Distributed Generation Using Indirect Matrix Converter ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 3, MARCH 2013

Distributed Generation Using Indirect Matrix Converter in Reverse Power Mode Xiong Liu, Student Member, IEEE, Poh Chiang Loh, Senior Member, IEEE, Peng Wang, Member, IEEE, Frede Blaabjerg, Fellow, IEEE, Yi Tang, Student Member, IEEE, and Essam A. Al-Ammar, Member, IEEE

Abstract—Indirect matrix converter (IMC) is an alternative for ac/ac energy conversion, usually operated with a voltage steppeddown gain of only 0.866. For applications like distribution generation where voltage-boost functionality is required, the traditional style of operating the IMC is therefore not appropriate. Like most power converters, the operation of the IMC can surely be reversed to produce a boosted gain, but so far its relevant control principles have not been discussed. These challenges are now addressed in this paper with distributed generation suggested as a potential application. Simulation and experimental results for validating various performance aspects of the proposed control schemes can be found in a later section of this paper. Index Terms—Grid-connection, indirect matrix converter, islanded operation, voltage-boost functionality.

I. INTRODUCTION C/AC energy conversion can commonly be found in traditional industry applications like adjustable speed motor drives, power quality conditioners, and many others. Most recent demand for ac/ac energy conversion would likely be distributed generation (DG), where a sizable number of decentralized sources need to be tied to the utility distribution grid. Common examples include wind energy conversion systems (WECS), diesel generators, and microturbines. The direct connection of these sources to the distribution grid is usually not possible because of mismatches in amplitude and/or frequency (usually variable for the sources, but fixed for the grid). Proper ac/ac power electronic converters are thus needed for interfacing the sources to the grid. For that purpose, two commonly investigated alternatives are the back-to-back (B2B) converter [1]–[4] and matrix converter [5]–[21]. The usual concern quoted with the B2B converter is its large dc-link electrolytic capacitor being a common

A

Manuscript received August 4, 2011; revised February 29, 2012; accepted July 2, 2012. Date of current version October 12, 2012. Recommended for publication by Associate Editor J. W. Kolar. X. Liu and P. Wang are with the School of Electrical and Electronic Engineering, Energy Research Institute@NTU, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]; [email protected]). P. C. Loh and Y. Tang are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]; [email protected]). F. Blaabjerg is with the Department of Energy Technology, Aalborg University, Aalborg East 9220, Denmark (e-mail: [email protected]). E. A. Al-Ammar is with the Department of Electrical Engineering, King Saud University, Riyadh 11411, Saudi Arabia (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2012.2209205

cause of premature failure, even though it has high energy density and is relatively low in price. To extend the lifetime of the converter, a foil capacitor can be used instead, especially if the intention is to provide filtering rather than to store enough energy for temporary ride-through. Regardless of the type used though, including the dc capacitor would demand for an additional sensor and control scheme for regulating its voltage so as to avoid damages caused by overvoltages and to compensate for lower frequency ripples if smaller capacitance is used. It is therefore tempting to remove the dc capacitor, which after all is the main attractiveness of the “all-semiconductor” matrix converter. In its earliest form, matrix converter is usually drawn like a 3 × 3 matrix with a total of nine bidirectional or eighteen unidirectional switches. Such arrangement provides full bidirectional power flow flexibility, which might not be useful for DG, where power is flowing from the sources to the distribution grid. Topological modifications to allow for only unidirectional power flow might therefore be of interest since they usually lead to the reduction of semiconductor switches. The reduction is however not possible with the 3 × 3 matrix converter, whose input and output functionalities are closely merged. Attention is therefore directed at the indirect matrix converter (IMC) [14]–[20], which is still a bidirectional converter if the same 18 unidirectional switches are used. The IMC can however be simplified for unidirectional power flow using lesser switches. The resulting converters are renamed as sparse matrix converters (SMCs), which in its simplest form uses only nine switches for transferring power from the high to low voltage port ([17], [18], subsequently also introduced in [15]). It is thus a step-down converter like most other matrix converters have been operated so far. In some senses, SMCs and IMC can also be viewed as similar to the B2B converter because of their common rectifier-to-inverter arrangement. Rectifier and inverter of the SMCs and IMC are however of complementary types with the rectifier always of the current-source (CS) type and inverter always of the voltage-source (VS) type. Both converters are joined at their common fictitious dc-link without any passive components, and hence leading to a more compact design with a longer lifespan. Other advantages shared by the SMCs include sinusoidal input and output waveforms, and smoother commutation at zero dc-link current [16]. The common voltage gain of IMC and SMCs is however still restricted to a maximum of 0.866, which is certainly not suitable for DG whose source voltages are usually lower than the grid voltage. In spite of this, there are still some discussions about using a matrix converter (as a buck converter) for grid-interfacing [20], [21]. Those would probably work after

0885-8993/$31.00 © 2012 IEEE

LIU et al.: DISTRIBUTED GENERATION USING INDIRECT MATRIX CONVERTER IN REVERSE POWER MODE

Fig. 1.

