A Digital Controlled PV-Inverter With Grid
Impedance Estimation for ENS Detection
Lucian Asiminoaei,Student Member,IEEE,Remus Teodorescu,Senior Member,IEEE,Frede Blaabjerg,Fellow,IEEE,
and Uffe Borup,Member,IEEE
Abstract—The steady increa in photovoltaic(PV)installations calls for new and better control methods in respect to the utility grid connection.Limiting the harmonic distortion is esntial to the power quality,but other requirements also contribute to a more safe grid-operation,especially in disperd power generation net-works.For instance,the knowledge of the utility impedance at the fundamental frequency can be ud to detect a utility failure.A PV-inverter with this feature can anticipate a possible network problem and decouple it in time.This paper describes the digital implementation of a PV-inverter with different advanced,robust control strategies and an embedded online technique to determine the utility grid impedance.By injecting an interharmonic current and measuring the voltage respon it is possible to estimate the grid impedance at the fundamental frequency.The prented tech-nique,which is implemented with the existing nsors and the CPU of the PV-inverter,provides a f
ast and low cost approach for on-line impedance measurement,which may be ud for detection of islanding operation.Practical tests on an existing PV-inverter val-idate the control methods,the impedance measurement,and the islanding detection.
Index Terms—Digital signal processors(DSPs),discrete Fourier transform(DFT),fixed-point arithmetic,grid impedance measure-ment,power system monitoring.
I.I NTRODUCTION
I N THE last ten years the number of photovoltaic(PV)-sys-
tems connected to the grid[1]has been incread.In addition to the typical power quality regulations concerning harmonic distortion,distortion immunity,and EMI limits, PV-systems must also meet specific power generation re-quirements like islanding detection,or even certain various technical recommendations in different countries like the grid impedance change detection in Germany.Such extra-require-ments contribute to a safe operation to the grid especially when the equipment is connected in disperd power generating networks.
The European standard EN50330-1(draft)[2]describes the ENS(the German abbreviation of Mains m
onitoring units with allocated Switching Devices)requirement,which ts the utility fail-safe protective interface for the PV-inverters.The goal is
Manuscript received October6,2004;revid April13,2005.This work was supported by PSO-Eltra under Contract4524and the Danish Technical Rearch Council under Contract2058-03-0003.Recommended by Associate Editor K. Ngo.
L.Asiminoaei,R.Teodorescu,and F.Blaabjerg are with the Power Elec-tronics Systems Section,Institute of Energy Technology,Aalborg University, Aalborg SE DK-9220,Denmark(e-mail:las@iet.aau.dk;ret@iet.aau.dk; fbl@iet.aau.dk).
U.Borup is with the Development Department,PowerLynx A/S,Sonderborg DK-6400,Denmark(e-mail:uffe.).
Digital Object Identifier10.1109/TPEL.2005.857506to isolate the supply within5s after an impedance change
of
0.5,which may be associated with a grid failure.The main impedance is typically detected by means of a tracking and step change evaluation at the fundamental frequency.Therefore, a method to measure the grid impedance value and its changes should be implemented into existing PV-inverters.
One solution is to attach a parate device developed only for the measuring purpo but this solution is more expensive and probably more difficult to integrate with the existing log-ical control.Another solution is to u the existing nsors and the CPU of the PV-inverter to implement the measuring method. Numerous publications exist in thisfield,which offer measuring solutions for the grid impedance for a wide frequency range from dc up to typically1kHz[18]–[22].Unfortunately,even being well treated in the literature[17]–[24],the methods cannot always be e
mbedded easily into a nondedicated , PV-inverters.Thus,specific limitations like real-time computa-tion,A/D(analog/digital)conversion accuracy,fixed point nu-merical limitations,etc.,make some of the existing techniques unsuitable for a fast and reliable measurement[11],[12].
