THE modular multilevel converter (MMC), presented

Transcription

1 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL., NO. 4, DECEMBER Internal Power Flow of a Modular Multilevel Converter With Distributed Energy Resources Theodore Soong, Graduate Student Member, IEEE, and Peter W. Lehn, Senior Member, IEEE Abstract This paper examines the internal power flow mechanisms that exist within a generalized modular multilevel converter (MMC) and examines alternatives for integration of distributed energy resources (DERs) within the MMC structure. Each phase leg of the MMC consists of two series connected strings of submodules, where each string of submodules is referred to as a phase arm. Based on analytically developed inter-arm power flow relations, a control methodology is proposed, which provides fully independent control of each arm s real power flow, facilitating extreme levels of inter-arm power transfer. This eliminates the need for uniform integration of DER units across all submodules of the MMC. Among others, viable operating configurations are shown to include DERs only integrated in the upper (or lower) phase arms and DERs integrated only in the upper and lower phase arms of a single phase leg. Power balance is maintained internal to the MMC via dc and ac currents circulating within the converter without distorting input dc or output ac currents. To maximize conversion efficiency, a mechanism for minimizing the necessary circulating ac currents under any inter-arm power flow condition is also identified. Comprehensive simulation results validate both the developed model and controls. Index Terms AC DC power converters, energy resources, energy storage, multilevel systems, power conversion. I. INTRODUCTION THE modular multilevel converter (MMC), presented in [1], has garnered increasing research attention in [] and [3]. Originally developed for mediumand high-voltage dc transmission and distribution applications [1], [4], [5], its modular structure also enables integration of distributed energy resources (DERs) [6], whether they be photovoltaic systems [7], [8] or energy storage [9] [1]. These proposals to integrate DERs typically suggest utilizing a dc/dc converter to control power from one DER into each submodule of the MMC. The MMC, shown in Fig. 1(a), consists of three phase legs, each with two phase arms. A phase arm is composed of N submodules and a small inductor. The inductors are used to limit the rate of change of current during switching transitions in the phase arms and to provide filtering of output currents. The composition of the submodule may vary, but the Manuscript received January 30, 014; revised April 8, 014 and July 8, 014; accepted July 1, 014. Date of publication July 4, 014; date of current version October 9, 014. Recommended for publication by Associate Editor R. Burgos. The authors are with the Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 3G4 Canada ( theodore.soong@mail.utoronto.ca; lehn@ecf.utoronto.ca). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JESTPE Fig. 1. MMC with two submodule variants. (a) MMC converter structure. (b) S-SM. (c) DE-SM. most common submodule, used in [1], is shown as a standard submodule (S-SM) in Fig. 1(b). It consists of a half bridge and a capacitor, and this paper refers to an MMC composed of these submodules as a standard MMC. The submodule labelled distributed energy submodule (DE-SM) in Fig. 1(c) utilizes a chopper to interface with a power source, and is one example of a submodule used in an MMC with integrated DERs. To balance submodule capacitor voltages within phase arms, a sorting algorithm combined with a modulation method is typically used [1], [13] [16]; however, this control method does not ensure equalization of the submodule capacitor voltages between phase arms [17]. In addition, integration of DERs modifies the power flow within the MMC. If the DER power injections per phase arm are not equal, whether due to a shutdown or decrease in power from a particular DER, then power must be transferred between phase arms to maintain capacitor voltage balance. One possible method of balancing submodule capacitor voltages between phase arms of an MMC without DERs is identified in [17]. It proposes to change the dc component of modulating signals in each phase arm to cause unequal dc power transfer to upper and lower phase arm capacitors. This method relies on the existence of a dc arm current component, which may cease to exist when DERs are integrated. Alternatively, it was first noted in [18] and expanded upon in [19] that the presence of a fundamental frequency difference current can control power flow between the upper and lower phase arms of an MMC. This difference current is common to both upper and lower phase arms, yet does not affect the ac output current of the converter. In [18] and [0], the fundamental frequency difference current is used to balance the submodule capacitor voltages between phase arms IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 118 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL., NO. 4, DECEMBER 014 However, the presented control methods do not guarantee that a zero-sequence fundamental frequency difference current is eliminated. As the difference current is common to both the upper and lower phase arms, a zero-sequence fundamental frequency difference current would flow into the dc link and distort the input dc current of the MMC. Reference [1] does present a balancing method that accounts for the zero-sequence fundamental frequency difference current. This paper differs from [1] in that it yields a simpler control structure, which does not utilize periodic gains, and it is a more intuitive method of controlling