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Topology of proposed matrix converter in reverse power mode.

taking precautionary steps to raise the source voltages, which so far has not been explicitly mentioned in those references. If modifying the sources is not intended or possible, a recent recommendation is to add a Z-source LC network to the fictitious dc-link of an IMC or SMC [22]–[24]. The resulting converter has voltage-boost ability, but can no longer be viewed as “allsemiconductor.” To avoid adding passive components, an alternative recommendation is discussed here for boosting voltage. Like most power converters, power flowing through a 3 × 3 matrix converter or IMC can be reversed, as mentioned in [25], whose focus is more on developing an appropriate modulation scheme. For an IMC, if forward flowing is not required, its topology can further be simplified with lesser switches used. Power flow is then permanently reversed. Note that for the SMCs, the same thought is applied, but power flow is restricted to the forward direction, which is not suitable for DG application. Relevant details on how to control the reversed matrix converter for DG have also not been discussed, even though the required schemes are likely to be more involved than simply reversing the power flow of a dc/dc or dc/ac converter. These challenges are now scoped for investigation here in both grid-connected and islanded modes. Proper operation of the proposed converter and control schemes has already been validated in simulation and experiment using a 1-kW prototype.

II. TOPOLOGY AND MODULATION A. Topology Fig. 1 shows the studied DG system, where a unidirectional IMC with 12 switches is explicitly shown. Six of the switches have antiparallel diodes, and are arranged as a front-end VS rectifier (VSR). The other six switches must either be of the reverse-blocking type or have series diodes for forming a rearend CS inverter (CSI). A clamping circuit inclusive of a diode in series with a small foil capacitor is also shown connected to the fictitious dc link. As its name implies, this clamping circuit helps to clamp the dc voltage as a mean of protecting the converter. During normal operation, it is always “deactivated” since its capacitor voltage is always slightly higher than the dc-

link voltage, hence reverse-biasing the series diode in turn. The resulting converter shown in Fig. 1 always has its power flow directed from the VS to CS terminals, which rightfully is the reverse direction of a traditional matrix converter. The reversal is justifiable since DG usually demands for voltage boosting of its sources with power flowing from them to the grid or local loads only. VS and CS terminals of the converter should, therefore, be connect to the three-phase ac source and grid or local loads, respectively, as demonstrated in Fig. 1. B. Modulation of CSI [6], [14]–[19], [30] CSI is normally operated with one upper and one lower switch ON at all instants. If the ON switches are from different phaselegs, an active state is formed with power transferred to the grid or load. In response, line voltage across two output filter capacitors Cf would appear across the fictitious dc link. Its value is approximately equal to the grid or load voltage vxy (x and y = R, Y, or W, but x = y), if voltage drop across the filter inductor Lf is negligible. In contrast, if the ON switches are from the same phase-leg, a null state is formed with the fictitious dc-link voltage shorted to zero. Current hence circulates within the IMC, instead of flowing to the grid or load. In total, six active and three null states can be formed with their corresponding ON switches and placements on the vector plane shown in Fig. 2(a). The figure also includes a reference current phasor drawn in sextant 1 as an example. The nearest vectors chosen for reproducing the reference would then be SC1 and SC6. Note that unlike normal CS modulation [26], [27], no null state is used here since there is a more efficient alternative to replace it with the same input and output responses produced. To demonstrate that the input line voltages and output currents of the IMC are first noted to be zero when in a CS null state regardless of the VS state. The same responses can be produced by turning ON either the upper or lower three switches of the VSR to form a VS null state [28]. Comparing both options, the VS null state is more attractive since it leads to zero dclink current, and hence no losses in the inverter. All three CS null states are hence not recommended, leaving only SC1 and SC6 in sextant 1 for inverter modulation. These active states cause switch SR to turn ON for the full switching period, hence

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Fig. 3. cycle. Fig. 2.

Normalized local average value of dc-link voltage over a fundamental

Space vector representations of (a) CSI and (b) VSR.

follows: clamping phase R to the upper dc rail. Distinction between the states is introduced by modulating the lower switches (SY and SW ) so that the other two phases are alternately connected to the lower dc rail. Line voltages appearing across the fictitious dc link would then be vR Y and vR W . The same interpretation can be applied to the other five sextants with only a small difference observed for the even sextants. Instead of positive rail clamping, even sextants clamp one phase to the lower dc-rail with the other two modulated to the upper dc rail in accordance to their computed duty ratios. Returning to the example in sextant 1, the corresponding active duty ratios (do1 and do2 ) for the CSI can be determined by first assuming the following three-phase current references (i∗R , i∗Y , and i∗W ): i∗R = Iom cos θR θ R = ωo t

i∗Y = Iom cos θY

θY = θR − 2π/3

i∗W = Iom cos θW

θW = θR + 2π/3

(1)

where Iom is their common amplitude, and θR , θY , and θW are their respective phase angles. Noting next that the sum of threephase currents is zero, do1 and do2 can eventually be determined as follows: cos θR + cos θY + cos θW = 0, − do1 = − cos θY /cos θR

cos θY cos θW − =1 cos θR cos θR

do2 = − cos θW /cos θR . (2)