In the actual approach the grid impedance is estimated with the purpo to detect a step change of
0.5as required in[2]. Therefore,an exact determination of the grid impedance over a wide frequency range[18]–[22]will possibly provide much more data than needed.Such knowledge about the frequency characteristic of the grid is certainly uful for the PV-inverter control[6]and also for estimating the voltage distortion created over the grid impedance[18]due to the PV-inverter current. But implementing a complex method that gives the frequency characteristic over a wide frequency range may overload the ex-isting control algorithm which already has the task of grid cur-rent control,grid synchronization,dc-voltage regulation,max-imum power point tracking,etc.
In the prent study,a solution is found by injecting a test signal through the inverter modulation proc
ess.This signal, an interharmonic current with a frequency clo to the funda-mental,determines a voltage drop due to the grid impedance, which is measured by the existing PV-inverter nsors.Then, the same CPU unit makes both the control algorithm and gives the grid impedance value.
This approach provides a fast and low cost solution to meet the required standards.By implementing the prented methods it is possible to estimate,at any instant,the power supply line impedance.
The paper describes the PV-inverter topology and the con-trol strategies ud to reduce the harmonic distortion to meet the references of the international regulations,even under the condition that the grid is distorted.The grid impedance esti-mation method is described,implemented,and tested on an ex-
0885-8993/$20.00©2005IEEE
Fig.1.System diagram of the PV-inverter with implementation of the grid impedance estimation.
isting PV-inverter.The control performance as well as the anti-islanding detection (ENS detection)are demonstrated.
II.PV-I NVERTER C ONTROL S TRATEGIES
A system diagram of the PV-inverter with current control and grid impedance estimation technique is shown in Fig.1.Besides the inverter block,Fig.1also shows the photovoltaic cells,the dc –dc converter,which is boosting the voltage,a digital signal processor (DSP)board,and finally a computer that allows soft-ware development and communication with the DSP board.The PV-inverter consists of a full-bridge power converter
and
an
(T-filter)output filter.The output voltage and current are measured.A tripping and protection unit is also implemented in the PV-inverter (e Fig.1).In the DSP,the control algorithm and the impedance estimation method are implemented.
An improved current control is required in order to obtain compliance with the new power quality standards IEEE929and IEC61727that impo a limit of 5%for the grid current Total harmonic distortion (THD)with individual limits of 4%for each odd harmonic from third to ninth and 2%for 11th to 15th.A classical proportional integral (PI)-controller will fail in the ca of voltage harmonic distortion [26].Proportional resonant (PR)controllers as reported [26],[27]can instead be ud both for a good tracking performance of the line frequency reference as well as for harmonic compensation and does not exhibit sta-tionary error and provide rejection of higher harmonic distur-bances.The current control loop of the PV-inverter using PR and harmonic compensators (HC)is shown in Fig.2,
where is the inverter voltage reference and is the inverter current reference.
As it can be obrved in Fig.2,the typical voltage feed-for-ward using the network voltage ud with PI controllers has been eliminated.
The PR current
controller is de fined as [26],
[27]
(1)
where
is the
gain,is the integral constant,
and is the resonance frequency.
The double integrator in (1)achieves an in finite gain at a cer-tain frequency,also called resonance
frequency ,and almost no attenuation exists outside this frequency.Thus,it can also be ud as a notch filter in order to outcompensate the harmonics in a very lective
way.
Fig.2.Current loop of PV-inverter with proportional resonant (PR)and harmonic compensator (HC)
controllers.
Fig.3.Bode plot of disturbance rejection (current error ratio disturbance)of the proportional resonant and harmonic compensator (PR +HC ),proportional integral (PI),and proportional (P)current controllers.
The harmonic
compensator is de fined as
[26]
(2)矩阵管理
where
(the integral constant for the speci fic harmonic)is designed to compensate lected harmonics third,fifth,and v-enth,as they are the most prominent harmonics in the current
spectrum.A processing delay,which is typical equal
to
for the PV-inverters,is introduced
in .
The output filter transfer
function is expresd in (3)
as
(3)
where
and .The current error –disturbance ratio rejection capability at null reference,which is the ca of the harmonics,is de fined
as
(4)
where is current error and the grid
果果日记
voltage is considered as the disturbance for the system.
