Energy and conductance state modeling of power electronic converters for DC microgrids

This document will demonstrate the methodology used to create an energy and conductance based model for power electronic converters. The work is intended to be a replacement for voltage and current based models which have limited applicability to the network nodal equations. Using conductance-based modeling allows direct application of load differential equations to the bus admittance matrix (Y-bus) with a unified approach. When applied directly to the Y-bus, the system becomes much easier to simulate since the state variables do not need to be transformed. The proposed transformation applies to loads, sources, and energy storage systems and is useful for DC microgrids. Transformed state models of a complete microgrid are compared to experimental results and show the models accurately reflect the system dynamic behavior.

Local degradation of structural, mechanical, electrical and chemical properties of membrane electrode assembly in polymer electrolyte fuel cell

Polymer electrolyte fuel cell (PEMFC) is promising source of clean power in many applications ranging from portable electronics to automotive and land-based power generation. However, widespread commercialization of PEMFC is primarily challenged by degradation. The mechanisms of fuel cell degradation are not well understood. Even though the numbers of installed units around the world continue to increase and dominate the pre-markets, the present lifetime requirements for fuel cells cannot be guarantee, creating the need for a more comprehensive knowledge of material’s ageing mechanism. The objective of this project is to conduct experiments on membrane electrode assembly (MEA) components of PEMFC to study structural, mechanical, electrical and chemical changes during ageing and understanding failure/degradation mechanism. The first part of this project was devoted to surface roughness analysis on catalyst layer (CL) and gas diffusion layer (GDL) using surface mapping microscopy. This study was motivated by the need to have a quantitative understanding of the GDL and CL surface morphology at the submicron level to predict interfacial contact resistance. Nanoindentation studies using atomic force microscope (AFM) were introduced to investigate the effect of degradation on mechanical properties of CL. The elastic modulus was decreased by 45 % in end of life (EOL) CL as compare to beginning of life (BOL) CL. In another set of experiment, conductive AFM (cAFM) was used to probe the local electric current in CL. The conductivity drops by 62 % in EOL CL. The future task will include characterization of MEA degradation using Raman and Fourier transform infrared (FTIR) spectroscopy. Raman spectroscopy will help to detect degree of structural disorder in CL during degradation. FTIR will help to study the effect of CO in CL. XRD will be used to determine Pt particle size and its crystallinity. In-situ conductive AFM studies using electrochemical cell on CL to correlate its structure with oxygen reduction reaction (ORR) reactivity

Design, construction, and testing of a research quality electric machine testbed

With energy demands and costs growing every day, the need for improving energy efficiency in electrical devices has become very important. Research into various methods of improving efficiency for all electrical components will be a key to meet future energy needs. This report documents the design, construction, and testing of a research quality electric machine dynamometer and test bed. This test cell system can be used for research in several areas including: electric drives systems, electric vehicle propulsion systems, power electronic converters, load/source element in an AC Microgrid, as well as many others. The test cell design criteria, and decisions, will be discussed in reference to user functionality and flexibility. The individual power components will be discussed in detail to how they relate to the project, highlighting any feature used in operation of the test cell. A project timeline will be discussed, clearly stating the work done by the different individuals involved in the project. In addition, the system will be parameterized and benchmark data will be used to provide the functional operation of the system. With energy demands and costs growing every day, the need for improving energy efficiency in electrical devices has become very important. Research into various methods of improving efficiency for all electrical components will be a key to meet future energy needs. This report documents the design, construction, and testing of a research quality electric machine dynamometer and test bed. This test cell system can be used for research in several areas including: electric drives systems, electric vehicle propulsion systems, power electronic converters, load/source element in an AC Microgrid, as well as many others. The test cell design criteria, and decisions, will be discussed in reference to user functionality and flexibility. The individual power components will be discussed in detail to how they relate to the project, highlighting any feature used in operation of the test cell. A project timeline will be discussed, clearly stating the work done by the different individuals involved in the project. In addition, the system will be parameterized and benchmark data will be used to provide the functional operation of the system.