Equation (2), when multiplied by their associated output line voltages (vR Y and vR W ), gives the average dc-link voltage in (3) with Vom and φo representing the phase voltage amplitude and output power factor angle, respectively. In order to guarantee that the fictitious dc-link voltage vR Y and vR W are no less than zero, the output power factor angle φo should be within the range from −π/6 to π/6 [29] 3Vom 2 cos θR π π · cos φo , − ≤ θR ≤ . 6 6

Vdc(av ) = do1 vR Y + do2 vR W =

(3)

The same mathematical procedure can be applied to the other five sextants with their obtained equations generalized as

Vdc(av ) =

3Vom Iom · cos φo , 2|im ax |

for positive rail clamping

Vdc(av ) =

3Vom Iom · cos φo , 2|im in |

for negative rail clamping (4)

where im ax = maxim ax = max(i∗R , i∗Y , i∗W ), and im in = min(i∗R , i∗Y , i∗W ). Equation (4) clearly states that the fictitious dc-link voltage is time varying with its normalized local average value over a fundamental period shown in Fig. 3 for unity power factor (φo = 0). The observed sixth-order ripple must properly be compensated when modulating the VSR so as to produce sinusoidal waveforms. C. Modulation of VSR [6], [14], [16] Being a normal six-switch bridge, the VSR can be modulated by a standard carrier based [6], [14], [16] or the space vector modulator [15], [17]–[19] after compensating for the varying dc-link voltage expressed as (4). The resulting state sequence must have VS null states for boosting voltage since they are more efficient than CS null states [28], as explained earlier. VS null states are in fact the only null type recommended here, and are introduced by turning ON either all upper (SA, SB, SC) or all lower switches (SA , SB , and SC ) of the VSR. That means for a carrier-based modulator, amplitude of the modulating references must be lower than the triangular carrier peak if both active and null states are to be produced within each carrier period. Fig. 2(b) shows all active and null states that a VSR can produce, and a reference phasor whose amplitude is determined by a suitably designed closed-loop controller. Details of the controller are presented in the next section. Besides lower than the carrier peak, amplitude of the references must be normalized to compensate for the average fictitious dc-link variation before sinusoidal input and output currents can be produced. Assuming that the three-phase references before normalization are represented by vA , vB , and vC , the eventual modulating reference dA for phase A is written as follows for illustration: dA =

Vm · cos(ωi t + θA ) + Voff vA + Voff = Vdc(av ) /2 Vdc(av ) /2

Voff = −0.5(max(vA , vB , vC ) + min(vA , vB , vC ))

(5)


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III. CONTROL ALGORITHMS FOR DG APPLICATIONS Steady-state sinusoidal input/output waveforms of the matrix converter are guaranteed by the discussed modulation scheme, which alone is insufficient for DG application. Suitable higher level control schemes must be designed for both grid-connected and islanded modes, while operating the converter permanently in the reverse power mode. Relevant control objectives are now defined and compared with those of a B2B ac/dc/ac converter, before realization details are discussed.

A. Control Objectives

Fig. 4.

Coordination of CSI and VSR modulations.

where Vm , ωi , and θA are the amplitude, angular frequency, and phase angle of vA , and Voff is the triple offset commonly added to gain a 15% increase in modulation index [30]. The fictitious dc-link current Idc(av ) can then be computed using (5) and the three-phase input currents. Because of (5), the resulting dc current would vary in inverse proportion to Vdc(av ) , which when applied to the example in Fig. 2(a) leads to Idc(av ) = Idc cos θR in sextant 1, where Idc is the amplitude. This dc-link current, when used to compute the output currents (iR , iY , and iW ), results in (6), which are clearly three-phase sinusoids, as demanded iR = Idc(av ) = −(iY + iW ) ∝ cos θR iY = do1 × Idc(av ) ∝ cos θY iW = do2 × Idc(av ) ∝ cos θW .

(6)

Another observation noted with the modulation is the presence of two instantaneous dc-link voltage values per switching cycle. This requires some forms of coordination between CS and VS modulations to avoid volt–sec error. More precisely, the requirement is to have a full VS state sequence for each dc-link voltage value. This can be done by comparing a standard triangular carrier with do1 from (2) for the CSI [14], [16], as demonstrated at the top of Fig. 4. It helps to divide period Ts into two expressed as do1 Ts and do2 Ts , within which the two dc-link voltages would, respectively, prevail. To next insert a full VS state sequence per subperiod, the rising and falling edges of the second triangular carrier used for VS modulation must occupy the two subperiods fully, as demonstrated at the bottom of Fig. 4. The variable-gradient carrier when compared with the VS references then leads to the full VS sequence of N1 ↔ A1 ↔ A2 ↔ N0 per subperiod. Here, A1 and A2 represent the two nearest active states, and N1 and N0 represent the redundant null states placed at the start and end of each carrier edge. This placement of nulls has the advantage of introducing zero current switching to the CSI, hence solving commutation problems commonly faced by the matrix converter.

