Negative Half Cycle Research Articles

Investigation of Partial Discharge Transformation Characteristics in Polyimide (PI) Insulations under High-Frequency Electric Stress.

This research delves into the primary issue of polyimide (PI) insulation failures in high-frequency power transformers (HFPTs) by scrutinizing partial discharge development under high-frequency electrical stress. This study employs an experimental approach coupled with a plasma simulation model for a ball-sphere electrode structure. The simulation model integrates the particle transport equation, Poisson equation, and complex chemical reactions to ascertain microscopic parameters, including plasma distribution, electric field, electron density, electron temperature, surface, and space charge distribution. The effect of the voltage polarity and electrical energy on the PD process is also discussed. The contact point plays a pivotal role in triggering partial discharges and culminating in the breakdown of PI insulation. Asymmetry phenomena were found between positive and negative half-cycles by analyzing the PD data stage by stage. A significant number of PDs increased at every stage and the PD amplitude was higher during the negative cycle at the initial stage, but in later stages, the PD amplitude was found to be higher in the positive half-cycle, and scanning electron microscopy (SEM) revealed that the maximum damage occurred near the contact point junction. The simulation results show that the plasma initially accumulates the electron density near the contact point junction. Under the action of the electric field, plasma starts traveling at the PI surface outward from the contact point. Before the PD activity, all parameters have higher values in the plasma head. The microscopic parameters reveal maximum values near the contact point junction, during PD activities where significant damage takes place. These parameter distributions exhibit a decreasing trend over time as when the PD activity ends. The model's predictions are consistent with the experimental data. The paper lays the foundation for future research in polymer insulation design under high-frequency electrical stress.

Elucidation of discharge mechanisms in He- and Ar-flexible μ-tube plasmas by temporally and spatially resolved plasma optical emission phoresis spectroscopy

A Helium- and Argon-flexible μ-tube plasma (FμTP) driven by a square wave high voltage were investigated by means of temporally and spatially resolved spectroscopy to characterize the discharge mechanisms. These two discharge gases show different discharge behavior in the same FμTP-configuration. The mixtures of different concentration of propane in Ar were used as discharge gases to confirm the role of Ar+ in an Ar-FμTP by tuning the discharge behavior. It was demonstrated that, N2+ are mainly responsible for the excitation and ionization and only small amount of He+ are produced in a He-FμTP, whereas Ar-FμTP lives from Ar+. These ions as well as excited species do not propagate beyond the capillary during the negative half cycle, resulting in a negligible contribution for protonation in this half cycle. The present study proposes a new method to data analysis, Plasma Optical Emission Phoresis Spectroscopy, which allows to distinguish noble gas ions from excited noble gas species.

Design and implementation of an innovative single-phase direct AC-AC bipolar voltage buck converter with enhanced control topology

Direct AC–AC converters are strong candidates in the power converting system to regulate grid voltage against the perturbation in the line voltage and to acquire frequency regulation at discrete step levels in variable speed drivers for industrial systems. All such applications require the inverted and non-inverted form of the input voltage across the output with voltage-regulating capabilities. The required value of the output frequency is gained with the proper arrangement of the number of positive and negative pulses of the input voltage across the output terminals. The period of each such pulse for low-frequency operation is almost the same as the half period of the input grid or utility voltage. These output pulses are generated by converting the positive and negative input half cycles in noninverting and inverting forms as per requirement. There is no control complication to generate control signals used to adjust the load frequency as the operating period of the switching devices is normally greater than the period of the source voltage. However, high-frequency pulse width modulated (PWM) control signals are used to regulate the output voltage. The size of the inductor and capacitor is inversely related to the value of the switching frequency. Similarly, the ripple contents of voltage and currents in these filtering components are also inversely linked with PWM frequency. These constraints motivate the circuit designer to select high PWM frequency. However, the alignment of the high-frequency control input with the variation in the input source voltage is a big challenge for a design engineer as the switching period of a high-frequency signal normally lies in the microsecond. It is also required to operate some high-frequency devices for various half cycles of the source voltage, creating control complications as the polarities of the half cycles are continuously changing. This requires at least the generation of two high-frequency signals for different intervals. The interruption of the filtering inductor current is a big source of high voltage surges in circuits where the high-frequency transistors operate in a complementary way. This may be due to internal defects in the switching transistors or some unnecessary inherent delay in their control signals. In this research work, a simplified AC–AC converter is developed that does not need alignment of high-frequency control with the polarity of the source voltage. With this approach, high-frequency signals can be generated with the help of any analog or digital control system. By applying this technique, only one high-frequency control signal is generated and applied in AC circuits, as in a DC converter, without applying a highly sensitive polarity sensing circuit. So, controlling complications is drastically simplified. The circuit and configuration always avoid the current interruption problem of filtering the inductor. The proposed control and circuit topology are tested both in computer-based simulation and practically developed circuits. The results obtained from these platforms endorse the effectiveness and validation of the proposed work.