The Bode plots of the disturbance rejection for the PR con-troller are shown in Fig.3where for comparison purpos the equivalent disturbance rejections for PI-and P-controllers also have been shown.As it can be en,around the fundamental fre-quency the PR-controller provides 140-dB attenuation while the PI-controller only provides 17dB.Moreover,around the fifth and venth harmonics the situation is even wor,the PR-con-troller attenuation being around 125dB and the PI-controller attenuation is only 8dB.Moreover,from Fig.3it is clear that
the PI-controller rejection capability at the fifth and venth har-monic is comparable with that of a simple proportional con-troller,the integral action being irrelevant.
Thus,the superiority of the PR-controller is demonstrated compared to the PI-controller in terms of harmonic current re-jection.
The size of the proportional
gain
from the PR-controller determines the bandwidth and pha margin stability,in the same way as the
classical PI-controller.A gain equal
to
2leads to a bandwidth of about 650Hz.This was considered satisfactory in respect to a ud sampling frequency of 8.5kHz.The pha margin (PM)is determined to be equal to 72indi-cating a high stability.The integral
constant acts to eliminate the steady-state error [26].Another aspect is
that determines the bandwidth centered at the resonance frequency,which in this ca is the grid frequency,where the attenuation is positive.Usu-ally,the grid frequency is stiff and is only allowed to vary in a narrow range,
typically 1%.A value
of 300was deter-mined by simulations in order to eliminate the steady-state error at the grid frequency.
Having the fundamental component current controller de-signed,the harmonic compensator is being added.In this ca,the integral
constant has the same effect as for the fundamental ,eliminating the steady-state error,just that the resonance frequencies are synchronous with the third,fifth,and venth harmonics.In this way,a lective harmonic compensation can be achieved without affecting the fundamental controller dynamics.
III.L INE I MPEDANCE M EASUREMENT T ECHNIQUES This ction gives a survey of the commonly ud methods for line impedance measurement.An extended work can be found in [3]that describes in different general approaches for mea-suring the network harmonic impedance either in single-or in three-pha systems,for low-,medium-,and high-voltage in-stallations.In this ction,the methodologies are prented in respect to the actual purpo of the ,PV-inverter.Therefore,as the methods are described hereafter,different lim-itations are shown and argued for the chon method.
It is noticeable that the grid impedance measuring methods are usually using dedicated hardware devices.Once the input signals are acquired by voltage and current measurement,the processing par
t follows,which typically involves large mathe-matical calculations in order to obtain the impedance value.[4]Fig.4shows the usual technique for impedance measuring.The dedicated measuring device is denoted by “Z ”-block and
is normally a parated part of the
inverter.
,
圣诞节假期
and are the grid lumped resistance,capacitance,and inductance,while V stands for the voltage supply.The “”argument shows the model dependency on the harmonic order.
The state of the art [3]divides the measuring solutions into two major categories:passive and active methods.
Passive methods u the information about the noncharacter-istic harmonics voltages and currents that are already prent in the system.Therefore,as the methods depend on the existing background distortion of the voltage [3],[8]and,in many cas,the distortion does have either the amplitude or the repetition rate to be properly measured,this turns out to be very dif ficult for a PV
implementation.
Fig.4.Diagram of the PV-inverter connected to the grid.The grid impedance is measured with an external device (Z ).
