Optimality Gap Research Articles

Design and Simulation of a High-Efficiency Micro-Transformer for Photovoltaic Application

This paper presents the design and analysis of a micro-transformer model aimed at achieving high efficiency in photovoltaic applications. The proposed micro-transformer structure consists of two circular planar coils made of copper mounted on PCB (FR4) and Si substrates. The Mohan formula is employed to calculate the micro-transformer’s geometric parameters, ensuring alignment with flyback converter specifications. Consequently, the inductance, quality factors, and coupling factor variation parameters versus frequency, and the impact of the gap between the coils (500, 750, and 1000 µm) on them were analyzed. The simulation findings unequivocally demonstrated that a judicious reduction in gap thickness to 500 µm resulted in a remarkable enhancement of the coupling factor by an impressive 91%. Moreover, finite element-based software was used to analyze the thermal, magnetic, and electric performance of the micro-transformer across varying gap sizes. The investigation led to the determination of the optimal gap thickness that achieves adequate temperature, current, and magnetic flux distribution in the micro-transformer. Finally, the simulation circuit of a photovoltaic system that incorporates a flyback converter including the proposed micro-transformer was performed. Overall, the results revealed that the proposed micro-transformer model with its circular planar coil design offers high efficiency in PV applications.

Influence of battery cell spacing on thermal performance of phase change material filled lithium-ion battery pack

The era of electric mobility has started, and petrol/diesel vehicles are being replaced by electric vehicles (EVs). The phase change material (PCM) is a trending field of research in its application of energy storage and thermal management. PCM-based thermal management method is found to be quite simple and effective for battery packs. However, its commercialization is difficult due to its low thermal conductivity and extra weight addition to the battery pack. Hence, the present research focuses on the battery performance with PCM. The experimental setup for a 48V, 25Ah battery pack is developed, and its performance is explored with and without PCM. The numerical model for same sized battery pack is developed, and validated with experimental results. The major objective of the present research is to find the optimal gap between two battery cells so that a sufficient amount of PCM can be filled inside the battery pack. Initially, inline and staggered cell arrangements are examined, and no significant difference in thermal performance is found. Further, cell spacing of 5 mm, 3 mm, and 1 mm are examined, and maximum temperature and temperature difference are compared along with the weight and volume of the battery pack. For a single charging process, 1 mm cell spacing is found sufficient, considering the weight of the battery pack and thermal performance. However, with 1 mm cell spacing, temperature increases significantly after each charging and discharging. At the same time, 3 mm and 5 mm are found as feasible solutions considering single and double charging-discharging cycles, respectively. 3 mm cell spacing is better option when weight is a critical issue, while 5 mm cell spacing is better when thermal performance is a critical issue. The current study offers guidance in the advancement of battery packs, particularly in cases where space constraints are a concern.

Demand Steering in a Last-Mile Delivery Problem with Home and Pickup Point Delivery Options

To increase the efficiency of last-mile delivery, online retailers can adopt pickup points in their operations. The retailer may then incentivize customers to steer them from home to pickup point delivery to reduce costs. However, it is usually uncertain whether the customer accepts this incentive to switch to pickup delivery. This setup gives rise to a new last-mile delivery problem with integrated incentive and routing decisions under uncertainty. We model this problem as a two-stage stochastic program with decision-dependent uncertainty. In the first stage, a retailer decides which customers to incentivize. However, customers’ reaction to the incentive is stochastic: they may accept the offer and switch to pickup point delivery, or they may decline the offer and stick with home delivery. In the second stage, after customers’ final delivery choices are revealed, a vehicle route is planned to serve customers via the delivery option of their choice. We develop an exact branch-and-bound algorithm and propose several heuristics to improve the algorithm’s scalability. Our algorithm solves instances with up to 50 customers, realizing on average 4%–8% lower last-mile delivery costs compared with the commonly applied approaches in the industry that do not use incentives or offer incentives to all customers. We also develop a benchmark policy that gives very fast solutions with a 2% average optimality gap for small instances and up to 2% average cost increase compared with the heuristic solutions. Funding: This project received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [Grant 765395]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0287 .

