An Improved Frequency Measurement Method from the Digital ... - MDPI

electronics Article

An Improved Frequency Measurement Method from the Digital PLL Structure for Single-Phase Grid-Connected PV Applications Byunggyu Yu 1,2 1 2

ID

Division of Electrical, Electronic & Control Engineering, Kongju National University, Cheonan-si 31080, Korea; [email protected]; Tel.: +82-41-521-9162 Institute of IT Convergence Technology, Cheonan-si 31080, Korea

Received: 12 July 2018; Accepted: 18 August 2018; Published: 20 August 2018







Abstract: The Phase Locked Loop (PLL) technique has been studied to obtain the phase and frequency information in grid-connected distributed generations for the sake of synchronizing the grid voltage and the inverter output current. In particular, the line frequency information, such as the anti-islanding function, is very important for the grid connection requirement. This paper presents a novel frequency measurement method from the digital PLL control structure for single-phase grid-connected PV applications. The conventional PLL controller uses the phase information to calculate the frequency of PV inverter output voltage after every line cycle and has shown a relatively low accuracy. This paper uses the angular frequency to directly measure the frequency after every line cycle. To verify the validity of the proposed method compared with the conventional method, a simulation was conducted. According to the simulation results, the measurement error of the proposed method is 80 times lower than the conventional one. Keywords: phase locked loop; grid-connection; photovoltaic generation; frequency measurement; PV inverter

1. Introduction The grid interactive PV system has the fastest growth rate in the world energy industry and has started to play the dominant role in that industry [1–3]. To obtain grid synchronization between the grid voltage and the inverter output current, it is very important to obtain grid voltage information, such as the phase, frequency, and magnitude [3–9]. The frequency measurement, used in the PV inverter controller, is especially important, since it plays a key role in the inverter current command, such as the anti-islanding function [10–15]. In general, PLL control methods are commonly used to estimate the phase and frequency of PV inverter output voltage in order to synchronize them with the utility voltage in distributed power systems. The simple Zero Crossing Detection (ZCD) method has been used to obtain voltage phase information by detecting the zero-crossing points of the PV inverter output voltage [16,17]. The ZCD method has several disadvantages, such as low detection speed and possible inaccurate phase information between the two crossing points [16–18]. Another method, called the digital PLL, uses the quadrature of the input waveform, shifted by 90 degrees, and has been studied widely until the present day [18]. In a three-phase system, the dq transformation of the three-phase variables has the same properties as the digital PLL, and the PLL can be implemented easily [18]. However, in a single-phase system, it must achieve an additional signal, introducing a phase shift of 90 degrees with respect to the fundamental frequency of the power system. Single-phase PV systems have received considerable attention because of their emerging applications, such as PV micro-inverter systems, as well as vehicle-to-grid and grid-to-vehicle connections [19,20]. Electronics 2018, 7, 150; doi:10.3390/electronics7080150

