GB2591724A

GB2591724A - A charger

Info

Publication number: GB2591724A
Application number: GB1917138.8A
Authority: GB
Inventors: Li Yun; Ahmed Rishad; Long Teng; Fang Haiping; Shen Yanfeng; Zhao Hui
Original assignee: Cambridge Enterprise Ltd; Zhuzhou CRRC Times Electric UK Innovation Center
Current assignee: Cambridge Enterprise Ltd; Zhuzhou CRRC Times Electric UK Innovation Center
Priority date: 2019-11-25
Filing date: 2019-11-25
Publication date: 2021-08-11
Also published as: GB201917138D0

Abstract

A charger compatible with 1 phase and 3 phase supplies. With a 1 phase supply, the 1 phase source is connected between two of the three input lines of the charger. Each of the three input lines is coupled to an LCL filter 20 comprising grid and converter inductors with a filter capacitor between them. Each of the LCL filter legs is coupled to a respective leg of a 3 phase rectifier 30. With a 1 phase input, the three legs work in an unbalanced technique to control the power flow into the LCL filter to compensate the double-line frequency power pulsation. With a 1 phase input, when the rectifier is driven by a Space Vector Pulse Width 10 Modulation (SVPWM) scheme, the modulation range and DC voltage utilization of the charger is increased. The charger may be an on board charger for an electric vehicle.

Description

A Charger

FIELD OF THE INVENTION

The present invention relates to a charger, in particular a charger for charging an electrical energy storage device such as a battery.

BACKGROUND OF THE INVENTION

The chargers, especially the on-board chargers (OBCs) for Electric vehicles (EVs) are attracting increasing attention [1-4] because of a rapid uptake of transport electrification [5, 6]. Major automobile production and consumption countries such as the U.S. and the U.K. have set ambitious EV development roadmaps in which the OBC has been defined as an important aspect [7, 8]. By 2035, the gravimetric and volumetric power densities of the OBC are expected to achieve 50 kW/kg and 60 kW/L according to the roadmap, which are approximately seven times higher than existing products [8].

The Level 2 charging in which an AC supply with the current up to 60 A is fed has been commonly considered as a mandatory requirement for OBCs in the domestic and street- side charging [9, 10]. The voltage of such AC supplies can be either single or three-phase. In fact, without additional upgrade on circuit breakers, three phase supplies can effectively increase the charging rate by three times, showing a sensible and affordable solution for EV charging. The three-phase supply is commonly available in premises and thus it is commercially valuable to equip the EV OBCs with both single-phase (14) and three-phase (34) grid connections [11, 12]. Yet most of commercial OBCs are only compatible with a 1-$ supply and it is hardly seen literature on combined 1-4) and 3OBCs except for US2019/288539, proposed a combined 1-0 and 34 OBC using a Vienna rectifier and 2 LLC converters. However, for 14 operation the circuit configuration needs to be changed (re-grounding) and control for AC-DC rectifier of the OBC is complex. The potentials of practical combined 1-0 and 34 OBC technology and solution have been overlooked by both the industry and academia.

However, the difference and challenge of combining single and three-phase OBCs are beyond only adding one more leg in the AC-DC rectifier of the OBC. When the OBC is connected to a 1-0 supply, a large power pulsation at double line frequency [13] is generated at the AC-DC rectifier, which would not appear when connecting to a 34 supply. The ACDC rectifier of the OBC as shown in Fig. 1 is focused to enable both single-and three-phase OBC connection and achieve high power density.

TABLE I summarizes the techniques dealing with this double-line frequency power pulsation.

Method DC link Charging Main issues voltage current DC Large DC capacitor capacitor storage Fluctuate charging current Variable DC voltage Impair battery Voltage stress, Over modulation Active 11dr Extra switching power filter (APF) devices for control; Extra passive devices for energy storage * I

Table I

Conventional techniques usually employ a bulk DC capacitor bank to reduce the voltage pulsation at the DC link of the rectifier. The power density is low due to the large number of capacitors at the DC link. The reliability is also limited because the use of less reliable electrolytic capacitors is usually inevitable in this technique to achieve large capacitance.

To increase the power density, [14] boldly directs the low frequency power pulsation into the batteries so the capacitance of the DC link can be significantly reduced but the DC current provided by the OBC contains a large AC ripple at the double-line frequency although the impact of the low frequency ripple current at to the battery is unclear. Some literature [15, 16] shows that the current pulsation will cause adverse impact on the battery[17] such as the temperature increase, the capacity degradation and the gassing.

Advanced control techniques can eliminate the current distortion caused by the double-line frequency power pulsation. [18] employs a repetitive algorithm and a feed-forward controller to eliminate the output current distortion. [19] applies a feedback controller to reduce the current pulsation. However, those special control techniques are based on using the inconstant DC link voltage largely pulsating at the double-line frequency to smooth the output DC current and a high control bandwidth must be employed. The pulsating DC voltage will cause voltage stress and over-modulation of semiconductors at the peak and bottom of the pulsation respectively.

The active power filter (APF) can divert and store the double-line frequency power pulsation by using much smaller energy storage components. There are different APF circuit topologies depending on the location of the APF and the type of components used for energy storage in the APF [13, 19-30].

The APF can be implemented at the DC side [24, 25, 27] as shown in Fig. 2 (a) or AC side as shown in Fig. 2 (b) [13, 29, 31]; there are inductor-based APFs [24] and capacitor-based APFs [13, 20, 21, 27]. To identify the optimal location and the type of the energy storage components used in APFs, the unified equations among these techniques are necessary.

Reducing the cost and size of the APFs are important. [20] uses split-capacitors to control the current in both the rectifier and APF, and thus no extra switches are required. However, extra passive components are still needed to store the pulsating power. [30, 32] use novel topologies to reduce the capacitance but the voltage ratings of the capacitors and the semiconductor devices must be increased. Since the passive components storing the pulsating energy can dominate the volume and weight of the APF, it is important to investigate the volume! weight of the energy storage components.

The present invention acknowledges that there is a need for a universal converter that is compatible with both a 1-4) and 3-0 supplies.

SUMMARY OF THE INVENTION

The present invention provides a charger in accordance with the independent claim appended hereto. Advantageous embodiments are provided by the dependent claims, also appended hereto.

We describe a charger for charging an electrical energy storage device, comprising: first, second and third AC inputs for receiving up to three respective phases of AC voltages from an AC source; first, second and third LCL filters connected to each of the respective first, second and third AC inputs; and a three-phase rectifier having first, second and third legs, each of the first, second and third legs connected to respective ones of the LCL filters, the rectifier for rectifying the up to three phase AC source voltages; and a controller connected to the three-phase rectifier to control the three-phase rectifier to produce a DC output voltage from an AC input voltage, the charger having a single-phase mode of operation in which a single-phase AC source is connected between the first and second AC inputs and the controller controls the first, second and third legs of the three-phase rectifier to generate a DC output.

Advantageously, unlike some other chargers in which the third leg of the rectifier is redundant when connected to a 14 supply, the proposed technique utilizes the third leg as part of the AC side APF to address the double-line frequency power pulsation issue while the other two legs are connected to the single phase AC supply. This therefore provides a charger that is compatible with 14 and 34 supplies whilst being able to handle the power pulsation problems associate with connecting to 1-4) supplies and whilst maintaining a small form factor for the filter capacitors.