Single Power-Conversion Active-Clamped AC/DC Converter Employing Si/SiC Hybrid Switch

This article proposes a single power-conversion voltage-fed active-clamped ac/dc converter that uses an Si IGBT/SiC MOSFET hybrid switch. By incorporating two switches at the primary side of the circuit, we removed the full-bridge diode rectifier, and thereby reduced the required number of power devices. Inherent bidirectional active-clamp circuit naturally limits the voltage spike at bottom switches and reuses the energy accumulated in the leakage inductor during both positive and negative grid half-cycles. Also, it offers dual-resonant power transfer paths, so it can deliver the high power with less circuit components. The alternating switching modulation makes one of the bottom switches turn off with hard switching per grid half-cycle while holding other bottom switch on to conduct the current. In contrast, top switches are softly switched with low root-mean-square current. Therefore, the converter with proposed switching modulation enables direct substitution of Si IGBT for an SiC MOSFET at the top on the primary side, and thereby which cuts down the circuit implementation cost. We built a 1 kW prototype converter and confirmed its validity.

Corrosion Behavior of X80 Steel in a Simulated Soil Solution Under Square-Wave Current Interference

The buried pipeline is disturbed by the dynamic direct current (DC) stray current with the subway as the main leakage source, which has the safety risk of accelerating corrosion, resulting in pipeline failure, which not only causes economic losses but also threatens personal safety. Therefore, it is necessary to study the corrosion behavior of pipeline steel under dynamic DC interference. The corrosion behavior of X80 steel under dynamic DC interference were studied by a mass loss test, alternating current impedance, circuit simulation, x-ray diffraction, and a Pourbaix diagram. Combined with the corrosion efficiency and Pourbaix diagram of the Fe-H2O system, the reversible process and reduction process mechanism in the Faraday process are proposed. The reason why the corrosion efficiency slows down in the process of non-Faraday is analyzed by the electric double-layer model of equivalent circuit calculation. In addition, based on the above corrosion process, the corresponding conceptual model of the corrosion mechanism is proposed. The experimental results show that with the asymmetry of positive and negative half-cycle interference duration and the increase of current density, the corrosion efficiency, and current corrosion efficiency of X80 steel decrease, and local corrosion intensifies. The length of the negative half-cycle interference affects the capacitive charge-discharge effect at the metal/solution interface and the reduction reaction process of corrosion products, resulting in corrosion slowing down and corrosion efficiency reduction. This is also an important reason for the reduction of corrosion mass loss observed in the experiment compared with steady-state DC.

New boost type single phase inverters for photovoltaic applications with reduced device count.

In recent years, single-stage boost inverters with common ground have shaped the inverter markets due to the many benefits associated with these types of inverters, including their high efficiency, single control scheme, and integrated boost converter. A new boost-type inverter that utilizes a common ground and has fewer switches is proposed in this article. It uses two DC-link capacitors connected in parallel and discharged independently while being charged simultaneously. The voltage for the positive and negative half cycles is supplied by the capacitors located at the top and bottom of the circuit, respectively. In addition, a comparison is made between the proposed circuit and the boost inverter already in use in the literature. Using PLECS as the computing software, the efficiencies are determined depending on the various percentages of output power. To validate performance, present experimental data, and attain the best possible efficiency of 97%, a 400 W prototype model is constructed. In addition to that, the breakdown of the costs is shown.