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considerable attention because of their emerging applications, such as PV micro-inverter systems, as well as vehicle-to-grid and grid-to-vehicle connections [19,20]. Usually,PLL PLL is is used used to to detect detect voltage voltage information information [21,22]. [21,22]. The The conventional conventional PLL PLL controller controller uses uses Usually, phase information PVPV inverter output voltage after every line line cycle, and phase information to tocalculate calculatethe thefrequency frequencyofof inverter output voltage after every cycle, has shown a relatively low accuracy [23–28]. This paper presents a novel frequency measurement and has shown a relatively low accuracy [23–28]. This paper presents a novel frequency measurement method, with withhigh highaccuracy, accuracy,from fromthe the digital PLL control structure single-phase grid-connected method, digital PLL control structure forfor single-phase grid-connected PV PV applications. Unlike the conventional technique, the PLL method proposed in this paper applications. Unlike the conventional PLLPLL technique, the PLL method proposed in this paper usesuses the the angular frequency to directly measure the frequency every line cycle. angular frequency to directly measure the frequency afterafter every line cycle. This paper paper consists consists of of three three sections. sections. Firstly, the control control system system for for aa digital digital PLL, PLL, using using an an all all This Firstly, the pass filer, is described. Secondly, the proposed PLL method for a novel line frequency measurement pass filer, is described. Secondly, the proposed PLL method for a novel line frequency measurement is is explained, analyzed, and compared the conventional method. Lastly, measurement a frequency explained, analyzed, and compared with thewith conventional method. Lastly, a frequency measurementcomparison performance comparison between the proposed method andone, the conventional one, is performance between the proposed method and the conventional is discussed through discussed through several simulation results for a 350 W single-phase PV micro-inverter. several simulation results for a 350 W single-phase PV micro-inverter. 2. System Configuration Configuration In a three-phase three-phasesystem, system,utility utilityvoltage voltage information, such as the magnitude the information, such as the magnitude and and angleangle of theofgridgrid-voltage vector, easily obtained. a single-phasesystem, system,the thegrid grid voltage voltage information is voltage vector, can can easily be be obtained. In In a single-phase is obtained by detecting detecting the the zero-crossing zero-crossing point. point. However, the zero-crossing zero-crossing detection detection method is not not practical practical due due to to its its sensitivity sensitivity to to noise. noise. Therefore, two two virtual virtual phases phases of PLL PLL operation operation must must be used used for for aa single-phase single-phase system. system. To To use use the the reference reference frame frame theory theory for for aa simple simple control, control, the the single-phase single-phase voltage voltage should should be be virtual virtual two-phase PLL forfor a two-phase voltage voltage that thathas hasaa90-degree 90-degreeout-of-phase out-of-phasecomponent. component.Based Basedon onthis thisconcept, concept,the the PLL single-phase system consists of of two stages: AA two-phase generator and a phase controller, as shown in a single-phase system consists two stages: two-phase generator and a phase controller, as shown Figure 1. 1. in Figure

Figure 1. Block diagram of PLL for a single-phase PV inverter controller. Figure 1. Block diagram of PLL for a single-phase PV inverter controller.

2.1. Two-Phase Generator 2.1. Two-Phase Generator In Figure 1, Vqs is defined as a 90-degree lagging component of Vds. There are a few ways to In Figure 1, V is defined as a 90-degree lagging component of Vds . There are a few ways to calculate Vqs. In thisqspaper, an all-pass filter is used to achieve the 90-degree out-of-phase component calculate Vqs . In this paper, an all-pass filter is used to achieve the 90-degree out-of-phase component in the utility voltage, as shown in Figure 2. When the input resistance Ri is equal to the feedback in the utility voltage, as shown in Figure 2. When the input resistance Ri is equal to the feedback resistance Rf, there is no magnitude attenuation. resistance Rf , there is no magnitude attenuation.  Vout  1 − j 2 fRC  Vout =  1 − j2π f RC  (1) =  1 + j 2 fRC  (1) V in Vin 1 + j2π f RC

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Figure 2. Analog lagging all-pass filter topology. Figure 2. Analog lagging all-pass filter topology.

The output voltage phase will be changed to the transfer function in (1), based on the input The output voltage phase will be changed to the transfer function in (1), based on the input voltage. voltage. Vout C ∠θ C 1 1 (2π f RC ) out = C1111 = C11 ∠θ − θ = −2 tan−− 2 = = Vin C2 ∠θ2 C2 11 −  2 = −2 tan 2 fRC

Vin

C 2  2

(

C2

1∠θ = −2 tan−1 (2π f RC ) = −90◦ , RC =

1 = −2 tan −1 ( 2 fRC ) = −90, RC = Vout −s + a 1 = , a= = 2π f Vin s+a RC

V

)

1 1f 2π

2 f

(2) (2) (3)

(3) (4)