Both B2B and matrix converters use a rectifier and an inverter for performing ac energy conversion. Besides semiconductor, the only difference noted between them is the presence of a dc-link capacitor in the B2B topology. The capacitor helps to decouple the rectifier and inverter, hence allowing them to operate separately for different control objectives [1]–[4]. For grid interfacing, it is presently well accepted that the grid inverter of the B2B converter should be controlled to keep the dc-link voltage constant, while the source rectifier should be controlled to track the dispatch power. When islanded, the inverter should switch to high-quality voltage regulation, while the rectifier should regulate the dc-link voltage. In both modes, powers transferred through the rectifier and inverter need not be balanced instantaneously since any mismatch can flow through the dc-link capacitor to charge or discharge it. Reactive power regulation also remains separately controlled for the rectifier and inverter in both modes of operation. The control objectives described earlier are however not fully applicable to the proposed matrix converter since it does not have a dc-link capacitor, and hence does not need any dc-link voltage regulation. Instantaneous active powers at the input and output of the converter are also always balanced, meaning that only one of them needs to be regulated for dispatch tracking in the grid connected mode. Reactive power regulation remains separated for the input and output ports, but there is a constraint to note, as explained in the following section. When transferred to the islanded mode, supplying of high-quality system voltage remains the control objective, but with no requirement to balance the dc-link voltage, which is no longer a control state variable.

B. Realization of Grid-Connected Control As defined earlier, the single objective in grid-connected mode is to track the dispatch power. Control diagram for realizing it is shown in Fig. 5, where current command Iref is obtained by dividing the demanded kilovoltampere command with the source rms voltage. Three-phase ac command i∗A B C is then obtained by multiplying Iref with cos θA B C , where θA B C = (ωt + φi , ωt − 2π/3 + φi , ωt + 2π/3 + φi ) and φi is the input power factor angle synchronized to the source voltage. For unity power factor operation, φi is set to zero. The computed current reference is subsequently tracked by the measured source current by feeding their error to a proportional-resonant (PR) controller, whose transfer function is written as [31], [32]

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Fig. 5.


Control of the matrix converter in grid-connected mode.

Fig. 6.

follows: ki s Gpr (s) = kp + 2 s + 10s + ωi2

(7)

where kp and ki are the controller gains. Equation (7) is implemented in the stationary frame with its resonance frequency set as the input frequency ωi to provide a high gain there for forcing the tracking error to zero. Alternatively, if the power or d–q current commands are given, the synchronous-frame proportional-integral (PI) controller can be used instead, whose effects are the same as the PR controller [31], [32]. The controller output is fed to a negative unity gain for signifying the reversal of power before sent to the modulator explained in Section II-C. Controlling the VSR in this way ensures that the dispatch power flows to the fictitious dc link, and then to the grid since there is not any passive component for storing it. A feedback controller for regulating the dc-link voltage is thus not needed with power channeled to the grid automatically so long as the CSI is properly modulated, as described in Section II-B. Reactive power to the grid can also be adjusted by setting the power factor angle φo appropriately. Caution must however be taken to ensure that the increase in φo is not excessive since it leads to a reduction in dc-link voltage according to (4). In theory, its allowed range is only from −π/6 to π/6.

Control of the matrix converter in islanded mode.

neously send to the loads since storage is absent in the converter. It must subsequently be multiplied by cosθA B C to form the reference currents i∗A B C to be tracked by the source inductive current iA B C . The corresponding current error (i∗A B C − iA B C ) is fed to a PR controller, whose output is inverted by a negative gain to signify reverse power flow before feeding to the VSR modulator. At the CSI, modulation is again performed by calculating the duty ratios in accordance to (2). Current references used for computing these ratios are likely not in phase with the output voltages because of the inductive nature of most loads. They should lag the output voltages by a demanded power factor angle. IV. COMPARISON WITH OTHER TOPOLOGIES A three-phase ac/ac converter with input-to-output voltage boost can be realized by the B2B converter, Z-source matrix converter (ZMC), and proposed matrix converter in reverse power mode (RMC). Brief mentioning about their similarities and differences has already been given in Sections I and III. This section continues with the discussion by stating some of their basic component requirements before viewing at functionalities achievable by them. Recommendation and precautions to note while using the RMC as a DG converter then follow. A. Basic Component Requirements

