Approximation of durrmeyer type operators depending on certain parameters

Motivated by a number of recent investigations, we consider a new analogue of Bernstein-Durrmeyer operators based on certain variants. We derive some approximation properties of these operators. We also compute local approximation and Voronovskaja type asymptotic formula. We illustrate the convergence of aforementioned operators by making use of the software MATLAB which we stated in the paper

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects

Modulation and control strategies for neutral-point-clamped converters

This thesis presents modulation and control strategies for neutral-point-clamped (NPC) converters. These converters produce ac voltages with lower harmonic distortion and the switches operate with less switching frequencies than traditional two-level voltage-source converters. NPC converters are widely employed in grid integration of renewable energy sources like solar and wind energy, high-power motor drives, shunt active power filters, etc. The NPC converters suffer from challenges such as, the subsequent increase in switching losses while controlling the capacitor voltage (CV) ripples, neutral-point (NP) voltage instability arising in the presence of nonlinear loads enriched in even-order harmonics, and the divergence of CVs in the presence of nonzero average NP current. The focus of this thesis is to address these challenges and develop more efficient modulation and control techniques for the NPC converters. In order to find a trade-off solution between the CV ripple magnitude and the switching power losses, a new feedforward compensated modulation technique for the three-phase NPC converter is proposed in this thesis. With this technique, the CVs are limited within a predefined voltage band. An innovative feedforward compensation is introduced to avoid low-frequency distortion on the output voltages of the converter arising due to oscillations in the CVs. Limiting the CV ripples helps in the design of the NPC converter, since the maximum voltage that the dc-link capacitors and the power semiconductors have to withstand is predefined. Though the proposed feedforward compensated modulation strategy offers a trade-off between the CV ripples and switching losses, its performance deteriorates in the presence of extreme nonlinear loads due to the tendency of the CVs to frequently bounce out of the voltage band leading to higher switching losses. In order to address this drawback, a band-limited three-level (BL-3L) modulation technique is proposed which aims to balance the average CVs without any substantial increase in the switching losses, thereby concentrating mainly on enhancing the steady state performance of the system. In addition to the predefined voltage band (applied to the CVs), a variable current band is applied to the phase currents. The size of the current band is varied based on the tendency of the operational condition to unbalance the NP. Therefore, the BL-3L modulation is another approach to have a trade-off between the CV ripples and the switching power losses, which ensures the average CVs are balanced even in the presence of nonlinear loads enriched in even-order harmonics. For bipolar dc-bus applications of NPC converters like feeding multiterminal dc-loads, back-to-back systems and grid-connected photovoltaic (PV) systems, the main challenge is to generate the required nonzero average NP current which, if not compensated, causes the CVs to diverge and hence destabilizes the converter. In order to address this issue, a dual-mode modulation technique is proposed which utilizes the inherent capability of the NPC converter to generate the required average NP current and does not employ any additional hardware. This technique is developed analytically using ac-side voltages and currents, and is applicable for all bipolar dc-bus applications of the NPC converter with balanced CVs. The analytical solution also provides the maximum average NP current injection capacity of the NPC converter, which defines the stable operating region of the converter. The applications of dual-mode modulation technique are limited to systems with balanced CVs. In order to extend this analysis to applications of the NPC converter with unbalanced CVs, a dual-input NPC inverter-based grid-connected PV system is considered. A control strategy is proposed for this system to asymmetrically control the PV arrays without incorporating any additional external circuit. This is achieved by employing an analytically developed linearization block, similar to the dual-mode modulation technique, which helps in generating the required NP current to counter for the difference in the PV currents. Experimental results are obtained on a laboratory developed prototype to validate all the proposed modulation techniques under different operating conditions. Finally, this thesis summarizes the work that has been done and presents some directions for future research.Doctor of Philosoph

Enhancing the natural voltage balancing capability of neutral-point-clamped converters under carrier-based pulsewidth modulation

In this paper, a new modulation technique is presented which aims to enhance the natural voltage balancing capability of neutral-point-clamped converters. The traditional carrier-based pulsewidth modulation technique with zerosequence injection faces some drawbacks, namely, its inability to balance initial capacitor voltage imbalances quickly and the divergence of the capacitor voltages in the presence of nonlinear loads with even harmonics. This paper aims to find a trade-off between voltage balance performance and switching losses by reducing the difference between the average capacitor voltages without incorporating any external circuitry. A reference neutralpoint (NP) current is generated using the average difference between the capacitor voltages. Depending on the reference NP current and predicted NP current, appropriate duty cycles are applied to switch the three phases. These duty cycles are directly linked to the voltage unbalance between the capacitor voltages and thus provides the necessary ‘push’ to mitigate deviations in natural balancing characteristics. To validate the proposed modulation technique, simulation results are presented for linear loads as well as for nonlinear loads with even harmonics.Accepted versio

Balancing average capacitor voltages in neutral-point-clamped converters using band-limited three-level modulation

In this paper, a band-limited three-level modulation scheme is presented which aims to balance the average capacitor voltages in neutral-point-clamped converters under all load operating conditions. Compared to previous three-level modulation schemes, the proposed scheme provides a trade-off between voltage balancing performance and switching losses. Consequently, helping in optimizing the system’s footprint and its operating cost. A variable current band is calculated in order to provide the necessary control action for balancing the average (as opposed to instantaneous) capacitor voltages. The proposed modulation scheme is tested under both linear and nonlinear loads. A comparison is also performed between the proposed band-limited three-level modulation and other modulation schemes presented in the literature.Accepted versio

Adaptive control scheme for three-phase four wire grid tied SPV system with DSTATCOM capabilities

This paper proposes an adaptive modified least mean fourth (MLMF) control scheme with perturb and observe (P and O) technique for a voltage source converter (VSC) connected to solar photovoltaic array (SPV), three single-phase non-linear loads in a three-phase, 4-wire system with DSTATCOM (Distributed Static Compensator) capabilities. The adaptive control scheme based on MLMF shows low mean square error and converges faster. The system is modelled and simulated for power factor correction and zero voltage regulation modes. Due to single stage topology, the system shows high efficacy at high voltages. The neutral load current is well compensated by the VSC's fourth leg current. The harmonics in grid currents are well under the IEEE-519 standard