, this 𝑔𝑟𝑖𝑑 .On makes the obtained angular displacement θ distorted as is shown in Figure 7b. Onvoltages. the Figure 8fluctuation shows the simulation results for the MAF-PLL scheme under the distorted grid It contrary, Figure 8 shows the simulation results for the MAF-PLL scheme under the distorted grid can be clearly observed that the dynamic response of the MAF-PLL is comparable to that achieved voltages. It can be clearly observed that the dynamic response of the MAF-PLL is comparable to that by the SRF-PLL. The MAF-PLL, however, provides attractive steady-state response as a result of an achieved by the SRF-PLL. The MAF-PLL, however, provides attractive steady-state response as a excellent filtering capability of the MAF. of the MAF. result of an excellent filtering capability
7. Dynamic response of the conventional synchronous reference frame phase lock loop Figure Figure 7. Dynamic response of the conventional synchronous reference frame phase lock loop (SRF-PLL) under the distorted grid voltages: (a) angular frequency; and (b) angular displacement. (SRF-PLL) under the distorted grid voltages: (a) angular frequency; and (b) angular displacement. Energies 2016, 9, 190
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Figure 8. Dynamic response of the moving average filter phase lock loop (MAF-PLL) under the
Figure 8. Dynamic response of the moving average filter phase lock loop (MAF-PLL) under the distorted grid voltages: (a) angular frequency; and (b) angular displacement. distorted grid voltages: (a) angular frequency; and (b) angular displacement. To highlight the effectiveness of the proposed control scheme, the comparative simulation results withthe the effectiveness conventional control for acontrol grid-connected are also presented. The results To highlight of the scheme proposed scheme,inverter the comparative simulation conventional control scheme comprises a synchronous PI decoupling current controller and a SRFwith the conventional control scheme for a grid-connected inverter are also presented. The conventional PLL. In order to point out the weakness of the conventional control scheme, the simulation results control both scheme comprises a synchronous decoupling current controller and a SRF-PLL. In order to under the ideal and distorted grid PI voltages are shown in Figures 9 and 10, in which 𝑖𝑎 , 𝑖𝑏 , and 𝑖𝑐 denote three-phase inverter currents. As can be observed from the output current waveforms in Figure 9, the conventional control scheme shows a good steady-state performance under the ideal grid voltages. In the abnormal grid conditions, however, the output current waveforms, illustrated in Figure 10, are highly distorted due to the poor sinusoidal disturbance rejection capability of the PI controller both in current controller and in PLL.
Figure 8. Dynamic response of the moving average filter phase lock loop (MAF-PLL) under the distorted grid voltages: (a) angular frequency; and (b) angular displacement. Energies 2016, 9, 190
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To highlight the effectiveness of the proposed control scheme, the comparative simulation results with the conventional control scheme for a grid-connected inverter are also presented. The point out the weakness of scheme the conventional scheme, the simulation both conventional control comprises a control synchronous PI decoupling currentresults controller andunder a SRF-the ideal and distorted grid voltages are shown in Figures 9 and 10 in which i , i , and i denote three-phase PLL. In order to point out the weakness of the conventional control scheme, results a b the simulation c both under the ideal and distorted grid voltages are shown in Figures 9 and 10, in which 𝑖 , 𝑖 , and inverter currents. As can be observed from the output current waveforms in Figure 9, the 𝑎 𝑏conventional 𝑖 denote three-phase inverter currents. As can be observed from the output current waveforms 𝑐 control scheme shows a good steady-state performance under the ideal grid voltages. In the in abnormal Figure 9, the conventional control scheme shows a good steady-state performance under the ideal grid conditions, however, the output current waveforms, illustrated in Figure 10, are highly distorted grid voltages. In the abnormal grid conditions, however, the output current waveforms, illustrated due to the poor sinusoidal disturbance rejection capability of the PI controller both in current controller in Figure 10, are highly distorted due to the poor sinusoidal disturbance rejection capability of the PI and in PLL. controller both in current controller and in PLL.
9. Inverter currents of the conventional proportional-integral proportional-integral (PI) (PI) decoupling controller under under Figure Figure 9. Inverter currents of the conventional decoupling controller the ideal grid voltages: (a) phase-currents; and (b) q-axis and d-axis currents. the2016, ideal Energies 9, grid 190 voltages: (a) phase-currents; and (b) q-axis and d-axis currents. 12 of 21
Figure Inverter currents currents of of the PI decoupling controller under under the Figure 10. 10. Inverter the conventional conventional PI decoupling controller the distorted distorted grid grid voltages: (a) phase-currents; and (b) q-axis and d-axis currents. voltages: (a) phase-currents; and (b) q-axis and d-axis currents.