Simulation design and analysis 9-level H-bridge single phase stepdown cyclo inverter

This DC-to-AC voltage converter is designed for output frequency controlled by a 9-level cascade H-bridge cyclo inverter with pulse width adjustment. The aim of the study was to determine the pattern and format of the voltage, output frequency, and Total Harmonic Distortion index of a 9-level IGBT cyclo inverter. The method used is to build a unidirectional power converter design modeling into 9 alternating levels with cyclo converter-controlled frequency settings using the Simulink MATLAB tool. The cyclo converter section is constructed with two P and N converters in a parallel arrangement. The frequency and trigger pulse width of both converters control the output voltage and frequency format of the cyclo inverter. The test results show a series of ladder waves with an output frequency, of (1/2f, 1/3f, 1/4f, 1/5f, 1/6f, 1/7f, 1/8f, 1/9f, and 1/10f). The simulation results show that the nth input frequency divider waveform is characterized by the emergence of a number of step pulses of n positive half cycles and negative half cycles. The Total Harmonic Distortion Index gets bigger when the system circuit is designed at a low frequency. This modeling can be implemented into a prototype that is used for variable-speed DC motor drivers.

Discharge Characteristics of Needle Plate Electrode in Transformer Oil Under Low-frequency AC Voltage

Low-frequency transformer is the key equipment of flexible low-frequency AC transmission systems for offshore wind power. As the low-frequency voltage is applied, the transformer has significantly different insulation characteristics from those of the conventional transformer, it is necessary to study the typical characteristics of partial discharge of oil-paper insulation under such voltage. In this dissertation, the characteristics of discharge of needle plate electrodes in transformer oil under power frequency to low-frequency voltage are experimentally researched by adopting the pulse current method, and the discharge statistics, discharge atlas as well as feature parameters are analysed. With the decreasing of voltage frequency, the inception voltage (IV) value of partial discharge slightly increases, the extinction voltage (EV) phases of positive half-cycle (PHC) voltage waveform, as well as negative half-cycle (NHC) voltage waveform appear earlier, and the maximum discharge (MD), average discharge (AD), and pulse repetition rate (PRR) all show a downward trend.

A Single-Phase Seven-Level Triple Boost Inverter for Grid-Connected Transformerless PV Applications

A new seven-level common ground (CG) switched capacitor (SC)-based grid tied transformerless inverter has been introduced in this paper, which has three times boosting capability of input voltage. Thus, this inverter is preferable for low voltage PV applications without any boost conversion stage. To step-up the input PV voltage and facilitate seven steps in output voltage, two SC cells are connected in parallel. A virtual dc link capacitor serves key role for negative half cycle on behalf of H-Bridge and helping in constructing topology with common ground. The common grounding configuration of this inverter helps in bypassing the stray capacitance, which eliminates the leakage current and consequently reduces EMI considerably. Hence, further no requirement of any electro-magnetic interference (EMI) filter for electro-magnetic compatibility (EMC). Additionally, this inverter handles reactive power during the grid's lagging/leading power factor (pf) condition. To regulate active and reactive grid power, a proportional resonant (PR) current controller is designed. The proposed modulation scheme helps in balancing capacitor's voltages at their base values with allowable ripple. A detailed comparison also has been presented with other contemporary seven level inverters. The inverter circuit details, control technique, PWM scheme, thermal modeling, and loss analysis with component design guidelines are described in detail. Experimental results are presented to validate the effectiveness and feasibility of this proposed inverter.

Design of Light Emitting Diode-Based Fiber Optic Current Sensor and Its Application in Pollution Flash Prevention in Digitalized Substations

Prevention of pollution flash in electrical equipment in digitalized substations and transmission lines has always been a crucial part of power operation. In order to prevent pollution flash, it is essential to detect the contamination of electrical equipment. The measurement of leakage current is a fundamental aspect of preventive pollution flash work in electrical equipment. Applying fiber optic current sensors to online monitoring systems in the power system offers advantages such as resistance to harsh environments, immunity to electromagnetic interference, and resistance to chemical corrosion. This study designs a unidirectional half-wave fiber optic current sensor based on Light Emitting Diodes (LED) for selectively observing the positive and negative half-cycles of leakage current. Due to the light emission and unidirectional conduction characteristics of LED, with a well-designed circuit, LED performs photoelectric conversion on the current, allowing the sensor to selectively measure the positive and negative half-cycles of leakage current. Subsequently, a combination circuit of silicon detectors and amplifiers is used to complete the photoelectric conversion, facilitating voltage signal measurement. In experiments, the response of the unidirectional half-wave LED fiber optic current sensor reached 37.8 mV/mA, with a detection bandwidth range between [1.2 kHz, 9.8 kHz]. In leakage current tests, using the leakage current of insulators as a reference, experiments were conducted using the voltage boosting method. As the applied voltage increased, the leakage current displayed on the sampling resistor increased, and the measurement waveform indicated that the sensor could correctly select the unidirectional half-wave. In leakage current and salt density tests, the designed fiber optic sensor accurately reflected the exponential relationship between insulator leakage current and contamination, demonstrating the practical value of the designed fiber optic current sensor.