−s + a

out of (5) into (4), the 1 discrete all-pass filter equation can be drawn After applying a bilinear transformation = (4) a= = 2 f V s + a as Equations (6) and (7). in RC , 2 z−1 s= (5) After applying a bilinear transformation of (5) Ts into z + 1(4), the discrete all-pass filter equation can be drawn Equations (6) and (7). where Tas is the sampling period

s

2 z −1

1− − β + sz−=1 Vout (z) T, sβ z=+ 1 = − 1 Vin (z) 1 − βz 1+

aTs 2 aTs 2

=

1−

πf fs πf fs

1+ where Ts is the sampling period Vout [n] = − β · Vin [n] + Vin [n − 1] + β · Vout [n − 1]

(5) (6)

(7)

aTs 1 −  f 1 − To obtain a 90-degree out-of-phase component from the the filter resistance and fvoltage, s 2 input 1  resistance = =is 1 kΩ, Vout (by z ) (3).− If + z −filter capacitance should be determined the then the filter capacitance (6) will aTs f = 1 + 1 + − 1 be 1.5315 µF. In that case, the βV is( z0.963, based ) 1and −  zit can be simulated f s on (7), as shown in Figure 3. 2 in

, Obviously, the output signal has a 90-degree out-of-phase lag with respect to the input voltage. With the grid voltage V and the calculated 90-degree out-of-phase lagging voltage (7) Vqs , Vout dsn = −  Vin  n + Vin  n − 1 +  Vout  n − 1 the active and reactive component in the reference frame can be drawn by applying the reverse obtain a 90-degree out-of-phase the input resistancephase and ParkTo transformation as (8). In (8) and (9), component the rotatingfrom reference framevoltage, is basedthe on filter the estimated capacitance be determined byω, the filter ˆ(3).asIfshown angle θˆ and should the estimated frequency in resistance Figure 4. is 1 kΩ, then the filter capacitance will be 1.5315 μF. In that case, the β is 0.963, and based on (7), as shown  it can be!simulated   in Figure 3. !  ∧ ∧ ∧ ∧ Obviously, the output signal cos hasθa 90-degree lag with respect to the input voltage. Vde sin θ  out-of-phase Vds +V qs · sin θ   Vds · cos θlagging = Vds and ∧the calculated · 90-degree = out-of-phase (8) With the grid voltage voltage ∧ ∧ ∧ Vqs, the active Vqe Vqs − sin θ cos θ − V · sin θ + V · cos θ qs ds by applying and reactive component in the reference frame can be drawn the reverse Park transformation as (8). In (8)∧ and (9), the∧rotating reference frame is based on the estimated∧phase angle ∧ ∧ Vde = Vds frequency · cos θ + Vqs𝜔 θ = Vmin sinFigure θ · cos4.θ − Vm cos θ · sin θ = Vm sin(θ − θ ) (9) 𝜃̂ and the estimated ̂,· sin as shown    Vde   cos   =   Vqe   − sin  

      sin    Vds   Vds  cos  + Vqs  sin    =     V   qs    −Vds  sin  + Vqs  cos    cos    

(8)

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





Vde = Vds  cos  + Vqs  sin  = Vm sin   cos  − Vm cos   sin  = Vm sin( −  ) Electronics 2018, 7,V150 de = Vds  cos  + Vqs  sin  = Vm sin   cos  − Vm cos   sin  = Vm sin( −  )

(9)

4 of(9) 11

(a) (a)

(b) (b) Figure 3. Digital all-pass filter simulation results for 90-degree out-of-phase lagging. Figure Figure3.3.Digital Digitalall-pass all-passfilter filtersimulation simulationresults resultsfor for90-degree 90-degreeout-of-phase out-of-phaselagging. lagging.

Rotating Rotating imaginary axis imaginary Vqe axis Vqe

Stationary Stationary imaginary axis axis Vimaginary qs Vqs 

  

 

Rotating Vde Rotating Vde real axis real axis Vds Stationary Stationary Vds real axis real axis

Figure 4. Estimated reference frame for a single-phase system. Figure Figure4.4.Estimated Estimatedreference referenceframe framefor fora asingle-phase single-phasesystem. system.

