Power Factor Research Articles

Strategic control of excess tellurium to achieve high figure-of-merit in Te-rich Bi0.5Sb1.5Te3

Abstract Increasing the Te content in stoichiometric Bi0.5Sb1.5Te3 facilitates effective control over the anti-site defects and nanostructure; however, arresting excess Te in the host matrix is challenging. Herein, we report the success of a saturation-annealing treatment in a vacuum, followed by air-quenching as a promising approach for synthesizing high figure-of-merit (zT) Bi0.5Sb1.5Te3+xTe (x = 0, 2, 5 and 10 wt%) materials. A remarkably high-power factor (α 2 σ ~ 6 mW at 300 K) is achieved in p-type Bi0.5Sb1.5Te3 + 5 wt% Te composition due to high carrier concentration (n) and good carrier mobility (µ). Microstructural analysis revealed the formation of densely interconnected polycrystalline grains featuring fine grain boundaries, planar/point defects, and strain field domains, contributing towards wide-length scale phonon scattering. The cumulative effect of drastically reduced thermal conductivity (κ ~ 0.8 W/m-K at 300 K), and enhanced power factor resulted in a record zT value ~ 2.2 at 300 K in Bi0.5Sb1.5Te3 + 5 wt% Te, with an average zT value up to 1.35 in temperatures ranging from 303 to 573 K. The COMSOL simulations predict a maximum conversion efficiency (η max ) of ~ 15%, at a temperature gradient (∆T) of 270 K, for a single-leg thermoelectric generator (TEG) developed using this material.

High Conductivity and Thermoelectric Power Factor in p-Type MoS2 Nanosheets

High Conductivity and Thermoelectric Power Factor in p-Type MoS2 Nanosheets

Enhancing the Thermoelectric Performance of Bi2O2Se Ceramics via Multi-Element Doping

Bi2O2Se, as the n-type counterpart of p-type BiCuSeO, has garnered considerable attention. The lower carrier concentration leads to reduced electrical conductivity, prompting extensive research efforts aimed at enhancing its electrical performance. This study prepared Bi2−3x(CeTiSn)xO2Se (x = 0, 0.02, 0.03, and 0.04) ceramics using a combination of high-energy ball milling and cold isostatic pressing techniques. Results demonstrated that the incorporation of multiple elements led to an increase in the carrier concentration within the Bi2O2Se system, thereby improving electrical conductivity. The electrical conductivity increased from 5.1 S/cm for Bi2O2Se to 154.1 S/cm for Bi1.88(CeTiSn)0.04O2Se at 323 K. Furthermore, the maximum power factor value of Bi1.88(CeTiSn)0.04O2Se was 112 μW m−1 K−2 at 763 K. Doping led to a slight increase in thermal conductivity. The figure of merit ZTmax value of Bi1.88(CeTiSn)0.04O2Se was ~0.16, marking a significant enhancement of about 1.45 times compared to that of the pure sample (~0.11).

Rectifier Fault Diagnosis Based on Euclidean Norm Fusion Multi-Frequency Bands and Multi-Scale Permutation Entropy

With the emphasis on energy conversion and energy-saving technologies, the single-phase pulse width modulation (PWM) rectifier method is widely used in urban rail transit because of its advantages of bidirectional electric energy conversion and higher power factor. However, due to the complex control and harsh environment, it can easily fail. Faults can cause current and voltage distortion, harmonic increases and other problems, which can threaten the safety of the power system and the train. In order to ensure the stable operation of the rectifier, incidences of faults should be reduced. A fault diagnosis technique based on Euclidean norm fusion multi-frequency bands and multi-scale permutation entropy is proposed. Firstly, by the optimal wavelet function, information on the optimal multi-frequency bands of the fault signal is selected after wavelet packet decomposition. Secondly, the multi-scale permutation entropy of each frequency band is calculated, and multiple fault feature vectors are obtained for each frequency band. To reduce the classifier’s computational cost, the Euclidean norm is used to fuse the multi-scale permutation entropy into an entropy value, so that each frequency band uses an entropy value to characterize the fault information features. Finally, the optimal multi-frequency bands and multi-scale permutation entropy after fusion are used as the fault feature vector. In the simulation system, it is shown that the method’s average accuracy is 78.46%, 97.07%, and 99.45% when the SNR is 5 dB, 10 dB, and 15 dB, respectively. And the fusion of multi-scale permutation entropy can improve the accuracy, recall rate, precision, and F1 score and reduce the False Alarm Rate (FAR) and the Missing Alarm Rate (MAR). The results show that the fault diagnosis method has high diagnosis accuracy, is a simple feature fusion method, and has good robustness to working conditions and noise.