Effect of powered electrode configuration on plasma structure of surface micro-discharge array

Surface micro-discharge (SMD) has received growing interest for its great prospect in various emerging applications spanning the fields of biomedicine, manufacturing, and agriculture. Discharge properties and the nature of the chemical species are heavily dependent on the electrode configuration. However, insight into the effect of electrode configuration on SMD remains scarce. This paper reports on the effect of the geometry of the powered planar electrode on the dynamic evolution of plasma in a helium SMD array at atmospheric pressure. The observed symmetric and asymmetric luminous patterns correspond to odd and even numbered current pulses in negative half-cycle, respectively. When the powered electrode is not covering the full area of the mesh unit of the grounded electrode, the luminous pattern dominated by the negative pattern consists of three parts: the distinct luminous channel, the flabelliform luminous area, and the discontinuous cambered channels under the incomplete powered electrode condition. The distinct luminous channel is ascribed to the propagation of the bullet-like plasma volume originated at the middle part of the mesh side before merging with other plasmas. The merging plasma forms a cambered front and continuous to propagate, leading to the formation of a flabelliform area. The discontinuous cambered channels result from the propagation of bullets ignited at the mesh corners, especially the slide of luminous area with maximum emission intensity along the streamer. Moreover, the mesh element without a powered electrode can also initiate breakdown due to the sufficiently high voltage and the propagation of surface charges, suggesting that the grounded mesh electrode should be extended to avoid redundant discharges.

A Bridgeless Cuk-BB-Converter-Based BLDCM Drive for MEV Applications

This article presents a brushless DC motor (BLDCM) drive for a maritime electric vehicle (MEV) application. The presented BLDCM drive uses a bridgeless Cuk-buckboost (BL-Cuk-BB) converter for input-side power factor (PF) improvement. The BL-Cuk-BB converter uses the buckboost converter for the negative half-cycles of the input AC voltages and the Cuk converter for the positive half-cycles. In the case of MEVs, the drive systems are generally fed by diesel engine generators (DEGs). The asymmetric BL-Cuk-BB converter is operated in a discontinuous inductor current mode (DICM) in the present work to attain better power quality. The usage of a second-order buckboost converter with a fourth-order Cuk converter results in a decrement in the net order of the system. Additionally, the input inductor of the Cuk converter also participates as the filter component along with capacitor C2 during buckboost converter operation to enhance the power quality. The total component count reduction in the BL-Cuk-BB converter is also achieved by eliminating the usage of extra/external back-feeding diodes, which are generally used in bridgeless schemes. The present scheme uses the inbuilt anti-parallel diodes for the same purpose. The lesser components requirement in the BL-Cuk-BB-converter-based BLDCM drive implies lesser cost and volume, along with greater reliability, lower conduction losses, and lower weight of the BLDCM drive, which adds to the merits of the model. The paper includes a detailed mathematical model and stability analysis using pole-zero maps and bode plots of the BL-Cuk-BB converter for each half-supply AC voltage cycle. The BL-Cuk-BB-converter-based BLDCM drive for an EV application has been developed on the MATLAB/Simulink platform for a DICM operation, and the MATLAB simulation results have been presented for validation of the BL-Cuk-BB-converter-based BLDCM drive.

A Single-Phase Grid-Connected Boost/Buck–Boost-Derived Solar PV Micro-Inverter Topology Having Power Decoupling Capability

A boost/buck–boost-derived solar photovoltaic (PV) micro-inverter suitable for interfacing a 35 V 220 W PV module to a 220 V single-phase ac grid is proposed in this article. It uses only six switches, of which two switches operate at high frequency (HF), two at line frequency (LF), and the remaining two switches at HF during either positive half cycle (PHC) or negative half cycle (NHC) of the grid voltage. To achieve high gain and negligible turn on losses for the HF switches, the micro-inverter is operated in discontinuous mode of conduction for all possible operating conditions. The negative terminal of the PV module is directly connected to the grid neutral, and hence the magnitude of leakage flow is zero. The instantaneous power mismatch between the dc side and the ac side is addressed by achieving inherent power decoupling in the proposed topology without incorporating any additional active power decoupling circuit (APDC). The detailed analyses of the proposed micro-inverter are carried out. A 220 W laboratory prototype of the proposed micro-inverter is fabricated, and experimental studies are carried out in detail to confirm the viability of the proposed scheme.

