IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018 1957
Input Current Ripple and Grid Current HarmonicsRestraint Approach for Single-Phase Inverter Under
Battery Input Condition in ResidentialPhotovoltaic/Battery Systems
Bin Liu , Lina Wang , Member, IEEE, Dongran Song , Mei Su , Jian Yang , Member, IEEE, Deqiang He ,Zhiwen Chen , and Shaojian Song
Abstract—When an existing photovoltaic (PV) system is up-graded to a residential PV/battery system, the single-phase PVinverter under both input conditions of battery and PV shouldbe properly controlled to restrain the input current ripple andgrid-current harmonics. To do this, equivalent circuits of PV arrayand Li-ion battery pack are first constructed and respectively an-alyzed. The analysis results show that the input current under thebattery pack may contain serious ripple component due to the lowinternal impedance of the battery pack, which cannot suppress theripple current caused by the inherent power coupling problem ofthe grid-connected single-phase inverter. Then, based on the smallsignal model of the boost dc–dc convertor, a novel active controlmethod is proposed for mitigating the input current ripple, whichadopts double-channel current feedbacks including an additionalripple current feedback channel and the normal one. To providethe feedback signal, a third-order general integrator is introducedto extract the current ripple. Besides, a proportional-resonant con-troller is used to restrain the grid-current harmonics. Finally, thecontrol parameters are obtained using MATLAB toolbox, andthe proposed control strategies are validated by the experimentalresults on a 5 kW prototype.
Index Terms—Residential PV/ battery system, single-phase PVgrid-connected inverter, third-order general integrator, doublefeedback control.
Manuscript received October 29, 2017; revised February 13, 2018; acceptedMarch 14, 2018. Date of publication March 28, 2018; date of current versionSeptember 18, 2018. This work was supported in part by the National NaturalScience Foundation of China under Grants 51765006, and in part by the NaturalScience Foundation of Guangxi Province under Grants 2016GXNSFBA380241and 2017GXNSFDA198012. Paper no. TSTE-00982-2017. (Corresponding au-thors: Lina Wang; Dongran Song.)
B. Liu is with the School of Electrical Engineering, Guangxi Univer-sity, Nanning 530004, and also with the School of Information Science andEngineering, Central South University, Changsha 410083, China (e-mail:,[email protected]).
L. Wang is with the School of Automation Science and Electrical Engineering,Beihang University, Beijing 100191, China (e-mail:,[email protected]).
D. He and S. Song are with the School of Mechanical Engineering,Guangxi University, Nanning 530004, China (e-mail:, [email protected];[email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TSTE.2018.2820507
NOMENCLATURE
L Boost inductor.C DC-link capacitor.uin, iin Input voltage and input current.ug, ig Grid voltage and grid current.Idc, ir DC and ripple component of input current.udc, ur DC and ripple component of DC-link voltage.ω Angular frequency of grid voltage and cur-
rent.pac, pdc AC and DC power.Z Equivalent impedance.zPV, zLi Equivalent impedances of PV array and the
Li-ion battery.R1 , R2 Equivalent resistances of battery model.Rs, Rp, Rd, Rsh Equivalent resistances across PV model.Cd, Cj, Cp Equivalent capacitances of PV and battery
models.D0 Average duty of boost converter.d, d, d0 Instantaneous value of sum, average, small
disturb of boost converter duty.λ Power allocation split ratio.I∗gdc, i∗gdc DC component and AC component of grid
current reference.Ag Amplitude of fundamental grid current.v Input signal of third-order general integrator.δ, δ1 Initial phase angle of fundamental and
second-harmonic component.m The attenuation coefficient in third-order gen-
eral integrator.φ Phase delay of third-order general integrator.ωt Angular frequency of input signal of third-
order general integrator.A0 , A DC amplitude and AC amplitude of the sec-
ond harmonic.ka, kb Determinate cCoefficients of the proposed
third-order general integrator.kpi, kii PI parameters of current controller.kpv, kiv PI parameters of voltage controller.kRF Coefficient of ripple current feedback.kGP, kGR Parameters of resonant controller.
1958 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018
I. INTRODUCTION
DUE to the depletion of fossil fuels, the distributed gen-eration of photovoltaic (PV) energy [1] and wind energy
[2] have been popular across the world. As PV energy is inter-mittent and unreliable, the integration between a distributed PVpower generation system (hereinafter referred to as PV system)and a distributed energy storage (DES) is a promising solutionto improve the reliability and efficiency of the distributed PVsystem. Energy storage devices, such as batteries and fuel cells,have drawn great attentions and the demand of energy storagefor the PV systems has been dramatically increased [3]–[5].Moreover, the increase of the PV generation self-consumptionrate has a significant impact on improving the conversion effi-ciency and the lifetime of the storage devices in a PV-storagehybrid system. As a result, the residential PV/battery system forthe optimization of PV-self-consumption becomes popular, andattracts more and more research attentions [6]–[8].
