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Showing papers on "Topology (electrical circuits) published in 2010"


Journal ArticleDOI
TL;DR: The operation of modular multilevel converter is described, an emerging and highly attractive topology for medium- and high-voltage applications and a new pulsewidth-modulation scheme for an arbitrary number of voltage levels is introduced and evaluated.
Abstract: This paper describes the operation of modular multilevel converter, an emerging and highly attractive topology for medium- and high-voltage applications. A new pulsewidth-modulation (PWM) scheme for an arbitrary number of voltage levels is introduced and evaluated. On the basis of this PWM scheme, the semiconductor losses are calculated, and the loss distribution is illustrated.

899 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method.

517 citations


Journal ArticleDOI
TL;DR: In this paper, the ground current in a 1.5kW PV installation is measured under different conditions and used to build a simulation model, which allows the study of the influence of the harmonics injected by the inverter on the ground currents.
Abstract: For low-power grid-connected applications, a single-phase converter can be used. In photovoltaic (PV) applications, it is possible to remove the transformer in the inverter to reduce losses, costs, and size. Galvanic connection of the grid and the dc sources in transformerless systems can introduce additional ground currents due to the ground parasitic capacitance. These currents increase conducted and radiated electromagnetic emissions, harmonics injected in the utility grid, and losses. Amplitude and spectrum of the ground current depend on the converter topology, the switching strategy, and the resonant circuit formed by the ground capacitance, the converter, the ac filter, and the grid. In this paper, the ground current in a 1.5-kW PV installation is measured under different conditions and used to build a simulation model. The installation includes a string of 16 PV panel, a full-bridge inverter, and an LCL filter. This model allows the study of the influence of the harmonics injected by the inverter on the ground current.

418 citations


Journal ArticleDOI
TL;DR: Based on the concept of control topology, an impulsive controller is designed to achieve the exponential synchronization of CDNs, and moreover, the exponential convergence rate can be specified.
Abstract: In this paper, the synchronization of complex dynamical networks (CDNs) with system delay and multiple coupling delays is studied via impulsive distributed control. The concept of control topology is introduced to describe the whole controller structure, which consists of some directed connections between nodes. The control topology can be designed either to be the same as the non-delayed coupling topology of the network, or to be independent of the intrinsic network topology. Based on the concept of control topology, an impulsive controller is designed to achieve the exponential synchronization of CDNs, and moreover, the exponential convergence rate can be specified. Illustrated examples have been given to show the effectiveness of the proposed impulsive distributed control strategy.

395 citations


Journal ArticleDOI
TL;DR: This new topology has the potential to increase the efficiency and reduce the cost of high-power pickups by minimizing the reactive currents in the pickup coil and the reflected VAR loading on the power supply.
Abstract: This paper describes the design of a new unity-power-factor inductive-power-transfer (IPT) pickup using an LCL tuned network for application in high-power systems. This new topology has the potential to increase the efficiency and reduce the cost of high-power pickups by minimizing the reactive currents in the pickup coil and the reflected VAR loading on the power supply. In a practical system, the rectifier and associated processing circuitry distorts the current waveforms, adding an effective inductive loading to the pickup circuit. A series compensation capacitor is added to correct this loading. A design strategy is developed for the new topology, and two example circuits are constructed and compared experimentally with a traditional parallel-tuned (LC) pickup operating on a monorail-based IPT system.

355 citations


Journal ArticleDOI
TL;DR: In this paper, a general voltage source converter high voltage direct current (VSC MTDC) model is derived mathematically, which is valid for every possible topology of the DC circuit.
Abstract: In this paper, a new general voltage source converter high voltage direct current (VSC MTDC) model is derived mathematically. The full system model consists of the converter and its controllers, DC circuit equations, and coupling equations. The main contribution of the new model is its valid for every possible topology of the DC circuit. Practical implementation of the model in power system stability software is discussed in detail. The generalized DC equations can all be expressed in terms of matrices that are byproducts of the construction of the DC bus admittance matrix. Initialization, switching actions resulting in different topologies and simulation of the loss of DC lines amount to a simple calculation or recalculation of the DC bus admittance matrix. The model is implemented in Matlab. Examples on a two- and six-terminal system show that the new model is indeed capable of accurately simulating VSC MTDC systems with arbitrary topology.