PID CONTROLLER FOR SPEED CONTROL OF PMSM BASED ON MAYFLY OPTIMIZATION ALGORITHM

Permanent magnet synchronous motor (PMSM) is extensively employed in AC servo drives owing to their superior torque-to-inertia ratio, power density, efficiency, and power factor compared to other motors. So, it is a crucial point to regulate the PMSM speed. Conventional proportional, integral, and differential (PID) is a simple controller and easy to implement but it is coefficients are essentially determined by experience when used in PMSM to control the speed. This invariably produces unacceptable outcomes, in addition when it comes to low-power application drives, PID controller gains typically produce adequate results but, when it comes to high-power application drives, an untuned PID does not deliver satisfactory performance. The optimization algorithm offers an effective method to produce optimal PID gains. Therefore, to optimize the PID coefficients to regulate the PMSM speed, this study suggests a mayfly optimization algorithm (MA). Recently, the MA was introduced as a new intelligent optimization method with exceptional optimization capabilities. Nuptial dancing and random flight improve the ability of the algorithm to balance its features of exploitation and exploration while assisting in its escape from local optima. This suggested approach has been verified with MATLAB, and the outcomes are compared with the standard particle swarm optimization technique (PSO) and conventional PID. The outcomes show that compared to the standard PSO or conventional PID, the PID parameters adjusted by the MA method can produce faster speed responses and less overshoot. Furthermore, the system's optimal ITAE index value, as determined by the MA technique, is smaller (0.794) as compared to other techniques 1.503 and 1.906 respectively.

Investigation on phase formation and thermoelectric transport properties of CoTe2-CoSe2 solid solution alloys.

CoTe2 and CoSe2 alloys have garnered considerable attention in thermoelectric applications due to their high electrical conductivity, tunable electronic properties, and potential for high power factors. In this study, the phase formation behavior and thermoelectric transport properties of a CoTe2-CoSe2 solid solution alloy were investigated by synthesizing a series of Co(Te1-xSex)2 compositions, where x = 0, 0.25, 0.50, 0.75, and 1.0. For x = 0, 0.25, and 0.50, the orthorhombic phase of CoTe2 was observed, while for x = 0.75, the orthorhombic phase of CoTe2 and cubic phase of CoSe2 coexisted. Up to x = 0.50, the power factor decreased slightly as the Hall mobility and the density-of-state effective mass decreased. The total thermal conductivity decreased as x increased to 0.50, owing to a decrease in the electronic and lattice thermal conductivity. Despite the decrease in total thermal conductivity, no significant increase in zT values was observed in the range of x = 0.25-0.50 due to a more pronounced decrease in the power factor. Nevertheless, cubic phase CoSe2 exhibited higher power factors and thus higher zT of 0.13 at 700K. Further analysis based on single Kane band model suggests that significant enhancement in the power factor and zT could be achieved by reducing the carrier concentration from ∼1021 to ∼1019 cm-3 for all compositions.