Development of room temperature operating single electron transistor using FIB etching and deposition technology

The single-electron transistor (SET) is one of the best candidates for future nano electronic circuits because of its ultralow power consumption, small size and unique functionality. SET devices operate on the principle of Coulomb blockade, which is more prominent at dimensions of a few nano meters. Typically, the SET device consists of two capacitively coupled ultra-small tunnel junctions with a nano island between them. In order to observe the Coulomb blockade effects in a SET device the charging energy of the device has to be greater that the thermal energy. This condition limits the operation of most of the existing SET devices to cryogenic temperatures. Room temperature operation of SET devices requires sub-10nm nano-islands due to the inverse dependence of charging energy on the radius of the conducting nano-island. Fabrication of sub-10nm structures using lithography processes is still a technological challenge. In the present investigation, Focused Ion Beam based etch and deposition technology is used to fabricate single electron transistors devices operating at room temperature. The SET device incorporates an array of tungsten nano-islands with an average diameter of 8nm. The fabricated devices are characterized at room temperature and clear Coulomb blockade and Coulomb oscillations are observed. An improvement in the resolution limitation of the FIB etching process is demonstrated by optimizing the thickness of the active layer. SET devices with structural and topological variation are developed to explore their impact on the behavior of the device. The threshold voltage of the device was minimized to ~500mV by minimizing the source-drain gap of the device to 17nm. Vertical source and drain terminals are fabricated to realize single-dot based SET device. A unique process flow is developed to fabricate Si dot based SET devices for better gate controllability in the device characteristic. The device vi parameters of the fabricated devices are extracted by using a conductance model. Finally, characteristic of these devices are validated with the simulated data from theoretical modeling.

LOCAL DIGITAL CONTROL OF POWER ELECTRONIC CONVERTERS IN A DC MICROGRID BASED ON A-PRIORI DERIVATION OF SWITCHING SURFACES

In power electronic basedmicrogrids, the computational requirements needed to implement an optimized online control strategy can be prohibitive. The work presented in this dissertation proposes a generalized method of derivation of geometric manifolds in a dc microgrid that is based on the a-priori computation of the optimal reactions and trajectories for classes of events in a dc microgrid. The proposed states are the stored energies in all the energy storage elements of the dc microgrid and power flowing into them. It is anticipated that calculating a large enough set of dissimilar transient scenarios will also span many scenarios not specifically used to develop the surface. These geometric manifolds will then be used as reference surfaces in any type of controller, such as a sliding mode hysteretic controller. The presence of switched power converters in microgrids involve different control actions for different system events. The control of the switch states of the converters is essential for steady state and transient operations. A digital memory look-up based controller that uses a hysteretic sliding mode control strategy is an effective technique to generate the proper switch states for the converters. An example dcmicrogrid with three dc-dc boost converters and resistive loads is considered for this work. The geometric manifolds are successfully generated for transient events, such as step changes in the loads and the sources. The surfaces corresponding to a specific case of step change in the loads are then used as reference surfaces in an EEPROM for experimentally validating the control strategy. The required switch states corresponding to this specific transient scenario are programmed in the EEPROM as a memory table. This controls the switching of the dc-dc boost converters and drives the system states to the reference manifold. In this work, it is shown that this strategy effectively controls the system for a transient condition such as step changes in the loads for the example case.

Study of and design procedure for dual circularly polarized waveguide slot arrays

For the past sixty years, waveguide slot radiator arrays have played a critical role in microwave radar and communication systems. They feature a well-characterized antenna element capable of direct integration into a low-loss feed structure with highly developed and inexpensive manufacturing processes. Waveguide slot radiators comprise some of the highest performance—in terms of side-lobe-level, efficiency, etc. — antenna arrays ever constructed. A wealth of information is available in the open literature regarding design procedures for linearly polarized waveguide slots. By contrast, despite their presence in some of the earliest published reports, little has been presented to date on array designs for circularly polarized (CP) waveguide slots. Moreover, that which has been presented features a classic traveling wave, efficiency-reducing beam tilt. This work proposes a unique CP waveguide slot architecture which mitigates these problems and a thorough design procedure employing widely available, modern computational tools. The proposed array topology features simultaneous dual-CP operation with grating-lobe-free, broadside radiation, high aperture efficiency, and good return loss. A traditional X-Slot CP element is employed with the inclusion of a slow wave structure passive phase shifter to ensure broadside radiation without the need for performance-limiting dielectric loading. It is anticipated this technology will be advantageous for upcoming polarimetric radar and Ka-band SatCom systems. The presented design methodology represents a philosophical shift away from traditional waveguide slot radiator design practices. Rather than providing design curves and/or analytical expressions for equivalent circuit models, simple first-order design rules – generated via parametric studies — are presented with the understanding that device optimization and design will be carried out computationally. A unit-cell, S-parameter based approach provides a sufficient reduction of complexity to permit efficient, accurate device design with attention to realistic, application-specific mechanical tolerances. A transparent, start-to-finish example of the design procedure for a linear sub-array at X-Band is presented. Both unit cell and array performance is calculated via finite element method simulations. Results are confirmed via good agreement with finite difference, time domain calculations. Array performance exhibiting grating-lobe-free, broadside-scanned, dual-CP radiation with better than 20 dB return loss and over 75% aperture efficiency is presented.