the internal power flow of the MMC. The purpose of this paper is to analyze the power flow of a generalized MMC that includes DERs integrated into submodules. This will enable the identification of alternatives for distributing DERs into a subset of phase arms in the MMC. From the power flow analysis, a control method is developed to provide power balance between phase arms in the presence of DERs. Power balance is achieved through the manipulation of circulating ac and dc currents within the MMC, and the paper focuses on achieving power balance without affecting the ac grid or dc link currents. Of greatest significance, a means of achieving power balance while maximizing conversion efficiency through the minimization of circulating current with the MMC is presented. This paper begins with a review of the operation and modeling of a generalized MMC with DERs integrated into each submodule. For clarity, the power flow between the upper and lower phase arms for a single-phase MMC is analyzed first. The results are then extended to develop a methodology for voltage balance across all arms of a three-phase MMC. Simulation is used to validate the analyses and the proposed control methodology. II. SINGLE-PHASE MMC MODELING In this paper, the general MMC with DERs integrated into each submodule is studied. The DERs may consist of a variety of energy source technologies, for example, battery or supercapacitor energy storage. The analysis focuses on the power flow between phase arms of the MMC in steady state. For individual submodules within the phase arms, it is assumed that a sorting algorithm together with phase disposition pulsewidth modulation [5], [] maintains the submodule capacitor voltage balance (as justified in [18]). This section considers the single-phase representation of the general MMC with DERs integrated into each submodule. Conclusions are then drawn from the single-phase analysis for application to the three-phase MMC. A. Single-Phase MMC Model and Principle of Operation For the following discussion, the operation of the MMC is briefly reviewed. Fig. shows a single-phase model of the MMC. To generalize the model for use with DERs integrated into each submodule, P inj,u and P inj,l have been introduced as shown. The terms P inj,u and P inj,l represent the total average power injected by the DERs into the submodules of the upper and lower arms, respectively. Fig.. Circuit model of a single-phase MMC. The voltages v (t) ± v (t) and v s (t) are referenced to ground. The analytical model of Fig. is developed based on the following assumptions: 1) high number of submodules enabling near-sinusoidal output voltages (as justified by [18]); ) equal arm impedances with no coupling between inductances (for simplicity of mathematical derivations); 3) power injection per arm is equally divided between submodules (as readily ensured via DER current regulation by the DE-SM DER side converter). In Fig., the voltages synthesized by the submodules of each arm are represented as low-frequency averaged voltage sources. Thus, the upper and lower phase arm voltages are denoted by v U (t) and v L (t). Applying KVL to Fig., v U (t) and v L (t) are related to V DC, v (t), and v (t) as follows: v U (t) = V DC v (t) v (t) (1a) v L (t) = V DC + v (t) v (t). (1b) The voltage v (t) is the voltage required to drive the ac output current, i (t), andv (t) is the voltage required to drive the difference current, i (t). The difference current is a circulating current, common to both upper and lower phase arms, which does not enter the ac grid. The coordinate system is employed to decouple quantities related to the external ac grid and internal circulating current of the MMC. Thus, the internal power flow of an MMC with DERs would primarily depend upon the difference current quantities. The voltages v (t) and v (t) can be explicitly defined in terms of voltage drops across impedances and the ac grid voltage, v S (t), as follows: ( v (t)=v S (t)+ R G + R ) A v (t) = R A i (t) + L A d dt i (t). ( i (t)+ L G + L ) A d dt i (t) (a) (b) Note that v (t) is the voltage drop across the arm impedances, L A and R A, due to i (t). As the arm reactance and resistance are small, the term v (t) may be neglected for the power flow analysis of Sections II and III. The negligible influence

3 SOONG AND LEHN: INTERNAL POWER FLOW OF A MODULAR MULTILEVEL CONVERTER 119 of v (t) will be justified via simulation results provided in Section V. The phase arm currents i U (t) and i L (t) shown in Fig. are also defined in terms of the current quantities. This relates the composition of the phase arm currents to the ac output and circulating currents, which results in i U (t) = i (t) + i (t) (3a) i L (t) = i (t) i (t). (3b) As revealed by (3), each phase arm need only conduct half the ac output current in addition to the difference current, i (t). The difference current can be composed of currents at any frequency. For a generalized MMC with DERs, the difference current is chosen to consist of a dc and fundamental frequency component. The dc component allows for power to be transferred from the dc link to both the upper and lower phase arms, while the fundamental frequency component enables power transfer between the upper and lower phase arms [18] [0]. Thus i (t) = I 0 + i (t) (4) where I 0 denotes the dc component and i (t) denotes the fundamental frequency component. As previously stated, the difference current need not only consist of dc and fundamental frequency components. Other frequency components can be included to yield additional benefits, such as employing a second harmonic frequency component to achieve submodule capacitor voltage ripple reduction [3], [4]. However, in this paper, all