The charger has a three-phase mode of operation in which each respective phase of a three-phase AC source is connected to the respective first, second and third AC inputs, and the controller controls each of the first, second and third legs of the three-phase rectifier to generate a DC output.

Each of the LCL filters may comprise a grid-side inductor connected to the respective AC input, a converter side inductor connected in series between the grid-side inductor and a respective one of the legs of the rectifier, and a filter capacitor between the grid-side inductor and converter-side inductor. The filter capacitor of the first LCL filter may be connected between the grid-side inductor and the converter-side inductor of the first and second LCL filters, the filter capacitor of the second LCL filter may be connected between the grid-side inductor and the converter-side inductor of the second and third LCL filters, and the filter capacitor of the third LCL filter may connected between the grid-side inductor and the converter-side inductor of the third and first LCL filters.

In the single-phase mode, the rectifier operates as an unbalanced rectifier.

In the single-phase mode, the rectifier may be driven by a Sinusoidal Pulse Width Modulation (SPWM) scheme or a Space Vector Pulse Width Modulation (SVPWM) scheme.

In the single-phase mode, the third leg of the rectifier is controlled to control the power flow resulting from a double-line frequency power pulsation by diverting the power flow into the LCL filter.

In the single-phase mode, the LCL filters are configured to attenuate harmonic current. In the single-phase mode, the LCL filters are configured to store energy from a double-line frequency power pulsation.

In any of the above, the charger may be an on-board charger for an electric vehicle.

The AC source may be a grid voltage.

LIST OF FIGURES

The present invention will now be described, by way of example only, and with reference to the accompanying drawings, in which: Figure 1 shows an EV charger with a 14 grid; Figure 2a shows a typical APFs for the DC side APF; Figure 2b shows a typical APFs for the AC side; Figures 3a and 3b show the relationship between the volume! weight and the maximum energy storage for the inductors and film capacitors: 3(a) the energy vs the volume, and 3(b) the energy vs the weight; Figures 4a to 4d show the waveforms for inductors as energy storage components: (a) the current waveform for DC side APF, (b) the voltage waveform for DC side APF, (c) the current waveform for AC side APF, and (d) the voltage waveforms for AC side APF; Figures 5a to 5d show the waveforms for capacitors as energy storage components: 5(a) the voltage waveform for DC side APF, 5(b) the current waveform for DC side APF, 5(c) the voltage waveform for AC side APF, and 5(d) the current waveforms for AC side APF; Figures 6a and 6b show the proposed universal converter when coupled to a (a) three-phase grid, and (b) with single-phase grid; Figures 7a and 7b show the equivalent circuits of Figures 6a and 6b with a 34 and 1-0 grid: 7(a) the single-phase equivalent circuit with a 3-0 grid, and 7(b) the equivalent circuit with a 1-0 grid; Figures 8a, 8b and Sc show the equivalent circuits with a 14 grid: 8(a) the equivalent circuit with current sources, 8(b) positive-sequence equivalent circuit, and 8(c) negative sequence equivalent circuit; Figure 9 shows an open-loop control block for the 14 connection Figure 10 shows the diagram of typical solution trajectories with the boundaries of both SPWM and SVPWM (l/dc = 650V, P100= 3.3kW).

Figure 11 a shows the flowchart of deriving the minimal Cf; Figure 11 b shows the derived minimal Cf with different power ratings and Vdc (modulation index = 1); Figures 12a and 12b show the total 12(a) volume and 12(b) weight of the LCL filter versus KvoL; Figure 13 shows the required DC capacitance comparison between moo and PSW. Pdc = 3 kW, Vdc = 650 V, AV = 13 V (2% of Vete); Figure 14 shows the simulated waveforms of the converter with 3-4) power supply at 400 V and 10 kW. The Vdc = 650 V; Figures 15a and 15b show the simulated waveforms of the conventional method but small DC capacitance connected to a 1-4) grid: 15(a) Vg = 230V, P0 = 3 kW and 15(b) Vg = 120 V, Po = 300W; Figure 16 shows the simulated waveforms of the proposed method of the converter connected to a 1-4) grid; Figures 17a, 17b and 17c show test set-up of 17(a) overall converter, 17(b) the capacitor bank for the dc capacitor storage technique, and 17(c) the film capacitor for the proposed technique; Figures 18a to 18c show experimental results of the proposed technique with Po = 300W and 10pF dc capacitors: 18(a) waveforms, 18(b) DC voltage spectrum in percentage, 18(c) current spectrum versus standard limit; Figures 19a to 19c show experimental results of the proposed technique with Pg = 500W with 10 pF dc capacitors: 19(a) waveforms, 19(b) DC voltage spectrum in percentage, 19(c) current spectrum versus standard limit; Figures 20a to 20c show experimental results of the proposed technique with Pg = 3000W with 10 pF dc capacitors: 20(a) waveforms, 20(b) DC voltage spectrum in percentage, 20(c) current spectrum versus standard limit; Figure 21 shows the 100 Hz dc voltage ripple percentage at various load with 10 pF dc capacitor with the proposed technique Figure 22 shows the experimental efficiency comparison between the proposed technique with 10 pF dc capacitor and the conventional 1-4) converter with 1.3 mF dc capacitor at various loads.

Figures 23a to 23c show experimental results of conventional single-phase converter with Po = 300W with 10 pF dc capacitors: 18(a) waveforms, 18(b) DC voltage spectrum in percentage, 18(c) current spectrum versus standard limit; Figures 24a to 24c show experimental results of conventional single-phase converter with P, = 500W with 10 pF dc capacitors: 24(a) waveforms, 24(b) DC voltage spectrum in percentage, 24(c) current spectrum versus standard limit; Figure 25 shows the equivalent circuit of the proposed technique for a 1-4) grid; and Figure 26 shows the equivalent circuit of Figure 20 when only vo"to exists.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In brief, unlike some other chargers [11, 12] in which the third leg of the rectifier is redundant when connected to a 14 supply, the proposed technique utilizes the third leg as part of the AC side APF to address the double-line frequency power pulsation issue while the other two legs are connected to the single phase AC supply.

Furthermore, the low frequency power pulsation is diverted into the LCL filter between grid and converter and the capacitor at the LCL filter is used to store the power pulsation. Therefore, neither extra semiconductor nor passive components are required. From control's perspective, unlike the conventional APF technique, which decouples and separately controls the dc power and the double-line frequency power pulsation, the proposed control operates three legs as an unbalanced converter when connected with a 14 supply. Therefore, some benefits from 34 converters can be utilized, namely, the Y/A transformation and space vector pulse width modulation (SVPWM) can be applied to amplify the equivalent capacitance in LCL filters for APF power pulsation storage and achieve higher DC voltage utilization compared with sinusoidal pulse width modulation (SPWM), respectively. When connected with a 34 supply, the third leg is used with the other two legs as a normal three phase rectifier and no APF is needed because no double-line frequency power pulsation exists.

We will discuss the derivation of the universal equations to evaluate the optimal APF circuit. The we will discuss a proposed circuit and discuss its operating principle. We will then discuss the parameter design procedure of the LCL filter for this combined single-and three-phase rectifiers along with the size and weight comparison with the conventional circuit. Finally, we will discuss simulations and experiments to verify the design.