On differential privacy for federated learning in wireless systems with multiple base stations

AbstractIn this work, we consider a federated learning model in a wireless system with multiple base stations and inter‐cell interference. We apply a differentially private scheme to transmit information from users to their corresponding base station during the learning phase. We show the convergence behavior of the learning process by deriving an upper bound on its optimality gap. Furthermore, we define an optimization problem to reduce this upper bound and the total privacy leakage. To find the locally optimal solutions of this problem, we first propose an algorithm that schedules the resource blocks and users. We then extend this scheme to reduce the total privacy leakage by optimizing the differential privacy artificial noise. We apply the solutions of these two procedures as parameters of a federated learning system where each user is equipped with a classifier and communication cells have mostly fewer resource blocks than numbers of users. The simulation results show that our proposed scheduler improves the average accuracy of the predictions compared with a random scheduler. In particular, the results show an improvement of over 6%. Furthermore, its extended version with noise optimizer significantly reduces the amount of privacy leakage.

Optimal and heuristic solutions for placing multiple finite-size rectangular facilities in an existing layout

In a companion paper (Date, K., and R. Nagi. [(2023) Optimal Placement of Multiple Finite-size Rectangular Facilities in an Existing Layout. International Journal of Production Research, THIS ISSUE]) we investigated a new problem of optimal placement of multiple finite-size rectangular facilities with known dimensions in the presence of existing rectangular facilities. We introduced the requisite theory to arrive at a solution by dividing the feasible region into sub-regions whose boundaries provide the candidates for the optimal placement. In this paper, we focus on developing optimal and heuristic solution methods for solving problem instances with various facility counts. To solve small instances with fewer facilities, we develop two optimal methods: (1) efficient explicit enumeration based on a tree state-space representation and (2) an implicit enumeration scheme that uses a flow-decomposition-based lower bound to reduce the search space and time. To solve industrial-sized instances, we have to resort to a family of construction and improvement heuristics given that the problem is NP-hard. The heuristic procedures perform well for non-pathological cases with an acceptable optimality gap. The main contribution of this paper is a range of optimal to heuristic methods that can be applied by the practitioner depending on their problem characteristics and desired efficiency.

Narrowing band gap and enhanced optoelectronic properties in methylammonium lead chloride perovskite under pressure

In this study, we explore the impact of hydrostatic pressure on the structural stability, elastic properties, mechanical behavior, thermodynamics, and optoelectronic characteristics of lead halide perovskite, specifically focusing on CH3NH3PbCl3. Through high-level ab initio simulation techniques, we investigate the lattice squeezing effects on this methylammonium lead chloride perovskite. Our findings reveal that applying hydrostatic pressure squeezes lattice parameters, influences the electronic profile, and results in spin-split band edges. The band gaps in compressed perovskites are observed to be narrower, with the potential for pressure-induced closures, offering new electronic features under various thermodynamic conditions. Because of the high-quality crystal and its optimal optical band gap, we successfully construct an efficient UV-photodetector, highlighting its promising applications in optoelectronics. This work contributes to a deeper atomistic understanding of inorganic halide perovskite behavior under external pressure and demonstrates the potential for realizing enhanced electronic functionalities through pressure conditions.

Two efficient logarithmic formulations to solve nonconvex economic dispatch

To solve economic dispatch (ED) with nonconvex nonlinear generation cost functions, this paper adopts a global optimization technique where piecewise linear approximation (PLA) functions replace the nonlinear functions. However, a problem with this technique is that the PLA model requires incorporating many discrete variables into the optimization model, which may render the model computationally expensive. This paper presents two efficient representation techniques of the PLAs, which scale logarithmically, including binary zig-zag (ZZB) and general integer zig-zag (ZZI). We replace the nonconvex cost functions in the ED with their PLAs and obtain an alternative ED formulation where two logarithmic techniques model the PLAs. Then, one can efficiently solve the alternative ED model with the standard branch-and-cut/bound-based algorithms to the desired optimality gap. To verify the techniques’ efficacy, we consider test systems having 13, 38, 40, 80, and 160 units. The numerical evaluations show that the logarithmic techniques presented can yield high-quality optimal solutions in less than 2 seconds in the considered cases, illustrating the techniques’ efficiency.