Design and implementation of a 3D computer game controller using inertial MEMS sensors

Though 3D computer graphics has seen tremendous advancement in the past two decades, most available mechanisms for computer interaction in 3D are high cost and targeted for industry and virtual reality applications. Recent advances in Micro-Electro-Mechanical-System (MEMS) devices have brought forth a variety of new low-cost, low-power, miniature sensors with high accuracy, which are well suited for hand-held devices. In this work a novel design for a 3D computer game controller using inertial sensors is proposed, and a prototype device based on this design is implemented. The design incorporates MEMS accelerometers and gyroscopes from Analog Devices to measure the three components of the acceleration and angular velocity. From these sensor readings, the position and orientation of the hand-held compartment can be calculated using numerical methods. The implemented prototype is utilizes a USB 2.0 compliant interface for power and communication with the host system. A Microchip dsPIC microcontroller is used in the design. This microcontroller integrates the analog to digital converters, the program memory flash, as well as the core processor, on a single integrated circuit. A PC running Microsoft Windows operating system is used as the host machine. Prototype firmware for the microcontroller is developed and tested to establish the communication between the design and the host, and perform the data acquisition and initial filtering of the sensor data. A PC front-end application with a graphical interface is developed to communicate with the device, and allow real-time visualization of the acquired data.

Managing server energy and reducing operational cost for online service providers

The past decade has seen the energy consumption in servers and Internet Data Centers (IDCs) skyrocket. A recent survey estimated that the worldwide spending on servers and cooling have risen to above $30 billion and is likely to exceed spending on the new server hardware . The rapid rise in energy consumption has posted a serious threat to both energy resources and the environment, which makes green computing not only worthwhile but also necessary. This dissertation intends to tackle the challenges of both reducing the energy consumption of server systems and by reducing the cost for Online Service Providers (OSPs). Two distinct subsystems account for most of IDC’s power: the server system, which accounts for 56% of the total power consumption of an IDC, and the cooling and humidifcation systems, which accounts for about 30% of the total power consumption. The server system dominates the energy consumption of an IDC, and its power draw can vary drastically with data center utilization. In this dissertation, we propose three models to achieve energy effciency in web server clusters: an energy proportional model, an optimal server allocation and frequency adjustment strategy, and a constrained Markov model. The proposed models have combined Dynamic Voltage/Frequency Scaling (DV/FS) and Vary-On, Vary-off (VOVF) mechanisms that work together for more energy savings. Meanwhile, corresponding strategies are proposed to deal with the transition overheads. We further extend server energy management to the IDC’s costs management, helping the OSPs to conserve, manage their own electricity cost, and lower the carbon emissions. We have developed an optimal energy-aware load dispatching strategy that periodically maps more requests to the locations with lower electricity prices. A carbon emission limit is placed, and the volatility of the carbon offset market is also considered. Two energy effcient strategies are applied to the server system and the cooling system respectively. With the rapid development of cloud services, we also carry out research to reduce the server energy in cloud computing environments. In this work, we propose a new live virtual machine (VM) placement scheme that can effectively map VMs to Physical Machines (PMs) with substantial energy savings in a heterogeneous server cluster. A VM/PM mapping probability matrix is constructed, in which each VM request is assigned with a probability running on PMs. The VM/PM mapping probability matrix takes into account resource limitations, VM operation overheads, server reliability as well as energy effciency. The evolution of Internet Data Centers and the increasing demands of web services raise great challenges to improve the energy effciency of IDCs. We also express several potential areas for future research in each chapter.