Evaluations of double line frequency APFS based on Unified Equations Various APFs exist to filter the double line frequency power pulsation of a 1-4) rectifier.

Fig. 2 (a) and (b) show the APF at the DC side AC side respectively. Either the inductor L or capacitor C or both can be used at the AC and DC side as energy storage components. Because both the topology and type of energy storage components can affect the current! voltage waveforms so does the power density of the APF, identifying the optimal circuit is complicated. A unified expression is derived to assess the performance of different type of APFs as well as the volume expressions for the passive components are defined to support the selection of the APF in order to minimize the size of the passive components.

A. Evaluating the Size and Weight of Inductors and Capacitors as Energy Storage Devices for APFs To discuss the relationship between the volume / weight versus the maximum stored energy, Fig. 3 (a) and (b) records 241 different capacitors and 121 different inductors from the market, including 49 inductors with silicon steel cores from the Hammond Manufacturing [33], 36 inductors with MPP power cores from the Magnetics Inc[34], 36 inductors with MPP power cores from ChangSung Corp [35], 53 film capacitors from KEMET [36], 49 film capacitors from Vishay [37], and 139 film capacitors from TDK [38]. It should be noted that the weight information of 39 capacitors from C4AE series is not available in the datasheets so the Energy v.s Weight relationship shown in Fig. 3 (b) contains 199 capacitors while Fig. 3 (a) contains all 238 capacitors to illustrate the Energy v.s Volume relationship. Moreover, to calculate the size and volume of inductors with MPP cores, the maximum magnetic flux density is set as 0.1 T and the fill factor = 0.4 is used as a typical value suggested in Magnetics Inc's design guides [39] for toroidal cores. For the commercialized inductors, the maximum current uses the rated current 1.rated, (donated by / which is the maximal value of the saturation current (donated by /sat) and the current for temperature rise (donated by urns).

Fig. 3 shows that, although the size / weight difference with different manufacturers / series, the volume / weight of both the inductors and capacitors are approximately linear with their maximum energy storage. This linear relation can be expressed as (1) and (2) for inductors and capacitors: Eng, = -1!irate,2 = FVOLL Eng, = -1LI rate, =Kw,-WET, 2 Eng, = -1CVra",2 = K"_VOL, 2 Eng = Cl/rateci2 = KweLWET, where 'rated. / -V rated is the rated maximum current! voltage, VOLL/ WETL and VOL c I WETc are the volume! weight of the inductor and capacitors, Kw_ I Km and Kvc / Kwc the energy density coefficients per unit volume / weight for inductors and capacitors. Large energy density coefficients can result in small volume / weight. In Fig. 3, all the energy density coefficients can be obtained by choosing specific point (as highlighted with blue in Fig. 3). For film capacitors, Kvc 10-4 J/mms, and Kwc 0.1 J/g; for silicon steel inductors, KVL 10-6 J/mm3, and Km --r% 2x10-4 J/g; for inductors with MPP cores, Kw_ 5x10-7 J/mm3, and Km/Lt 1x 10-4 J/g.

B. Unified Voltage and Current Equations of APF at the DC and AC Sides To derive the equation, an inductor is used for storing energy at the DC side APF as shown in Fig. 2 (a). The double-line frequency (notated as subscript 100 as the line frequency is considered as 50 Hz) power pulsation ploo(t) = Pioosin(2wgt+e) needs to satisfy: v, (0= Ldi dtJt) i, (0= P," sin (2ogt +0) (3) where the if(t) and vi(t) are the inductor current and voltage respectively; L is the inductor; wg and 19 are the grid's angular frequency and phase angle respectively, ploo(t) is the double line frequency power pulsation, and P100 is its magnitude. (1) (2)

The solution of (3) is (4), i, (0= ±,IPa.1(K -cos(2cogt + en rogL v, =4/9"cogL sin(2wat +0) (4) where K is the constant in general solutions of the differential equations, determined by i40) as: Because 40) can be controlled by setting specific value, K is determined by the control strategy. ii(t) must be a real number so K 1 is required. Specially, when K = 1, (4) can be further simplified as, Fig. 4 (a) and (b) show the waveforms of il(t) and v/(t) at different K for the DC side APF. When K>1, the DC offset of the inductor current occurs and both the mean and peak values increase when K increases. As shown in Fig. 4(a)-(b), the blue/red curves represent the positive/negative solutions in (4). When K= 1, the shape of the 14t) is sinusoidal within both [0, 10] ms and [10, 20] ms as the grey curves, but h(t) flips over at the communication point when t = 10 ms so its polarity remains unchanged. This flip-over of if(t) will flip vf(t) because vr(t) = Ldif(Oldt.

If L is installed at the AC side, the equation to compensate P100 is as same as (3) and the solution remains as same as (4). However, the value K can only be 1 because the il(t) of the AC side APF needs a natural commutation point to change the polarity and there is no DC offset. Therefore, K = 1 is mandatory. il(t) and v/(t) are shown in Fig. 4 (c) and (d). From existing literature, (4) has be verified by both DC side APFs in [27, 40] and AC side APFs in [13].

\12P oigL v, (0= ±,I2P,00co0L cos w t+-e g 2, 1(K -cos(2cogt +On (5) C. Volume / Weight Expression of Passive Components Based on the unified solution in (4), the magnitude of i/(t) for AC side APF and DC side APF has the same expression as shown in (6).

mag (i, (0) = (cogo."(K +1) (6) From (6), it is obvious that the AC side inductor current equals to the smallest value of that in the DC side APF for storing the same amount of energy, i.e. K = 1. The inductance L and inductor current if(t) determine the volume of inductors. Substituting (6) into (1) yields (7).

VOLL =1 Lcdted2 /KvL = (K + 7 \ 2 2cogK" ir t d 2 /K w, (K +1) Pico WET, = L ( 1 \ 2, 2rogK""L Eq. (7) shows that the volume / weight of the required inductance is determined by the power pulsation (Pim), the material (Kw_ /KwL), and the control stratagem (i.e. the value of K) from (6).

When a capacitor is applied as the energy storage device, similar to the derivation of using the inductor, the double-line power pulsation needs to satisfy (8), where ve and fa are the voltage and current of the capacitor used in APF respectively. The general solutions of (7) are given in (9) and the volume expressions are in (10). As aforementioned, the solution and volume expressions of capacitor based APF in (8) and (9) are applicable for both the AC and DC side APFs. For DC side APF, K 1. For AC side APF, K = 1. The voltage and current waveforms of the capacitor at the DC and AC side APF are shown in Fig. 5.

va ic (t) = vc (t)C dvciGt(t) Pi" sin(2cogt +19) (8) tct (t) -±\119" V K -cos (2co gt + 8) cogC i (0 -± sin (2o)gt + e) Pw° i a) gC V(K -cos(2cogt ± 19)) (7) (9) mag(ve (0) \i,Plog°c° 1 C V 2 AC 2 rated V C Vrated2 j/K VOL, = WET, = Ploo (K +1) 20.),Kvc wc 2::K7",c (K +1) (10) where VOLc / WETc is the volume! weight of the capacitor, and Kvc / Kwc is the energy density per unit volume! weight.

Because (10) has the same form to (7), one unified equation can be used to assess the volume and weight of the APF passive components, which depends on the location of the APF in terms of the value K and the type of the passive components in terms of the value of KL and KC.