frequency components of i (t) except for the dc and fundamental are eliminated to yield enhanced conversion efficiency [18], [5], [6]. B. Power Flow of the Phase Arms In this section, the upper and lower phase arm voltages and currents given by (1) and (3) are used to derive the power balance relationship across submodule capacitors of each arm. By computing the average power out of the upper and lower submodule capacitors, the following relationships are found: P CU = 1 [ ] [ ] ˆV Î ˆV Î cos(φ) + cos(γ ) }{{}}{{} P P P CL = 1 1 [V DCI 0 ] P }{{} inj,u (5a) P [ DC ] [ ] ˆV Î ˆV Î cos(φ) cos(γ ) } {{ } P } {{ } P 1 [V DCI 0 ] }{{} P inj,l (5b) P DC where P CU and P CL is the average power out of the submodule capacitors. The variables γ and φ are the phase angles of i (t) and i (t), respectively, relative to v (t). In this paper, the current entering the ac grid is only composed of a fundamental frequency component (i.e., i (t) = i (t)). Fig. 3. Power flow diagram of a generalized MMC with DERs in each submodule. Based on (5), the different sources of power transfer can be related to currents i (t) and i (t). The ac grid current, i (t), transfers power out of the upper and lower submodule capacitors to the ac grid. This real power transfer is denoted as P. The dc difference current, I 0, transfers an equal amount of power into the upper arm and lower arm submodule capacitors from the dc link. This real power transfer is denoted as P DC. The fundamental frequency difference current, i (t), transfers power from the upper arm to the lower arm submodule capacitors. This real power transfer is denoted as P. The power transfer mechanisms are shown in Fig. 3. In addition to the real powers, the reactive powers Q and Q are also labelled in Fig. 3. The reactive power Q is the reactive power transferred from the MMC to the ac grid, and Q is defined as the reactive power transferred from the upper arm to the lower arm submodule capacitors. These quantities are given by Q = ˆV Î sin(φ) (6a) Q = ˆV Î sin(γ ). (6b) For values of γ not equal to 0 or π, there exists a reactive current component to the fundamental frequency difference current. That is, the total apparent power due to the difference current is equal to P + jq. It is important to note that the reactive current component of the fundamental frequency difference current supplies none of the reactive power required by the ac grid nor does it transfer any average power between arms. In this paper, the phase angle γ is chosen such that zero reactive power circulates within the MMC. III. THREE-PHASE MMC INTERNAL POWER FLOW This section extends the power flow analysis from a singlephase to a three-phase MMC, and develops a methodology to achieve voltage balance across all submodules of a three-phase MMC without affecting the dc input or ac output currents. Specific focus is on: 1) power transfer between phase arms within an individual phase leg and ) power transfer between phase legs. This is achieved through the independent control of the difference current in each phase (i.e., i x (t) for a

4 1130 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL., NO. 4, DECEMBER 014 currents may be unbalanced but their sum must be equal to zero (i a (t)+i b (t)+i c (t) = 0). This can be achieved by allowing the three fundamental frequency difference currents to contain positive and negative sequence currents, while enforcing null zero-sequence current. For example, if P b were to be nonzero, and P a and P c were zero, then reactive power must circulate in phases a and c such that fundamental frequency current does not enter i dc (t). Defining i (t) for phases a, b, andc with positive and negative sequence components results in Fig. 4. Three-phase MMC depicting independent currents i a (t), i b (t), and i c (t). given phase x). As i x (t) for each phase is independent, the results from Section II can be adapted. Thus, to accomplish the power transfer objectives, the difference current is once more composed of a dc (I 0x ) and fundamental frequency current component (i x (t)). A. Power Transfer Between Phase Legs As introduced in Section II-B, the dc difference current transfers power from the dc link to both the upper and lower arms [see (5)]. Thus, the dc difference current can be used to facilitate power transfer between phase legs and the dc link. In Fig. 4, the power delivered from the dc link to the phase leg x is determined by the dc difference current I 0x. For a standard MMC in steady state, an equal amount of power is delivered from the dc link to each phase leg (I 0a = I 0b = I 0c ). In a generalized MMC with DERs, it is not necessary for I 0x to be equal for all phases. Thus, freedom to arbitrarily assign I 0x enables compensation of unequal power injection from the DERs between phase legs. B. Power Transfer Between Phase Arms In addition to power transfer between phase legs, complete control of power flow within the MMC requires independent power transfer between phase arms within each phase. As introduced in Section II-B, the fundamental frequency difference current, i (t), assigns the power exchange between the upper and lower phase arms (P in Fig. 3) within the phase leg. The analysis can be extended for application to three-phase systems. Critical to the analysis of the three-phase MMC will be the minimization of circulating current to enable maximum conversion efficiency. In Fig. 4, the three-phase MMC must achieve independent power transfer between the upper and lower arms of each phase by utilizing the fundamental frequency difference current i x (t) for a given phase x. However, it is desired that power transfer is executed without affecting i x (t) and i dc (t). It has already been established