Crystal structure manipulation to achieve better thermoelectric performance in Te-substituted GeSe

GeSe has recently gained attention for its structural similarity to SnSe, an excellent thermoelectric material. However, for the orthorhombic GeSe, the maximum zT is limited to ∼0.2 at 700 K. A significant improvement in the thermoelectric performance is observed when GeSe is stabilized in a rhombohedral or cubic structure; thus, the crystal structure plays an important role in GeSe for improved zT. In this study, we investigated the structural transitions and thermoelectric properties of Te-substituted GeSe. Increasing Te substitution in GeSe1-xTex (x = 0.00–0.50) induces a transition from orthorhombic to rhombohedral crystal structure at ambient conditions with the maximum zT ∼ 0.58 observed in rhombohedral GeSe0.6Te0.4 at 573 K. The improved thermoelectric performance in the rhombohedral phase is due to a concurrent increase in the power factor and a decrease in lattice thermal conductivity. The phonon dispersion calculation tells that the high-frequency optical phonon modes significantly increase the phonon–phonon scattering for the rhombohedral phase, enhancing the lattice anharmonicity and reducing the lattice thermal conductivity. This behavior aligns with the presence of metavalent bonding in rhombohedral GeSe. Additionally, peak broadening observed in the Raman spectra of the rhombohedral phase indicates pronounced lattice anharmonicity and phonon modes softening due to the metavalent bond character.

Justification of the application of a distributed network of photoelectric converters to power a linear motor of magnetolevitation transport

Modern high-speed transport is the basis of sustainable economic and social development of the state, society in compliance with environmental requirements. The concept of power supply of a linear motor of magneto-levitation transport from a distributed network of photovoltaic converters is substantiated. The basic power element of a track power plant is proposed in the form of a completed unit consisting of a solar panel, a storage device and an inverter, which operates on a load in the form of a "short" track coil. The use of a "short" track coil allows reducing electrical energy losses, since the traction force is formed only in the zone of interaction with the rolling stock, energy is not transmitted to unused sections of the track structure. By reducing the length of the working section, other energy indicators of the system as a whole are significantly suspended, in particular the power factor and effi-ciency. Reducing the length of the working sections in conditions of high speeds of rolling stock will lead to increased requirements for reliability and speed of operation of track switches. The track switches are created on the basis of power semiconductor switches, which are controlled by modern microcontrollers. The effectiveness of the proposed structure de-pends on the solar activity in the region of the transport artery. The estimated solar activity indicators allow us to state that the weight indicators of the rolling stock that must move on the track with a "short" section correspond to the available resources.

Integration of Boron Nitride Into Tin‐Enriched SnSe2 for a High‐performance Thermoelectric Nanocomposite with Optimized Electrical Transport and Mechanical Properties

AbstractThermoelectric materials with high figures of merit are essential for efficient energy conversion and cooling applications. This study integrates boron nitride (BN) into tin‐enriched SnSe₂ to form a multi‐phase composite with synergistic thermoelectric and mechanical properties. The incorporation of BN into SnSe2 offers the dual benefit of optimizing both carrier concentration and carrier mobility. Notably, the BN/SnSe2 composite exhibits a significant increase in the Seebeck coefficient, attributed to an increased bandgap and electronic density of states near the Fermi level, as corroborated by density functional theory calculations. Consequently, an impressive power factor of 940 µWm−1K−2 is achieved for the sample with a mere 0.8 wt.% BN content. This power factor enhancement, coupled with a notable ≈37% reduction in lattice thermal conductivity due to increased phonon scattering from lattice strain induced by Se vacancies, contributes to a remarkable ZTmax value of 0.68 at 767 K, exceeding the performance of pristine SnSe2 by ≈76%. Additionally, BN enhances stress distribution and deformation behavior, improving stability and reliability under diverse thermal and mechanical conditions. This study demonstrates an effective approach for advancing SnSe₂ thermoelectric materials and provides a foundation for composite design and energy band engineering to achieve high‐performance thermoelectric devices.