290 citations


Journal ArticleDOI
TL;DR: Comparisons among the modulation techniques are discussed, and it is proven that the proposed modulation for two- and three-level inverters presents the best results.
Abstract: In some photovoltaic (PV) applications, it is possible to remove the transformer of a system in order to reduce losses, cost, and size. In transformerless systems, the PV module parasitic capacitance can introduce leakage currents in which the amplitude depends on the converter topology, on the pulsewidth modulation, and on the resonant circuit comprised by the system components. Based on the common-mode voltage model, modulation techniques are proposed to eliminate the leakage current in transformerless PV systems without requiring any modification on the converter and any additional hardware. The main drawback is that the proposed modulation technique for two-level inverters can only be used with 650-V dc link in the case of a 110-V (rms) grid phase voltage. Comparisons among the modulation techniques are discussed, and it is proven that the proposed modulation for two- and three-level inverters presents the best results. To validate the models used in the simulations, an experimental three-phase inverter is used.

288 citations


Proceedings ArticleDOI
Kurt Friedrich1
04 Jul 2010
TL;DR: In this article, the authors present an actual view into the development of high voltage direct current (HVDC) converter stations build in Modular Multilevel Converter (MMC) topology.
Abstract: This paper presents an actual view into the development of High Voltage Direct Current (HVDC) converter stations build in Modular Multilevel Converter (MMC) topology. Explanations are given how voltage sourced converters (VSC) of large active power transmission capacity and independent controlled reactive power exchange capability are designed for terminals of HVDC Links. This modern type of self-commutated converters has been developed under brand name HVDC PLUS by Siemens for use in electric power systems.

280 citations


Journal ArticleDOI
TL;DR: An algorithm is proposed that generates random topology power grids featuring the same topology and electrical characteristics found from the real data.
Abstract: In order to design an efficient communication scheme and examine the efficiency of any networked control architecture in smart grid applications, we need to characterize statistically its information source, namely the power grid itself. Investigating the statistical properties of power grids has the immediate benefit of providing a natural simulation platform, producing a large number of power grid test cases with realistic topologies, with scalable network size, and with realistic electrical parameter settings. The second benefit is that one can start analyzing the performance of decentralized control algorithms over information networks whose topology matches that of the underlying power network and use network scientific approaches to determine analytically if these architectures would scale well. With these motivations, in this paper we study both the topological and electrical characteristics of power grid networks based on a number of synthetic and real-world power systems. The most interesting discoveries include: the power grid is sparsely connected with obvious small-world properties; its nodal degree distribution can be well fitted by a mixture distribution coming from the sum of a truncated geometric random variable and an irregular discrete random variable; the power grid has very distinctive graph spectral density and its algebraic connectivity scales as a power function of the network size; the line impedance has a heavy-tailed distribution, which can be captured quite accurately by a clipped double Pareto lognormal distribution. Based on the discoveries mentioned above, we propose an algorithm that generates random topology power grids featuring the same topology and electrical characteristics found from the real data.

271 citations


Journal ArticleDOI
TL;DR: In this article, a set of basic rules for generating multiple-input converter topologies is proposed for hybrid power systems, where all the input sources can power the load simultaneously or individually, and only one power source can transfer energy to the load at a time.
Abstract: Hybrid power systems continuously deliver power to the load from several renewable energy sources. For such systems, the use of a multiple-input converter (MIC) has the advantage of simpler circuit structure and lower cost, compared to the use of several single-input converters. By decomposing converters into basic cells, namely, pulsating source cells and output filters, a set of basic rules for generating multiple-input converter topologies is proposed. Specifically, two families of multiple-input converters are systematically generated. In the first family of MICs, all the input sources can power the load simultaneously or individually. In the second family, only one power source is allowed to transfer energy to the load at a time. Furthermore, some isolated MICs are simplified for reducing the complexity of the circuit configuration.