that the fundamental frequency difference current does not affect i (t), buti dc (t) should also not contain any fundamental frequency component. Therefore, the three fundamental frequency difference i a (t) = Î (p) cos ( ωt +γ (p)) + Î (n) cos ( ωt +γ (n)) (7a) i b (t) = Î (p) (ωt cos + γ (p) π ) 3 + Î (n) (ωt cos + γ (n) + π ) (7b) 3 i c (t) = Î (p) cos (ωt + γ (p) + π 3 + Î (n) cos (ωt + γ (n) π 3 ) ). (7c) Since grid currents are independent from the difference currents, the voltage v (t) remains positive sequence. Hence, the average power delivered by the difference current at the fundamental frequency can be found by multiplying the positive sequence v (t) with the positive and negative sequence fundamental frequency difference current i (t) and integrating over one period. This results in the following relations: P a = ˆV Î (p) P b = ˆV Î (p) P c = ˆV Î (p) cos ( γ (p)) + ˆV Î (n) cos ( γ (p)) + ˆV Î (n) cos cos(γ (p) ) + ˆV Î (n) cos cos ( γ (n)) ( γ (n) π 3 ( γ (n) + π 3 ) (8a) (8b) ). (8c) Using a similar approach, a reactive difference power (Q x for a given phase x) can also be identified for each phase, and results in Q a = ˆV Î (p) Q b = ˆV Î (p) Q c = ˆV Î (p) sin(γ (p) ) ˆV Î (n) sin(γ (n) ) sin(γ (p) ) ˆV Î (n) sin sin(γ (p) ) ˆV Î (n) sin ( γ (n) π 3 ( γ (n) + π 3 ) (9a) (9b) ). (9c) According to (8) and (9), three real and three reactive power flows exist, but only four independent variables (Î (p), Î (n),γ(p), and γ (n) ) are available. This is a result of choosing a difference current comprising only positive and negative sequence components. Hence, to enable independent active power control, only a single reactive power constraint may be imposed. To maximize conversion efficiency, the net reactive power, Q, given in (10) is chosen to be minimized. Minimizing Q prevents unnecessary circulating current within the MMC, which does not aid in power transfer;

5 SOONG AND LEHN: INTERNAL POWER FLOW OF A MODULAR MULTILEVEL CONVERTER 1131 thus, Q is assigned to zero in this paper Q = Q x = 3 ˆV Î (p) sin ( γ (p)). (10) x={a,b,c} According to (8) and (10), P a, P b, P c,and Q can be related to four independent variables. Choosing independent variables to be Î (p), Î (n),γ(p), and γ (n) would result in nonlinear relation between variables and multiple solutions. Instead the independent variables are chosen as Î (p) cos(γ (p) ), Î (p) sin(γ (p) ), Î (n) cos(γ (n) ), and Î (n) sin(γ (n) ) to simplify computation. This yields the following relations, which are readily computed with a real-time controller: where P a P b P c Q A = ˆV = A Î (p) cos ( γ (p)) Î (p) sin ( γ (p)) Î (n) cos ( γ (n)) Î (n) sin ( γ (n)) (11) Provided a nonzero ˆV, the matrix A is full rank and invertible; therefore, the positive and negative sequence fundamental frequency difference currents can be uniquely determined for agivenp a, P b, P c,and Q. Full control over the power transfer between the upper and lower phase arms of all three phases is thereby achieved, while not being detrimental to i (t) and i dc (t). By manipulating the difference current to contain a dc and fundamental component, power can be transferred between the upper and lower phase arms of any phase, and between phase legs. This allows for independent control of power to all six phase arms of the MMC and guarantees submodule voltage balance between phase arms even for large inter-arm power transfers. The proposed approach does not distort the dc link current by ensuring that null zero sequence fundamental frequency difference current is imposed and maximizes efficiency by minimizing unnecessary reactive fundamental frequency difference current. C. Impact of Integrating DERs Into an MMC To discuss the effect of integrating DERs into an MMC, phasor diagrams are used to visualize the fundamental frequency currents and their relation to the power flow between arms given in (5). The phasor diagrams are shown for an exemplary phase of the three-phase MMC in Fig. 5. The currents are aligned to V of its respective phase, which implies that the projection of current vectors to the real axis is proportional to active power transfer, and projection of the currents onto the imaginary axis is proportional to reactive power transfer. From the submodule capacitor power balance (5), (P DC /)+ P inj,u must be delivered by the upper arms through Fig. 5. This rms phasor current diagram relates the fundamental frequency output current, difference current, upper arm and lower arm currents. To maintain power balance for each phase arm, vector I U1 must lie on dashed line 1, while vector I L1 must lie on dashed line. Dashed lines 1 and are associated with power flow ((P DC /) + P inj,u )/ V and ((P DC /) + P inj,l )/ V, respectively, from (5). Fig. 6. This rms phasor current diagram relates the output current and the fundamental frequency upper and lower arm currents. To maintain power balance for each phase arm, vector I U1 must lie on dashed line 1, while vector I must lie on dashed line. Dashed lines 1 and are associated with power flow ((P DC /) + P inj,u )/ V and (P DC + P inj,l + P inj,u )/ V, respectively, from (5). the fundamental frequency components of i U (t). Similarly, (P DC /)+ P inj,l must be delivered by the lower arms through the fundamental frequency components of i L (t). Thus, the dashed lines in Fig. 5 show where the tip of phasors I U and I L must lie for power balance to be maintained. In addition, these two vectors must sum up to I, as shown in Fig. 6. Inspection of Fig. 6 reveals that power from the dc link (P DC ) is reduced by the sum of injected powers (i.e., P inj,u + P inj,x ). As previously stated, γ in Fig. 5 is chosen to equal π such that zero reactive power circulates within the MMC (if