Reducing main memory access latency through SDRAM address mapping techniques and access reordering mechanisms

As the performance gap between microprocessors and memory continues to increase, main memory accesses result in long latencies which become a factor limiting system performance. Previous studies show that main memory access streams contain significant localities and SDRAM devices provide parallelism through multiple banks and channels. These locality and parallelism have not been exploited thoroughly by conventional memory controllers. In this thesis, SDRAM address mapping techniques and memory access reordering mechanisms are studied and applied to memory controller design with the goal of reducing observed main memory access latency. The proposed bit-reversal address mapping attempts to distribute main memory accesses evenly in the SDRAM address space to enable bank parallelism. As memory accesses to unique banks are interleaved, the access latencies are partially hidden and therefore reduced. With the consideration of cache conflict misses, bit-reversal address mapping is able to direct potential row conflicts to different banks, further improving the performance. The proposed burst scheduling is a novel access reordering mechanism, which creates bursts by clustering accesses directed to the same rows of the same banks. Subjected to a threshold, reads are allowed to preempt writes and qualified writes are piggybacked at the end of the bursts. A sophisticated access scheduler selects accesses based on priorities and interleaves accesses to maximize the SDRAM data bus utilization. Consequentially burst scheduling reduces row conflict rate, increasing and exploiting the available row locality. Using a revised SimpleScalar and M5 simulator, both techniques are evaluated and compared with existing academic and industrial solutions. With SPEC CPU2000 benchmarks, bit-reversal reduces the execution time by 14% on average over traditional page interleaving address mapping. Burst scheduling also achieves a 15% reduction in execution time over conventional bank in order scheduling. Working constructively together, bit-reversal and burst scheduling successfully achieve a 19% speedup across simulated benchmarks.

Fabrication and characterization of room temperature operating single electron transistors using focused ion beam technologies

The single electron transistor (SET) is a Coulomb blockade device, whose operation is based on the controlled manipulation of individual electrons. Single electron transistors show immense potential to be used in future ultra lowpower devices, high density memory and also in high precision electrometry. Most SET devices operate at cryogenic temperatures, because the charging energy is much smaller than the thermal oscillations. The room temperature operation of these devices is possible with sub- 10nm nano-islands due to the inverse dependance of charging energy on the radius of the conducting nano-island. The fabrication of sub-10nm features with existing lithographic techniques is a technological challenge. Here we present the results for the first room temperature operating SET device fabricated using Focused Ion Beam deposition technology. The SET device, incorporates an array of tungsten nano-islands with an average diameter of 8nm. The SET devices shows clear Coulomb blockade for different gate voltages at room temperature. The charging energy of the device was calculated to be 160.0 meV; the capacitance per junction was found to be 0.94 atto F; and the tunnel resistance per junction was calculated to be 1.26 G Ω. The tunnel resistance is five orders of magnitude larger than the quantum of resistance (26 k Ω) and allows for the localization of electrons on the tungsten nano-island. The lower capacitance of the device combined with the high tunnel resistance, allows for the Coulomb blockade effects observed at room temperature. Different device configurations, minimizing the total capacitance of the device have been explored. The effect of the geometry of the nano electrodes on the device characteristics has been presented. Simulated device characteristics, based on the soliton model have been discussed. The first application of SET device as a gas sensor has been demonstrated.

Multi-node TOA-DOA cooperative LOS-NLOS localization : enabling high accuracy and reliability