Active methods make u of a provoked disturbance into the power supply network followed by acquisition and signal pro-cessing.The way of “disturbing ”the network can vary,therefore active methods are also divided into two major categories:tran-sient methods and steady-state methods.A.Transient Active Methods
Transient methods are well suited for obtaining fast results,due to the short time of the disturbing effect on the network.Brie fly,with this technique the device (
“”in Fig.4),generates a transient current into the network (e.g.,a resistive short-cir-cuit),and then measures the grid voltage and current at two different time instants,before and after the impul occurrence (short-circuit).The impul will contain harmonics in a large spectrum.A similar approach is reported in [5]where the tran-sient is a damped oscillation created by connecting a known ca-pacitor.The results obtained give the network respon over a large frequency range,making such methods well suited in ap-plications where the impedance must be known at different fre-quencies.However,the methods must involve high performance A/D acquisition devices and also must u special numerical techniques to eliminate noi and random errors [12],[13].The requirements are dif ficult to be achieved on a nonded-icated harmonic analyzer platform like a PV-inverter even if a powerful DSP is ud,becau the DSP already has speci fic and important tasks a
s mentioned in Section II.B.Steady-State Active Methods
Steady-state methods typically inject a known and periodical distortion into the grid and then make the analysis in steady-state.One technique propos the development of a dedicated inverter topology [16]where the pha difference between the supply voltage and the inverter voltage is measured and ud to calculate the line impedance.Another method us the tech-nique of repetitively connecting a capacitive load to the network and measuring the difference in pha shift between the voltage and current [17].
The technique ud in this paper is also reported in [23]which is a steady-state technique that injects an interharmonic current into the network and records the voltage change respon.The input signals are procesd by means of Fourier analysis at the particular injected harmonic frequency.In this way,the method has the entire control of the injected current and the computa-tion needs only a few Fourier-terms for obtaining the final re-sult.As the pre-existing harmonics on the grid do not overlap on the frequency ud for the interharmonic current injection,their effects are small,and this has the advantage of using low signal level for measurement [3].This technique can be ud to
obtain the frequency characteristic of the grid for a wide fre-quency range from 0to 2.5kHz [14]–[16]if
the method repeats the measurements at different frequencies [10]followed by an interpolation of the results.Such knowledge about the frequency characteristic of the grid is certainly uful for the PV-inverter control [6]and also for estimating the voltage distortion cre-ated by the PV-inverter current over the grid impedance [18].But an exact determination of the grid impedance over a wide frequency range will provide too many data than required for the actual purpo,since the grid impedance must be known at the fundamental frequency only.The method may not be very preci for the entire frequency range [10],as it depends on the injecting signal levels,length and type of the windowing func-tion,lected sampling frequency,available resolution for the A/D converter,existing noi and disturbances on the grid,etc.However,as this method does not require any special hardware but still has control over the measurement process,it is very con-venient for a practical implementation in PV-inverters [7].
IV .P RINCIPLE OF O PERATION
In this ction,the underlying principle of the lected method to estimate the impedance is explained and its integra-tion into PV-inverters is described.As it was shown in Fig.4,the characteristic harmonics from the grid (denoted by “”argument)have to be taken into account.That leads to the idea of analyzing the grid as a complex structure characterized by its harmonic compon
ents.This model is further depicted in Fig.5by decomposing the complex model into individual frequencies [9].
The supply voltage
V contains the fundamental fre-quency and the background voltage distortion (harmonics).It can be en in Fig.5that if the injection is done with a characteristic harmonic frequency then the results are in fluenced by the existing predistortion.One solution is to measure the background distortion before the harmonic injection and then subtract the result from the current measurements.Since this approach requires signi ficant DSP processing power and also larger memory storage,the real implementation should avoid such solution.
To facilitate the algorithms,an interharmonic current is ud instead.The network model at the frequency of the interhar-monic (referred to
as )is shown in Fig.6.
V
is no longer prent if it is assumed that the respective interharmonic is not prent in the network.A further assumption,such as the in-jected harmonic can be of low frequency,eliminates the parallel capacitor from the system diagram becau its effect is negli-gible at low frequency.
The PV-inverter injects the harmonic current by adding a har-monic signal to the voltage reference.This eliminates the need of a parate current generator.By using the same nsors (de-noted
by
and
V )as for the control loop,the PV-inverter records the time-domain respon waveforms.The measure-ments are procesd with Fourier analysis for the speci fic in-terharmonic ud,and finally the voltage and current at this fre-quency are obtained.
Next,the grid impedance is obtained
as
(5)
Fig.5.Decomposition of complex harmonic model of the grid into multiple individual models.Each individual model corresponds to a characteristic voltage harmonic existing in the
grid.