the power injected into the upper arm was greater than that of the lower arm then γ would be chosen as zero). This angle choice for γ will cause I U1 and I L1 to be composed of half the necessary ac output current with the minimum difference current to achieve power balance. In a standard MMC, a steady-state fundamental frequency difference current is not required as it would unbalance submodule capacitor voltage between arms. However, a steady-state fundamental frequency difference current is required in a generalized MMC with DERs integrated into a subset of submodules. The phasor diagrams of Figs. 5 and 6 represent a convenient method of visualizing the steady-state effect of integrating DERs into a subset of submodules. D. Special Case: Pseudo-Cascaded Converter with DC Link From the analysis of the phasor diagrams, a special case can be observed that serves as a link between the MMC and a cascaded converter with active power capabilities [7], [8]. This special case of the generalized MMC with DERs is

6 113 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL., NO. 4, DECEMBER 014 Fig. 8. Main control diagram for the MMC. v x (t) for x in {αβz} is generated by the difference current controller shown in Fig. 9. i α (t) and i β (t) have been low-pass filtered to remove switching harmonics. Fig. 7. Current flow in a Pseudo-cascaded converter with dc link when P DC = 0. referred to as the Pseudo-cascaded converter with DC link. Using Fig. 6 for reference, consider the case where the upper arms contain no DERs, thus P inj,ux = 0forx in {a, b, c}, and I U1x is placed in line with its respective V x. Reactive output of the upper and lower arms may be adjusted by moving I U1x and/or I L1x along dashed lines 1 and, respectively. In this case, the upper arm is being used only for exchanging real power (P DC /) with the dc link, while all DER power injection and var production occurs on the lower arm. If we further stipulate that zero power is exchanged with the dc link (P DC = 0), we obtain the operating mode shown in Fig. 7 for a three-phase MMC. The upper arms transfer zero power and merely provide the voltage difference between V DC and the lower arms. The upper arms are redundant if no dc link exists. Meanwhile, the lower arms act as a cascaded converter composed of half-bridge submodules, and must conduct the rated output current, hence the name Pseudo-cascaded converter with dc link. From this discussion, it is evident that the fundamental frequency difference current can be used to transfer any desired amount of active or reactive power between the upper and lower phase arms, thus balancing the submodule capacitor voltages in a balanced three-phase MMC. This is valid even in the extreme case where no DERs are implemented in the upper arms, thus creating the Pseudo-cascaded converter with dc link. By symmetry, it is equally possible to operate the MMC with DERs integrated only into the upper arms. IV. CONTROL SYSTEM FOR GENERALIZED MMC WITH DERS In this section, the control system for a generalized three-phase MMC with DERs integrated into submodules is developed based on the discussions of Section III. To maximize efficiency, reactive fundamental frequency difference current is minimized as per the results of Section III-B. To further enhance efficiency, the controller also removes any undesired harmonic difference currents. Undesired harmonics includes harmonics that result from steady-state fundamental difference currents, which are not present in standard MMCs. A control structure akin to [9], [30] is used where a series of resonant controllers is used for each harmonic that requires regulation. Resonant controllers are used due to their ability to track both positive and negative sequence current components [31]. In comparison to the balancing methods in [18] and [0], which control the amplitude of the fundamental frequency difference current, the resonant controllers allow for control of both amplitude and phase. Control feedback to achieve power balance of the MMC is based only on the total submodule capacitor voltages of the arms. The management of DERs is decoupled from the control of the MMC. A. MMC Grid and Difference Current Control Structure The control architecture employed for the MMC is shown in Fig. 8. The controllers are divided into grid and difference current controllers. A pair of resonant controllers regulates the grid currents in the α and β frame to achieve a desired P s and Q s. The difference current i (t) is controlled via the difference voltage v (t) in the αβz 1 frame by the control structure of Fig. 9. Each αβz-axis controller of Fig. 9 consists of four current controllers that control the: 1) dc; ) fundamental frequency; 3) second harmonic; and 4) third harmonic components of i (t). The dc current controllers in the αβz reference frame assign the power P DCx for each phase via proportional integral (PI) control. The fundamental current controllers in the αβz reference frame assign the real and reactive power transfer between the upper and lower phase arms (i.e., P x and Q x ) via resonant control. The second harmonic current controllers suppress undesired second harmonic currents to minimize arm conduction loss via resonant control. From [19], it is known that the fundamental and third harmonic difference currents are coupled. Thus, the introduction of a fundamental frequency difference current induces a third harmonic difference current in the MMC. As the third harmonic current is not used for power transfer, the elimination of this third harmonic is desired. The third harmonic current controller suppresses undesired third harmonic currents via resonant control. 1 The zero sequence component is identified by z.