2.2. Phase Controller 2.2. 2.2.Phase PhaseController Controller As shown in (9), the reactive voltage component Vde should be maintained at zero for the unity As shown inin(9), the voltage component VV be at zero for the shown (9), thereactive reactive voltage should bemaintained maintained zero theunity unity dedeshould powerAs factor of the estimated phase angle component 𝜃̂ to be equal to the real phase angleatθ. To for control the θˆ 𝜃̂totobebeequal power factor ofofthe estimated phase angle totothe real phase angle θ.θ.To control the power factor the estimated phase angle equal the real phase angle To control the estimated phase angle error, Δω is obtained using a PI controller. Δω is added to the initial value ω ff estimated phase angle error, ∆ω is obtained using a PI controller. ∆ω is added to the initial value ω estimated phase angle error, Δω is obtained using a PI controller. Δω is added to the initial value ω ff ff ̂ to achieve the estimated frequency 𝜔 ̂ and the estimated phase angle 𝜃, as shown in Figure 1. ˆ as totoachieve and thethe estimated phase angle θ, in Figure 1. 1. achievethe theestimated estimatedfrequency frequencyωˆ 𝜔 ̂ and estimated phase angle 𝜃̂, shown as shown in Figure 3. The Line Frequency Measurement Techniques from the Digital PLL The accurate line frequency information from the PLL controller is very significant for the evaluation of the system’s safety status, which is required to meet national and international grid

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3. The Line Frequency Measurement Techniques from the Digital PLL Electronics 2018, 7, 150

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The accurate line frequency information from the PLL controller is very significant for the evaluation of the system’s safety status, which is required to meet national and international grid inverter controller controller code requirements [29–31]. In addition, this information is used to generate the PV inverter command, such as the anti-islanding function and the Active Frequency Drift (AFD) method [10–12,14]. command, such as the anti-islanding function and the Active Frequency Drift (AFD) method [10– This section discusses both the conventional PLL technique and the one one to calculate the 12,14]. This section discusses both the conventional PLL technique andproposed the proposed to calculate lineline frequency. the frequency. 3.1. The The Conventional Conventional Method Method 3.1. The operational principle of of the the conventional PLL technique technique to to calculate calculate the the line line frequency of The operational principle conventional PLL frequency of ˆ PV inverter output voltage is shown in Figure 5. Angular frequency information ( ω), as shown in PV inverter output voltage is shown in Figure 5. Angular frequency information (𝜔 ̂), as shown in Figure 1,1,isisalso used to calculate phase information. Based Based on the phase the line frequency Figure also used to calculate phase information. on theinformation, phase information, the line is calculated by the relationship between the sampling frequency (f ) and the number of the sampling frequency is calculated by the relationship between the sampling frequency (fsampling) and the number counter (F_N) during a line cycle, as shown in Figure 5. After a line cycle, the phase information of the counter (F_N) during a line cycle, as shown in Figure 5. After a line cycle, the phase information (wt_vco) match the the exact exact one-line one-line cycle cycle phase phase 2π, 2π, because because the the incremental incremental phase (dwt_vco) is is (wt_vco) does does not not match phase (dwt_vco) not small enough. Since the sampling frequency is limited by the microcontroller performance, it is not small enough. Since the sampling frequency is limited by the microcontroller performance, it is hard to to increase increase the the sampling sampling frequency. frequency. In In other other words, words, the the incremental incremental phase phase is is not not small small enough. enough. hard Thus, difference between wt_vco, after a line cycle, andand 2π has Thus, the the amount amountof oferror errorcaused causedbybythe thephase phase difference between wt_vco, after a line cycle, 2π a negative effect on the calculated line frequency measurement. Thus, the conventional PLL technique has a negative effect on the calculated line frequency measurement. Thus, the conventional PLL to measuretothe line frequency has shownhas lowshown accuracy. technique measure the line frequency low accuracy.

Figure 5. Flowchart of the conventional PLL technique to calculate the line frequency. Figure 5. Flowchart of the conventional PLL technique to calculate the line frequency.