Factors Contributing to Sibling Rivalry Among Preschool Children

Background: Sibling rivalry is a form of relationship between siblings that is negative. Such relationships come with competition, jealousy, anger, and even hatred. In Indonesia, almost 75% of children experience sibling rivalry in the age range of 3-5 years. Sibling rivalry can refer to a child's developmental stage that is so emotionally immature that the child doesn't know how to get attention or start games with their siblings.
 Objectives: The purpose of this study is to determine the factors contributing to Sibling Rivalry in preschool children.
 Methods: The research method used is quantitative with a Cross-Sectional Study design. This research has been conducted in Preschool, Lubuk Begalung District from 6 to 9 June 2022. The population in this study were mothers who had young children with the criteria of being willing to sign informed consent. The sample in this study was 55 respondents. Data were analyzed univariately in the form of frequency distribution and bivariate using the Chi-Square test.
 Results: Based on the research results, it was found that there is a contribution from parental attitudes, favoritism, and children's age gap which can trigger sibling rivalry, with details of all variables having a significant sign (p-value < 0.05).
 Conclusion: Parents are expected to show the same level of affection for their children, educate them according to their developmental stage, implement a combination of parenting patterns according to the child's needs, and determine an optimal pregnancy gap of more than two years between children. We encourage parents to motivate children to look for ways to make things better. Parents just need to give their children time to process their feelings before they can forgive their siblings because children can forgive more quickly. make peace with the situation, respect each other, defend your rights, and ask permission if you want to borrow something. It is hoped that future researchers will carry out further research using other methods such as conducting health education so that picker parents know more about sibling rivalry. Future researchers could explore how to manage emotions when conflict occurs between siblings.

Two-dimensional Janus AgBiP2X3X[formula omitted] (X, X[formula omitted] = S, Se, Te): Efficient intrinsic electric field regulatory strategy for photocatalytic overall water-splitting

Exploring highly efficient catalysts that utilize visible light for water-splitting shows immense potential in addressing energy and environmental challenges. However, most photocatalysts are faced with challenges such as low carrier migration ability, high carrier recombination rate, and insufficient driving force for water-splitting reactions. Here, based on the two-dimensional (2D) AgBiP2X6 (X = S, Se, Te) structures, we construct Janus AgBiP2X3X3′ (X, X′ = S, Se, Te) monolayers and theoretically investigate their photocatalytic performance. The results indicate that the Janus method effectively regulate the energy band structure and intrinsic electric field (EF) of the materials. The Janus AgBiP2S3Te3 structure possesses an optimal band gap and band edge position in comparison to AgBiP2X6. Among all the investigated materials, AgBiP2S3Te3 possesses the largest intrinsic EF. The vertical intrinsic EF in Janus AgBiP2S3Te3 facilitates spatial separation of photogenerated electrons and holes, allowing hydrogen evolution reaction (HER) to take place on its top surface and oxygen evolution reaction (OER) to occur on its bottom surface, thereby effectively preventing carrier recombination. The limiting potentials for OER and HER reactions are significantly reduced. The OER can proceeds spontaneously under neutral conditions. The Gibbs free energy change (ΔG) of the HER is 0.075 eV under acidic conditions at pH = 0, which closely approaches the optimal value of 0. Simultaneously, the Janus AgBiP2S3Te3 exhibits kinetic and thermal stability, suitable appfavorableropriate electron and hole mobility, and excellent visible light absorption capability. Our work not only predict a series of new 2D materials, but also paves a strategy for improving the photocatalytic properties of 2D ferroelectric materials.