7 SOONG AND LEHN: INTERNAL POWER FLOW OF A MODULAR MULTILEVEL CONVERTER 1133 by summing all submodule capacitor voltages of the phase x upper and lower arms, respectively. The fundamental frequency difference current reference generator of Fig. 10 creates current references to equalize upper and lower arm submodule capacitor voltages, while minimizing circulating reactive current. This reference generator is developed from Section III-B equations where the average powers P a, P b,andp c were shown to be independently controllable by including positive and negative sequence components in the fundamental frequency difference currents. To simplify computation, the positive and negative sequence components are determined by choosing the following four independent variables: 1) Î (p) cos(γ (p) ); ) Î (p) sin(γ (p) ); 3) Î (n) cos(γ (n) ); and 4) Î (n) sin(γ (n) ). For control, the variables are mapped onto a fundamental frequency space vector Fig. 9. Difference current controller for creation of v x (t) for x in {αβz}. The current i x (t) has been low-pass filtered to remove switching harmonics. The reference i x (t) is created with the structure shown in Fig. 10. Fig. 10. Reference creation for difference current controllers. The voltages v CUx (t) and v CLx (t) denote the sum of all submodule capacitor voltages in the upper or lower arm of a given phase x. H(s) is a low-pass filter. B. Generation of Difference Current Controller Reference From the discussion in Section III, it was found that the dc power, P DCx, and average difference power, P x,foragiven phase x can be independently controlled for each phase. The power P DCx is controlled with the dc difference current I 0x, and P x is controlled with the fundamental frequency difference current i x (t). The process for generating the difference current references to maintain power balance across all phase arms is shown in Fig. 10. From the figure, reference generation is divided into fundamental frequency difference currents and dc difference currents reference generators. Feedback for both reference generators is based solely on the total submodule capacitor voltages of the phase arms, denoted by v CUx (t) and v CLx (t) for a given phase x. These quantities are computed i α (t)+ ji β (t) = [Î (p) + cos ( γ (p)) + j Î (p) sin ( γ (p))] e θ (t) [Î (n) cos ( γ (n)) j Î (n) sin ( γ (n))] e θ (1) where θ is the angle of v α (t) + jv β (t). The fundamental frequency difference current reference generator shown in Fig. 10 regulates the mean difference between v CUx (t) and v CLx (t) to create a P x reference for a given phase x via PI control. Given the knowledge of P inj,ux and P inj,lx, a feedforward term, (Pinj,Ux P inj,lx /), is also added to improve response time. The reference power commands P x and Q are then mapped onto the references iα (t) and i β (t) using (11) and (1) to create fundamental frequency difference current references in the αβz frame. The dc difference current reference generator of Fig. 10 regulates the mean sum of v CUx (t) and v CLx (t) to create a I 0x current reference for a given phase x via PI control. The individual phase references are converted into the αβz reference frame for use by the current controllers. The dc difference current in the α and β axes manipulates the dc power transfer between the phase legs. The z-axis current, I 0z, gives the dc current flowing from the external dc grid. The summation of the dc and fundamental frequency difference current references in the αβz reference frame completes the difference current reference computation. C. Control of Power Injection by DERs In a general MMC with DERs integrated into each submodule, all submodules are assumed to have DERs integrated into them. Since the underlying sorting algorithm accounts for balance of submodule capacitor voltages within a phase arm for this analysis, it is sufficient to assume that each submodule injects P inj,ux /N or P inj,lx /N into their respective arms where N is the number of submodules in each arm. Fig. 11 shows how the power command, P inj,ux /N or P inj,lx /N, is translated into a current command for the DER chopper. The DER chopper operates with a current controller to deliver the desired power.

8 1134 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL., NO. 4, DECEMBER 014 Fig. 11. DER control diagram for a given phase x, with x in {a, b, c}. The current i DER (t) has been low-pass filtered to remove switching harmonics. Three simulated scenarios are considered in this section. The first simulation focuses on the MMC operating as a Pseudo-cascaded converter with DC link, thus demonstrating the ability of fundamental frequency difference current to transfer power between the upper and lower arms. The second simulation verifies that the fundamental frequency difference currents, when composed of only positive and negative sequence components, have the ability to transfer an arbitrarily specified amount of power between the lower and upper arms on each phase independently. The final simulation validates that power transfer between phase legs is also possible. In all cases, both MMC input and output currents remain undistorted despite the varying internal power transfers within the converter. Fig. 1. Diagram of the simulated system. TABLE I SIMULATION PARAMETERS OF THE MODEL V. SIMULATION RESULTS A full-switched PSCAD/EMTDC model of the MMC with DERs integrated into submodules was developed to verify the power flow relations and the proposed submodule balancing algorithm of the converter. The simulated system, shown in Fig. 1, is composed of an MMC connected to the grid through an ideal transformer with a one-to-one conversion ratio (L G and R G may be viewed as the leakage inductance and winding resistance of the transformer). Table I summarizes all model parameters used in the simulation. The modulation method used in this simulation is the phase disposition pulsewidth modulation method []. Due to the low number of modules in the simulated MMC, a carrier frequency of 5.5 khz is used and arm inductances are set to 0.06 pu. The DERs are modeled as a constant voltage source due to the short duration of the simulation. A. Scenario 1: MMC Power Flow With DERs Integrated Into Submodules of the Lower Arms Only It was concluded in Section III-C that the fundamental frequency difference current can be used to transfer power between the upper and lower arms of an MMC. An extreme case occurs if an MMC operates with power