This dissertation investigates high performance cooperative localization in wireless environments based on multi-node time-of-arrival (TOA) and direction-of-arrival (DOA) estimations in line-of-sight (LOS) and non-LOS (NLOS) scenarios. Here, two categories of nodes are assumed: base nodes (BNs) and target nodes (TNs). BNs are equipped with antenna arrays and capable of estimating TOA (range) and DOA (angle). TNs are equipped with Omni-directional antennas and communicate with BNs to allow BNs to localize TNs; thus, the proposed localization is maintained by BNs and TNs cooperation. First, a LOS localization method is proposed, which is based on semi-distributed multi-node TOA-DOA fusion. The proposed technique is applicable to mobile ad-hoc networks (MANETs). We assume LOS is available between BNs and TNs. One BN is selected as the reference BN, and other nodes are localized in the coordinates of the reference BN. Each BN can localize TNs located in its coverage area independently. In addition, a TN might be localized by multiple BNs. High performance localization is attainable via multi-node TOA-DOA fusion. The complexity of the semi-distributed multi-node TOA-DOA fusion is low because the total computational load is distributed across all BNs. To evaluate the localization accuracy of the proposed method, we compare the proposed method with global positioning system (GPS) aided TOA (DOA) fusion, which are applicable to MANETs. The comparison criterion is the localization circular error probability (CEP). The results confirm that the proposed method is suitable for moderate scale MANETs, while GPS-aided TOA fusion is suitable for large scale MANETs. Usually, TOA and DOA of TNs are periodically estimated by BNs. Thus, Kalman filter (KF) is integrated with multi-node TOA-DOA fusion to further improve its performance. The integration of KF and multi-node TOA-DOA fusion is compared with extended-KF (EKF) when it is applied to multiple TOA-DOA estimations made by multiple BNs. The comparison depicts that it is stable (no divergence takes place) and its accuracy is slightly lower than that of the EKF, if the EKF converges. However, the EKF may diverge while the integration of KF and multi-node TOA-DOA fusion does not; thus, the reliability of the proposed method is higher. In addition, the computational complexity of the integration of KF and multi-node TOA-DOA fusion is much lower than that of EKF. In wireless environments, LOS might be obstructed. This degrades the localization reliability. Antenna arrays installed at each BN is incorporated to allow each BN to identify NLOS scenarios independently. Here, a single BN measures the phase difference across two antenna elements using a synchronized bi-receiver system, and maps it into wireless channel’s K-factor. The larger K is, the more likely the channel would be a LOS one. Next, the K-factor is incorporated to identify NLOS scenarios. The performance of this system is characterized in terms of probability of LOS and NLOS identification. The latency of the method is small. Finally, a multi-node NLOS identification and localization method is proposed to improve localization reliability. In this case, multiple BNs engage in the process of NLOS identification, shared reflectors determination and localization, and NLOS TN localization. In NLOS scenarios, when there are three or more shared reflectors, those reflectors are localized via DOA fusion, and then a TN is localized via TOA fusion based on the localization of shared reflectors.

Time-domain models for power system stability and unbalance

It is an important and difficult challenge to protect modern interconnected power system from blackouts. Applying advanced power system protection techniques and increasing power system stability are ways to improve the reliability and security of power systems. Phasor-domain software packages such as Power System Simulator for Engineers (PSS/E) can be used to study large power systems but cannot be used for transient analysis. In order to observe both power system stability and transient behavior of the system during disturbances, modeling has to be done in the time-domain. This work focuses on modeling of power systems and various control systems in the Alternative Transients Program (ATP). ATP is a time-domain power system modeling software in which all the power system components can be modeled in detail. Models are implemented with attention to component representation and parameters. The synchronous machine model includes the saturation characteristics and control interface. Transient Analysis Control System is used to model the excitation control system, power system stabilizer and the turbine governor system of the synchronous machine. Several base cases of a single machine system are modeled and benchmarked against PSS/E. A two area system is modeled and inter-area and intra-area oscillations are observed. The two area system is reduced to a two machine system using reduced dynamic equivalencing. The original and the reduced systems are benchmarked against PSS/E. This work also includes the simulation of single-pole tripping using one of the base case models. Advantages of single-pole tripping and comparison of system behavior against three-pole tripping are studied. Results indicate that the built-in control system models in PSS/E can be effectively reproduced in ATP. The benchmarked models correctly simulate the power system dynamics. The successful implementation of a dynamically reduced system in ATP shows promise for studying a small sub-system of a large system without losing the dynamic behaviors. Other aspects such as relaying can be investigated using the benchmarked models. It is expected that this work will provide guidance in modeling different control systems for the synchronous machine and in representing dynamic equivalents of large power systems.