A General Framework for Providing Interval Representations of Pareto Optimal Outcomes for Large-Scale Bi- and Tri-Criteria MIP Problems

The Multi-Objective Mixed-Integer Programming (MOMIP) problem is one of the most challenging. To derive its Pareto optimal solutions one can use the well-known Chebyshev scalarization and Mixed-Integer Programming (MIP) solvers. However, for a large-scale instance of the MOMIP problem, its scalarization may not be solved to optimality, even by state-of-the-art optimization packages, within the time limit imposed on optimization. If a MIP solver cannot derive the optimal solution within the assumed time limit, it provides the optimality gap, which gauges the quality of the approximate solution. However, for the MOMIP case, no information is provided on the lower and upper bounds of the components of the Pareto optimal outcome. For the MOMIP problem with two and three objective functions, an algorithm is proposed to provide the so-called interval representation of the Pareto optimal outcome designated by the weighting vector when there is a time limit on solving the Chebyshev scalarization. Such interval representations can be used to navigate on the Pareto front. The results of several numerical experiments on selected large-scale instances of the multi-objective multidimensional 0–1 knapsack problem illustrate the proposed approach. The limitations and possible enhancements of the proposed method are also discussed.

Intermediate bands and p-orbital tuning of the band structure of BiFeO3 for photovoltaic application.

BiFeO3 is a lead-free inorganic ferroelectric material that holds promise for photovoltaic applications. However, its larger band gap poses a challenge for efficient sunlight absorption, limiting its efficiency in such applications. In this work, nitrogen, which has lower electronegativity compared to oxygen, was selected to tune the band gap of BiFeO3. It was discovered that the band gap of BiFeO3-xNx (x = 0.125, 0.25, 0.375, and 0.5) was reduced from the original value of 3.1 eV for the parent phase to 1.45-1.77 eV, which originated from the intermediate bands caused by the stronger interaction between Fe 3d and N 2p and the valence band maximum shifted towards higher energy levels caused by the introduction of N 2p. In particular, the band gaps of 1.45 and 1.49 eV for BiFeO2.75N0.25 and BiFeO2.625N0.375, respectively, were closer to the optimal band gap of approximately 1.4 eV for photovoltaic materials. Accompanied with the reduction in the band gap, the optical absorption coefficient of N-substituted BiFeO3 in the visible range was evidently increased. Noticeably, N-substituted BiFeO3 showed good ferroelectricity with a decreased band gap and increased optical absorption. The presented results thus demonstrate that N substitution is a promising way to improve the ferroelectric photovoltaic properties of BiFeO3.

Effect of two-fold single-atom substitutions (S, Se; C, N) in band gap engineered donor-acceptor conjugated microporous polymers on the efficient aerobic photooxidation of aryl sulfides.

Substitution of a single atom in a photoactive system is capable of vastly altering its optoelectronic properties leading to the generation of an efficient photocatalyst. In this study, we explore the impact of two-fold single-atom substitutions on the optoelectronic properties and photocatalytic performance of donor-acceptor type conjugated microporous polymers (D-A CMPs). For this, three isostructural triphenylamine (TPA)-based D-A CMPs were synthesized namely PTPA-BT, PTPA-BS, and PTPA-PS containing 2,1,3-benzothiadiazole, 2,1,3-benzoselenadiazole and [1,2,5]selenadiazolo[3,4-c]pyridine as the acceptor moieties, respectively. Firstly, PTPA-BT and PTPA-BS were synthesized using the S to Se single-atom substitution strategy, followed by the synthesis of PTPA-PS employing a second C to N single-atom substitution. The effect of single-atom substitution demonstrated drastic changes in their band gap, conductivity, and charge carrier dynamics, which in turn impacted their photocatalytic activity, although the change in their porosity was not much pronounced. In terms of photocatalytic detoxification of sulfur mustards, the activities of D-A CMPs follow the trend: PTPA-BS > PTPA-PS > PTPA-BT. In comparison with PTPA-BT (containing C, S) and PTPA-PS (containing N, Se), PTPA-BS (containing C, Se) exhibits a higher photocatalytic activity towards the photooxidation of thioanisole with >99% conversion and ∼93% isolated yield under visible-light illumination, which is attributed to its lower interfacial charge transfer resistance, stronger photocurrent response, optimal band gap and higher activity to generate superoxide anion radicals. Therefore, the two-fold single-atom substitution strategy is crucial for optimizing D-A CMPs for the photocatalytic oxidation of aryl sulfides. This approach allows fine-tuning of the optoelectronic properties to enhance photocatalytic efficiency and performance.