3.2. The Proposed Method 3.2. The Proposed Method The operational principle of the proposed PLL technique to calculate the line frequency of PV The operational principle of the proposed PLL technique to calculate the line frequency of PV inverter output voltage is shown in Figure 6. Unlike the conventional method, this method uses the inverter output voltage is shown in Figure 6. Unlike the conventional method, this method uses the angular frequency to directly measure the frequency after every line cycle. As shown in Figure 6, by angular frequency to directly measure the frequency after every line cycle. As shown in Figure 6, summing the angular frequency (wt_vco) during a single line cycle, the summation of angular by summing the angular frequency (wt_vco) during a single line cycle, the summation of angular frequency wt_vco_s can be achieved. After a line cycle, the averaged angular frequency information frequency wt_vco_s can be achieved. After a line cycle, the averaged angular frequency information can can be generated by dividing the number of the counter F_N for a line cycle. It could be converted to be generated by dividing the number of the counter F_N for a line cycle. It could be converted to the line frequency with an appropriate scaling factor k. The scaling factor k is related to several parameters,

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the line frequency with an appropriate scaling factor k. The scaling factor k is related to several such as the sampling frequency of the microcontroller, the nominal line frequency, etc. In this paper, parameters, such as the sampling frequency of the microcontroller, the nominal line frequency, etc. the scaling factor k was easily determined by using only one example case. Unlike the conventional In this paper, the scaling factor k was easily determined by using only one example case. Unlike the method, there is little relationship between the proposed method and the phase error, causing a phase conventional method, there is little relationship between the proposed method and the phase error, difference between wt_vco and 2π. With the proposed method, the phase error only affects the number causing a phase difference between wt_vco and 2π. With the proposed method, the phase error only of affects the counter, and its of impact is negligible. Therefore, averagedTherefore, angular frequency information the number the counter, and its impact isthe negligible. the averaged angular is quite reliableinformation for calculating the reliable line frequency. frequency is quite for calculating the line frequency.

Figure 6. Flowchart of the proposed PLL technique to calculate the line frequency. Figure 6. Flowchart of the proposed PLL technique to calculate the line frequency.

4. Simulation Results 4. Simulation Results To verify the performance accuracy of the proposed PLL method, a simulation was conducted To verify the performance PV accuracy of the proposed PLL simulation was electrical conducted using a 350 W grid-connected micro-inverter application, asmethod, shown inaFigure 7. Further specifications of the simulation are shownapplication, in Table 1. as According toFigure the related international using a 350 W grid-connected PVcircuit micro-inverter shown in 7. Further electrical standards, such as simulation IEEE Std. 1547, the are normal frequency was determined to be between 59.3 specifications of the circuit shown in Tablerange 1. According to the related international Hz and 60.5 standards, suchHz as[21]. IEEE Std. 1547, the normal frequency range was determined to be between 59.3 Hz First, the steady-state responses were discussed. Throughout the normal frequency range, and 60.5 Hz [21]. measured line frequency information usingThroughout both the conventional PLLfrequency technique and First, the steady-state responses was wereobtained discussed. the normal range, the proposed one, shown in Figures 8–12. In these figures, the actual frequency means frequency measured line frequency information was obtained using both the conventional PLLthe technique and command of the grid voltage V grid, as shown in Figure 7. As shown in Figure 8, when the grid voltage the proposed one, shown in Figures 8–12. In these figures, the actual frequency means the frequency source is operated at 60 Hz, the PV inverter output current is maintained in phase with the PV command of the grid voltage Vgrid , as shown in Figure 7. As shown in Figure 8, when the grid inverter output voltage. The line frequencies are measured by two different PLL techniques, as shown voltage source is operated at 60 Hz, the PV inverter output current is maintained in phase with the in Figure 8. While the measurement error of the line frequency using the conventional method PV inverter output voltage. The line frequencies are measured by two different PLL techniques, changes from −0.048 Hz to +0.096 Hz, the measurement error of the line frequency using the proposed as shown in Figure 8. While the measurement error of the line frequency using the conventional method varies from –0.004 Hz to +0.003 Hz. Obviously, the proposed method shows a measurement method changes from −0.048 Hz to +0.096 Hz, the measurement error of the line frequency using the error at least 10 times smaller than that of the conventional method. Similarly, the measured line proposed method from –0.004 Hzare to 60.5 +0.003 Obviously, proposed method frequencies, whenvaries the grid frequencies Hz Hz. and 59.3 Hz, are the shown in Figures 9 andshows 10. a measurement error at least 10 times smaller than that of the conventional method. Similarly, According to the results shown in Figures 9 and 10, the proposed method shows higher accuracies thethan measured line frequencies, when the gridanalysis frequencies areaccuracy 60.5 Hzofand 59.3 Hz,techniques are shown the conventional one. The quantitative of the both PLL is in Figures 9 and 10. According to the results shown in Figures 9 and 10, the proposed method shows summarized in Table 2. Using the proposed method, the measurement error is around 80 times lower higher accuracies than the conventional one. The quantitative analysis of the accuracy of both PLL that using the conventional one. techniques is summarized in Table 2. Using the proposed method, the measurement error is around 80 times lower that using the conventional one.