D. Optimal Circuit Selection From Figure 5, it is obvious that the capacitor shows higher energy density than inductors considering both the size and weight, i.e. Kvc >> KVL and Kwc >> KWL, so the APF is in favour of using film capacitors for storing energy. However, as shown in Figure 2, the voltage source APF with a capacitor needs an extra inductor for ripple current damping and limiting, which needs to be considered in the design.

Existing techniques [25, 30, 41] use capacitance per watt (FA/V) to identify the optimal circuit, and propose the APFs with small capacitance but a high voltage rating. However, the volume! weight of capacitors in different types of the APF have not been compared.

The unified volume expression in (10) can be used to identify the circuit with optimal volume and weight.

In (10), P100, &lg. Km are constant, and the only controllable parameter is K. To achieve the minimal volume, K = 1 should be selected no matter AC side or DC side APFs.

However, when K = 1 of the DC side APF, the control variables, capacitor current and voltage ia(t) and vc(t), are non-sinusoidal with sharp changes as shown in Fig. 4 and Fig. 5, The widely spread spectrums of the voltage and current require a high control bandwidth to be implemented at the APF and the filtering performance is inevitably compromised [27]. Furthermore, the parasitic components might dominate the high-frequency impedance, resulting in errors of the instantaneous power equation in (7).

Instead, K must be 1 when the AC side APF and both the voltage and current are sinusoidal. The control of AC side APF is much easier than the DC counterpart for the same power density of the APF so the filtering performance of the APF at the AC side is better.

In conclusion, the APF using capacitors at the AC side has the advantages of low volume, low bandwidth control requirements, high filtering performance and robustness with parasitic parameters thus it has been selected for this invention.

Proposed Universal 1-th and 3-th topology and control for AC-DC rectifier used in OBCs The proposed universal 14 and 34 circuit is as shown in Figures 6a and 6b. Figure 6a shows the circuit connected with a 34 source whereas Figure 6b is shown connected with a 14 source The AC sources 10 each are connected to a leg of the charger. Each leg of the charger is connected to LCL filters 20. Each of the filters comprising a grid-side inductor Lg in series with a converter-side inductor Ls and a filter capacitor Cf connected between the inductors. The filter capacitor of the first LCL filter is connected between the grid-side inductor and the converter-side inductor of the first and second LCL filters, the filter capacitor of the second LCL filter is connected between the grid-side inductor and the converter-side inductor of the second and third LCL filters, and the filter capacitor of the third LCL filter is connected between the grid-side inductor and the converter-side inductor of the third and first LCL filters.

Each of the legs of the LCL filter 20 is connected to a respective leg of a 34 rectifier 30.

The output may be smoothed via the DC side Capacitor C. When connected with a 14 supply (as shown in Figure 6b), the 1-source is connected between two of the three input lines. The third leg of the rectifier 30 can be utilized to control (via a controller, not shown) the power flow to compensate the double-line frequency power pulsation, therefore no extra power electronic switches are required for the APF functionality. Moreover, the LCL filter between the supply and the converter can be utilized as energy storage components thus no extra passive components are required. Because the LCL filter inherently has inductors, no additional ripple current damping inductors are required in the APF.

The LCL filter in Figures 6a and 6b is highlighted in blue to emphases that it not only attenuates the switching harmonics but also stores the unbalanced power pulsation when used as part of the APF for a 14 connection.

A. Double-Line Frequency Power Pulsation in Form of Sequence Networks The instantaneous power p(t) can be written in the form of sequence network, where the subscripts 0, 1, 2 donate the zero sequence, positive sequence, and negative sequence respectively. If no zero-sequence current exists, the expression of p(t) is shown as (11): (t) p(t) = v" i" _v" _ " (t) = V (OT /1(0 + (OT /2 + (OT /1(0 + (t)T /2 (0 (11) There are six components in (11), and their contributions can be summarized in TABLE II. TABLE II shows that moo is generated by coupling the positive and negative sequence. When connected with a balanced 34 supply, no negative-sequence voltage and current exist so pm) is zero.

Table 2

A 1-4) supply can be considered as an unbalanced 3-0 supply, whereas the three phase voltages and the three phase currents are as (12): (12) By using the abc/zpn transformation, the voltages and currents in sequence network can be expressed as (13): g O' /g1, 192 Tabc2 zpn Pga, cb, /go 9 I El 1/ 9 [0 -30' , 1/30" Vo, V9,1, V9,2 Tabc2zpn[v go, v gh, 'go uoI 1; 1 ° (13) 1 is the matrix to compute the sequence components where T" 2zpri = (positive, negative, and zero) from three phase abc system, and a = 1L -30 is the complex operator for the 2r/3 rotation Substituting (13) into TABLE II derives (14) which is the expression of (the phasor of the double-line frequency power pulsation generated by grid) in form of sequence network: Li 31 °" _I 1 ° The Y/A Ploo-vg 3 = -j-V 2 -Vg L _ 3 _I 3'1 ' \' -I Z30° (14) = -j- II II / -j-V -f--V9 capacitors is preferred.

=-; / 92 91 2 91 '92 APF with B. Operating Principles above, 1 ° \ As concluded -/gZ-30° the AC side transformation can amplify the equivalent capacitance provided by the LCL filter.

When connected with a 34 supply as shown in Fig. 6 (a), the three phases of converter are balanced. A 14 equivalent circuit is shown in Fig. 7 (a). Because p100 = 0, there is no double-line frequency power pulsation. The voltage phasor of the rectifier is controlled n as Vgvt =Vg+ jog (Lg + LG)Ig The subscript cvt donates the voltage generated by the converter (rectifier).

When connected with a 14 supply as shown in Fig. 6 (b), the equivalent circuit is shown in Fig. 7 (b) where vevta, vo,g, and vc"t, are the three phase voltages of the converter, and vaa, vgfg and vac are the three phase voltages across the Cf. Both the power supply and impedance are asymmetrical, and the circuit needs to be simplified. By using the superposition theory, the unconnected terminal (Phase-C) is substituted by a current source with the current as zero, i.e. i = 0. The Phase-A and Phase-B form the line and neutral of the single phase where the current is ig and -ig respectively as shown in Fig. 8 (a). The sequence network circuits in terms of the forward and backward sequence are shown in Fig. 8 (b) and (c) where the positive sequence current is and the negative sequence current is /or, and the negative sequence current is /g2. The controlled voltage of the rectifier at each phase (v0wg, v,,tb, and v,,te) can be expressed in the positive sequence (i.e. Vevt1) and the negative sequence (i.e. V0vt2) as shown in Fig. 8(b) and (c) Two requirements need to be satisfied: 1) the I, needs to be controlled as (15), and 2) the capacitor Cr should store all double-line frequency power pulsation generated by the

L

grid, P100 Cf = P100 vg as (16).

E I 0 0 (15) Vg-Vcia-Vcfb)= jOu2Ly Ig (1b) P100-Cf = P100-Vg 0 _I where P 100-Cf and P * 100 vg are the double-line frequency power generated by capacitors and the grid respectively.