injected from DERs in the upper or lower arm only. In this case, all the output current is conducted by the upper or lower arms only. This type of operation was classified in Section III-D as the Pseudo-cascaded converter with DC link. The simulation results presented in this section provide evidence of this extreme case. The simulation results are shown in Fig. 13. From t = 0.0 to 0.05 s, the MMC operates with the dc link source providing all input power to the converter. Beginning at 0.05 s, the DERs in the lower arm submodules provide power to the MMC in place of the dc link source. With DERs, power can also be transferred from the MMC to the grid without utilizing the dc link. The output current of a representative DER in each of the six phase arms is shown by i DER,Ux (t), andi DER,Lx (t) where Ux and Lx denote the location of the DER. The subscript specifically denotes whether the DER is located in the upper or lower arm of phase x. As seen in Fig. 13, i DER,La (t), i DER,Lb (t), andi DER,Lc (t) start to increase at 0.05 s, delivering power into the lower phase arms. The fundamental frequency difference current becomes nonzero to transfer power from the lower arms to the upper arms, and the total submodule capacitor voltage of each phase arm converges to its nominal value. In steady state, the difference currents all contain fundamental components, but no dc component since all power is provided by the DERs in the lower phase arms. From the submodule capacitor voltage waveforms, the total submodule capacitor voltages of each phase arm converge to their nominal total voltage of 6.4 kv. However, focusing on the total submodule capacitor voltages in the lower arms (v CLx (t) for a given phase x), the voltage ripple has noticeably changed compared with its initial ripple. This is due to the ac output current flowing through the lower arms only, thus increasing the capacitor current, and in turn the voltage ripple, of the capacitor. In addition, since no current is flowing through the upper arms, there is an absence of

9 SOONG AND LEHN: INTERNAL POWER FLOW OF A MODULAR MULTILEVEL CONVERTER 1135 Fig. 13. This simulation shows the MMC transitioning from operation with power provided by the dc link source to operation with power provided by the DERs in the lower arms of all phases only. At t = 0.05 s, the total DER output power in the lower arms is assigned to equal the grid power (indicated by the ider variables). After the initial transients, the difference current of all three phases contains a fundamental frequency difference current, which transfers power from the lower to the upper arm. Output voltages and currents are measured at the node between the grid interface impedance and the MMC. Fig. 14. This simulation shows the MMC operating with power delivered from the dc link source and DERs in the lower arm of phase a. At t = 0.05 s, the DERs in the lower arm of phase a begin injecting power into the phase arm (indicated by ider,la (t)). To compensate, power is transferred from the lower arm to the upper arm of phase a without affecting power transfer in phases b and c. Power balance between the upper and lower phase arms is shown to be internal to the MMC with the dc and ac terminals unaffected. Output voltages and currents are measured at the node between the grid interface impedance and MMC. voltage ripple in the total submodule capacitor voltages of the upper arms (v CUx (t)). This simulation shows that an MMC can operate with power injected into the lower arms only by utilizing the fundamental frequency difference current. Operation in this manner resembles that of a Pseudo-cascaded converter with DC link. phase of a three-phase MMC. Simulation is used to validate that power can be transferred between the upper and lower arms in a single phase, while no power transfer occurs in the other phases. The simulation results are shown in Fig. 14. From t = 0.0 to 0.05 s, the MMC operates with the dc link source providing all input power to the converter. Beginning at 0.05 s, the DERs in the lower arm of phase a begin to inject one third of the rated output power into the lower arm (indicated by i DER,La (t)). This implies that the DERs in the lower phase a arm supply enough power such that the phase leg a does B. Scenario : MMC Power Transfer Between Phase Arms In Section III, a method was developed to control the power transfer between the upper and lower arms of each independent

10 1136 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL., NO. 4, DECEMBER 014 not require any power transfer from the dc link. Both phases b and c continue to operate with power transferred from the dc link source only. Thus, P a is transferring power from the lower arm to the upper arm, while P b and P c remain zero. Once the MMC settles into its new operating point, it can be seen that i DC (t) has dropped by one third, indicating that phase leg a no longer requires power from the dc link. The currents i a (t), i b (t), andi c (t) all contain a fundamental frequency component, but the dc component of the difference current only changes in i a (t). This indicates that dc power is not delivered into the phase leg a. The total submodule capacitor voltages of each arm converge to their nominal value of 6.4 kv as required. Similar to the previous simulation, the submodule capacitor voltage ripple in v CLa (t) has increased due to the increased fundamental current conducted by the lower arm of phase leg a, and the total submodule capacitor voltage of the phase leg a upper arm (v CUa (t)) shows little to no ripple. The simulation shows that power can be transferred between the upper and lower phase arms of a single phase without affecting power transfer of the other phases. The difference between the upper and lower arm submodule capacitor voltages also converges to zero. The ac output currents are unaffected by this balancing, and there is negligible distortion of the dc link source current. As anticipated in the model development, neglecting the voltage drop across the arm chokes (i.e., v (t)) in the internal power flow analysis and control design has no impact on voltage balancing performance. C. Scenario 3: MMC Power Transfer Between Phase Legs As described in Section III, the MMC can transfer power between phase legs by utilizing the dc link. The simulation results presented in this section demonstrate power transfer between phase legs using only the DERs in phase leg a to provide power to phases b