255 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a novel converter topology that interfaces four power ports: two sources, one bidirectional storage port, and one isolated load port, which can achieve zero-voltage switching for all four main switches.
Abstract: This paper proposes a novel converter topology that interfaces four power ports: two sources, one bidirectional storage port, and one isolated load port. The proposed four-port dc/dc converter is derived by simply adding two switches and two diodes to the traditional half-bridge topology. Zero-voltage switching is realized for all four main switches. Three of the four ports can be tightly regulated by adjusting their independent duty-cycle values, while the fourth port is left unregulated to maintain the power balance for the system. Circuit analysis and design considerations are presented; the dynamic modeling and close-loop design guidance are given as well. Experimental results verify the proposed topology and confirm its ability to achieve tight independent control over three power-processing paths. This topology promises significant savings in component count and losses for renewable energy power-harvesting systems.

Patent
26 Jan 2010
TL;DR: In this paper, a data communication system and an associated network node implementation is disclosed that, in certain embodiments, uses single-channel bi-directional communication links between nodes to send frames of data.
Abstract: A data communication system and an associated network node implementation is disclosed that, in certain embodiments, uses single-channel bi-directional communication links between nodes to send frames of data. The network nodes can be connected together in a ring or daisy chain topology with data frames sent in alternating directions through the bi-directional links. Such networks initially configured in a physical ring topology can tolerate single point failures by automatically switching to a logical daisy chain topology.

Proceedings ArticleDOI
01 Nov 2010
TL;DR: In this paper, the steady-state analysis of the converter has been carried out, giving some guidelines for the design (considering soft switching limits and the amount of reactive current) and a small-signal model of the topology.
Abstract: The increase demand of an intermediate storage of electrical energy in battery systems, in particular due to the use of renewable energy, has resulted in the need of bidirectional DC/DC power converters with galvanic isolation Uninterruptible Power Supplies (UPS), battery charging systems, photovoltaic equipment and auxiliary power supplies in traction applications are examples of some fields of application of this kind of converters A Dual Active Bridge (DAB) bidirectional DC/DC converter is a topology with the advantages of decreased number of devices, soft-switching commutations, low cost, and high efficiency The use of this topology is proposed for applications where the power density, cost, weight, and reliability are critical factors In the present paper the steady-state analysis of the converter has been carried out, giving some guidelines for the design (considering soft switching limits and the amount of reactive current) and a small-signal model of the topology Simulations and experimental results are also presented

Journal ArticleDOI
TL;DR: A three-level nonisolated dc-dc converter as a candidate for ultracapacitor applications is proposed and analyzed and experimentally verified on a general-purpose controlled electric drive.
Abstract: Electrochemical double-layer capacitors, which are well known as ultracapacitors, have intensively been used in power conversion applications such as controlled electric drives, active filters, power conditioners, and uninterruptible power supplies. The ultracapacitor is employed as the energy storage device that can be fully charged/discharged within a few seconds. To achieve better flexibility and efficiency, the ultracapacitor is connected to the power conversion system via an interfacing dc-dc power converter. Various topologies are used as the dc-dc power converter: nonisolated two-level single-phase or multiphase interleaved converters and many varieties of isolated soft-switched dc-dc converters. A three-level nonisolated dc-dc converter as a candidate for ultracapacitor applications is proposed and analyzed in this paper. The topology is theoretically analyzed, and design guidelines are given. The modeling and control aspects are discussed. A 5.5-kW prototype was designed, and the proposed topology was experimentally verified on a general-purpose controlled electric drive. Experimental results are presented and discussed.

Journal ArticleDOI
TL;DR: A new approach based on the interval analysis is introduced to solve the DOCRs coordination problem considering uncertainty in the network topology, and the application of the proposed method to the IEEE 14- and 30-bus test systems proves the ability of the interval method in modeling topology uncertainty inThe large-scale coordination problem.
Abstract: In real power systems, the network topology is subjected to uncertainty due to single-line outage contingencies, maintenance activities, and network reconfigurations. These changes in the network topology may lead to miscoordination of directional overcurrent relays (DOCRs). To overcome this drawback, corresponding to each primary/backup relay pair, a set of inequality coordination constraints which is related to different network topologies should be satisfied. In this paper, a new approach based on the interval analysis is introduced to solve the DOCRs coordination problem considering uncertainty in the network topology. The basic idea is to convert the set of inequality constraints corresponding to each relay pair to an interval constraint. In this situation, the DOCR coordination problem is formulated as an interval linear programming (ILP) problem. Using well-known mathematical theorems, the obtained ILP problem, which has no equality constraints, can be converted to standard linear programming (LP). As a result, the number of coordination constraints is significantly reduced in the proposed methods. The application of the proposed method to the IEEE 14- and 30-bus test systems proves the ability of the interval method in modeling topology uncertainty in the large-scale coordination problem.