In addition to the results obtained using the conventional PI control scheme, the simulations have been carried out for another harmonic compensation approaches for comparison. Figure 11 shows the steady-state responses of the inverter currents using PR controller with different distorted grid conditions. To eliminate harmonic contents in inverter currents, only the resonant terms to compensate the 5th and 7th harmonics are added together with the fundamental controller. As shown in Figure 11a, the compensation works well when the grid disturbance only contains 5th and 7th
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Figure 10. Inverter currents of the conventional PI decoupling controller under the distorted grid voltages: phase-currents; and (b) q-axis andthe d-axis currents. In addition to (a) the results obtained using conventional PI control scheme, the simulations have been carried out for another harmonic compensation approaches for comparison. Figure 11 In addition to the results obtained using the conventional PI control scheme, the simulations shows the steady-state responses of the inverter currents using PR controller with different distorted have been carried out for another harmonic compensation approaches for comparison. Figure 11 grid conditions. To eliminate harmonic contents in inverter currents, the resonant terms to shows the steady-state responses of the inverter currents using PR controlleronly with different distorted compensate the 5th and 7th harmonics are added together with the fundamental controller. As grid conditions. To eliminate harmonic contents in inverter currents, only the resonant terms to shown compensate 5th and 7th harmonics added together with the fundamental controller. As shown in Figure 11a, the the compensation works are well when the grid disturbance only contains 5th and 7th in Figure 11a, the compensation works well when the grid disturbance only contains 5th andthe 7thcontrol harmonics. However, when the grid has the harmonic disturbance in other frequencies, harmonics. However, when the grid has the harmonic disturbance in other frequencies, the control performance of this scheme is degraded dramatically.
performance of this scheme is degraded dramatically.
Figure 11. Inverter currents using controllerwith with different gridgrid conditions: (a) The(a) case Figure 11. Inverter currents using PRPR controller differentdistorted distorted conditions: The case when the grid disturbance only contains 5th and 7th harmonics. (b) The case when the grid when the grid disturbance only contains 5th and 7th harmonics. (b) The case when the grid disturbance disturbance contains 5th, 7th, 11th and 13th harmonics. contains 5th, 7th, 11th and 13th harmonics.
Another widely used compensation approach that employs nonlinear controller is the sliding mode control. As an illustration, Figure 12 shows the control performance under distorted grid conditions when the sliding mode control is employed for harmonic compensation. As stated earlier, this control scheme can guarantee a good steady-state performance of target system, as shown in Figure 12a. However, the chattering in control input signals is unavoidable as is observed in the waveforms of inverter reference voltages v˚q and v˚d in Figure 12b. Moreover, it is not easy to meet the trade-off between the transient responses and steady-state performance in designing the sliding mode controller.
conditions when the sliding mode control is employed for harmonic compensation. As stated earlier, this control scheme can guarantee a good steady-state performance of target system, as shown in 2016, 9, 190 13 of 21 Figure Energies 12a. However, the chattering in control input signals is unavoidable as is observed in the ∗ ∗ waveforms Another of inverter reference voltages 𝑣 and 𝑣 in Figure 12b. Moreover, it is not easy to 𝑞 𝑑 widely used compensation approach that employs nonlinear controller is the sliding meet Energies 2016, 9, 190 of 23 the trade-off between steady-state performance in designing the 14 sliding mode control. Asthe an transient illustration,responses Figure 12 and shows the control performance under distorted grid conditions when the sliding mode control is employed for harmonic compensation. As stated earlier, mode controller. this control scheme can guarantee a good steady-state performance of target system, as shown in Figure 12a. However, the chattering in control input signals is unavoidable as is observed in the waveforms of inverter reference voltages 𝑣𝑞∗ and 𝑣𝑑∗ in Figure 12b. Moreover, it is not easy to meet the trade-off between the transient responses and steady-state performance in designing the sliding mode controller.
Figure 12. 12. Control Control performance performance with with harmonic harmonic compensation compensation using using the the sliding sliding mode mode control control under under Figure distorted distorted grid gridconditions: conditions: (a) (a) inverter inverter phase phase currents; currents;and and(b) (b)inverter inverterreference referencevoltages. voltages. Figure 12. Control performance with harmonic compensation using the sliding mode control under distorted grid conditions: (a) inverter phase currents; and (b) inverter reference voltages.