Many distributed PV systems with two-stage grid-connectedinverter have been installed over the last decade, one feasi-ble scheme to construct PV/battery systems is to upgrade theexisting PV systems, namely, modify the control programs ofgrid-connected PV inverters and make them comply with newapplication scenarios [9]. As shown in Fig. 1, a typical residen-tial PV/battery system is composed of PV array, battery energystorage subsystem (BESS), single-phase PV grid-connected in-verter (PVGCI), energy management and control unit (EMCU),and DC/DC charger (with buck-boost topology). The PV arrayand PVGCI are the two key components of the existing PV sys-tems. Affected by the solar radiation, the residential PV/batterysystem operates in different modes:
1) Mode I. In the daytime when solar radiation is abundant,contactor K1 switches on and contactor K2 switches off.The PV energy charges BESS to full capacity firstly, andthe superfluous PV energy supplys the residential loadsor injects to the utility grid through the single-phase PVinverter.
2) Mode II. At night, or during the day when solar radia-tion is poor, contactor K1 switches off and contactor K2switches on. The energy stored in the battery units dis-charges to residential loads and the utility grid throughPVGCI to ensure power reliability, power quality, highself-consumption rate, high utilization rate of power elec-tronic devices, and the monetary expense reduction.
Therefore, in this application, PVGCI should be adapted totwo input conditions with different energy source: PV array orbattery pack.
Conventional PVGCIs with the configuration of two-stageenergy conversion toplology, boost converter in the precedingstage and DC/AC inverter in the second stage, are designedfor the application scenario of PV array, which show currentsource characteristics. Some papers, such as Ref [10], [11], ad-dressed the control of PVGCIs under the input of PV array andobtained good results. However, the battery pack has voltagesource characteristics. When the energy stored in the batterypack feeds PVGCIs, the inherent double-line-frequency powerpulsation on the grid side of PVGCIs may bring negative effects
Fig. 1. Schematic diagram of the residential PV/battery system.
on residential PV/battery systems. These negative effects, suchas current ripple at the power input side, voltage fluctuation inthe DC link, distortion in PVGCI output current, reduced lifeexpectancy of DC capacitors, and the reduction of the systemefficiency, impact the reliability and stability of the system [12],[13]. For the Li-ion battery pack, a second harmonic ripple inthe charging or discharging current results in additional heat-ing losses, adverse effects for cell voltage balancing, roundtripefficiency, and lifetime as studied in [14], [15]. Consequently,there is a urgent need to study the appropriate PVGCI operationcontrol strategies under the battery input condition [13].
As a passive power decoupling method, increasing the capac-itance of the DC-link capacitor is a straightforward and validsolution to the DC-link voltage ripple problem, which was re-ported in [16], [17]. However, larger DC-link capacitor leadsto lower power density, and the requirement of larger elec-trolytic capacitors contradicts the high reliability requirementof PV systems. Therefore, a number of active power decou-pling circuits and active control methods have recently beenproposed in order to reduce the DC-link capacitance require-ment. Refs [18], [19] use a parallel phase leg and an inductor inthe DC-link side as an auxiliary circuit to deal with the pulsat-ing power. By adding components, a three-port converter withpower decoupling capability was proposed in [20], but the sys-tem cost and complexity are increased. Alternatively, Ref [21]proposed a low frequency harmonic elimination PWM tech-nique, achieving low double-frequency ripple and reducing thecapacitance requirement significantly. Based on nonlinear con-trol, Ref [22] presented a new approach to get the trajectory ofthe reference current along with mitigating the second harmoniccurrent ripple. However, these methods are used for Z-sourceinverters or single-stage inverters, and they are not suitable forthe installed traditional PV grid-connected inverters. Refs [23],[24] proposed active control algorithms for current ripple re-duction in the preceding stage of the two-stage inverters. Nev-ertheless, it is difficult for these active control strategies to beused universally when there are different energy sources. Fur-thermore, the grid current control in the second DC/AC stagewas not considered. In conclusion, the existing methods arenot appropriate in the applications of residential PV/batterysystems.
LIU et al.: INPUT CURRENT RIPPLE AND GRID CURRENT HARMONICS RESTRAINT APPROACH FOR SINGLE-PHASE INVERTER 1959
Fig. 2. Topology of the two-stage PVGCI and the power flow.
Motivated by the above observations, this paper proposes anovel input current ripple and grid current harmonics constraintmethod for controlling PVGCIs under battery input conditionin the residential battery-supported PV system. To this end,the universal equivalent circuit models of the PV array andthe Li-ion battery are given, and different characteristics of thetwo energy sources are analyzed. Then, to address the issue ofthe inherent double-line-frequency power pulsation and smallequivalent impedance of the current ripple, a novel active inputcurrent ripple mitigating control algorithm is proposed basedon double-channel current feedback and the frequency-domainmodel of the boost circuit. Besides, to deal with the low-orderharmonics (especially the third-order harmonic) in the grid cur-rent, caused by the double-line-frequency voltage ripple in theDC-link, a ripple notch filter based on a third-order generalintegrator is designed in the DC-link voltage control loop.
The rest of this paper is organized as follows. Section IIdescribes the two-stage PVGCI topology and analyzes differenteffects brought by the two energy source inputs. Section IIIpresents the proposed control strategies to mitigate the inputcurrent ripple and the grid current harmonics. In Section IV, thedesign principle of the digital controller is discussed. Finally,Section V describes the experimental platform of a 5 kW PVGCIand experimental results of the proposed PVGCI control strategyunder the battery input condition.