Conditional Neural Heuristic for Multiobjective Vehicle Routing Problems.

Existing neural heuristics for multiobjective vehicle routing problems (MOVRPs) are primarily conditioned on instance context, which failed to appropriately exploit preference and problem size, thus holding back the performance. To thoroughly unleash the potential, we propose a novel conditional neural heuristic (CNH) that fully leverages the instance context, preference, and size with an encoder-decoder structured policy network. Particularly, in our CNH, we design a dual-attention-based encoder to relate preferences and instance contexts, so as to better capture their joint effect on approximating the exact Pareto front (PF). We also design a size-aware decoder based on the sinusoidal encoding to explicitly incorporate the problem size into the embedding, so that a single trained model could better solve instances of various scales. Besides, we customize the REINFORCE algorithm to train the neural heuristic by leveraging stochastic preferences (SPs), which further enhances the training performance. Extensive experimental results on random and benchmark instances reveal that our CNH could achieve favorable approximation to the whole PF with higher hypervolume (HV) and lower optimality gap (Gap) than those of the existing neural and conventional heuristics. More importantly, a single trained model of our CNH can outperform other neural heuristics that are exclusively trained on each size. In addition, the effectiveness of the key designs is also verified through ablation studies.

Batch Learning SDDP for Long-Term Hydrothermal Planning

We consider the stochastic dual dynamic programming (SDDP) algorithm - a widely employed algorithm applied to multistage stochastic programming - and propose a variant using experience replay - a batch learning technique from reinforcement learning. To connect SDDP with reinforcement learning, we cast SDDP as a Q-learning algorithm and describe its application in both risk-neutral and risk-averse settings. We demonstrate the superiority of the algorithm over conventional SDDP by benchmarking it against PSR's SDDP software using a large-scale instance of the long-term planning problem of inter-connected hydropower plants in Colombia. We find that SDDP with batch learning is able to produce tighter optimality gaps in a shorter amount of time than conventional SDDP. We also find that batch learning improves the parallel efficiency of SDDP backward passes.

Genetic Artificial Hummingbird Algorithm-Support Vector Machine for Timely Power Theft Detection.

Utilities face serious obstacles from power theft, which calls for creative ways to maintain income and improve operational effectiveness. This study presents a novel hybrid genetic artificial hummingbird algorithm-support vector machine classifier to detect power theft. The proposed algorithm combines the artificial hummingbird algorithm exploration phase with the genetic algorithm's mutation and crossover operators, to optimize the support vector machine's hyperparameters and categorize users as fraudulent or nonfraudulent. It utilizes 7,270 rows of labeled historical electricity consumption data from the Liberia Electricity Corporation over 15 independent runs. The methodology entailed data preprocessing, data split into training, validation, and testing sets in an 80-10-10 ratio, z-score normalization, optimization, training, validation, testing, and computation of six evaluation metrics. Its performance is compared with 13 metaheuristic classifiers and the conventional support vector machine. Findings indicate that the genetic artificial hummingbird algorithm-support vector machine outperforms the 13 rivals and the standard support vector machine in the six assessment measures with an accuracy score of 0.9986, precision of 0.9971, f_score of 0.9986, recall of 1, Matthews correlation coefficient of 0.9972, and g_mean of 0.9987. Furthermore, 90% of the time, Wilcoxon rank-sum tests revealed statistically significant differences between the algorithm and its rivals, demonstrating its superiority. The average run time is 4,656 seconds, the 3rd highest among its competitors. Despite the time complexity trade-off, its excellent performance on the unimodal and multimodal benchmark test functions, placing joint best in 7 out of 7 and 5 out of 6, respectively, provides important insights into the model's capacity to balance exploitation and exploration, improve local search, and avoid becoming stuck in the local optimum. These findings address important metaheuristic optimization gaps highlighting the model's potential for power theft detection.