01 Jan 2010
TL;DR: The ability of this topology to deal with abnormal conditions is demonstrated, especially its ability to keep control of the current despite the collapse of the DC bus voltage, e.g. a DCside fault.
Abstract: Voltage-Source Converters have brought numerous advantages to HVDC transmission. However, they suffer from high losses and are usually weak against faults on the DC-side. In this paper, a new topology which brings together some concepts from traditional Current Source Converters and multi-level converters, is presented. Two stacks of Hbridge cells alternate to construct the converter voltage using director switches made of IGBTs in series. The resulting converter generates AC current with low harmonic content and with low loss. Furthermore, the converter is still very responsive in case of a fault. This paper first explains the composition and the working of this converter, then detailed simulations at 20 MW illustrate the performances and low losses of this converter under normal conditions. The ability of this topology to deal with abnormal conditions is also demonstrated, especially its ability to keep control of the current despite the collapse of the DC bus voltage, e.g. a DCside fault.

Journal ArticleDOI
TL;DR: In this article, several research topics pertaining to the design and modeling of domestic induction appliances are reviewed, stressing its most significant advances and pointing to its future tendencies, and a bibliographic review showing some of the published papers during the last years is included.
Abstract: In this paper several research topics pertaining to the design and modeling of domestic induction appliances are reviewed. Each topic is summarized, stressing its most significant advances and pointing to its future tendencies. A bibliographic review showing some of the published papers during the last years is included. The emphases and relative contributions of some of them are also discussed.

Journal ArticleDOI
TL;DR: Simulation and experimental results show that the proposed method can obtain the desired voltage much faster and minimize commutation torque ripple more efficiently at both high and low speeds.
Abstract: Brushless dc motor still suffers from commutation torque ripple, which mainly depends on speed and transient line current in the commutation interval. This paper presents a novel circuit topology and a dc link voltage control strategy to keep incoming and outgoing phase currents changing at the same rate during commutation. A dc-dc single-ended primary inductor converter (SEPIC) and a switch selection circuit are employed in front of the inverter. The desired commutation voltage is accomplished by the SEPIC converter. The dc link voltage control strategy is carried out by the switch selection circuit to separate two procedures, adjusting the SEPIC converter and regulating speed. The cause of commutation ripple is analyzed, and the way to obtain the desired dc link voltage is introduced in detail. Finally, simulation and experimental results show that, compared with the dc-dc converter, the proposed method can obtain the desired voltage much faster and minimize commutation torque ripple more efficiently at both high and low speeds.

Journal ArticleDOI
TL;DR: Noise leads to a general, one-to-one correspondence between the dynamical correlation and the connections among oscillators for a variety of node dynamics and network structures, enabling an accurate prediction of the full network topology based solely on measuring the dynamicals correlation.
Abstract: We study the relationship between dynamical properties and interaction patterns in complex oscillator networks in the presence of noise. A striking finding is that noise leads to a general, one-to-one correspondence between the dynamical correlation and the connections among oscillators for a variety of node dynamics and network structures. The universal finding enables an accurate prediction of the full network topology based solely on measuring the dynamical correlation. The power of the method for network inference is demonstrated by the high success rate in identifying links for distinct dynamics on both model and real-life networks. The method can have potential applications in various fields due to its generality, high accuracy, and efficiency.

Journal ArticleDOI
TL;DR: In this paper, a single-switch non-isolated dc-dc converter with high voltage transfer gain and reduced semiconductor voltage stress is proposed, which utilizes a hybrid switched-capacitor technique for providing a high voltage gain without an extreme switch duty cycle and yet enabling the use of a lower voltage and RDS-ON MOSFET switch.
Abstract: In this paper, a new single-switch nonisolated dc-dc converter with high voltage transfer gain and reduced semiconductor voltage stress is proposed. The proposed topology utilizes a hybrid switched-capacitor technique for providing a high voltage gain without an extreme switch duty cycle and yet enabling the use of a lower voltage and RDS-ON MOSFET switch so as to reduce cost, switch conduction, and turn-on losses. In addition, the low voltage stress across the diodes allows the use of Schottky rectifiers for alleviating the reverse-recovery current problem, leading to a further reduction in the switching, and conduction losses. The principle of operation and a comparison with other high step-up topologies are presented. Two extensions of the proposed converter are also introduced and discussed. Simulation and experimental results are also presented to demonstrate the effectiveness of the proposed scheme.