Figure13 13 shows shows the the simulation simulation results results of of the the proposed proposed control control scheme scheme under under the the same same distorted distorted Figure grid voltages as Figure 10. In contrast to those in Figure 10, the phase current waveforms in Figure 13 shows simulationtoresults proposed control scheme underwaveforms the same distorted grid voltagesFigure as Figure 10. the In contrast thoseofinthe Figure 10, the phase current in Figure 13a 13a still remain sinusoidal. Also, as can be observed in the q-axis and d-axis current waveforms in grid voltages as Figure 10. In contrast to those in Figure 10, the phase current waveforms in Figure still remain sinusoidal. Also, as can be observed in the q-axis and d-axis current waveforms in 13a still remain sinusoidal. Also,scheme as can begives observed in the q-axis and d-axis current waveforms in phase Figure 13b, the proposed control nearly constant currents, which imply that Figure 13b, the proposed control scheme gives nearly constant currents, which imply that phase the proposed control scheme gives nearly constant currents, which imply that phase currentsFigure have13b, relatively lowharmonic harmonic contents. currents have relatively low contents. currents have relatively low harmonic contents.
Figure 13. Inverter currents proposed control control scheme under the the distorted grid voltages: Figure 13. Inverter currents of of thetheproposed scheme under distorted grid voltages: (a) phase-currents; and (b) q-axis and d-axis currents. (a) phase-currents; and (b) q-axis and d-axis currents.
Figure 13. Inverter currents of the proposed control scheme under the distorted grid voltages: (a) phase-currents; and (b)harmful q-axis and d-axis currents. Despite the fact that the disturbances in three-phase grid are mainly sinusoidal harmonics, any type of disturbance may occur in gird in extreme cases. Figure 14 shows the comparative current responses in the presence of random disturbances in three-phase grid voltages. Random values are generated as shown in Figure 14c and these values are added with grid voltages to generate random disturbances in three-phase. From the comparative simulation results between the proposed control scheme in Figure 14a and the conventional PI control scheme in Figure 14b, it is verified that the proposed control scheme is robust against even random disturbance in grid voltage.
harmonics, any type of disturbance may occur in gird in extreme cases. Figure 14 shows the comparative current responses in the presence of random disturbances in three-phase grid voltages. Random values are generated as shown in Figure 14c and these values are added with grid voltages to generate random disturbances in three-phase. From the comparative simulation results between the proposed control scheme in Figure 14a and the conventional PI control scheme in Figure1514b, Energies 2016, 9, 190 of 23it is verified that the proposed control scheme is robust against even random disturbance in grid voltage.
Figure 14. 14. Steady-state Steady-state current current responses responses with with random random limited-band limited-band disturbances: disturbances: (a) (a) using using the the Figure proposed control control scheme; scheme; (b) (b) using using the the conventional conventional PI PI controller; controller; and and (c) (c) waveform waveform of of random random proposed disturbances in in three-phase three-phasegrid gridvoltages. voltages. disturbances
Although low harmonic contents in inverter currents at steady state can be achieved even under Although low harmonic contents in inverter currents at steady state can be achieved even under the distorted grid voltages by using the proposed control scheme, the transient response of the the distorted grid voltages by using the proposed control scheme, the transient response of the proposed control scheme becomes worse than that of the conventional control scheme. The proposed control scheme becomes worse than that of the conventional control scheme. The degradation degradation in transient response is mainly caused by the phase delay of filters used for the harmonic in transient response is mainly caused by the phase delay of filters used for the harmonic extractor. extractor. Figure 15 shows the transient responses of the conventional control scheme, in which Figure 15 shows the transient responses of the conventional control scheme, in which Figure 15a Figure 15a shows the waveforms of phase currents and Figure 15b shows the waveforms of the q-axis shows the waveforms of phase currents and Figure 15b shows the waveforms of the q-axis and d-axis and d-axis currents with the q-aixs current reference 𝑖𝑞∗ . As can be observed form Figure 15b, the currents with the q-aixs current reference i˚q . As can be observed form Figure 15b, the conventional conventional scheme responds rapidly to the change of reference currents. However, as is seen in scheme responds rapidly to the change of reference currents. However, as is seen in Figure 16, the Figure 16, the transient response of the proposed control scheme is relatively slow due to the delay transient response of the proposed control scheme is relatively slow due to the delay introduced by introduced by the harmonic extractors. The transient response in Figure 16b is almost ten times the harmonic extractors. The transient response in Figure 16b is almost ten times slower than that of slower than that of the conventional control scheme. This result is unacceptable to be used for a the conventional control scheme. This result is unacceptable to be used for a current control loop in current control loop in DG systems because they are supposed to provide very fast response. DG systems because they are supposed to provide very fast response.