A Novel Approach on Dielectric Barrier Discharge Using Printed Circuit Boards

Drug-resistant bacteria, prions, and nosocomial infections underline the need of more effective sterilizing technologies. The cold plasma technology is expected to bring a benefit in this context. Six different plasma sources, based on printed circuit boards, were evaluated fourfold. This includes measurements of the power consumption, the ignition behavior by an ICCD-camera, and ozone formation by absorption spectroscopy at 254nm. To evaluate the biocidal effect, four bacterial test series were performed with Escherichia coli. The entirety of the tests analyzes the plasma inactivation process from the input parameters to the desired biocidal effect. The discharge current and time-resolved ignition behaviors indicated a simultaneous formation of filaments at the beginning of the negative half-cycle. The dynamics of the ozone production showed a saturated exponential growth upon a maximum value of 435ppm. Additionally, the microbiological test series unveiled differences between the plasma source concepts. A total reduction rate of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {10^{-4}}$ </tex-math></inline-formula> within a minute was achievable. An air flow through slits within the plasma sources destabilized the plasma. Minor changes of the electrode geometry changed all measured parameters. Hence, to develop a pathogen inactivating plasma source, these results recommend a comb-shaped electrode design, which is laminated on a dielectric.

A bridgeless AC-DC step up regulator circuit for piezoelectric energy harvester

Various applications of the piezoelectric energy in the modern world require an efficient AC-DC low power converter. As the two stages converter with bridge rectifiers may not be used because the diodes would not be suitable for low volt ranging between 100 to 200mv, these are considered an efficient element in the low volt circuits because of their entire losses. In this paper, a small and efficient AC-DC low power converter is presented. It directly converts low AC voltage to the required output DC voltage using one stage instead of bridge rectification. The proposed converter combines both boost and buck boost converters which are parallel constructed to condition the positive and negative half cycle of the input AC volt respectively. Two inductors and one capacitor are used for booth circuits in terms of reducing the size. The circuit is tested at 50 kHz switching frequency with two different duty cycles to rectify a 0.5 AC volt to about 3 DC volts with an estimated efficiency of 65%. The simulation result was 3.7 DC V from 0.5 ACV. The circuit analysis and the design guide line are explained. The circuit is designed and tested using Matlab (Simulink) software.

Asymmetric discharges of dielectric barrier discharge in atmospheric air

We report in this Letter a kind of asymmetric discharge mode in positive and negative half-cycles of dielectric barrier discharge in ambient air. This phenomenon is characterized by homogeneous and filamentary discharges occurring alternately in the two half-cycles, using two different materials of alumina ceramic and quartz as the dielectric barrier at each side. The discharge current waveforms, discharge images, optical emission spectra, and the averaged electron energy are significantly different for the asymmetric discharges. It is suggested that the seed electrons and secondary electron emission from the different dielectric materials acting as the temporary cathode are responsible for the different discharge modes.

A New Topology of Single-Phase Common Ground Buck-Boost Inverter With Component Voltage Rating Reduction

The combination of conventional front-end DC-DC converter and H-bridge inverter has been proposed with common-ground (CG) characteristic and voltage booting capability. However, it has drawback of low modulation index utilization which causes high component voltage rating and small conversion efficiency. In this paper, a new topology of a single-phase common-ground buck-boost inverter (1P-CG-BBI) is presented to overcome existing drawbacks of conventional CG inverters. The proposed 1P-CG-BBI uses one more active-switch and one more diode than traditional CG inverter. Note that the proposed inverter still shares the same ground for DC input source and AC output voltage, which completely eliminates the leakage current. A hybrid pulse width modulation (PWM) technique is introduced to control the buck-boost stage. Accordingly, the buck-boost stage of the 1P-CG-BBI operates similar to a conventional DC-DC boost converter in the positive half cycle. In the negative half cycle, this stage behaves as a traditional inverting DC-DC buck-boost converter. Accordingly, the DC-DC operation and DC-AC operation can be controlled, independently. Consequently, the modulation index can be significantly improved compared to previous CG inverters. High modulation index tends to reduce component voltage rating and increase system efficiency. A comparison study has been discussed to highlight these advantages. Simulation results conducted using PSIM software are considered to verify the operation of the proposed inverter. A laboratory prototype is also developed to further demonstrated the accuracy of theory. Accordingly, the proposed inverter obtains 93.12% and 91.83% efficiency at 550-W for buck and boost operating, respectively.