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Secondly, the transient responses using both PLL techniques were analyzed when the grid voltage Electronics 2018, 7, x FOR PEER REVIEW 7 of 11 frequency was changing dramatically. It was assumed that the grid voltage frequency was changing from the nominal frequency 60 Hz to two other states, 60.5 Hz and 59.3 Hz. This condition can be Secondly, the transient responses using both PLL techniques were analyzed when the grid implemented by changing the frequency command the gridthat voltage Vgrid at 0.3frequency s, as shown voltage frequency was changing dramatically. It wasof assumed the grid voltage was in Figure 8. The key waveforms of the PV inverter, when the grid voltage frequency is changing rapidly changing from the nominal frequency 60 Hz to two other states, 60.5 Hz and 59.3 Hz. This condition from to 60.5 Hz by at 0.3 s, are shown in Figure 11. Both have the time can60beHz implemented changing the frequency command of methods the grid voltage Vgridsame at 0.3transient s, as shown of 0.179 s. Similarly, both methods have the same transient time of 0.290 s when the grid voltage in Figure 8. The key waveforms of the PV inverter, when the grid voltage frequency is changing frequency is changing Hz shown to 59.3 in Hz at 0.311. s, as shown in Figure 12.same This transient is because rapidly from 60 Hz torapidly 60.5 Hzfrom at 0.360 s, are Figure Both methods have the both methods the same sampling forsame detecting a line cycle. time of 0.179have s. Similarly, both methodscounter have the transient time of 0.290 s when the grid voltage According to the simulation results, it can be stated technique a higher frequency is changing rapidly from 60 Hz to 59.3 Hz atthat 0.3 s,the asproposed shown in PLL Figure 12. This has is because both methods the same sampling detectingresponse a line cycle. accuracy than thehave conventional one and counter the samefortransient time. According to the simulation results, it can be stated that the proposed PLL technique has a higher Table 1. Electrical specification of the simulation circuit. accuracy than the conventional one and the same transient response time. Table 1. Electrical specification of the simulation circuit. Parameters Value

PV inverter nominal power, Pinv Parameters Nominal grid voltage, Vgrid PV inverter nominal power, Pinv Nominal grid frequency, fgrid Nominal grid voltage, Vgrid Number of phase Nominal grid frequency, Normal frequency range fgrid of phase TheNumber scaling factor, k The sampling Normalfrequency, frequencyfsampling range

350 [W] Value 220 [V] 350 [W] 60 [Hz] 220 [V] Single 60≤[Hz] 59.3 [Hz] f ≤ 60.5 [Hz] Single 0.1592 59.3 [Hz]25 ≤ f[kHz] ≤ 60.5 [Hz] The scaling factor, k 0.1592 The2.sampling frequency, fsamplingtwo different 25PLL [kHz] Table Measurement error using techniques.