II. GENERATION AND PROPAGATION OF
CURRENT RIPPLE IN PVGCI
A. Topology of the Two-Stage PVGCI and Analysis ofPower Pulsation
Fig. 2 shows the topology of the two-stage PVGCI and thepower flow. The two-stage PVGCI can reduce the required num-ber of series-connected PV modules and increase the systemreliability and MPPT efficiency [25]. In the two-stage PVGCI, aboost converter is applied in the preceding stage. L denotes theboost inductor, C denotes the DC-link capacitor, the voltage ofDC-link bus is denoted by udc, and the input voltage and currentis denoted by uin and iin, respectively. In the second stage, asingle-phase full bridge is used, and L1 , L2 are filters on theAC side. ug is the grid voltage. ig is the grid current injected byPVGCI.
Fig. 3. Equivalent propagation circuit of the current ripple.
When PVGCI works at the unitary power factor (PF), theinstantaneous power on the AC grid side can be written as:
pac = ug ig = Ug sin (ωt) Ig sin (ωt)
=12UgIg − 1
2UgIg cos (2ωt) . (1)
where ω is the grid angular frequency, pac and pdc represents theoutput power in the AC side of PVGCI and the input power inthe DC input side of PVGCI, respectively.
Equation (1) shows that there is double-line-frequency pul-sating power injectes into the grid. Assuming there is no powerloss in PVGCI, the output power pac is equal to the input powerpdc. Thus, the pulsating power leads to a second harmonic inuin or iin. Usually, a relatively large DC-link capacitor is usedto realize power decoupling. Assuming the bus voltage udc isapproximated by its mean value Udc, the input current iin can bederived as:
iin =pac
Udc=
UgIg
2Udc− UgIg
2Udccos (2ωt) = Idc + ir (2)
where Idc = Ug Ig2Ud c
, ir = −Ug Ig2Ud c
cos (2ωt)From (2), it can be seen that iin is composed of two compo-
nents, namely the DC component Idc and the current ripple ir,which will be penetrated into the input source.
B. Propagation of Current Ripple in PVGCI Under PV andBattery Input Condition
As described in Section I. PVGCI should work in two modes:Mode I and Mode II. Accordingly, PVGCI control algorithmshould be adapted to PV array or Li-ion battery pack as energysource. However, different energy source has different propaga-tion characteristics for current ripple, and thus control algorithmshould comply with the new work condition. Before that, thesecurrent ripple propagation characteristics should be analyzedfirstly.
Generally, the resulted current ripple ir could act as a currentsource in the equivalent circuit of the current ripple. As shown inFig. 3, z(jω) denotes the AC impedance of the energy sources,namely PV array or Li-ion battery pack. In order to evaluatethe current ripple penetrated by single-phase inverter, assumingthe same passivity-based control method is adopted in the boostconverter, the magnitude Z2ω of z(jω) at double grid frequency2 ω determines the value of the current ripple propagated intothe input energy sources.
1960 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018
The AC impedance models of the PV array and Li-ion batterystudied in [26]–[28], are respectively formulated by
zpv (jω) =
[Rs +
Rp
(ωRpCp)2 + 1
]− j
[ωR2
pCp
(ωRpCp)2 + 1
].
(3)
and
zLi (jω) =
[R1 +
R2
(ωR2Cj)2 + 1
]− j
[ωR2
2Cj
(ωR2Cj)2 + 1
].
(4)
where Rd is dynamic resistance, Rsh is shunt resistance con-nected in parallel, Cd is diffusion capacitance, and Ct is tran-sition capacitance, connected in parallel, for PV array ACimpedance model; R1 represents the series resistance, R2 andCj are the resistance and capacitance of the RC ladder, for ACequivalent impedance of Li-ion battery pack.
From (3) and (4), it can be seen that the AC impedance mod-els of the PV array and Li-ion battery pack have the same form.Therefore, evaluation of the current ripple could be done bycomparing the parameters of these models. When ω→ 200π,the impedances of the PV array and the Li-ion battery on thereal axis tend to Rs + Rp and R1 + R2 , respectively. Nor-mally, Rs + Rp is much larger than R1 + R2 [28], [29]. Atω = 200π rad/ s (fr = 100 Hz), the magnitude of zPV(200π) isof the order of ohm, as reported in [26], and the magnitude ofzLi(200π) is of the order of 10 mΩ, as reported in [14], [29],[30], |zPV(200π)| is much larger than |zLi(200π)|. Therefore, itis clear that the current ripple is much worse under the conditionof the Li-ion battery pack input (Mode II) than PV array input(Mode I). Current ripple rejection control strategy under batteryinput condition is of great demand.