3 1 I 3 2 Vc,12 J 2 Vrti /of 2 I I I \ Val jOic, (3C1 V012 0 E V012 j009 (3Cf Vcfl 0 E =9cogCf V cf1V 012 P100-01 = = (17) V of 0 V of 2 Substituting Vora V cfb 1 1 1 1 a2 a into (15) derives (18), and substituting (17) into (16) derives (19). Consequently, the two requirements are transformed in the form of sequence network: I I 1 II (1/30' )V cf 1+ (1/ _30*) V cf 2 = V REC "a L _ 1 nu -.I _I L Von V012 - r100-vg - V9 Ig 9COyc 18%C1 where V REC = V g -iNg2L9, Ig is a defined vector.

There are two variables (Von and V012) in the two equations,(18) and (19). The solution can be derived as (20): {- ( 1 L L°71 V cfl = V REC -± A -Z-301 1 1- L\ 71 V012 = ', -F IAt r v REC -.,,,,n," (18) (19) (20) where A = 1 112 VREc 4Ploo_v9 3 9cogC, is a defined vector.

From Fig.8 (b) and (c), the rectifier voltage in the positive and negative sequences need to be controlled as: V 0 V cfl frOg (3Cf)-g L-30 frogL, = V cf 1 + (21) V012 = V cf 2 + V02 j(09,(3c) -g ^Tic30° joaLe In order to increase the DC voltage utilization, the SVPWM is used, in which the voltage reference in the a,6 axis is required as: Vcvt, Ta102apTzgn2abc -0 - 1 1 H - (22) E V0,41 Vcvt0 -j j Vevti 0 Vcvtl V cvt2 V cvt2 where Ta "2 = 1 0 and T = 1 1 1 are the matrix to performs the 1 1 a2 a 2 1 a a2

Z

zpn to abc transformation, and the abc to ai3 transformation respectively.

Therefore, the open-loop control of this unbalanced operation for a 14 connection can be illustrated in Fig.9. With setting the complex power S, the sequence network voltages on the Cf, the sequence network voltages on the converter, and the converter voltage in the at5 axis are derived, and the switching signals are generated with SVPWM modulation block.

Figure 10 shows the trajectory of the required rectifier voltage by using the technique in Figure 9. Because the rectifier is operating in an unbalanced condition, the trajectory is not a circle but an ellipse. Because the SVPWM is applied, the modulation range is increased by 15% compared with the conventional SPWM techniques thus, without increasing the DC link voltage, the required voltage can be fully covered with a useful margin for other possible grid connection requirements such as voltage fluctuation and reactive power provision.

Parameter Design For LCL Filter and DC Capacitor A. LCL Filter Design and Size / Weight Evaluation The LCL filter, as shown in Fig 6, comprises the capacitor Cf, the grid-side inductor Lg, and the converter-side inductor Lc. Three requirements of parameters in the LCL need to be met for achieving both harmonics filtering and APF functions: 1) storage of the double-frequency power pulsation poo; 2) limitation of the converter side ripple current lc, and 3) Compliance with the grid code [42] of the grid side current lg.

The size of Cf is determined by the value of p100 and the capacitor voltage. Due to unbalanced operation, the maximum voltage of the capacitor is possibly larger than the peak value of the single-phase supply voltage.

For a fixed DC link voltage, the capacitor maximum voltage can be located at the trajectory of the AC voltage as shown in Fig. 10. To ensure linear modulation, the elliptical trajectory of the unbalanced voltage must be within the boundary of the circular trajectory of balanced voltage. If Cf is too small, the elliptical trajectory would exceed the circular boundary, resulting in non-linear modulation; if Cf is too large, the modulation index would be small, so the dc voltage utilization is compromised. As shown in Fig. 10, the SVPWM increases the inverted AC voltage by about 15% than the SPWM due to higher DC link voltage utilization, meaning smaller Cf when using SVPWM or additional voltage margin if the same Cf.

Fig. 11(a) shows the procedure to derive the required minimum C to avoid over-modulation under the premise of satisfying eqs. (18) and(19). As shown in Fig.11(b), Cf increases with the increase of the power rating. The capacitance value of Cf can be then defined by the voltage shown in Fig 10 and the power shown in Fig. 11(b).

The ripple current requirement (i.e. the requirement 2) needs the converter side inductor Lc to satisfy the limit of the current ripple required by the converter. The equation for the inductance calculation is given in [43] and shown as (23).

L > VDC (23) 6f,""aimax where fcw is the switching frequency and the Ai I the maximum ripple current allowed -*,nax.s at the converter circuit.

The grid current requirement (i.e. the requirement 3) is met by achieving the harmonics attenuation, which is calculated by using the transfer function of the LCL filter. The largest grid harmonic appears when the 14 grid is connected (see Appendix), giving the transfer function of the LCL filter for 14 connection: bar (s) G LCL bar (6 g 2 lc, "a, (s) szLgL" (3C, ) + s (La + ) Since fcw is much larger than the resonant frequency between the capacitor and inductor in the LCL filter, then s3LgL0Cf >> s(Lg-FL). Therefore, GLeL(s) can be simplified as (25) at 15: GLGL-har (s) ,s3LgLG (3C") where Vhar(s) is the harmonic voltage of the converter, and thar(s) is the harmonic current injected to the grid.

The closed-form expressions of the switching harmonic voltages are derived in [44], showing that the most significant harmonic has the frequency fcw. The magnitude of the most significant harmonic in a half-bridge is: 2 V" re V - J0 M 2V (26) Tc 2 it where Vhar is the most significant harmonic's magnitude, J is the first-order Besse! function and is always smaller than 1; M is the modulation index within [0, 1]. When M= 0, Vhar reaches its maximum value.

har VharGLCL-har (s jrasvi) ski (27) where Ltd is the maximum harmonic limit in the grid code. We apply IEEE Std 519 [42] as the grid limits in which lard =O. I rated when fcw > 35fg. (24) (25)

From (26) and(27), the minimal value of Lg is derived as: L 41/da (28) g ira'8w3c (3Cf)istd Fig.11, (23) and (28) can be used to determine Cf, Lc, and Lg respectively. The proposed technique requires larger Cf than the existing design because the value of Cf is determined by voltage modulation and energy storage given by Fig.10 andFig.11. The DC link voltage needs to be regulated at 650 V which is commonly used in OBCs and the single-phase power rating is set to be 10 kW, which covers the common 6.6 kW and 3.3 kW Level 2 and Level 1 charging standards.

The required Cf is 14.3 pF obtained from Fig.11, which is larger than 0.95 pF of the conventional method in [43]. However, (28)shows that the increase of Cf can lead to a decrease of Lg. The total volume and weight of the LCL filter need to be assessed.

Denoting KCf as the coefficient of quantifying the increase of Cf, considering Lc remains unchanged from (23), then Lg is decreased by KCf from(28). The volume and weight of the LCL filter are functions of Ku-, and can be expressed as (29) and (30) respectively: VOLTOT (K,,,)= 3 (kgf WOL, + voLL,IK" +VOLLg) (29) 1WETTOT (K,) = 3 (Kgf WET°, + WETLY/ + WETLg) (30) where VOLTor. VOLcf, VOLLg and VOL° WETTor WETcf, WE71g, and WETLG are the volume and weight of LCL filter, Cf, Lg, and Lo respectively.