and c. The simulation results are shown in Fig. 15. From t = 0.0 to 0.05 s, only the dc link source provides power to the MMC. Beginning at 0.05 s, DERs in phase leg a are used to provide power to the MMC (indicated by i DER,Ua (t) and i DER,La (t)). As power transfer is only required between phase legs, the difference current i a (t) is only composed of a dc component and is observed to decrease to a negative value, thus transferring power into the dc link, eventually causing i DC (t) to reach zero. Power from phase a allows the other phases to operate as they would in a standard MMC. Thus, the phase a difference current i a (t) is the negative of the sum of i b (t) and i c (t). As desired, the total submodule capacitor voltages converge to their nominal value. The ripple of the total submodule capacitor voltages of phase a, v CUa (t) and v CLa (t), has increased due to the higher dc difference current that phase a must conduct at this operating point. Since the dc difference current transfers power out of both the upper and lower phase arms, the ripple is equal on both v CUa (t) and v CLa (t). Fig. 15. This simulation shows the MMC transitioning from operation with the dc link source to operation with energy storage in phase a only. At t = 0.05 s, the DERs in phase a provide power to all phases. After the initial transients, the phase a difference current is seen transferring power to the other phase legs, while all other currents remain the same. Output voltages and currents are measured at the node between the grid interface impedance and MMC. Control of the phase leg dc difference current was shown to be independent of the other phases. The ac output currents are also unaffected after an initial transient. This simulation shows that DERs in one phase leg can support active power transfer to the other phase legs. VI. CONCLUSION This paper analyzes the power flow of a generalized MMC with DERs integrated into the submodules of individual phase arms. Based on the analysis, it is demonstrated that dc and fundamental frequency difference currents circulating within the generalized MMC can be used to maintain submodule

11 SOONG AND LEHN: INTERNAL POWER FLOW OF A MODULAR MULTILEVEL CONVERTER 1137 capacitor voltage balance across all submodules regardless of which phase arms include DERs. A control methodology that maintains capacitor balance is developed, which can accommodate arbitrary placement of DERs. When DERs are employed in only a subset of phase arms, steady-state fundamental frequency difference current is required. This results in an undesired third harmonic circulating current, which is not apparent in standard MMCs. However, the controller is shown to be able to eliminate both second and third harmonic current within the MMC to maximize efficiency. To further enhance efficiency, the proposed controller employs a mechanism to minimize reactive fundamental frequency difference current since it does not aid in power transfer between phase arms. Analysis and simulation results show that the proposed control methodology is able to maintain voltage balance even in the presence of large inter-arm power transfers. Thus, it is possible for DERs in any phase arm to provide power to all other phases or to the dc terminals of the MMC. Use of phasor diagrams that depict power balance of the converter, enables visualization of the circulating currents required for inter-arm power transfers. The proposed control methodology may be exploited to reduce the number of submodules that are equipped with DERs by interfacing only a subset of arms with DERs, or, alternatively, it may be employed to provide robustness of the system to DER failures. If DER failure or shutdown occurs, the system is still operable as phase arms with operational DERs can compensate for the absent DERs without influencing ac or dc terminal quantities. REFERENCES [1] A. Lesnicar and R. 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12 1138 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL., NO. 4, DECEMBER 014 [6] M. Hagiwara and H. Akagi, Control and experiment of pulsewidthmodulated modular multilevel converters, IEEE Trans. Power Electron., vol. 4, no. 7, pp , Jul [Online]. Available: [7] L. Maharjan, S. Inoue, H. Akagi, and J. Asakura, State-of-charge (SOC)-balancing control of a battery energy storage system based on a cascade PWM converter, IEEE Trans. Power Electron., vol. 4, no. 6, pp , Jun [Online]. Available: [8] M. R. Islam, Y. Guo, and J. Zhu, A high-frequency link multilevel cascaded medium voltage converter for direct grid integration of renewable energy systems, IEEE Trans. Power Electron., vol. 9, no. 8, pp , Aug [9] X. She, A. Huang, X. Ni, and R. Burgos, AC circulating currents suppression in modular multilevel converter, in Proc. 38th Annu. Conf. IEEE Ind. Electron. Soc., Oct. 01, pp [Online]. Available: [30] Z. Li, P. Wang, Z. Chu, H. Zhu, Y. Luo, and Y. Li, An inner current suppressing method for modular multilevel converters, IEEE Trans. Power Electron., vol. 8, no. 11, pp , Nov [Online]. Available: wrapper.htm?arnumber= [31] J.-W. Moon, C.-S. Kim, J.-W. Park, D.-W. Kang, and J.-M. Kim, Circulating current control in MMC under the unbalanced voltage, IEEE Trans. Power Del., vol. 8, no. 3, pp , Jul [Online]. Available: wrapper.htm?arnumber= Theodore Soong (SM 11) received the B.A.Sc. degree in engineering science and the M.A.Sc. degree in electrical engineering from the University of Toronto, Toronto, ON, Canada, in 009 and 01, respectively, where he is currently working toward the Ph.D. degree in electrical engineering. He is currently with the Department of Electrical and Computer Engineering, University of Toronto. His current research interests include the integration of renewable resources to the grid and modular converters. Peter W. Lehn (S 88 M 98 SM 05) received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Manitoba, Winnipeg, MB, Canada, in 1990 and 199, respectively, and the Ph.D. degree from the University of Toronto, Toronto, ON, Canada, in He joined the faculty at the University of Toronto in He spent six months as a Visiting Professor with the University of Erlangen-Nuremberg, Erlangen, Germany, in 001. He is currently with the Department of Electrical and Computer Engineering, University of Toronto. His current research interests include HVDC technologies, grid integration of solar and wind energy systems, and theoretical and experimental analysis of power electronics.