Proceedings ArticleDOI
23 Dec 2010
TL;DR: In this article, an alternative 3-level topology referred to as T-type is presented, which is very high efficient for medium switching frequencies (4-20 kHz) for low voltage converter.
Abstract: In the low voltage converter range, 3-phase 3-level VSC topologies are not wide spread in industry because of the increased part count and higher costs, although they are more efficient for higher switching frequencies. In this paper an alternative 3-level topology referred to as T-type is presented, which is very high efficient for medium switching frequencies (4–20 kHz). Additionally, it is shown that the total silicon chip area of a 3-level topology can be lower than in a 2-level topology since the losses are distributed over more components leading to only a small increase in the junction temperature. This allows for the design of a chip area and cost optimized 3-level bridge leg module for the mass market.

Journal ArticleDOI
TL;DR: The simulations and experimental results for a 15kW three-phase system, with nine voltage levels, validate the study presented and help clarify the structure and development of an equation in the load voltage for n levels using PWM phase-shifted multicarrier modulation.
Abstract: In this paper, a modular three-phase multilevel inverter specially suited for electrical drive applications is proposed. Unlike the cascaded H-bridge inverter, this topology is based on power cells connected in cascade using two inverter legs in series. A detailed analysis of the structure and the development of design equations for the load voltage with n levels are carried out using pulsewidth-modulation phase-shifted multicarrier modulation. Simulations and experimental results for a 15-kW three-phase system, with nine voltage levels, validate the study presented.

Proceedings ArticleDOI
C C Davidson1, D R Trainer1
01 Jan 2010
TL;DR: In this paper, the authors proposed a wave-shaping scheme for VSC-HVDC power transmission using a combination of IGBT valves using series-connected IGBTs and multilevel converters based on individual and isolated half-bridge and full-bridge submodules.
Abstract: Existing circuit topologies for VSC-HVDC power transmission fall into two distinct categories In the first category, low-pulse-number converters are used, employing large numbers of IGBTs in series in each valve, with Pulse Width Modulation (PWM) The second category, known as the M2C topology, uses a "Multi-Level" approach to achieve very high pulse numbers However, recent research work has highlighted a number of interesting possibilities for a new family of converters for use in VSC-HVDC schemes, combining the advantages of both approaches The new converters rely on using a combination of IGBT valves using series-connected IGBTs and multilevel converters based on individual and isolated half-bridge and full-bridge submodules ("cells") which provide a "wave-shaping" function Several options are possible, where the multilevel cells are connected in series or parallel with series IGBT "Director" valves and with the multilevel cells on either the AC or DC side of the converter (5 pages)

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a DC-DC multi-output boost (MOB) converter which can share its total output between different series of output voltages for low and high power applications.
Abstract: This study presents a new DC-DC multi-output boost (MOB) converter which can share its total output between different series of output voltages for low- and high-power applications. This configuration can be utilised instead of several single output power supplies. This is a compatible topology for a diode-clamed inverter in the grid connection systems, where boosting low rectified output-voltage and series DC link capacitors is required. To verify the proposed topology, steady-state and dynamic analyses of a MOB converter are examined. A simple control strategy has been proposed to demonstrate the performance of the proposed topology for a double-output boost converter. The topology and its control strategy can easily be extended to offer multiple outputs. Simulation and experimental results are presented to show the validity of the control strategy for the proposed converter.

Journal ArticleDOI
TL;DR: This paper proposes fractional-order formation control algorithms with absolute/relative damping and studies the conditions on the network topology and the control gains such that the formation control will be achieved under a directed fixed networkTopology.