Table 2. Measurement error using Positive two different Grid Frequency PLL Technique ErrorPLL (%)techniques. Negative Error (%)

No 1

No 1

2 3

Grid Frequency 60 Hz 60 Hz

2

60.5 Hz 60.5 Hz

3

59.3 Hz 59.3 Hz

PLL Technique Conventional Proposed Conventional Proposed Conventional Conventional Proposed Proposed Conventional Conventional Proposed Proposed

Positive Error (%) Negative Error (%) 0.096 Hz (0.160%) 0.048 Hz (0.080%) 0.003Hz Hz(0.160%) (0.005%) 0.048 0.004 (0.007%) 0.096 Hz Hz (0.080%) 0.003 Hz Hz (0.007%) 0.033Hz Hz(0.005%) (0.055%) 0.004 0.114 (0.190%) 0.033 Hz (0.055%) 0.114 Hz (0.190%) 0.002 Hz (0.003%) 0.004 Hz (0.007%) 0.002 Hz (0.003%) 0.004 Hz (0.007%) 0.082 Hz (0.137%) 0.058 Hz (0.097%) 0.082 Hz (0.137%) 0.058 Hz (0.097%) 0.001 Hz (0.002%) 0.003 Hz (0.005%) 0.001 Hz (0.002%) 0.003 Hz (0.005%)

Figure 7. Simulation circuit of a single-phase PV micro-inverter for evaluating the grid-connection. Figure 7. Simulation circuit of a single-phase PV micro-inverter for evaluating the grid-connection.

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Figure 8. Key waveforms of the PV inverter when the grid voltage frequency is 60 Hz. Figure 8. Key waveforms of the PV inverter when the grid voltage frequency is 60 Hz.

Figure 8. 8. Key waveforms whenthe thegrid gridvoltage voltage frequency is 60 Figure Key waveformsofofthe thePV PV inverter inverter when frequency is 60 Hz.Hz.

Figure 9. Key waveforms of the PV inverter when the grid voltage frequency is 60.5 Hz.

Figure 9. 9.Key waveforms inverter whenthe thegrid gridvoltage voltage frequency is 60.5 Figure 9.Key Key waveformsof ofthe thePV PVinverter inverterwhen when the grid voltage frequency 60.5 Hz.Hz. Figure waveforms of the PV frequency isis60.5 Hz.

Figure 10. Key waveforms of the PV inverter when the grid voltage frequency is 59.3 Hz. Figure 10. Key waveformsof ofthe thePV PVinverter inverterwhen when the grid voltage frequency 59.3 Hz.Hz. Figure Key waveforms of the voltage frequency isis59.3 Hz. Figure 10.10. Key waveforms inverter whenthe thegrid grid voltage frequency is 59.3

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Figure Key waveforms the PV inverter when grid Figure 11.11. Key waveforms voltagefrequency frequencyis rapidlychanging changing Figure 11. Key waveformsofof ofthe thePV PVinverter inverter when when the the grid grid voltage voltage frequency isisrapidly rapidly changing from 60 Hz to 60.5 Hz. from 60 Hz to 60.5 Hz. from 60 Hz to 60.5 Hz.

Figure 12. Key waveforms the PV inverter when the grid frequency is rapidly changing Figure Key waveformsofof ofthe thePV PVinverter inverter when when the the grid grid voltage voltage Figure 12.12. Key waveforms voltagefrequency frequencyisisrapidly rapidlychanging changing from 60 Hz to 59.3 Hz. from 60 Hz to 59.3 Hz. from 60 Hz to 59.3 Hz.

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5. Conclusions In this paper, a novel frequency measurement method for the digital PLL control structure for single phase grid-connected PV applications is presented. While the conventional PLL controller uses phase information to calculate the frequency of PV inverter output voltage after every line cycle, this paper uses the angular frequency to directly measure the frequency after every line cycle. Thus, the measured frequency of the proposed method is more accurate than that of the conventional one. According to the corresponding simulation, measuring the line frequency, the measurement error of the proposed method is around 80 times less than that of the conventional one. By using the proposed PLL technique, a more accurate line frequency can be achieved, and a more accurate control command, such as the anti-islanding function and over/under frequency protection, can be generated. Funding: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (grant number 2016R1C1B1007001). Conflicts of Interest: The author declares no conflict of interest.

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