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Figure 15. Transient Transientresponses responses the conventional PI decoupling controller under the Figure of of the PI decoupling currentcurrent controller under the distorted Figure 15. 15. Transient responses of conventional the conventional PI decoupling current controller under the distorted grid voltages: (a) phase-currents; and (b) q-axis and d-axis currents. grid voltages: phase-currents; and (b) q-axis d-axisand currents. distorted grid (a) voltages: (a) phase-currents; and and (b) q-axis d-axis currents.
Figure 16. Transient responses of the proposed current control scheme under the distorted grid Figure16. 16.Transient Transient responses of proposed the proposed current under the distorted grid Figure responses of the current controlcontrol schemescheme under the distorted grid voltages: voltages: (a) phase-currents; and (b) q-axis and d-axis currents. voltages: (a) phase-currents; and (b) q-axis and d-axis currents. (a) phase-currents; and (b) q-axis and d-axis currents.
Even though the major advantage of using the MAF in the harmonic extractor over BPF or LPF Even though though themajor majoradvantage advantageofofusing using theMAF MAFininthe theharmonic harmonic extractor over BPF LPF extractor over BPF or or LPF is thatEven the transientthe period introduced by filter isthe well reduced and predictable, this delay by the MAFis is that the transient period introduced by filter is well reduced and predictable, this delay by the MAF that thebetransient periodfurther introduced by filter is well the reduced and predictable, delay by the MAF should compensated in order to improve transient performancethis of current controller. should be be compensated compensated further further in in order order to to improve improve the the transient transient performance performance of current controller. should of current controller. A compensation method for phase delay has been proposed in [18]. Although this method reduces A compensation compensation method method for for phase phase delay delay has has been been proposed proposed in in [18]. [18]. Although Although this method method reduces reduces A the transient response of the MAF, the steady-state error is noticeably increased.this By considering that the transient response of the MAF, the steady-state error is noticeably increased. By considering that the reference transient currents responseare of the MAF, the steady-state error is noticeably By considering the generally obtained from the voltage control increased. loop or droop control loopthat in the reference reference currents currents are are generally generally obtained obtained from from the the voltage voltage control control loop loop or or droop droop control control loop in in the grid-connected inverter systems, it is always possible to detect the change in reference currents.loop Based grid-connected inverter systems, it is always possible to detect the change in reference currents. Based grid-connected inverter systems,the it istransient always possible to of detect the change reference currents. Based on this information, to improve response current control in loop, the q-axis and d-axis on this information, to improve the transient response of current control loop, the q-axis and d-axis harmonic currents 𝑖𝑞ℎ and 𝑖𝑑ℎ are temporally replaced during the transient period of the MAF with harmonic currents 𝑖𝑞ℎ and 𝑖𝑑ℎ are temporally replaced during the transient period of the MAF with
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on this information, to improve the transient 𝑖𝑞ℎ,𝑡response = 𝑖𝑞 − of 𝐼𝑞∗ current control loop, the q-axis and d-axis harmonic currents iqh and idh are temporally replaced during the transient period of the MAF with
𝑖𝑑ℎ,𝑡 = 𝑖𝑑 − ˚𝐼𝑑∗ iqh,t “ iq ´ Iq
(30)
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(30) (31)
where 𝑖𝑞ℎ,𝑡 and 𝑖𝑑ℎ,𝑡 are the approximated q-axis and d-axis harmonic currents based on the i “ id ´ Id˚ (31) assumption that the fundamental currents candh,treach theirs reference values instantly. where and idh,tthe are the approximated q-axis and harmonic currents based on the assumption Figure 17iqh,tshows simulation results of d-axis the proposed control scheme with temporary that the fundamental currents can reach theirs reference values instantly. replacement of the harmonic currents during the transient period of the MAF, which is one window Figure 17 shows the simulation results of the proposed control scheme with temporary length. In order to show the transient response of the proposed control scheme, the q-axis reference replacement of the harmonic currents during the transient period of the MAF, which is one window current islength. increased from 5 A the to 10 A at tresponse = 0.2 s, of and decreased to 7 Athe at tq-axis = 0.3reference s. As is clearly In order to show transient the then, proposed control scheme, observedcurrent in Figure 17b, thefrom q-axis can value to immediately, retaining is increased 5 Acurrent to 10 A at t =reach 0.2 s, its andreference then, decreased 7 A at t = 0.3 while s. As is clearly observed in Figure 17b, the q-axis current can reach its reference value immediately, while good harmonic suppression characteristics in phase currents. Although the replacement of the good harmonic suppression characteristics in phase currents. Although thecontents replacement harmonicretaining currents during transient period of the MAF may increase harmonic in inverter of the harmonic currents during transient period of the MAF may increase harmonic contents in current, the transient performance can be considerably improved. Moreover, the increase of the inverter current, the transient performance can be considerably improved. Moreover, the increase harmonicofcomponents in inverter in currents be negligible because it lasts during only one the harmonic components inverter can currents can be negligible because it lasts during only onewindow length ofwindow the MAF. length of the MAF.