A Novel Single Phase Grid Connected Transformer-Less Solar Micro-Inverter Topology With Power Decoupling Capability

A novel transformer-less micro-inverter topology suitable for interfacing a 35 V, 220 W solar PV module to a single phase 220–230 V ac grid is proposed in this paper. It employs only six switches, out of which two switches operate at high frequency, three at line frequency and one switch at high frequency during the negative half cycle of the grid voltage. The micro-inverter is operated in discontinuous conduction mode of operation for all possible operating conditions to achieve high gain as well as negligible turn on losses for the high frequency switches. In this topology the negative terminal of the PV module is shorted with the grid neutral which makes the magnitude of the leakage current flow to be zero. The power decoupling between the dc and ac sides is inherent in this topology, and it is achieved without incorporating any active power decoupling circuit. Thin film capacitors are utilized to improve the reliability of the micro-inverter. The detailed analyses of the proposed micro-inverter are carried out. The effectiveness of the proposed scheme is verified by performing detailed simulation studies. A 220 W laboratory prototype of the proposed micro-inverter is fabricated, and detailed experimental studies are carried out to confirm the viability of the proposed scheme.

Energy-saving actuation signal for magnetorheological valve train by leveraging hysteresis effect

• Analysis of electromagnetic hysteresis effect in magnetorheological valve train. • Customized pulse actuation signal for leveraging the hysteresis effect in magnetorheological valve train. • Pulse signal optimization for energy saving operation of VVL that improves the engine efficiency. • Customized pulse signal saves actuation energy of magnetorheological valve train. Smart, adaptive, and effective magnetorheological (MR) technology-based devices are replacing conventional brakes, clutches, valves, and dampers. MR valve improves engine performance by enabling variable valve actuation. Constructing an MR valve train is simpler than other active valve systems. However, similar to other electromagnetic valves, the MR valve train consumes considerable electrical energy in controlling the resistance force of the MR fluid such that the valve can remain partially open or fully closed. Thus, an engine equipped with an MR valve expends additional fuel for the actuation of the valve system. In this study, instead of conventional direct current (DC) actuation, an energy-saving customized pulse (CP) signal is proposed for valve actuation by leveraging the electromagnetic hysteresis effect. The applied CP signal causes fluctuations in the generated magnetic flux, resistance force, and consequent valve position. Therefore, the variation in MR resistance force at various duty cycles and negative half cycles was investigated and compared with the required force to perform variable valve lift (VVL). Simulations indicated that a 35% duty cycle with 75% current during the negative half cycle was able to maintain the required force but results in negligible deviation in the resistance force which doesn’t affect the VVL operation. Therefore, the proposed method is advantageous over conventional DC input, conferring actuation energy-savings of approximately 28%.

Effect of the high voltage waveform on the ionic wind produced by a needle-to-plate dielectric barrier discharge

Although corona discharges are used in many industrial applications because of their ability to produce chemical species, the ionic wind they induce is less known and often ignored. Therefore, the present study aims at investigating the ionic wind produced by a corona discharge ignited between a high voltage needle and a grounded plate electrode covered by a dielectric material. More specifically, the work focuses on the influence of the high voltage waveform on the temporal behavior of the ionic wind. The results highlight that the high voltage waveform plays a key role on the dynamics of the flow produced inside the discharge. On the one hand, for the sine, triangle and sawtooth waveforms, there is a flow acceleration during both the positive and the negative half-cycles, the positive discharge being more effective in velocity production. On the other hand, for the square waveform, the increase in velocity occurs during the rises and falls of the voltage, because of the strengthening of the electric field due to the ions remaining from the previous half-cycle at the wall of the dielectric material.