III. ACTIVE CONTROL STRATEGY FOR ALLEVIATING THE
INPUT CURRENT RIPPLE AND GRID HARMONICS CURRENT
A. Active Mitigating Algorithm for the Input Current RippleBased on Double-Channel Current Feedback
As analyzed in Section II, |zPV(200π)| is of the order of ohmand large enough to suppress the current ripple with the help ofa relatively large DC-link capacitor. Accordingly, the installedcommercial PVGCIs with PV array input rarely adopt the cur-rent ripple active mitigating algorithm. However, it is necessaryto take advanced control strategy to alleviate the current rip-ple, when the PVGCI operates under Li-ion battery pack inputcondition.
From (1), it can be seen that the output power of PVGCIcould be divided into two parts: DC power and AC ripple power.Thereby, AC ripple power can be described as:
pr =UgIg
2cos (2ωt) . (5)
Since the cut-off frequency of the grid filter, which consistsof the inductors L1 and L2 , is far higher than the double gridfrequency, this filter has a little impact on the current ripple. Thepower decoupling mainly depends on the DC-link capacitor C.
Assuming the internal impedance of the Li-ion battery packis much less than the impedance of boost inductor L at thepulsating frequency, the pulsating power pr is mainly absorbedby two passive components: the DC-link capacitor C and theboost inductor L. Suppose ur is the voltage ripple in the DC-link, the pulsating power absorbed by the DC-link capacitor canbe expressed as [18]:
Cudcdur
dt= λpr =
12λUgIg cos (2ωt) . (6)
where λ denotes the pulsating power absorption split ratio, and0 < λ < 1. Specially, if λ = 1, it means that all the pulsatingpower is absorbed by the DC-link capacitor.
By performing integration on both sides of (6) and omittingthe second-order item, ur can be derived as,
ur =UgIg
4ωCUdcλ sin (2ωt) . (7)
The other part of the pulsating power ((1 − λ)pr) is mainlyabsorbed by the boost inductor L. Omitting the second-orderitem, the input current ripple can be expressed as
ir = (1 − λ)UgIg
4ωLIisin (2ωt) . (8)
In (8), to reduce the current ripple component ir, the powerallocation split ratio λ should be set to a larger value, ideally, ifλ = 1, ir = 0.
To control the ratio λ at a suitable value and ensure the stabilityof control system, the model of boost converter as Ref [31] hasbeen introduced. Based on the averaging model of the boostconverter, and ignoring the ripple component in input voltageuin, the relationship between uin and udc can be formulated as
uin
udc=
Uin
Udc + ur=
Uin
Udc
(1 + λ
Ug Ig
4ωC U 2d c
sin (2ωt)) . (9)
where Uin denotes the average input voltage. Ignoring the ripplecomponent in the input voltage uin, uin = Uin, udc representsthe DC-link bus voltage. Normally, to guarantee the lifetimeof DC-link capacitor, the voltage ripple rate ur/Udc should bedesigned less than 5% [23]. Consequently, λ Ug Ig
4ωC U 2d c
sin(2ωt) is
a very small value (less than 0.05). Hence, assuming D0 is theaverage duty cycle of the boost converter, (9) can be rewrittenas
uin
udc≈ Uin
Udc
(1 − λ
UgIg
4 ωCU 2dc
sin (2 ωt))
= (1 − D0)(
1 − λUgIg
4 ωCU 2dc
sin (2 ωt))
≈ 1 −(
D0 + λUgIg
4 ωCU 2dc
sin (2 ωt))
. (10)
Since λD0 is a very small value, the second “�” in (10) istenable.
From (8), it can be inferred that an effective way to reduce ir
is to regulate λ to be a relatively large value. Derived by (7), the
LIU et al.: INPUT CURRENT RIPPLE AND GRID CURRENT HARMONICS RESTRAINT APPROACH FOR SINGLE-PHASE INVERTER 1961
Fig. 4. Control scheme diagram of the boost converter based on double-channel current feedback control. (a) Control scheme of boost with traditionalinner controller. (b) A novel active mitigating control algorithm for inner controlloop.
value of λ can be regulated by controlling the value of ur, as
λ =4 ωCUdcur
UgIg sin (2ωt). (11)
Furthermore, according to (10), the value of ur can be con-trolled by adding a small disturb duty signal d to the averageduty D0 . That is to say, an effective way to mitigate the currentripple is to add a small disturb duty signal d to the averageduty D0 , and form a new additional current channel to regu-late the voltage ripple ur. The added small duty signal d can beexpressed as
d = λUgIgUin
4ωCU 3dc
sin (2ωt) . (12)
Combining (7) and (8), d can be rewritten as
d =λLIinir
(1 − λ) CU 3dc
= krir . (13)
It is clear that, in the steady state, d is proportional to ir andkr, and the relationship of d and λ has been revealed.
When PVGCI operates in Mode II (Li-ion battery pack asinput source), a single control loop could be adopted in outercontrol loop for boost, without current ripple active mitigatingcontrols shown in Fig. 4(a). The controller samples uin and iin
in real time and calculates reference input current i∗in accordingto the state of charge (SOC) of the Li-ion battery. In this part,a novel active mitigating algorithm for the input current ripplewith double-channel current feedback control structure can beobtained, as shown in Fig. 4(b). The core of the proposed algo-rithm is that the input current ripple is mitigated by regulatingthe voltage ripple ur on the DC-link bus.