Figure 17. Transient responsesofof the the proposed current controlcontrol scheme under the distorted Figure 17. Transient responses proposed current scheme under grid the voltages distorted grid with temporary replacement of the harmonic currents during transient period: (a) phase-currents; and voltages with temporary replacement of the harmonic currents during transient period: (a) phase(b) q-axis and d-axis currents. currents; and (b) q-axis and d-axis currents.
Figure 18 shows the fast Fourier transform (FFT) result of a-phase current using the proposed
Figure 18 shows the fast Fourier grid transform result of a-phase current using proposed control scheme under the distorted voltages,(FFT) in which the harmonic limits according to thethe IEEE control scheme under the distorted grid voltages, in which according 1547 interconnection of distributed generation regulations arethe alsoharmonic indicated forlimits comparison. As cantobethe IEEE seen, the 5th and harmonics are significantly reduced andare all the harmonic components are within As can 1547 interconnection of7th distributed generation regulations also indicated for comparison. the limits. be seen, the 5th and 7th harmonics are significantly reduced and all the harmonic components are within the limits.
Figure 18 shows the fast Fourier transform (FFT) result of a-phase current using the proposed control scheme under the distorted grid voltages, in which the harmonic limits according to the IEEE 1547 interconnection of distributed generation regulations are also indicated for comparison. As can Energies 2016, 9, 190 18 ofare 23 be seen, the 5th and 7th harmonics are significantly reduced and all the harmonic components within the limits.
Figure18. 18.Fast FastFourier Fouriertransform transform(FFT) (FFT)result result a-phase current using proposed scheme under Figure of of a-phase current using thethe proposed scheme under the the distorted grid voltages with harmonic limits according to the IEEE std. 1547. distorted grid voltages with harmonic limits according to the IEEE std. 1547. Energies 2016, 9, 190
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5. Experimental Results 5. Experimental Results The proposed control scheme has been implemented in a 2 kVA three-phase grid-connected inverter as shown Figure has 19. The control algorithms arethree-phase implemented using 32-bit Thesystem proposed controlinscheme beenwhole implemented in a 2 kVA grid-connected floating-point DSP TMS320F28335 with clock frequency of 150 MHz [22]. The sampling period is inverter system as shown in Figure 19. The whole control algorithms are implemented using 32-bit set to 100 µs inDSP theTMS320F28335 experiments, which yields the switching 10sampling kHz. Theperiod intelligent floating-point with clock frequency of 150frequency MHz [22]. of The is set power (IPM) is employed for three-phase grid-connected The inverter power phase to 100 µmodule s in the experiments, which yields the switching frequency of inverter. 10 kHz. The intelligent currents are detected by the and are converted through internal 12-bit A/D module (IPM) is employed forHall-effect three-phasedevices grid-connected inverter. The inverter phase currents are converters. inverter reference are appliedthrough using the symmetrical space vector PWM detected by The the Hall-effect devices voltages and are converted internal 12-bit A/D converters. The method. The parameters theapplied experimental are summarized in Table 1. For distorted inverter reference voltagesofare using system the symmetrical space vector PWM method. The condition ofof the grid voltages, 10% of the and the seventh harmonics, respectively, andof1% the parameters the experimental system arefifth summarized in Table 1. For distorted condition theofgrid eleventh thirteenth harmonics, respectively, arerespectively, injected to the grid which results in voltages, and 10%the of the fifth and the seventh harmonics, and 1%voltage, of the eleventh and the the THD of 14.2%. thirteenth harmonics, respectively, are injected to the grid voltage, which results in the THD of 14.2%.