Journal ArticleDOI
TL;DR: Novel symmetric hybrid multilevel topologies are introduced for both single- and three-phase medium-voltage high-power systems, and the topology conception is presented in detail, where a three-level switching cell with low component count and its modulation pattern give the origin of the proposed converters.
Abstract: Novel symmetric hybrid multilevel topologies are introduced for both single- and three-phase medium-voltage high-power systems. The topology conception is presented in detail, where a three-level switching cell with low component count, and its modulation pattern give the origin of the proposed converters. Voltage sharing and low output-voltage distortion are achieved. The theoretical frequency spectra are derived. Switching devices are separated into high- and low-frequency devices, generating hybrid converters. Five-level three-phase topologies are generated from only three insulated dc sources, while the number of semiconductors is the same as for the cascaded H bridge. Both simulation and experimental results are provided showing the validity of the analysis.

Journal ArticleDOI
Bin Su1, Zhengyu Lu1
TL;DR: In this paper, an interleaved totem-pole boost bridgeless rectifier with reduced reverse-recovery problems for power factor correction is proposed. But it is not shown that the converter can achieve zero-voltage switching under low line input.
Abstract: An interleaved totem-pole boost bridgeless rectifier with reduced reverse-recovery problems for power factor correction is proposed in this paper. The proposed converter consists of two interleaved and intercoupled totem-pole boost bridgeless converter cells. The two cells operate in phase-shift mode. Thus, the input current can be continuous with low ripple. For the individual cells, they operate alternatively in discontinuous current mode and the maximum duty ratio is 50%, which allows shifting the diode current with low di/dt rate to achieve zero-current switching off. Zero-voltage switching is achieved in the MOSFETs under low line input. Furthermore, the merits of totem-pole topology are inherited. The common-mode (CM) noise interference is rather low. And the potential capacity of bidirectional power conversion is retained. In brief, the conduction losses are reduced, reverse-recovery process is improved, and high efficiency is achieved. The interleaved totem-pole cell can also be applied to bidirectional dc/dc converters and ac/dc converters. Finally, an 800 W, 100 kHz experimental prototype was built to verify the theoretical analysis and feasibility of the proposed converter, whose efficiency is above 95.5% at full load under 90 V.

Journal ArticleDOI
TL;DR: In this article, a high power-factor rectifier suitable for universal line base on a modified version of the single-ended primary inductance converter (SEPIC) is presented, where voltage multiplier technique is applied to the classical SEPIC circuit, obtaining new operation characteristics as low-switchvoltage operation and high static gain at low line voltage.
Abstract: A high-power-factor rectifier suitable for universal line base on a modified version of the single-ended primary inductance converter (SEPIC) is presented in this paper. The voltage multiplier technique is applied to the classical SEPIC circuit, obtaining new operation characteristics as low-switch-voltage operation and high static gain at low line voltage. The new configuration also allows the reduction of the losses associated to the diode reverse recovery current, and soft commutation is obtained with a simple regenerative snubber circuit. The operation analysis, design procedure, and experimental results obtained from a 650-W universal line power-factor-correction prototype of the proposed converter are presented. The theoretical analysis and experimental results obtained with the proposed structure are compared with the classical boost topology.

Journal ArticleDOI
TL;DR: A systematic approach to derive DI converters by using a single-pole triple-throw switch as a building block is presented.
Abstract: Hybridizing energy systems using storage devices has gained popularity in transportation and distributed electric power generation applications. Traditionally, several independent power electronic converters (PECs) were utilized in such practices. Due to their reduced part count, double-input (DI) PECs prove to be a promising choice in hybridizing energy systems. A few topologies for multi-input converters have been reported in the literature; however, there is no systematic approach to synthesize them. Furthermore, all possible topologies are not completely explored, and it is difficult to derive new converters from existing topologies. Therefore, in this paper, a systematic approach to derive DI converters by using a single-pole triple-throw switch as a building block is presented.

Journal ArticleDOI
TL;DR: The steady-state power balance in the cells of a single-phase two-cell CHB is studied and the limits of the maximum and minimum input active powers for a stable operation of the CHB are addressed.
Abstract: Multilevel cascaded H-bridge (CHB) converters have been presented as a good solution for high-power applications. In this way, several control and modulation techniques have been proposed for this power converter topology. In this paper, the steady-state power balance in the cells of a single-phase two-cell CHB is studied. The capability to be supplied with active power from the grid or to deliver active power to the grid in each cell is analyzed according to the dc-link voltages and the desired ac output voltage value. The limits of the maximum and minimum input active powers for a stable operation of the CHB are addressed. Simulation results are shown to validate the presented analysis.