In the new inner current loop control diagram, the duty of theboost converter switch consists of two parts:
D(s) = D0(s) + Df (s). (14)
where D(s), D0(s) and Df(s) are the complex images of d, d0and d, respectively; d is the instantaneous sum of two duty parts,and d0 is the instantaneous value of duty, calculated by averagemodel of the boost converter. D0(s), as shown in Fig. 4(b),represents the output of the regulator Hi(s), which is used to
Fig. 5. Control scheme for the DC/AC converter with a notch filter.
process the boost inductor current error i∗in − iin based on theaverage model of the boost converter. Df(s) is the ripple dutycomponent, obtained from iin by the filter Gf(s). In Fig. 4(b),Gid(s) is the duty-to-input current transfer function, which isformulated by [32].
Gid(s) =Ud cR s + 2Ud c
LC R
s2 + 1RC s + (1−D0 )2
LC
. (15)
where R represents the equivalent output load of the boost,C represents the DC-link capacitance, and D0 represents theaverage duty cycle of the boost converter.
B. Current Ripple and Voltage Ripple Extracting andMitigating Based on a Third-Order General Integrator
Control scheme of DC/AC grid-connected inverter for the twodiscussed modes is identical, as shown in Fig. 5. A digital phaselocked loop (PLL) based on a synchronous reference frame,extracts the phase information and the frequency information ofthe single phase grid according to the sampled ug. i∗g is derivedfrom multiplying amplitude I∗g by phase information sin(ωt),the output signal of PLL. Here, a zero phase is assumed. Inthe inner grid current control loop, a proportional-resonant (PR)controller is applied for the sine waveform control of the gridcurrent.
Since udc contains a second-harmonic component, I∗g alsocontains a second-harmonic component. Suppose I∗gdc and i∗gdcas DC component and AC component of I∗g , respectively, thegrid current reference i∗g can be expressed as
i∗g = I∗g × sin (ωt) =(I∗gdc + i∗gac
) × sin (ωt)
=(I∗gdc + I∗2ω sin (2ωt + δ1)
) × sin (ωt) . (16)
Where, I∗2ω and δ1 are the amplitude and initial phase angleof second-harmonic component, respectively. Simplifying (16)further yields to:
i∗g = Ag sin (ωt + δ) − 12I2ω cos (3ωt + δ1) . (17)
Among them, Ag and δ are the amplitude and phase angle offundamental grid current, respectively:
Ag =
√(I∗gdc −
12I∗2ω sin δ1
)2
+(
12I∗2ω cos δ1
)2
. (18)
δ = arccosI∗gdc − 1
2 I∗2ω sin δ1√(I∗gdc − 1
2 I∗2ω sin δ1
)2+
( 12 I∗2ω cos δ1
)2.
(19)
1962 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018
Fig. 6. Second-harmonic component extraction algorithm based on a third-order general integrator.
From (16), the grid current reference i∗g is contaminated bythe third-order-harmonic component, which may result in powerquality problem in the grid current. So, a notch filter N(s) isrequired in the DC-link voltage control loop, as described inFig. 5.
Thus, the extracting and filtering method for double-line-frequency pulsating components includes two steps:
1) Extracting and amplifying the double-line-frequency cur-rent by Gf(s) in the current ripple feedback channel inFig. 4(b).
2) Removing the second-harmonic voltage from udc by anotch filter N(s) in Fig. 5. Where, Hv(s) is a DC regulator,and GPR(s) is a AC regulator.
A second-harmonic extraction method based on a third-ordergeneral integrator is proposed in this paper, of which the struc-ture is described in Fig. 6.
Suppose the input v(t) is a biased sinusoidal signal with asecond harmonic:
v(t) = A0 + A sin (2ωt + ϕ) (20)
where A0 is the DC component, A is the amplitude of the secondharmonic, and ϕ is the initial phase of the second harmonic. Thetransfer functions of v1(s)/v(s) and v2(s)/v(s) can be writtenas T1(s) and T2(s):
T1(s) =v1(s)v(s)
=kaωts
s2 + 2kaωts + ω2t. (21)
T2(s) =v2(s)v(s)
=2kakbωt
[s2 + ω2
t]
(s + kbωt) [s2 + kaωts + ω2t ]
. (22)
where v(s) is the complex image of the input signal v(t), and ωt isthe resonance frequency. Performing inverse Laplace transformon (21) and (22), the steady-state expressions of v1(t) and v2(t)in time domain can be obtained [33]:
v1 (∞)(t) = mA sin (ωtt + ϕ + φ) , (23)
v2 (∞)(t) = kakbA0 , (24)
m =2kakbωωt√
(ω2t − 4ω2)2 + 4k2
ak2bωt
2ω2, (25)
φ = sgn [ωt − 2ω]π
2− a tan
2kakbωtω
ω2t − 4ω2
sgn(x) =
{+1 x ≥0
−1 x < 0. (26)
Fig. 7. Bode diagram and step response of Gf(s) for different values of ka.(a) Bode of Gf(s). (b) Step response of Gf(s).