C. Realization of Islanded Control Islanded mode of operation requires the matrix converter to output a set of high-quality three-phase voltages regardless of the amount of loading. That simply means keeping the voltage magnitude constant since sinusoidal input and output waveforms are already guaranteed by the converter modulation. The overall control scheme proposed is therefore in accordance to Fig. 6 with the load voltages (vR , vY , vW ) measured and their common amplitude Vom extracted by applying the following equations: 1 2 vY − v W √ vX = √ vR + √ vY = = vR − 90◦ 3 3 3 2 . Vom = vR2 + vX

(8)

∗ and then passing their Subtracting Vom from its reference Vom error through a PI controller lead to an inner current reference amplitude to be tracked by the VSR. This reference represents the amount of power that the source must supply and instanta-

The intention of this section is to view through the topological layouts of the three converters, and then list down some of their basic component requirements. Ratings considered for the converters are given in per unit (p.u.) with their common bases chosen as the grid nominal rms voltage and source nominal rms current. Beginning with the B2B converter shown in Fig. 7, 12 switches with antiparallel diodes can explicitly be seen. These switches are arranged as a six-switch VSR and a six-switch VS inverter (VSI). Between them is a dc-link capacitor, whose √ theoretical minimum voltage is expressed as Vdc -B2B = 2 2/1.15 = 2.45 p.u. (safety margins are usually added in practice). Voltage rating of all switches must thus be higher than this value. Current ratings of the switches are however different with those for the VSR rated higher than 1 p.u., and those for the VSI higher than 1/k p.u. The term k represents the input-to-output voltage gain, which is usually larger than 1 for grid interfacing. Implementing the B2B control is also comparatively more involved with sensing required for all voltages and currents on both sides of the converter. Moreover, with a


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TABLE I BRIEF COMPARISON OF THREE TOPOLOGIES FOR DG

Fig. 7.

Topology of the back-to-back converter.

Fig. 8.

Topology of the Z-source matrix converter.

dc-link capacitor, its voltage must be measured for regulation to avoid overvoltages. The number of sensors required is thus five for voltages and four for currents.1 Considering next the ZMC shown in Fig. 8, a Z-source LC network is explicitly shown added to the fictitious dc link of a traditional nine-switch SMC oriented in the direction of forward power flow. Although boost functionality is added, the ZMC with its usually more costly passive components is strictly not “all-semiconductor.” According to [22], voltage rating of its Z-source capacitor must also be higher than 2.45 × (1−dS T )/m p.u., while its VSI switch rating must be higher than 2.45/m p.u. The terms dS T and m here represent the shoot-through duty ratio and modulation index of the VSI, which must, respectively, be smaller than 0.5 and (1 − dS T ). Different from the VSI though, voltage rating of the CS rectifier (CSR) switches must be higher than the peak line voltage of the source expressed as 2.45/k. Current ratings of the switches on the source and grid sides can also be determined as higher than 1 p.u. and 1/k p.u., respectively. Control implementation wise, three-phase source and grid voltages, three-phase grid currents, voltage across the Z-source capacitor, and current through the Z-source inductor must be measured for adjusting dS T and m appropriately. The number of sensors required is thus five for voltages and three for currents.1 Unlike the earlier two, the proposed RMC shown in Fig. 1 uses no dc-link component for its normal power conversion even though it has a series diode and clamping foil capacitor for protection. It uses 12 switches in total, which together with the clamping capacitor, share a common voltage rating whose value is given by the maximum fictitious dc-link voltage. According to Section II-A, this√value√should be the peak line voltage of the grid, which means 2 × 3 = 2.45 p.u. In contrast, current ratings of the switches are different, whose values are determined as higher than 1 p.u. and 1/k p.u. for the source and grid sides, respectively. Sensor requirement can also be summarized as four 1 Three-phase quantities of a three-wire system can be measured using only two sensors. The third is just the negative sum of the other two.

for voltages and two for currents1 according to the description provided in Section III. All features noted are summarized in Table I to give a general overview. More specific comparison involving practical aspects of the converters like power density, power-to-mass ratio, lifespan, semiconductor chip area, electromagnetic interference filtering, and other auxiliary requirements is beyond the scope of this paper. Relevant comparative methodologies can be found in [3], [33] even though the application studied there is permanent-magnet synchronous motor drives. A conclusion drawn there is that the higher achievable power density and power-to-mass ratio of a matrix converter are usually outweighed by its narrower range of functionalities. It is therefore relevant to view at certain identified functionalities of the three converters before recommending on suitable application scope for the RMC related to DG. B. General Functionalities—Grid-Connected Mode Besides active power transfer during the grid-connected mode, a DG converter is sometimes expected to generate reactive power for grid support. For that the B2B converter with its dc-link capacitor is an ideal choice since its grid-side power factor angle can vary over the full unrestricted range of −π/2 to π/2. Such unrestricted performance can also be produced by the ZMC if its three-switch CSR shown in Fig. 8 is replaced by a more involved 12-switch bidirectional CSR. With its present three-switch CSR, the ZMC shown in Fig. 8 can only support an angle variation from −π/6 to π/6. This range is similarly shared by the RMC, which according to [34], can be extended by applying an improved hybrid modulation scheme.