Fig.6.Principle diagram of the PV-inverter that includes the grid impedance measuring method.A harmonic current is injected through the PWM modulation process,the voltage is measured and the grid impedance is calculated by the
PV-inverter.
(6)(7)
where
and (referring to Fig.6)reprent the grid resis-tance respective
inductance;
and reprent the frequency respective the pha angle of the injected
interharmonic .
Since the goal is to obtain the grid impedance at the funda-mental frequency further processing must be done.Equation (8)gives the value of the grid impedance at the frequency of 50Hz,by a simple mathematical substitution of the injected harmonic with the fundamental
frequency
50
法国斯特拉斯堡
Hz
(8)
An alternative of (8)is the assumption that the injected frequency is clor to the fundamental frequency;therefore the calculated impedances for both frequencies have clo values.Maybe a correction factor bad on the grid type and its characteristic can be implemented for saving processing time.However,since usually there is no prior information where the PV-inverter will operate,implementing such a correction factor turns out to be more likely a ca to ca practice,embedded into the final PV-product.
The principle of operation also takes into account that the duration of the interharmonic injection should not be perma-nent but limited to veral fundamental periods.The repetition is done in a way that multiple results (algorithm executions)are obtained and averaged within the required duration of 5s [2].In this way,random errors due to noi and A/D-flickering can be minimized.Moreover,decreasing the duration of the harmonic injection will limit the total current harmonic distortion.
Even this approach adds a certain degree of complexity.It has the advantage of allowing other similar PV-inverters(ex-ample:multiple inverters connected together in a PV farm)to operate on(to measure)the same grid.Thus,the inverter makes the injection,measures the effect,and then waits in an idle state. During this interval any other similar PV-inverter is allowed to measure the grid impedance without being disturbed.
As it can be en,the underlying principle is relatively simple and easy to be done with the PV-inverter,but there are different issues that must be taken into account in a digital implementa-tion,which will be described in the next ction.
V.I MPLEMENTATION
Regarding the implementation of the impedance measure-ment,there are two techniques of interest.
•A single-harmonic(SH)injection.When the grid is measured using a single interharmonic,then the results are translated from this frequency to the fundamental according to(6)–(8).
•Two-harmonic(TH)injections.When the measurement process injects two interharmonics then the two discrete Fourier transformation(DFT)results are interpolated to give the impedance at the fundamental frequency.
A.Single Harmonic(SH)Injection
The PV injects one interharmonic into the grid and measures the respon.The signals are derived with the DFT analysis.The DFT coefficients are calculated
as好看的图
(9)
where
number of samples per fundamental
period;
input signal(voltage or current)at
point
;
complex Fourier vector of the th harmonic of the
input
signal;
real part
of
;
imaginary part
of.
A reprentation model of the DFT algorithm using(9)is
shown in Fig.7and referred to as a vector-approach due to
the vector-type operations(the sampled signals are stored
into
-length vectors and the algorithm is performed only after the
last sample is acquired).
Both harmonic current and voltage are calculated in this way,
and then by using(6)the grid impedance value is obtained for
the frequency of the injected harmonic.
One last step should be done to translate the grid impedance
from the value obtained at this frequency into the grid
impedance value at the fundamental frequency.Here,a
frequency of75Hz is lected for the injection process.This
frequency is relatively clo to the fundamental frequency(in
this ca50Hz),therefore it is estimated that the translation
will not be
necessary.
Fig.7.Vector approach to calculate the
DFT.
Fig.8.Running-sum approach to calculate the
DFT.
Fig.9.Comparison of the DFT calculation approaches:(a)vector approach
and(b)running-sum approach.
If the algorithm is executed as explained before,careful atten-
tion must be paid to the time required for the DFT calculations.
Since the DFT can only be calculated after all samples are ac-
quired,the calculation can overload the DSP.It is estimated that
using the implementation shown in Fig.7the DSP will require a
long time for thefinal calculation.This will need a multitasking
programming technique specially developed for the impedance
calculation.Such situations must be avoided since one of the
goals is to embed the impedance estimation routine into the DSP春天里歌曲
in a straightforward way without extra resources.