In order to compare with the LCL design from [43] which was for 200 WA, the LCL filter is recalculated by using the same method in [43] to compare with the filter used in this proposed method at 10 kVA, 650 V DC link system. The LCL parameters of the conventional method at 200 kVA and 10 kVA are shown in TABLE III. For the 200 kVA system [43], Lc = 100 pH, Lg = 270 pH, Cf = 10 pF; the rated current and voltage are 240 A (rms) and 1200 V (peak). If a 30% margin is used for the inductor current and capacitor voltage, the required maximum energies stored in Lc, Lg, and Cr are EngLe= 0.5Lg (1.3x Nk x240)2 J = 9.78 J, EngLg = 0.5L0(1.3x x240)2 J = 26.4 J and Engei = 0.5C, (1.3x1200)2= 12.2 J. Their volume and weight can be evaluated with the energy density equation in (1). In [43], Lg used silicon steel inductors where Kw_ 10-6J/mm3 and Kwe-- 2* 10-4J/g, giving VOLLg = EngLal KvL= 26.4x 106 me and WElig = EngLc I KwL= 132x 103 g; Lc used nanocrystalline based inductor, and the volume is given as VOLLg = 6.78x 106 mms in [43], and WETL, = VOL, / density = 34x103 g when density ra KVL / KWL = 5.0 gicm3; Cf used film capacitors where Kvc 10-4 Jimm3, Kwc 0.1 Jig, and VOLcr = 121x103 mm3, giving WETcf = 121 g. Therefore, the total volume and weight for the system with K01= 1 can be derived as: VOLT0T(Kcf = 1) = 9.99x108 mm3; WETTor(Kcf = 1) = 4.98x105 g. From Fig. 12(a), the optimal volume can be achieved when Kcf = 15.25.

From(23), Lc remains unchanged; from (29) and (30), Lg is decreased to (270 pH / Kcf) = 17.7 pH and Cf is increased to (10 pF x Kcf) = 153 pF. From (29) and (30), the total volume and weight are VOLToT(Kcf = 15.25) = 3.11x 107 mm3 and WETTOT(Kcf = 15.25) = 1.33x 103 g, respectively. Similarly, from Fig. 13(b), the optimal weight can be achieved when KCf = 31.50. From (23), Lc remains unchanged; from (29) and (30), Lg is decreased to 270 pH / Kcf = 8.57 pH and C1 is increased to 10 pF x Kcr= 315 pF. According to (29) and (30), the total volume and weight are VOLT07(Kcf = 15.25) = 3.4x 107 mm3 and WETTor(Kcf = 15.25) = 1.3x10 g, respectively.

Table Ill

LCL parameters for the system by using a design technique in [43] S (kVA) f9 (Hz) f( Hz) Vg (V rms) Vg, (V) Lg (mH) (mH) C1 (pF) 60 20k 480 1200 0.27 0.1 10 50 50k 380 650 0.336 0.430 0.95 The total volume and weight of the LCL filter can be plotted by using (28) and (29) as illustrated in Fig. 12. It is clearly shown that the design in [43] can be improved by increasing Kcr so the total volume and weight of the LCL filter can be decreased. The optimal KCf for the total volume and weight can be calculated by setting the first d (VOLT0T) d (WETT") derivatives to be zero as 0 and _ 0. The solutions are: where Korloptimal volume dKVOL dKVOL weight respectively. 1K01 optimalvolume -VOL, (32) K0floptimal weight - VOLLg

WE

WET, (31) and Kal optimal weight are the KG/4°r the optimal volume and the optimal When (31) is met, KorVOLci =VOLLy/Kor, which means that the when Cr and Lg have the same volume, the optimal volume can be reached. Similarly, when the C1 and Lg have the same weight, (32)is met and the optimal weight can be reached. In the conventional design, both the volume and weight of Lg is much larger than Cr due to a small capacitance of Cr. However, in this proposed design, the increased capacitance Cf will enable the volume and weight of the Cr and Lg become closer to each other, thus the total volume and weight of the filter will become closer to the optimum.

For S = 10 kVA with parameters designed in [43] in the marker 4 of Fig. 12, The parameters of Lc, Lg, and C1 are 336 pH at 21.5 A, 420 pH at 21.5 A and 0.96 pF at 650 V, respectively. If a 30% margin is used for the inductor current and capacitor voltage, the currents for both Lc and Lg are 28.0 A, and the voltage for Cr is 845 V. Thus, the energy stored in Lc, Lg, and Cr are EngL, = 0.5 x 336 p x282 = 0.1311 J, Engrg = 0.5 x 336 p x282 = 0.1673 J, and Engcr = 0.5 x 0.9 p x 8452 = 0.3418 J, respectively. If both Lc and Lg use inductors with MPP cores with Kw_ rt 5x 10-7 J/mm3, and KwL 1x10-Jig as shown in Fig 1, the volume and weight are of inductors are: VOL, = 2.62x10 mm3, WE71, = 1.31x103 g, VOLLg = 3.34x 105 mm3, WETrg = 1.67x 103 g. For C1, Kvc = 1x 10-4 J/mm3, Kwc = 0.1 J/g, Eng = 0.5CV2 = 0.3418 J, therefore, VOLcr= Eng/Kvc = 3.42x 103 mm3, and WETcr = 3.42 g. To verify the designed effectiveness of the designed value, TABEL IVis added to compare the weight and volume between the designed parameters and the commercialized devices. The evaluated volume and weight are 1.8)005 mm3 and 8.95x103 g; the volume and weight of actual commercialized components are 1.8x106 mm3 and 8.95x103 g. The differences between evaluation and actual devices are small and show that the evaluation is valid. Table IV also shows that the differences come from two aspects: 1) the parameters of the standardized devices cannot match exactly compared with the designed parameters; 2) (1)-(2) are empirical equations, and the precision is limited. It should be noted that the differences in the volume of Cr and weight between evaluation and actual device are more significant than the differences in the comparison on Lg/Lc.

TABLE IV

Volume / Weight Comparison between Designed Value and System with Commercialized Devices of the LCL filter for the Conventional OBC with Kcf= 1.

(1) 7443763540470 is the inductor from Wurth Electronics Inc, and its volume/weight is 51660 mm' / 224.0g.

(2) MK1,1648510094K2 is the film capacitor from Vishay, and its volume/weight is 5472 mrns / 6g.

(3) Energy capacity equals 0.5LI2 for inductors and 0.5C1/2 for capacitors. For examples, the energy capacity for Lc with designed parameters is 0.5 x 336 pH x (28 A)" = 0.1311 J; the energy capacity for 13 with selected devices is 0.5. (47 pH x 7) . (31 A)" = 0.1581 Lc Designed Selected devices Energy capacity (J) Evaluated volume Evaluated weight (g) (5' Actual Actual weight LE, parameters (4) volume (9) Cf (mm') Designed Selected devices Designed Selected Designed Selected device parameters parameters devices parameters 336 pH @ 7443763540470,', 0.1310 0.1581 2.62.105 3.16.105 1310 1720 3.62.105 1568 28 A x7 0.1673 0.2033 3.35.105 4.06.105 1670 2202 4.65.105 2016 430 pH @ (329 pH, 31 A) 0.3418 0.4050 3418 4050 3.4 4.1 5472 6.0 28A 7443763540470 x 9 0.9 pF @ (423 pH, 31 A) MKP1848510094K2 '2) (1 pF. 900V) 845V J. (4) Eq. (1) shows that VOL = energy capacity / Kv,; eq. (2) shows that VOL° = energy capacity! Kvc Kw.'- dime and ((cc = Xi04.11mm' can be extracted from Fig. 3.