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With their added dc-link components, the B2B and ZMC converters can also keep their grid currents balanced and sinusoidal even under unbalanced and distorted grid conditions. Oscillating grid instantaneous power will definitely surface, but can be blocked from the source by the dc-link components. Alternatively, the grid instantaneous power can be regulated constant, whose resulting grid currents will no longer be balanced sinusoids [35]. Such flexibility is however not associated with the RMC, whose instantaneous source and grid powers must always be balanced, ignoring losses. Balancing oscillating instantaneous powers might not be possible give the usually variable frequency of the source. Therefore, the more likely approach is to regulate the instantaneous powers to be constant and equal. Performing that requires modifications to the basic modulation scheme according to [36], [37]. Other than that the same control scheme as in Fig. 5 can be used to keep a constant source and hence grid-side instantaneous power. A third concern linked to the RMC is its voltage-boost only operation, which certainly is more constrained than the voltagebuck-boost functionality shared by the B2B and ZMC converters. The source voltage of the RMC must therefore be designed such that it is always 1.15 times lower than the lowest grid voltage that can be triggered by a sag. Not ensuring this will cause stability problems, while ensuring it will have the added benefit of higher efficiency. The latter can be explained by noting that for a low source voltage, the amount of voltage-boosting demanded is higher. That means longer VSR null state, during which the CSI switches are not conducting, and hence producing lesser losses (also explained in [33] for motor drives).

from the generally high power density and power-to-mass ratio of the RMC especially at a high switching frequency [33], while yet tolerating its more restricted general capabilities. A strong grid supplying an almost linear aggregated load would certainly be the ideal condition. Other possibilities can include: 1) Small-scale low-power DG nearer to residential areas, where reactive power generation might be less demanding. Much of interest would be to operate at a high switching frequency (>20 kHz) needed to keep audible noise low, while maximizing the power density of the RMC. 2) In a microgrid, where different types of DGs and loads are tied together as a small local area network [38]. Functionality distribution can then be coordinated such that those DGs interfaced by B2B converters can concentrate on reactive power and harmonic regulation, while others with RMCs can concentrate on active power generation. The same functionality distribution can be applied to a traditional grid, where power factor correction capacitors, passive and active power filters already exist. The added RMC DG can then be viewed as retrofitting the existing grid with additional active power generation capacity.

C. General Functionalities—Islanded Mode Interest in matrix converters is mainly motivated by their smaller passive component size, which can eventually lead to greater compactness. This is unfortunately at the expense of a smaller internal energy storage, which can greatly limit the converter load tracking ability. Matrix converters are therefore more suitable for loads that demand lower dynamics [33] or have lesser fast-changing harmonics. The same applies to the RMC in its islanded mode, where harmonic (and unbalanced) load currents drawn will cause oscillating instantaneous powers at the grid and source sides. These oscillating powers will interfere with the converter voltage regulation, which generally is much less severe for the BSB and ZMC converters because of their larger internal energy storages. Besides this, reactive power generation of the RMC and ZMC converters remains constrained by the angle variation range of −π/6 to π/6, which surely is narrower than the −π/2 to π/2 range demonstrated by the B2B converter.

V. SIMULATION AND EXPERIMENTAL RESULTS Three-phase 30-Hz/69-V (phase rms) input ac source and 50-Hz/100V (phase rms) grid voltages were considered for the simulation and experiment. Parameters indicated in Fig. 1 were respectively realized as L1 /R1 = 5 mH/0.4 Ω, Lf /Rf = 3 mH/20 Ω and Cf = 40 μF with the 20-Ω resistor Rf added in parallel with Lf for damping purposes. These values were not optimized, but rather chosen from those available in the laboratory. The findings drawn would still be fine since the main theme here is to prove the feasibility of using RMC and its control schemes for DG, rather than to optimize on its circuit design. The proposed converter and control algorithms were then preliminary verified in simulation using MATLAB/Simulink and the PLECS power electronic libraries. For hardware verification, a 1-kW laboratory prototype was subsequently built. The control of the hardware converter was realized by a combination of digital signal processor (DSP) and field programmable gate array (FPGA). Closed-loop control schemes shown in Figs. 5 and 6, and the modulation of the CSI were implemented with the TMS320LF2407 A DSP from Texas Instruments. Variableslope 10-kHz triangular carrier together with the references obtained for VSR modulation was subsequently transmitted to the Xilinx FPGA for gating signal generation. Results for both gridconnected and islanded modes are presented as follows. A. Grid-Connected Mode

D. Scope of DG Application Unlike motor drives where matrix converters are mostly recommended at present, DG involving the grid is far more wideranging in scale and possibilities. It is also more common to have multiple DGs tied to the grid rather than just a single unit, which after all is the basic thought behind decentralized generation. There are, therefore, likely to be cases that can benefit

Fig. 9 shows simulation results obtained for grid-connected mode based on the control scheme shown in Fig. 5. The figure shows waveforms for 30-Hz source voltage and current, 50-Hz grid voltage and current, fictitious dc-link voltage and current. Findings verified are summarized as follows: 1) Sinusoidal input current iA tracks its commanded amplitude of 7 A at unity input power factor.