To overcome this limitation,a method with accumulators
(running-sum in Fig.8)is ud to perform the multiplications
and summations of the DFT terms(9).
Fig.9gives a comparison of both principles,the vector-ap-
proach and the running-sum.It can be en that the vector-ap-
proach involves much more calculation time for the DFT once
the samples are acquired and also larger memory space to store
the samples.
As the running-sum approach demonstrates faster results and
smaller memory space,it is lected for further test.
B.Two-Harmonic Injection
The TH injection consists of injecting two harmonics at the same moment,then the DFT calculates the amplitude for tho two particular injected harmonics.
The TH injection is uful when
both
and need to be calculated.Thus,by having the grid impedance value at two different
frequencies,
and are obtained
from
(10)
平板怎么截图
(11)(12)
where
injected harmonic
frequencies;
impedances calculated
at
;grid resistance and inductance.
Theoretically,this method gives the result of the grid impedance (and in addition the grid resistance and inductance),but simulations and further studies have not validated this method to be the best for the PV-inverter.If the interval be-tween the chon frequencies is too narrow then (11)and (12)can fall into numerical problems,especially with fixed-point DSP becau of a small denominator.On the opposite,if the interval is larger,then the highest chon frequency can be near a grid resonance point,which again gives a wrong estimation of the final result.
Thus,even if initially the TH method gains attention becau of the advantage of obtaining
the
牙马
and values,the draw-backs mentioned,also encountered later in the simulation and experimental pha,lean for the first method,the SH injection.VI.S IMULATION OF THE I MPEDANCE D ETECTION M ETHOD Different simulations have been performed before the imple-mentation.Thus,different numerical constants for scaling the fixed-point variables have been t and typical numerical prob-lems with over flow and low resolution have been anticipated.The simulation is done with the SH injection method on a grid model as shown in Fig.10.The grid model is compod from the fundamental voltage block,the background distortion block,and the grid impedance model.The SH injection is made by the harmonic current injection block added to the generated PV cur-rent.The
“
”block depicts the complex harmonic model of the grid impedance as
in
(13)(14)
where
different relevant harmonic
frequencies;
and grid resistance and inductance and are dependent
on the harmonic frequency de fined before.
The grid parameters are t
to
1
and 0.1mH.A simple simulation (not shown here)is first made with an ideal model for the PV-inverter.The results give the exact value for the grid impedance.Then the lected SH technique is
sim-Fig.10.Principle diagram of the simulation,where the grid is modeled as a complex harmonic structure.The harmonic injection process overimpod on the PV-inverter current allows the determination of the grid
impedance.
Fig.11.Simulation results using the SH injection method:(a)grid impedance estimation,(b)injected harmonic,and (c)PV grid current.
ulated with a more realistic PV model,which includes nonideal behaviors from A/D-device,antialiasing filters,PWM modula-tors,EMI filter,etc.
Fig.11shows the time domain waveforms of the impedance estimation,injected interharmonic and PV
grid current.The in-terharmonic has a frequency of 75Hz,an amplitude of 1.5A (rms),and a duration of 40ms (two fundamental cycles).Fig.11shows a burst of three injections of the interharmonic current.This injection creates a distortion in the PV-inverter current,which is proportional to the amplitude and the repetition rate of the interharmonic.Since such distortion effect increas the
current ,which is not desired for the operation of the in-verter,one of the challenges is to find the minimum values (am-plitude,duration,repetition rate)for the injection that still gives a good accuracy for the impedance estimation.
The results of the DFT calculations are available only at the end of the injection process,which explain the modi fication of the impedance estimation in a discrete way when the update instants occur.
It was noted that the impedance results initially had a 20%deviation from the real value.The error appeared becau of an internal delay given by the voltage antialiasing filter.This delay has a signi ficant impact on the angle calculation,leading to an incorrect estimation.If the additional pha shift due to antialiasing filter is taken into account then the estimation is improved.
Another test in Fig.11is the modi fication of the PV-inverter current.In practice the PV-inverter current
changes becau the