Figure 19. 19. Experimental test setup. setup. Figure Experimental test
Figure 20 shows the experimental results for the SRF-PLL and MAF-PLL algorithms under the Figure 20 shows the experimental results for the SRF-PLL and MAF-PLL algorithms under the distorted grid voltages for comparison. As can been seen, the angular frequency waveform obtained distorted grid voltages for comparison. As candue been the angular frequency waveform obtained by the SRF-PLL algorithm is highly distorted toseen, the existence of high frequency disturbances in by the SRF-PLL algorithm is highly distorted due to the existence of high frequency disturbances in three-phase grid voltages. In contrast, the angular frequency obtained from the MAF-PLL algorithm three-phase gridconstant voltages.inInthe contrast, the angular frequency obtained from thehighly MAF-PLL algorithm remains nearly steady-state even when the grid voltages are distorted. As a remains nearly constant in the steady-state even when the grid voltages are highly distorted. a result, the angular displacement is not influenced by the distorted grid voltages, which provesAs the effectiveness and robustness of the MAF-PLL.
Figure 19. Experimental test setup.
Figure 20 shows the experimental results for the SRF-PLL and MAF-PLL algorithms under the distorted grid voltages for comparison. As can been seen, the angular frequency waveform obtained by the SRF-PLL algorithm is highly distorted due to the existence of high frequency disturbances in Energies 2016, 9, 190 19 of 23 three-phase grid voltages. In contrast, the angular frequency obtained from the MAF-PLL algorithm remains nearly constant in the steady-state even when the grid voltages are highly distorted. As a result, the angular displacement is not influenced by the distorted grid voltages, which proves the robustness of of the the MAF-PLL. MAF-PLL. effectiveness and robustness
Figure 20. Experimental results for the SRF-PLL and MAF-PLL under the distorted grid voltages. Figure 20. Experimental results for the SRF-PLL and MAF-PLL under the distorted grid voltages.
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Figure 21 shows the experimental experimental results for inverter inverter output currents when when the the conventional conventional synchronous synchronous PI decoupling controller controller and SRF-PLL algorithm algorithm are employed under the distorted grid voltages. It is clearly observed in this figure that phase current waveforms are quite non-sinusoidal. non-sinusoidal. This control scheme failsfails to meet the high qualityquality in a realinsystem This indicates indicatesthat thatthe theconventional conventional control scheme to meet the power high power a real where exist sinusoidal disturbances. systemthere where there exist sinusoidal disturbances.
Figure 21. 21. Experimental Experimental results for inverter inverter output output currents currents using using the the conventional conventional PI PI decoupling decoupling Figure results for controller and and SRF-PLL SRF-PLL under under the the distorted distorted grid grid voltages. voltages. controller
Figure 22 shows the experimental results for inverter output currents using the proposed control Figure 22 shows the experimental results for inverter output currents using the proposed control scheme under the same conditions as Figure 21. Due to an effective compensating capability of the scheme under the same conditions as Figure 21. Due to an effective compensating capability of proposed control scheme, the inverter phase currents shows considerably sinusoidal waveforms the proposed control scheme, the inverter phase currents shows considerably sinusoidal waveforms regardless of the high distortion level in the grid voltages. regardless of the high distortion level in the grid voltages.
controller and SRF-PLL under the distorted grid voltages.
Figure 22 shows the experimental results for inverter output currents using the proposed control scheme under the same conditions as Figure 21. Due to an effective compensating capability of the proposed scheme, the inverter phase currents shows considerably sinusoidal waveforms Energies 2016,control 9, 190 20 of 23 regardless of the high distortion level in the grid voltages.
Figure 22. Experimental results for inverter output currents using the proposed control scheme under Figure 22. Experimental results for inverter output currents using the proposed control scheme under the distorted grid voltages. the distorted grid voltages.