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Fig. 10. Experimental fictitious dc-link voltage v d c , input line voltage v A B , source phase voltage v A , and current iA during grid-connected mode.

Fig. 9. Simulated fictitious dc-link voltage v d c , input line voltage v A B , source phase voltage v A and current iA , fictitious dc-link current id c , unfiltered output current iR , grid phase voltage v R , and filtered current iS R . Fig. 11. Experimental fictitious dc-link current id c , unfiltered output current iR , grid phase voltage v R and filtered current iS R during grid-connected mode.

2) Grid phase voltage vR and unfiltered output current iR are in phase signifying unity output power factor. 3) Filtered output current iS R is a sinusoid at 5-A peak, but has a phase lag with reference to the grid voltage. This slight phase lag is contributed by the 40 μF output filter capacitor, whose current remains unchanged for a fixed grid voltage. Its influence therefore becomes comparably smaller as iS R increases. 4) Fictitious dc-link voltage vdc and current idc vary with six-pulse per fundamental output cycle in accordance to the six sextants on a vector diagram. The findings were then verified experimentally in the gridconnected mode, where the RMC was started by first turning on its controller to synchronize with the source and grid voltages. Simultaneously, the CSI duty ratios were calculated since they depend only on the position of the grid voltage phasor on the space vector plane. Upon synchronized, the converter was turned ON with only short capacitor charging transient observed (could be shortened further if smaller optimized parameters were used). The results obtained are shown in Figs. 10 and 11, from which the same findings listed earlier can be observed, except for slight differences caused by losses in a real system. For example, the output peak current is measured as 4.9 A, which is slightly lower than the 5-A peak noted in simulation due to converter losses. To further verify that tracking is controlled appropriately, Fig. 12 shows the three-phase source currents, which indeed are at a peak of 7 A set as reference Iref in Fig. 5. The waveforms are also properly balanced.

Fig. 12. Experimental three-phase input phase currents iA , iB , and iC during grid-connected mode.

B. Islanded Mode In islanded mode, the ac source is controlled to power an external load through the RMC. Control scheme applicable is shown in Fig. 6, whose control objective is to keep a set of well-regulated three-phase voltages across the load. Simulation and experimental testing were performed on the scheme with similar results obtained. Because of the closeness in results, which has earlier been confirmed for the grid-connected mode, only experimental results are presented here for proving the islanded performances. Resistive load of 40 Ω per phase was used for the testing because it was the only option available at the time of experimentation. The findings are still applicable to most loads with combined resistive and inductive nature. The

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Fig. 13. Experimental fictitious dc-link voltage v d c , source phase voltage v A , and current iA , and input line voltage v A B during islanded mode.

Fig. 16. Experimental source voltage v A , source current iA , load voltage v R and filtered load current iS R during load power increase.

Fig. 14. Experimental fictitious dc-link current v d c , unfiltered output current iR , load phase voltage v R , and filtered current iS R during islanded mode.

Fig. 15. Experimental three-phase load phase voltages v R , v Y , and v W during islanded mode.

results are presented in Figs. 13 and 14 from which the following observations can be noted: 1) As intended, input current iA is a sinusoid with 5-A peak and unity power factor. 2) Output voltage vR is well regulated at 50 Hz/100 V (rms) even with no grid connected at the converter output. 3) Sinusoidal output current iS R is noted to have a peak of 3.5 A and unity power factor. The unfiltered output current iR would then be leading the regulated output voltage by a finite power factor angle. 4) DC-link voltage and current are again varying six times per fundamental output cycle. The Variation of the dc-link voltage is, however, no longer symmetrical because of the nonzero power factor angle between the output voltage and unfiltered output current.

Fig. 17. Experimental source voltage v A , source current iA , load voltage v R , and filtered load current iS R during load power decrease.

Fig. 15 proceeds to show the three-phase output voltages, which have slight voltage amplitude differences due to minor imbalances of the three-phase resistive load. Despite these small differences, the voltages are generally balanced and regulated at the demanded value of 100 V (rms). To further demonstrate its dynamic response, Figs. 16 and 17 show the corresponding input current and output voltage variations when the load resistance changes from 60 to 30 Ω and then back to 30 Ω. As marked by those dashed circles in the figures, the output voltage is disturbed only lightly at the instants of transition. It recovers fast and retains its 100 V (rms) regulated value as time progresses. The input current is also noted to increase and decrease fast without distortion as the load resistance decreases and then increases.