In (23), m represents the attenuation coefficient, φ denotes thephase delay brought by T1(s), ωt represents the input angularfrequency. From (24) and (25), it can be inferred that m = 1 andφ = 0, when ωt = 2ω. Consequently, T1(s) and T2(s) can beused for constructing the current ripple extracting filter Gf(s)and the second-harmonic notch filter N(s), namely, Gf(s) =T1(s), N(s) = T2(s).
The bode diagrams of the transfer functions Gf(s) and N(s)are shown in Figs. 7 and 8. It can be seen from Fig. 8 thatthe selective ability of the bandpass filter Gf(s) enhances whenka is smaller. But the time to settle down in the step responsebecomes longer.
From (22), it can be seen that the characteristics of N(s) isdetermined by ka and kb. As shown in Fig. 8, when ka = 1 andka · kb is set to a smaller value, the notch width is wider, and itsstep response time turns slower. Therefore, the value of ka andkb should be designed carefully.
IV. DESIGN OF CURRENT RIPPLE MITIGATING CONTROLLER
A. Design of the Inner Current Controller for the BoostDC/DC Converter
To evaluate the current ripple mitigating effect with the pro-posed double-channel current feedback control technique and
LIU et al.: INPUT CURRENT RIPPLE AND GRID CURRENT HARMONICS RESTRAINT APPROACH FOR SINGLE-PHASE INVERTER 1963
Fig. 8. Bode diagram of N(s) with ka = 1 and different values of kb. (a) Bodeof N(s). (b) Response of N(s).
the second-harmonic extractor based on a third-order generalintegrator, the open-loop transfer function Gio(s) of the innercurrent control loop described in Fig. 4(b) is derived,
Gio(s) =Hi(s)Gid (s)
1 − Gf (s)Gid (s). (27)
PI controller is adopted by Hi(s), namely,
Hi(s) = kpi +kii
s. (28)
Neglecting the equivalent series resistance (ESR) of passivecomponents, the specifications and steady-state parameters ofthe developed PVGCI prototype are listed in Table I.
In order to obtain high selectivity of Gf(s) and high dampingperformance of N(s), ka is set to be 0.5. Moreover, in order toadjust the damping effect of the current ripple conveniently, acoefficient kRF (kRF > 1) is added to the channel of the currentripple feedback, namely Gf(s) = kRFT1(s). By setting kRF to asuitable value, the current ripple ir in iin could be constrainedto a low value. With the aid of MATLAB “sisotool”, the Bodediagram of Gio(s) is plotted in Fig. 9, with kpi = 750, kii =30000. Fig. 9 demonstrates that, when kRF becomes larger, thecurrent ripple mitigating effect becomes stronger. However, dueto the local positive feedback of the current ripple, the trade-off
TABLE IPARAMETERS OF 5 KVA PROTOTYPE
Fig. 9. Bode diagram of first-stage current loop.
Fig. 10. Control block diagram of the proposed scheme for the DC-linkvoltage.
between control stability and ripple reduction effect should beconsidered. Too high value of kRF might undermine the stabilityof control system.
B. Design of DC-Link Voltage Controller
Considering the DC/AC control scheme with a notch filter,the new overall control diagram of the DC/AC stage is givenin Fig. 10, in which Hv(s) is a PI controller, PLL is the phaselocked loop, and GL(s) is the transfer function of L-type ACfilter. Neglecting the ESR of inductors L1 and L2 , we obtain
GL(s) =1
s (L1 + L2)(29)
GPR(s) is the proportional resonant (PR) controller for thegrid current, which is expressed as
GPR(s) = kGP +2kGRs
s2 + ω2 (30)
1964 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018
Fig. 11. Bode diagram of DC-link voltage loop.
where kGP and kGR are the proportional and resonant controllerparameters, respectively. ω(= 2π × 50 rad/s) is the grid angularfrequency.
Then, the equivalent closed-loop transfer function Ti(s) ofthe grid current control loop (in the dashed frame in Fig. 10)can be expressed as
Ti(s) =GPR(s)GL(s)
1 + GPR(s)GL(s). (31)
In Fig. 10, the error u∗dc − udc is filtered by N(s) and regulated
by Hv(s), then DC component I∗g is obtained. i∗g is obtained bymultiplying I∗g by the grid voltage information sin(ωt). Thecorresponding transfer function of this process in s-domain is,
Hsin(s) =i∗gI∗g
=ω
s2 + ω2 . (32)
Gui(s) in Fig. 10 is the transfer function relating the DC-linkvoltage udc to the grid current ig. Adopt the reduced order modelof Gui(s) formulated in paper [34], namely
Gui(s) =udc(s)ig(s)
= kvs2 + ω2
ω. (33)
where kv is the proportional coefficient.Therefore, the open-loop transfer function Guo(s) of
udc(s)/u∗dc(s) in Fig. 11 is
Guo(s) = kvN(s)Hv(s)Hsin(s)Ti(s)Gui(s)
= kvN(s)Hv(s)Ti(s). (34)
The transfer function of Hv(s) is
Hv(s) = kpv +kiv
s. (35)
Adding a proportional coefficient kv into kpv is a conve-nient way for designing the controller. Let kv = 1, ka = 0.5,kb = 0.01, kGP = 50, kGR = 2000. With the aid of MATLAB,kpv = 17.6 and kiv = 450 are obtained. The bode diagram ofthe designed open-loop transfer function Guo(s) is shown inFig. 11. Compensated by Hv(s), the phase margin of Guo(s)is 86° and gain margin is more than 100 dB. High attenuation
Fig. 12. The experimental setup photos.