As mentioned previously in Figure 16, the delay of the MAF might slow down the dynamic As mentioned in Figure 16,get therid delay of the MAF might slow downtechnique the dynamic response in inverterpreviously currents. In order to of this problem, a modification that response in inverter currents. In order to get rid of this problem, a modification technique thatresponse replaces replaces the harmonic current with temporary values has been used. The transient current the harmonic current with temporary haschange been used. transient current response of the of the proposed control scheme undervalues the step in theThe current reference is demonstrated in proposed control scheme under the step change in the current reference is demonstrated in Figure 23. Figure 23. As is shown, the q-axis inverter current instantly reaches its new reference value, which As is shown, inverter current instantly reaches its new reference value, which validates the validates the the fastq-axis dynamic response of the proposed control scheme. fast dynamic response of the proposed control scheme. Energies 2016, 9, 190 19 of 21
Figure 23. Step response of the inverter currents using the proposed control scheme under the Figure 23. Step response of the inverter currents using the proposed control scheme under the distorted distorted grid voltages. grid voltages.
Figure 24 shows the experimental FFT result of a-phase inverter current using the proposed Figure 24 shows the distorted experimental resultIt of a-phaseobserved inverter that current using the proposed control scheme under the grid FFT voltages. is clearly the low-order harmonic control scheme the distorted voltages.and It isthirteenth clearly observed low-order harmonic components inunder the fifth, seventh,grid eleventh, order that are the considerably reduced. components inall thethe fifth, seventh,components eleventh, and thirteenth order are considerably reduced. Furthermore, harmonic well satisfy the harmonic limits of IEEE std. Furthermore, 1547 [6]. all the harmonic components well satisfy the harmonic limits of IEEE std. 1547 [6].
distorted grid voltages.
Figure 24 shows the experimental FFT result of a-phase inverter current using the proposed control scheme under the distorted grid voltages. It is clearly observed that the low-order harmonic components in the fifth, seventh, eleventh, and thirteenth order are considerably reduced. Energies 2016, 9, 190 21 of 23 Furthermore, all the harmonic components well satisfy the harmonic limits of IEEE std. 1547 [6].
Figure 24. FFT result of a-phase current using the proposed control scheme under the distorted grid voltages. Figure 24. FFT result of a-phase current using the proposed control scheme under the distorted grid voltages.
As a result, the proposed control scheme has a good disturbance rejection capability in steady state as well as fast dynamic response. As a result, the proposed control scheme has a good disturbance rejection capability in steady state as well as fast dynamic response. 6. Conclusions In this paper, an improved current control strategy for a grid-connected inverter even in the 6. Conclusions presence of distorted grid conditions has been proposed for DG systems. The proposed control In this paper, an improved current control strategy for a grid-connected inverter even in the scheme is designed to overcome the limitation of the conventional PI type control schemes under presence of distorted grid conditions has been proposed for DG systems. The proposed control scheme adverse operation conditions of grid. Two significant enhancements in the proposed control scheme is designed to overcome the limitation of the conventional PI type control schemes under adverse are the implementation of a robust PLL algorithm and the additional harmonic suppression scheme. operation conditions of grid. Two significant enhancements in the proposed control scheme are the This is achieved by introducing the model decomposition method and MAF, by which the inverter implementation of a robust PLL algorithm and the additional harmonic suppression scheme. This is model can be decomposed into the fundamental and harmonic components. Based on the derived achieved by introducing the model decomposition method and MAF, by which the inverter model can models, the fundamental and harmonic currents are independently controlled by a decoupling PI be decomposed into the fundamental and harmonic components. Based on the derived models, the controller and a predictive basis controller, respectively. The principle and mathematical description fundamental and harmonic currents are independently controlled by a decoupling PI controller and a predictive basis controller, respectively. The principle and mathematical description of the proposed control scheme have been analyzed to emphasize the simplicity of the control structure. To verify the feasibility and effectiveness of the proposed control scheme, the whole control systems are constructed using 32-bit floating-point DSP TMS320F28335. It has been demonstrated through the comparative simulations and experimental results that the proposed control scheme is an effective way to improve the performance of a grid-connected inverter under the distorted grid voltages. Acknowledgments: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2056436). This work was supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry & Energy. (NO. 20154030200720). Author Contributions: Ngoc Bao Lai and Kyeong-Hwa Kim conceived the main concept of the control structure and developed the entire system. Ngoc Bao Lai carried out the research and analyzed the numerical data with the guidance from Kyeong-Hwa Kim. Ngoc Bao Lai and Kyeong-Hwa Kim collaborated to prepare the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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