Universally optimal staffing of Erlang-A queues facing uncertain arrival rates

In many service systems, the staffing decisions must be made before the arrival rate is known with certainty. Thus, it is more appropriate to consider the arrival rate as a random variable at the time of the staffing decision. Motivated by this observation, we study the staffing problem in a service system modeled as an Erlang-A queue facing a random arrival rate. For linear staffing costs, linear waiting costs, and a cost per customer abandonment, we propose a policy that is based on modifying the well-known square-root safety staffing policy to explicitly account for the randomness in the arrival rate. Our primary contribution is to show that our proposed policy is “universally optimal”, i.e., irrespective of the magnitude of randomness in the arrival rate, the optimality gap between our proposed policy and the exact optimal policy remains bounded as the system size grows large. This is important because earlier performance guarantees for Erlang-A queues either (1) are not universal and offer performance guarantees that depend on the magnitude of uncertainty in the arrival rate or (2) are universal but assume a deterministic arrival rate. The practical relevance of this provable robustness is that our proposed policy is a “one-size-fits-all” as it is guaranteed to perform well for all levels of arrival rate uncertainty.

An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation

We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound (B&B) framework, our algorithm adaptively refines the piecewise-linear approximations and iteratively solves convex approximation problems. The convergence analysis provides a bound on the optimality gap as a function of approximation errors. Based on this bound, we prove that the proposed B&B algorithm terminates in a finite number of iterations and the worst-case bound to obtain an ϵ-optimal solution reciprocally depends on the square root of ϵ. Numerical experiments on Cobb–Douglas production efficiency and equitable resource allocation problems support that the algorithm efficiently finds a highly accurate solution while significantly outperforming the benchmark algorithms for all the small size problem instances solved. A modified branching strategy that takes the advantage of non-linearity in convex functions further improves the performance. Results are also discussed when solving a dual reformulation and using a cutting surface algorithm to solve distributionally robust counterpart of the Cobb–Douglas example models.

Comparative study on performance of counter-flow dew-point indirect evaporative cooling systems via a more realistic and experimentally validated three-dimensional model

Dew-point indirect evaporative cooling (DPIEC) technology is designed and applied as a low carbon-emission and high energy-efficient air conditioning (AC) solution without employing non-environmentally friendly refrigerant and mechanical compressor for cooling in building sector. A more realistic three-dimensional (3-D) model of the DPIEC that better captures the fundamental thermodynamic of its operation is proposed. It considers the variability of air thermal properties and is employed to investigate the DPIEC's performance for three possible arrangements. The 3-D model is classified as configurations 1, 2 and 3 based on the relative flow direction between primary/secondary air and spray water. Experimental results indicate that the model can well evaluate the thermodynamic performance. Additionally, the influence of crucial factors on the performance is parametrically studied by employing three performance indexes. Comparison reveals that configuration 1 can achieve the highest effectiveness and cooling capacity. Results also show that the secondary-to-primary air ratio should be confined to around 0.3 to achieve maximum cooling capacity, and the optimal channel gap should be limited to the range from 3 to 4 mm. Comparatively, the relative flow direction between the spray water and the primary/secondary air has a greater effect on the thermodynamic performance than the spray water inlet velocity.