TABLE IIEXPERIMENTAL DATA IN DIFFERENT INPUT SOURCE
gain has been obtained for the second harmonic. It is effectiveto prevent the second-harmonic current from injecting into thegrid. Therefore, a better power quality is ensured.
V. EXPERIMENTAL RESULTS
In order to study and verify the proposed control strategies,a 5 kVA experimental prototype and a storage system are built.Fig. 12 shows the experimental setup photos. The Li-ion batterypack is composed of 76 battery cells with nominal voltage 3.25 Vin series, and the nominal voltage of battery pack is 247 V. Theactual output voltage is 245 V. The parameters of 5 kVA PVGCIare shown in Table I. All the control algorithms are implementedin a low-cost 16-bit digital signal processor chip TMS320F2808,with 100 MHz maximum operating frequency.
Fig. 13 shows the experimental waveforms without using theproposed control strategies, when PVGCI operates in Mode Iand Mode II. The experimental data with two input sources, arecompared in Table II.
It is obvious that more current ripple occurs on the batterypack input side, when PVGCI is operating in Mode II. Thisphenomenon is consistent with the analysis in the Section II.Therefore, it is necessary to improve the control strategies andavoid the adverse effects caused by the input current ripple.
Fig. 14(a) illustrates the experimental waveforms with the tra-ditional control strategy (double PI controller in outer and innercontrol loop) when PVGCI operates under the battery pack inputcondition, and produces a power of 4.5 kW. Due to the voltagesource characteristic of Li-ion battery, the input current ripple ofPVGCI is mainly absorbed by the boost inductor. Ripple ratio of
LIU et al.: INPUT CURRENT RIPPLE AND GRID CURRENT HARMONICS RESTRAINT APPROACH FOR SINGLE-PHASE INVERTER 1965
Fig. 13. Waveforms of the input voltage and current under different inputsource conditions. (a) PV array input condition (Mode I). (b) Battery pack inputcondition (Mode II).
the input current is approximately 25.87% and the voltage ripplein DC-link bus voltage is small. Measured by the power analyzerWT1800, the THD of the grid-connected current is 3.01%, andthe third-order-harmonic current content is 1.95%, as illustratedin Fig. 14(b). For comparison, Fig. 14(c) illustrates the experi-mental waveforms with the proposed current ripple mitigatingcontrol algorithm, when PVGCI operates under the PV array in-put condition. The input current ripple is dramatically reduced,and the ripple ratio is 7.14%. Meanwhile, it is observed thatboth the voltage ripple in DC-link bus and the third-order har-monics of the grid current are increased apparently. The THDof the grid current is 3.43%, the third-order-harmonic currentcontent is 2.47%, as shown in Fig. 14(d). It is indicated that,the second-harmonic power shifts from the boost inductor tothe DC-link capacitor, by the proposed double-channel currentfeedback control algorithm. Therefore, the constraint methodfor mitigating grid current harmonics is necessary to adopt.
To validate the proposed integrated method of double-channelcurrent feedback control algorithm and the second-harmonicvoltage mitigating technique based on the third-order generalintegrator, another experiment has been carried out. Fig. 15 il-lustrates the experimental results, where PVGCI is operated atfull load (5 kW) under the battery pack input condition. WithkRF = 10, the current ripple ratio of the input current decreasesto 2.5%, and the voltage ripple in DC-link bus is 32 V (peak-to-peak voltage). Obviously, with the proposed second-harmonic
Fig. 14. Experimental waveforms without and with the double-channel cur-rent feedback control in the boost stage. (a) Waveforms with traditional control.(b) Grid current harmonic analysis with traditional control. (c) Waveforms withdouble-channel current feedback control. (d) Grid current harmonic analysiswith double-channel current feedback control.
1966 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018
Fig. 15. Experimental results with the proposed double-channel current feed-back control algorithm and the second-harmonic voltage mitigating methodbased on a third-order general integrator.
Fig. 16. Dynamic transient responses with proposed ripple mitigating control.
voltage mitigating method based on a third-order general inte-grator, the effect brought by the bus voltage ripple reduces. Asshown in Fig. 15(b), the THD of the grid current is 2.01%, andthird-order-harmonic current content is 1.57%, much less thanthe relevant standard values [35].
To evaluate the adaptability of the proposed control strategy,transient experiments have been performed under the batteryinput condition. Observed from the bode diagram in Fig. 9,dynamic performance and static performance may be differentwith different coefficient kRF. By taking kRF = 7.5, both dy-namic and static performance can be ensured. The experimentalwaveforms are shown in Fig. 16. In this experiment, the powerinjected into the grid changes from 3 kW to 5 kW. Experimental
results indicate that PVGCI with the proposed control strate-gies can stabilize again in less than half power cycle. That is tosay, good dynamic performance can be ensured when the loadchanges. During the transition phase, the input current ripple hasbeen constrained to a low value, 3.25 A (maximum peak-to-peakcurrent), which satisfies the stability and safety requirements forPVGCI operating under battery input condition.
