The fundamental frequency component in the arm currents of a modular multilevel converter is a necessity for the operation of the converter, as is the connection and bypassing of the submodules. ...Inevitably, this will cause alternating components in the capacitor voltages. This paper investigates how the arm currents and capacitor voltages interact when the submodules are connected and bypassed in a sinusoidal manner. Equations that describe the circulating current that is caused by the variations in the total inserted voltage are derived. Resonant frequencies are identified and the resonant behaviour is verified by experimental results. It is also found that the effective values of the arm resistance and submodule capacitances can be extracted from the measurements by least square fitting of the analytical expressions to the measured values. Finally, the analytical expression for the arm currents is verified by experimental results.
Many publications have been presented on the modulation and control of the modular multilevel converter, some of which are based on phase-shifted carrier modulation. This paper presents an analysis ...of how the switching frequency affects the capacitor voltages, circulating currents, and alternating voltages using phase-shifted carrier modulation. It is found that switching frequencies that are integer multiples of the fundamental frequency should be avoided as they can cause the capacitor voltages to diverge. Suitable switching frequencies are derived for which the arm and line quantities will be periodic with symmetric operating conditions in the upper and lower arms. Thus, the practical outcome of this paper is a detailed description of how the switching frequency should be chosen in order to achieve advantageous operating conditions. The theoretical results from the analysis are validated by both simulations and experimental results.
This paper presents a new modulation method for the modular multilevel converter. The proposed method is based on a fixed pulse pattern where harmonic elimination methods can be applied. In the ...proposed modulation method, the pulse pattern is chosen in such a way that the stored energy in each submodule remains stable. It is shown that this can be done at the fundamental switching frequency without measuring the capacitor voltages or using any other form of feedback control. Such a modulation scheme has not been presented before. The theoretical results are verified by both simulations and experimental results. The simulation results show successful operation at the fundamental switching frequency with a larger number of submodules. When a smaller number of submodules are used, harmonic elimination methods may be applied. This is verified experimentally on a converter with eight submodules per phase leg. The experimental results verify that stable operation can be maintained at the fundamental switching frequency while successfully eliminating the fifth harmonic in the ac-side voltage.
The balancing of the capacitor voltages in modular multilevel converters becomes increasingly difficult when the switching frequency is reduced. Typically, a reduced switching frequency will increase ...the spread in the capacitor voltages and, thus, the voltage ripple in the individual submodules. This paper presents a capacitor voltage balancing strategy which aims to combine a low switching frequency with a low capacitor-voltage ripple. This is done by a predictive algorithm that controls the converter in such a way that the stored charge in the submodule capacitors is evenly distributed among all the submodules when the capacitor voltages reach their maximum values. In this way, it is possible to limit the peak voltages in the submodule capacitors at switching frequencies as low as 2-3 times the fundamental switching frequency. The proposed capacitor voltage balancing strategy is validated by both simulations and experimental results with 130-Hz and 140-Hz switching frequency. In the simulations, the capacitor voltage ripple was reduced by 24% compared to the case when a conventional sorting algorithm is used, and the experimental results show that it is possible to combine the proposed voltage balancing strategy with a circulating-current controller.
The internal control of a modular multilevel converter aims to equalize and stabilize the submodule capacitor voltages independent of the loading conditions. It has been shown that a submodule ...selection mechanism, included in the modulator, can provide voltage sharing inside the converter arm. Several procedures for controlling the total stored energy in each converter arm exist. A new approach is described in this paper. It is based on estimation of the stored energy in the arms by combining the converter electromotive force reference, the measured alternating output current, and the known direct voltage. No feedback controllers are used. Experimental verification on a three-phase 10 kVA prototype is presented along with the description of the new procedure.
Modular multilevel converters (M2Cs) are increasingly used in high-voltage direct current (HVDC) systems. The efficiency of M2Cs is influenced by the modulation and cell selecting methods, which ...determines the switching frequency and capacitor voltage ripple in the converter station. A new approach to modulation of the M2C is presented in this paper. Tolerance band methods are employed to obtain the switching instants, and also cell selection. The proposed methods overcome the modulation problem for converters with few cells on one hand and also reduce the sorting efforts for cell balancing purposes of many cells converter on the other hand. Three different algorithms are also proposed to balance the cell capacitor voltages. The evaluation is done in time-domain simulation by which the performance of each method is studied in both the steady-state and transient cases. It is observed that using tolerance band methods not only reduces the switching frequency but also allows for handling severe fault cases in a grid-connected system. Eventually, the most promising tolerance band method has been implemented and verified in a real-time digital simulator, RTDS®. The average switching frequency of 70 Hz has been achieved for the system under study, while the capacitor voltage ripple is limited to 10% of the nominal cell voltage.
In modular multilevel converters, there is a tradeoff between the switching frequency and the voltage ripple in the submodule capacitors. The reason for this is that it becomes increasingly difficult ...to balance the capacitor voltages when the switching frequency is reduced. This paper presents a new submodule circuit, which improves the balancing of the capacitor voltages at low switching frequencies. The proposed submodule circuit consists of two capacitors and eight switches, forming a three-level submodule. Ideally, the voltage and current ratings of the switches can be chosen such that the combined power rating of the semiconductors is the same as for the equivalent solution with conventional half-bridge submodules. The proposed submodule circuit provides the possibility of connecting the two capacitors in parallel when the intermediate voltage level is used. This will reduce the capacitor voltage ripple, especially at low switching frequencies, and thus, allow for a reduction of the size, weight, and cost of the submodule capacitors. The proposed submodule circuit is validated by both simulations and experimental results. It is found that the parallel connection of the submodule capacitors will, in fact, significantly improve the balancing of the capacitor voltages.
Recent evidence has suggested that clades of dioecious angiosperms have fewer extant species on average than those of cosexual (hermaphroditic and monoecious) relatives. Reasons for the decrease in ...speciation rates and/or increase in extinction rates are only beginning to be investigated. One possibility is that dioecious species suffer a competitive disadvantage with cosexuals because only half of the individuals in a dioecious population are seed bearing. When only females produce seed, offspring will be more spatially clumped and will experience more local resource competition than when every individual produces seed. We examine two spatially explicit models to determine the effect of a reduction in seed dispersers on the invasibility and persistence of dioecious populations. Even though dioecious females were allowed to produce twice as many seeds as cosexuals, our results show that a reduction in the number of seed dispersers causes a decrease in the ability of dioecious progeny to find uninhabited sites, thus reducing persistence times. These results suggest that the maintenance of dioecy in the presence of hermaphroditic competitors requires a substantial increase in relative fitness and/or a large dispersal advantage of dioecious seeds. Corresponding Editor: M. Morgan
In this paper, previously developed stability results for open-loop sum-capacitor-voltage control of modular multilevel converters are extended. To give improved damping, circulating-current feedback ...is included in the control law. With the output-current control loop and a first-order measurement lag taken into account, global asymptotic stability is proven. Careful consideration of the on-line sum-capacitor-voltage reference computation is given, since this is the most critical part of the control system.
Material Rauši settlement and cemetery The case study looks at a site located on Dole Island, a centre of the Iron Age Daugava Liv population (Fig. 1). During the excavation of Rauši settlement, the ...food waste macro remains (animal bones) were identified by species and noted in the documentation (INV Nr Pd 14514). ...on the basis of visual assessment, it seems that we see evidence of a reuse of the household pottery in the burials (see Rice 1992, 233). In the excavation notes a list of excavated bones (fish, bird, large stock, small stock, sheep, pig, cow, horse, beaver, wild boar, deer or elk) was made for each feature.