The effect of space charge neutralization on the parametric design of photon enhanced thermionic solar converters

Photon-enhanced thermionic emission (PETE) is a promising method for increasing current density at relatively low cathode temperatures, but is susceptible to the space charge effect. In this study, we propose a novel PETE device model in which the space-charge barrier is relaxed by photon-excited cesium ions. The decrease in maximum efficiency with interelectrode gap is more gradual compared to previous studies. We investigate the effects of cathode materials properties (band gap and electron affinity) and operating conditions (cathode temperature and interelectrode gap) on PETE performance, and identify optimal performance conditions. Our findings show that the optimal gap range exceeds 5 μm and near field radiation loss can be minimized, providing an important opportunity for designing PETE device with larger interelectrode gaps and higher solar flux concentrations.

The Next Frontier of Solar Energy: Transparent Photovoltaics

The development of "Transparent Photovoltaics" (TPVs[1]), i.e., solar cells that are transparent to visible light, has become more and more popular in recent years due to their contribution to low CO2 emissions through "window power generation" in fully glazed buildings (building-integrated photovoltaics: BIPV) and the growing demand for development in the promotion of farm-based solar power; Agrivoltaics [2, 3]. So far, selective light-transmission photovoltaics (SLTPVs), in which conventional bulk and thin-film solar cells are fabricated into long and thin strips and arranged like a window shade at intervals or by reducing the film thickness, have already been put into practical use [3, 4], allowing part of the incident light to escape to the rear. However, the installation applications of SLTPVs are limited since blocking the line of sight outside the window and preventing a sufficient amount of light from reaching the interior or farmland surface. If TPVs that are uniformly transparent or tinted-transparent like window glasses can be commercialized, the range of applications is expected to expand significantly.TPVs are perceived by humans as being "nearly colorless" if they have a visible light transmittance of 80% or more, including the substrate material. Depending on the application, it is possible to produce red, and dark colors by adjusting the material characteristics so that only the short wavelength side of the visible light wavelength range, the long wavelength side, or the entire wavelength range is uniformly absorbed [2, 3]. These visible light-transmissive solar cells with visible light transmittance of 80% or less are referred to as semitransparent photovoltaics (STPVs).It is crucial to consider the theoretical limiting efficiency (TLE) for the practical application of TPVs. Recent reports have simulated TLs for single-junction and multi-junction cells with optical absorption in the UV and NIR regions, yet not in the visible region [5]. The results demonstrate that practical conversion efficiencies of 11% and 21% can be obtained for single-junction and 16-junction cells respectively, with 80% visible transmission. The optimal band gap for cells with 100% Vis-EQE (an external quantum efficiency in the visible light range of 435 to 670 nm) is around 1.5 eV, while for cells with 0% Vis-EQE and full transmission in the visible region, the optimal Eg shifts to the lower energy side of 1.1 to 1.2 eV. To use only the UV region without using the NIR region, 2.8 to 3.0 eV or higher can be easily approached with existing technology.Transparent photovoltaic cells (TPVs) and semi-transparent photovoltaic cells (STPVs) developed to date can be broadly classified into the following four types of power generation methods: TPVs (1) Heterojunction and homojunction with 3.0 eV and more wide-gap semiconductors as generating layers [6-8].(2) Glass plate (+ wavelength conversion material) with Si solar cells installed on the end face of the glass plate to form a module [9]. STPVs (3) Increased visible light transmittance by wider-gap semiconductor materials (colored transparent type) [3].(4) SLTPVs [4].If TPV can be made more cost-effective, it can be applied to various applications such as low CO2 emissions in buildings, photovoltaic power generation for agriculture, no external power source required for electric bulletin boards, auxiliary power source for electric vehicles, and so on. Research and development are categorized into the above areas (1) through (4), with (1) through (3) in particular requiring basic research and development from a materials perspective. The number of groups involved in research and requests for practical applications is increasing, and accelerated progress is expected.