VI. CONCLUSION A voltage-boost matrix converter operating in reverse power mode has been introduced in this paper for DG application. Suitable control schemes for achieving dispatch power tracking in grid-connected mode and high-quality voltage regulation in islanded mode have been developed. Sinusoidal input and output characteristics have been shown to be retained by the presented modulation scheme, which also features flexible input and output power factor tuning. Simulation and experimental results have validated these advantages, which collectively would strengthen the attractiveness of the reverse-mode matrix converter for DG application.


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Poh Chiang Loh (S’01–M’04–SM’12) received the B.Eng. (Hons.) and M.Eng. degrees in electrical engineering from the National University of Singapore, Singapore, in 1998 and 2000, respectively, and the Ph.D. degree from Monash University, Clayton, Australia, in 2002. From 2003 to 2009, he was an Assistant Professor with Nanyang Technological University, Nanyang, Singapore, where since 2009, he has been an Associate Professor with the School of Electrical and Electronic Engineering. Dr. Loh was the recipient of two third paper prizes from the IEEE Industry Applications Society Industrial Power Converter Committee Prizes in 2003 and 2006. He is currently serving as an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS.

Yi Tang (S’10) received the B.Eng. degree in electrical engineering from Wuhan University, Wuhan, China, in 2007, and the M.Sc. degree from Nanyang Technological University, Nanyang, Singapore, in 2009, where he is currently working toward the Ph.D. degree in the School of Electrical and Electronic Engineering. During the summer of 2007, he was a Visiting Scholar with the Institute of Energy Technology, Aalborg University, Aalborg, Denmark, where he focused on the control of grid-interfaced inverters and uninterruptible power supplies.

Peng Wang (M’00) received the B.Sc. degree from Xian Jiaotong University, Xian, China, in 1978, the M.Sc. degree from the Taiyuan University of Technology, Taiyuan, China, in 1987, and the M.Sc. and Ph.D. degrees from the University of Saskatchewan, Saskatoon, Canada, in 1995 and 1998, respectively. He is currently an Associate Professor in the School of Electrical and Electronic Engineering, Nanyang Technology University, Nanyang, Singapore.

Frede Blaabjerg (S’86–M’88–SM’97–F’03) received the M.Sc. degree in electrical engineering and the Ph.D. degree from the Institute of Energy Technology both from Aalborg University, Aalborg, Denmark, in 1987 and 1995, respectively. He was employed at ABB-Scandia, Randers, from 1987 to 1988. From 1988 to 1992, he was a Ph.D. student at Aalborg University, Denmark, where he was an Assistant Professor in 1992, an Associate Professor in 1996, and a Full Professor in power electronics and drives in 1998, and is currently with the Department of Energy Technology. He has been a Part-Time Research Program Leader at Research Center Risoe in wind turbines. During the period of 2006–2010, he was the Dean of the Faculty of Engineering, Science and Medicine the same place and became a Visiting Professor at Zhejiang University, Zhejiang, China, in 2009. His research interest includes power electronics and its applications like wind turbines, photovoltaic systems, and adjustable speed drives. Dr. Blaabjerg has been a Editor-in-Chief of the IEEE TRANSACTIONS ON POWER ELECTRONICS, since 2006 as well as he was a Distinguished Lecturer for the IEEE Power Electronics Society from 2005 to 2007. It is followed up as a Distinguished Lecturer for the IEEE Industry Applications Society from 2010 to 2011. He received the 1995 Angelos Award for his contribution in modulation technique and the Annual Teacher prize at Aalborg University, in 1995. In 1998, he received the Outstanding Young Power Electronics Engineer Award from the IEEE Power Electronics Society. He has received ten IEEE Prize paper awards and another prize paper award at PELINCEC Poland 2005. He received the IEEE Power Electronics Society Distinguished Service Award in 2009 as well as the EPE-PEMC 2010 Council award.

Essam A. Al-Ammar (S’01–M’07) was born in Riyadh, Saudi Arabia. He received the B.S. degree (Hons.) in electrical engineering from King Saud University, Riyadh, Saudi Arabia, in 1997, and the M.S. degree from the University of Alabama, Tuscaloosa, in 2003, and the Ph.D. degree from Arizona State University, Phoenix, in 2007. From 1997 to1999, he was a Power/Software Engineer at Lucent Technologies, Riyadh. He was an Instructor at King Saud University from 1999 to 2000. He is currently an Associate Professor in Department of Electrical Engineering, King Saud University. Since November 2008, he has been an Advisor at the Ministry of Water and Electricity, and become a Coordinator of Saudi Aramco Chair in electrical power. He was an Energy Consultant at Riyadh Techno Valley between October 2009 and October 2011. His current research and academic interests include high-voltage engineering, power system transmission, distribution, and protection. Solar and wind energies are part of his research interest too. He is involved in different technical committees, and has authored more than 45 technical papers in different power aspects. Dr. Al-Ammar is a member of IEEE since 2007 and Saudi Engineering Committee since 1997.