(5) Eq. K)a lx 104 J/g and Kw° = 0.1 J/g are From Fig. 3 to evaluate the weight.

Fig. 12 clearly shows that volume and weight can be decreased with increased KD/. The LCL filter reaches the optimal volume and weight when Kcf = 10.28 and 22.93 respectively. If Cf is set as 16 pF in this proposed method, then Kcf = 16.67, VOLTor = 1.02x106 mrnsand WETTor = 4406 g, which are closer to the optimum. The volume and weight of the LCL filter with K01 = 16.67 (the marker 7 in Fig. 12) can be reduced by 76.47% and 103.4% respectively compared to the conventional design with Kcf = 1 (the marker 4 in Fig. 12).

Parameter Design for the DC-Link Capacitor For the conventional it rectifier, the capacitance required to smooth the 100 Hz power pulsation is given as [45]: Cdc > Pdc dc (33) ( 1 \ CD V AV (2 (,) g,V" -AVdc dc dc The proposed APF technique can eliminate the double-line frequency power pulsation.

Therefore, the switching harmonics determine the DC capacitance.

The closed-form expressions of the switching harmonic voltages in [44] show that the most significant harmonics locates at the switching frequency fsw. The magnitude of the most significant harmonic is: = 2 V" j 77 n; 2 V" (34) v sw x ° , 2, 7r where Jo is the Bessel function of the first kind, and M is the modulation index. When M = 0, Vsw reaches its maximum value.

If the AC output voltage and current are: vsw(t) = Vansin(cuswt+es",") and i5(t) = /swsin(cuswt-Fes,#), where es. and El.; are the initial phase of v3(t) and isw(t). The instantaneous power at the AC output is p(t) = (V gsin(cogt) + V swsin(c,o swt+61sw")) x (I gsi n(cugt) + I swsin(wsvvt+esw,)). Because ls,, needs to be smaller than 4% of the grid current Ig to comply with the grid code [42], it can be neglected. Therefore, the expression of Psw(t) and its magnitude Psw are: ps,, (t)....-)Vs,,,c si n (co gt) si n (co swt + (35) Psw = -2 Vs",/g Because the semiconductors do not store energy, Psw also donates the magnitude of the instantaneous power at the DC link. The Pswfor an unbalanced 3-4) converter is three times smaller than that in a half-bridge. The required capacitance needs to meet: 6Psw C" > (36) 11 cos,"V"A Vdc 03swIldc ',AVcIc Fig. 13 shows the comparison of the required DC capacitance for the Psw at switching frequency and for the moo at the double-line frequency. The Cds for P sw is significantly smaller than the Cds for pica, especially for the applications with a large &mi. Because the proposed technique only needs Cdc for Psw, the size and volume can be greatly reduced. For f5 = 50 kHz, Cds 6.1 pF, and a 10 pF capacitor is used for Cds.

Simulations and Experimental Results Simulations The proposed circuit is shown in Fig. 6, and the parameters are shown in TABLE V. Fig. 14 and Fig. 15 shows the simulation results of the rectifier fed by 1-4) supply at 3 kW and 3-4) supply at 10 kW respectively. The proposed OBC will have two connectors, single (regulated by BS13363) and three-phase (regulated by IEC 62196), for users to select. Once the corresponding plug has been connected, the OBC will work accordingly for that connection, either single-or three-phase. It is obvious that the charging voltage remains the same during each charging event, either single or three phases for each charging event thus there is no need of dynamic switching between single and three phases within one charging event. However, the additional three-phase charging opportunity offered by the technology discussed here will benefit motorists by using three-phase charging facility for three times higher charging rate by using the one single and three phases compatible OBC.

Fig. 14 shows that both the DC link voltage and the AC line current were smooth when connected with a 3-4) grid. The performance of the rectifier with a small DC capacitor and without using the APE was firstly assessed to highlight the significance of the distortion caused by the double-line power pulsation. When connected with a 1-4) grid using the conventional single-phase converter (the H-bridge circuit with the LCL filter inTABLE V, 10 pF dc capacitor, and the SPWM modulation technique) for the rated 3 kW operation, as shown in Fig. 15(a), both the DC voltage and the AC current were greatly distorted due to the 100 Hz power pulsation. The voltage ripple was 780.7 V which was more than the nominal DC voltage of 650 V, and the maximum value reached 95.1 V. The grid current was also significantly distorted because of the DC voltage ripple. Because the voltage and current stress were significantly higher than the nominal voltage and current and the magnitude of the over current and voltage depend on the power, it is impractical to verify the results with experiment at the rated power if using the same rating of the devices in the rectifier. Instead, a scaled-down test set-up with Vg= 120 V and Pg= 300 W was conducted experimentally thus a 300 W simulation as shown in Fig 14 (b) was also presented for comparison. If the proposed technique was applied, the DC link voltage ripple was greatly reduced from (995.1 -214.4) V = 780.7 V in Fig. 15(a) to 11.7 V in Fig. 16 with the same DC capacitance Cdo = 10 pF.

TABLE I

Circuit Parameters grid voltage Vg grid frequency fg grid side inductor Lg converter side inductor L, LCL capacitor Cf dc-link capacitor Cdc dc-link voltage Vac output power Ps switching frequency fsw 230 V (RMS, 1-4)) 400 V (RMS, 3-4)) Hz pH 350 pH 16 pF pF 650 V 3 kW (1-ph) kW (3-ph) kHz It worth noting that, for the conventional technique with the bulk DC capacitor bank, Cc is calculated by using(33). To achieve AVdg = 11.7 V, Cdc = 3000 / (314x650x 11.7) F = 1.13 mF; in comparison, to achieve AV& = 11.7 V, simulation with the proposed APF technique uses Cdc = 10 pF as shown inTABLE IV. Therefore, the proposed APF only requires less than 1% DC capacitance of the DC capacitor required in the conventional bulk DC capacitor bank technique, which leads to a significant reduction of the volume of the rectifier and the OBC.

Experiments The experiment test set-up was shown in Fig. 17(a). The comparison between Fig. 17(b) and (c) showed that the size reduction of the DC link capacitor is significant. The significant reduction of the DC capacitance allowed using the film capacitors at the DC link, which improved the reliability and lifetime of the OBC due to higher robustness of the film capacitor than its electrolytic counterpart.

Fig. 18, 19 and 20 showed the experiments with the proposed APF technique at 300W, 500W, and 3 kW rated power respectively. The waveforms in Fig. 18(a), 19(a) and 20(a) showed that the DC link voltage was smooth, and the grid current was sinusoidal with acceptable small distortion; the dc ripple spectrum in Fig. 18(b), 19(b) and 20(b) showed that the 100 Hz voltage pulsations were small at various load condition; the grid current spectrum showed that at various load condition, the grid current could satisfy the IEEE 519 requirements. The experimental results matched the simulations shown in Fig. 16 well. Fig. 21 showed that the proposed technique can limit the magnitude of the 100 Hz voltage ripple with the various loads to less than 1.5% of the DC voltage (650V) from 300 W to 3000 W. Fig. 22 showed the efficiency comparison between the proposed technique with 10 pF dc capacitor and the conventional single-phase converter (the H-bridge circuit with the LCL filter in TABLE V. and the SPWM modulation technique) with 1.3 mF dc capacitors.