Spin-strain coupling in a 3-D transition metal oxides

ab-initio Hartree Fock (HF), density functional theory (DFT) and hybrid potentials were employed to compute the optimized lattice parameters and elastic properties of perovskite 3-d transition metal oxides. The optimized lattice parameters and elastic properties are interdependent in these materials. An interaction is observed between the electronic charge, spin and lattice degrees of freedom in 3-d transition metal oxides. The coupling between the electronic charge, spin and lattice structures originates due to localization of d-atomic orbitals. The coupling between the electronic charge, spin and crystalline lattice also contributes in the ferroelectric and ferromagnetic properties in perovskites. The cubic and tetragonal crystalline structures of perovskite transition metal oxides of ABO3 are studied. The electronic structure and the physics of 3-d perovskite materials is complex and less well considered. Moreover, the novelty of the electronic structure and properties of these perovskites transition metal oxides exceeds the challenge offered by their complex crystalline structures. To achieve the objective of understanding the structure and property relationship of these materials the first-principle computational method is employed. CRYSTAL09 code is employed for computing crystalline structure, elastic, ferromagnetic and other electronic properties. Second-order elastic constants (SOEC) and bulk moduli (B) are computed in an automated process by employing ELASTCON (elastic constants) and EOS (equation of state) programs in CRYSTAL09 code. ELASTCON, EOS and other computational algorithms are utilized to determine the elastic properties of tetragonal BaTiO3, rutile TiO2, cubic and tetragonal BaFeO3 and the ferromagentic properties of 3-d transition metal oxides. Multiple methods are employed to crosscheck the consistency of our computational results. Computational results have motivated us to explore the ferromagnetic properties of 3-d transition metal oxides. Billyscript and CRYSTAL09 code are employed to compute the optimized geometry of the cubic and tetragonal crystalline structure of transition metal oxides of Sc to Cu. Cubic crystalline structure is initially chosen to determine the effect of lattice strains on ferromagnetism due to the spin angular momentum of an electron. The 3-d transition metals and their oxides are challenging as the basis functions and potentials are not fully developed to address the complex physics of the transition metals. Moreover, perovskite crystalline structures are extremely challenging with respect to the quality of computations as the latter requires the well established methods. Ferroelectric and ferromagnetic properties of bulk, surfaces and interfaces are explored by employing CRYSTAL09 code. In our computations done on cubic TMOs of Sc-Fe it is observed that there is a coupling between the crystalline structure and FM/AFM spin polarization. Strained crystalline structures of 3-d transition metal oxides are subjected to changes in the electromagnetic and electronic properties. The electronic structure and properties of bulk, composites, surfaces of 3-d transition metal oxides are computed successfully.

Theoretical estimation of optical absorption and photoluminescence in nanostructured silicon; an approach to improve efficiency in nanostructured solar cells

Renewable energy is growing in demand, and thus the the manufacture of solar cells and photovoltaic arrays has advanced dramatically in recent years. This is proved by the fact that the photovoltaic production has doubled every 2 years, increasing by an average of 48% each year since 2002. Covering the general overview of solar cell working, and its model, this thesis will start with the three generations of photovoltaic solar cell technology, and move to the motivation of dedicating research to nanostructured solar cell. For the current generation solar cells, among several factors, like photon capture, photon reflection, carrier generation by photons, carrier transport and collection, the efficiency also depends on the absorption of photons. The absorption coefficient,α, and its dependence on the wavelength, λ, is of major concern to improve the efficiency. Nano-silicon structures (quantum wells and quantum dots) have a unique advantage compared to bulk and thin film crystalline silicon that multiple direct and indirect band gaps can be realized by appropriate size control of the quantum wells. This enables multiple wavelength photons of the solar spectrum to be absorbed efficiently. There is limited research on the calculation of absorption coefficient in nano structures of silicon. We present a theoretical approach to calculate the absorption coefficient using quantum mechanical calculations on the interaction of photons with the electrons of the valence band. One model is that the oscillator strength of the direct optical transitions is enhanced by the quantumconfinement effect in Si nanocrystallites. These kinds of quantum wells can be realized in practice in porous silicon. The absorption coefficient shows a peak of 64638.2 cm-1 at = 343 nm at photon energy of ξ = 3.49 eV ( = 355.532 nm). I have shown that a large value of absorption coefficient α comparable to that of bulk silicon is possible in silicon QDs because of carrier confinement. Our results have shown that we can enhance the absorption coefficient by an order of 10, and at the same time a nearly constant absorption coefficient curve over the visible spectrum. The validity of plots is verified by the correlation with experimental photoluminescence plots. A very generic comparison for the efficiency of p-i-n junction solar cell is given for a cell incorporating QDs and sans QDs. The design and fabrication technique is discussed in brief. I have shown that by using QDs in the intrinsic region of a cell, we can improve the efficiency by a factor of 1.865 times. Thus for a solar cell of efficiency of 26% for first generation solar cell, we can improve the efficiency to nearly 48.5% on using QDs.