VI. CONCLUSION
The difference of the second-harmonic input impedance ofPVGCI under different input conditions has been revealed by theanalysis on the equivalent impedance models. The impedanceof Li-ion battery pack in double-frequency is much less thanthat of PV arrays. To be specific, the former is only a fewpercent of the latter. Thereby, much more input current rippleappears, when Li-ion battery pack is used as the energy sourcefor PVGCI in the residential photovoltaic/battery system. Toaddress the problems of the serious second-harmonic current onthe input source side and the third-order-harmonic current onthe grid side, this paper has proposed an active input currentripple and grid harmonics current mitigating control method forPVGCI under the battery pack input. With the aid of MATLABsimulation, suitable controller parameters have been designed.Experimental results of prototype have shown that the inputcurrent double-frequency ripple can be limited to 2.5% or less,when PVGCI is operated at the full load. Simultaneously, THDof the grid current is 2.01%, which is within the limits imposedby standards such as VDE-AR-N4105. Besides, the static anddynamic performance of PVGCI has been proved to meet therequirement of grid-connected standards .With the proposedcontrol strategies, the original PV system can easily be upgradedto a residential PV/battery system. Consequently, the practicalsignificance of this research is ensured. In the future research,the feasibility of the proposed control scheme to mitigate thedouble-frequency ripple in PV/battery systems with other typesof batteries, such as lead-acid batteries and fuel cells, should beevaluated and verified.
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Bin Liu received the Ph.D. degree from the School ofInformation Science and Engineering, Central SouthUniversity, Changsha, China, in 2014. He is cur-rently working as a Postdoctoral member with Cen-tral South University, and a Lecturer with the Schoolof Electrical Engineering, Guangxi University,Nanning, China. His research interests include thegeneral area of power electronics and energy conver-sion, with particular emphasis on converter topolo-gies, modeling, and control.
Lina Wang (S’04–M’16) was born in Zhengzhou,China, in 1977. She received the B.Sc. degree inelectrical engineering and the Ph.D degree in controltheory and control engineering, both from the Cen-tral South University, Changsha, China, in 1998 and2003, respectively. From January 2004 to December2005, she was a Postdoctor with the Department ofElectrical Engineering, Tsinghua University, Beijing,China. She became an Associate Professor of PowerElectronics with Beihang University in 2006. Hercurrent research interests include power electronic
converters, application of SiC devices, distributed control and optimization ofmicrogrids, and electrical actuators for aircraft.
Dongran Song received the B.S., M.S., and Ph.D.degrees from the School of Information Sci-ence and Engineering, Central South University,Changsha, China, in 2006, 2009, and 2016, respec-tively. Since 2018, he has been as an Associate Profes-sor with the Central South University. He was an Elec-trical and Control Engineer with China Ming YangWind Power, Zhongshan, China, from 2009 to 2013.His research interests include wind turbines, powerelectronics, and renewable energy system.
1968 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018
Mei Su received the B.S., M.S., and Ph.D. degreesfrom the School of Information Science and Engi-neering, Central South University, Changsha, China,in 1989, 1992, and 2005, respectively. Since 2006,she has been a Professor with the School of Informa-tion Science and Engineering, Central South Univer-sity, Changsha, China. Her research interests includematrix converter, adjustable speed drives, and windenergy conversion systems.
Jian Yang received the Ph.D. degree in electricalengineering from the University of Central Florida,Orlando, FL, USA, in 2008. He was a Senior Electri-cal Engineer with Delta Tau Data Systems, Inc., LosAngeles, CA, USA, from 2007 to 2010. Since 2011,he has been with Central South University, Chang-sha, China, where he is currently a Professor with theSchool of Information Science and Engineering. Hismain research interests include control application,motion planning, and and power electronics.
Deqiang He received the Ph.D. degree fromChongqing University, Chongqing, China, in 2004.He is currently a Professor with the School of Me-chanical Engineering, Guangxi University, Nanning,China. His main research interests include fault diag-nosis and the intelligent maintenance of rail transit.
Zhiwen Chen received the B.E. degree in electronicinformation science and technology and the M.Sc. de-gree in electronic information and technology fromthe Central South University, Changsha, China, in2008 and 2012, respectively, and the Ph.D. degreein electrical engineering and information technologyfrom the University of Duisburg-Essen, Duisburg,Germany, in 2016. His research interests include con-trol engineering and fault diagnosis.
Shaojian Song received the B.S. degree in industrialelectrical automation and the M.S. degree in controltheory and control engineering from Guangxi Uni-versity, Nanning, China, in 1994 and 2001, respec-tively. He is currently a Professor with the School ofElectrical Engineering, Guangxi University. His cur-rent research interests include modeling, optimiza-tion and control for complex system, electric vehicleand V2G, active distribution network, power elec-tronics and energy conversion with particular em-phasis on converter modeling, control, and variousapplications.