The efficiency of the proposed technique decreased because of the extra APF (the third leg) consumed power, and the peak efficiency was 97.6% at 3000 W. Fig. 23(a) and Fig. 24(a) showed that the conventional 11 converter (which is a H-Bridge with the LCL filter) with 10 pF dc capacitance suffered great distortion from both the DC link voltage and the grid current. When operating at 500W, the experiment of non-APF was conducted with reduced Vg (120 V) and Vdc (325 V) to avoid the over voltage! current failure caused by power pulsation. Fig. 23(b) and Fig. 24(b) shows that the 100 Hz ripple was 49.97% (324.8 V) and 84.89% (275.8 V) respectively. The experiment matched the simulations shown in Fig. 15(b) as well.

Conclusion

We have discussed a voltage source converter which is compatible with both a 14 and 31 grid. The circuit is based on a 31 converter, but the control stratagem and the LCL filter are redesigned to address the issue of the power pulsation at double-line the grid frequency. When connected with a 14 grid, the power pulsation at double-line the grid frequency is diverted and stored into the LCL filter by utilizing the third leg of the rectifier circuit. Therefore, neither extra active switches nor passive components are required. The advantages of the proposed technology can be summarized as below: 1. Good compatibility: the charger can work with both 34 and 14 grids without changing the topology. When connected with a 14 grid, the third leg is used and no extra active switches are required.

2. Simple circuit: Cf in the LCL filter is utilized to store the pulsating power. Lg and Lc are utilized to damping the ripple current. Therefore, no extra passive components are required.

3. LCL filter's size/volume reduction: Although the Cf of the LCL filter is increased to store the pulsating power, the total volume and weight of the LCL filter can be reduced by 76.47% and 103.4% due to the reduction of the Lg.

4. DC-link capacitance reduction: The DC-link capacitance can be reduced by 130 times at the same switching frequency of the rectifier compared with the conventional DC capacitor storage techniques as mentioned in the experimental section.

5. Unified equations for size evaluation: the unified equations are obtained to identify the optimal circuit for AC/DC APFs with capacitors/inductors as energy storage devices and can be used to optimize the size/weight of the LCL filter.

6. High dc-voltage utilization: when connected with a 14 grid, the system operates in an unbalanced 34 condition. Therefore, the advantages of the 34 system can be utilized to increase the DC voltage utilization by 15% and increase the utilization of the LCL capacitor by three times because of applying the SVPWM and Y/A transformation provided by the three-phase systems.

Appendix Grid Harmonic Current With 1-4) Grid When operating with under 14 voltage, the circuit is as shown in Fig. 25, which is a 4-node network. Write the nodal equations in the matrix format as follows: Vcvla _vcIrtc _ where Y is the bus admittance matrix, and its value is: Y = +(0.5K, + + Ycf YCf -(0.5Ka + Y01) YLg YCT ± (0 5Kg YCf YCf VC/ YCf YLc F \i/Cf F \f/Cf where Kg, YLe, and Ycf are the admittance of Lg, Lg, and Cf respectively. YLt

Because Ig = (V, -1/4)/(2SLy), Ig can be derived in the matrix format as: 1 1 (37) 2sLg [1 1 0] = 2sLg [1 1 0]17-1Y, l/2, and can be simplified as:

_ Vo,de Ig -

ssLgL, (3C, + s (Lg +L) Because the most significant harmonic is Vhar, and VcvtaSKar, Vcvib'SVhar. The maximum value of Ig is as (38), c-har szcLe (3C,)+ s(L, +L) Define GLamar as the maximum harmonic transfer function, then, GLoL bar vc,,,t_har s3L,Lc(3C,)+ s(Lg + Lc) (38) (39) With a balanced 3-4) system, G _Lcc_ha, s3L9L0 (3C,)+ s (Lg + Le) scenario for Ig harmonics happens when connected to a 1-0 grid.

Therefore, the worst Eq. (37) shows that V0 has no contribution to lg. To analyse the reason, the superposition theory is applied. Thus, all the voltage sources except l/cc are shorted as shown inFig. 26. It is seen that Node 1 and Node 2 are in the equal voltage potential points of a balanced Wheatstone bridge when the only vc,40 is applied. Therefore, lc, is independent of Vow, Although the present invention has been described hereinabove with reference to specific embodiments, the present invention is not limited to the specific embodiments and modifications will be apparent to a skilled person in the art which lie within the scope of the claims. Any of the embodiments described hereinabove can be used in any combination with one or more of the other embodiments.

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Claims

CLAIMS: 1. A charger for charging an electrical energy storage device, comprising: first, second and third AC inputs for receiving up to three respective phases of AC voltages from an AC source; first, second and third LCL filters connected to each of the respective first, second and third AC inputs; and a three-phase rectifier having first; second and third legs, each of the first, second and third legs connected to respective ones of the LCL filters, the rectifier for rectifying the up to three phase AC source voltages; and a controller connected to the three-phase rectifier to control the three-phase rectifier to produce a DC output voltage from an AC input voltage, the charger having a single-phase mode of operation in which a single-phase AC source is connected between the first and second AC inputs and the controller controls the first, second and third legs of the three-phase rectifier to generate a DC output.
2. A charger according to claim 1, wherein the charger has a three-phase mode of operation in which each respective phase of a three-phase AC source is connected to the respective first, second and third AC inputs, and the controller controls each of the first, second and third legs of the three-phase rectifier to generate a DC output.
3. A charger according to claim 1 or 2, wherein each of the LCL filters comprises a grid-side inductor connected to the respective AC input, a converter side inductor connected in series between the grid-side inductor and a respective one of the legs of the rectifier, and a filter capacitor between the grid-side inductor and converter-side inductor.
4. A charger according to claim 3, wherein the filter capacitor of the first LCL filter is connected between the grid-side inductor and the converter-side inductor of the first and second LCL filters, the filter capacitor of the second LCL filter is connected between the grid-side inductor and the converter-side inductor of the second and third LCL filters, and the filter capacitor of the third LCL filter is connected between the grid-side inductor and the converter-side inductor of the third and first LCL filters.
5. A charger according to any preceding claim, wherein, in the single-phase mode, the rectifier operates as an unbalanced rectifier.
6. A charger according to any preceding claim, wherein, in the single-phase mode, the rectifier is driven by a Sinusoidal Pulse Width Modulation (SPWM) scheme or a Space Vector Pulse Width Modulation (SVPWM) scheme.
7. A charger according to any preceding claim, wherein, in the single-phase mode, the third leg of the rectifier is controlled to control the power flow resulting from a double-line frequency power pulsation by diverting the power flow into the LCL filter.
8. A charger according to any preceding claim, wherein, in the single-phase mode, the LCL filters are configured to attenuate harmonic current.
9. A charger according to any preceding claim, wherein, in the single-phase mode, the LCL filters are configured to store energy from a double-line frequency power pulsation
10. A charger according to any preceding claim, wherein the charger is an on-board charger for an electric vehicle.
11. A charger according to any preceding claim, wherein the AC source is a grid voltage.