The Experimental Study on the Thermoelectric Properties of Sputtered Amorphous Molybdenum Disulfide Films

ABSTRACT Molybdenum disulfide (MoS2), a promising two-dimensional material, has attracted significant attention due to its unique electronic and thermal properties, making it a potential thermoelectric material Extensive research is underway to improve the thermoelectric properties of MoS2 by enhancing the figure of merit (ZT). However, there is currently limited research on the effects of thickness and temperature on the thermoelectric properties of MoS2 films prepared by magnetron sputtering. In this paper, amorphous MoS2 films with different thicknesses were first deposited using magnetron sputtering, ranging from 43nm to 231nm. The Frequency Domain Thermoreflectance (FDTR) system was established to measure the thermal conductivity of MoS2 film. The experimental results indicate a thermal conductivity range of 0.49 to 0.53W/m·K, with thickness showing minimal impact. The thermal boundary conductance between the sputter-deposited MoS2 film and the SiO2 substrate is measured at 12±5MW/m2 ·K. The electrical conductivity and Seebeck coefficient were measured in the temperature range of 300 K to 450 K using LSR-3 equipment. The results indicate that the MoS2 films prepared in this study were all p-type semiconductors, with electrical properties increasing with temperature. Within the temperature range of 300–430 K, the power factor of all films increases with the rise in temperature, reaching a maximum value of 0.36 µW/cm·K2

Investigating the Multifunctional Role of Sr2FeMnO6 Double Perovskite in Spintronic and Thermoelectric Properties

Herein, the double‐perovskite Sr2FeMnO6 is investigated using density functional theory to investigate its electronic, magnetic, thermoelectric, and thermodynamic properties. The Sr2FeMnO6 show the ferromagnetic phase stability with the formation energy of about −2.53 eV. Spin‐polarized band structure and density of states (DOS) calculations, performed using the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE‐GGA) and modified Becke–Johnson (GGA + mBJ) methods, confirm a half‐metallic nature. The system exhibits metallic behavior in the spin‐up channel, whereas the low‐spin counterpart demonstrates semiconducting characteristics with a bandgap of about 1.38 eV. A total magnetic moment of 7 μB per formula unit is observed, predominantly originating from Fe and Mn atoms, with induced magnetism in oxygen attributed to Mn‐3d, Fe‐3d, and O‐2p orbital interactions. The thermoelectric behavior of the system is studied by employing the semiclassical Boltzmann theory‐based BoltzTraP code for both spin channels, revealing zT values of 0.98 and 0.94 for spin‐down and spin‐up channels, respectively, with zT decreasing and the power factor increasing with temperature. These findings highlight Sr2FeMnO6 as a promising candidate for spintronics, spin dynamics, and energy‐harvesting applications, offering insights into its multifunctional potential.

Cascaded AC-DC parallel boost-flyback converter for power factor correction

A two-stage power factor correction (PFC) topology achieves a higher power factor quality and lower harmonic distortion than a single-stage converter. This paper introduces a two-stage PFC topology using a parallel boost and flyback converter which is employed as a voltage regulator The main boost converter is used for PFC and the other is the active filter circuit. The filter is implemented to improve the quality of phase-current and eliminate the switching loss. Furthermore, a reaction curve of Ziegler-Nichol’s method determines the controller parameter for cascaded PFC converter circuit. Simulated and experimental results are presented to validate the proposed method. The total harmonic distortion (THD) value decreases significantly from 83.35% become 0.98% in the simulation. In addition, experimental results show that the current response has good performances, including less harmonics, higher power factor, and lower THD value compared to without a PFC circuit. The PF increased from 0.43 become 0.96, the THD value decreased from 49.4% become 16.2%, and contains a small number of harmonics. The proposed controller method has better responses than the conventional one, including small steady-state error, fast rise time and settling time. A microcontroller (MCU), type STM32F407VG, produced by STMicroelectronics is used to execute the proposed control in both converters.

Scrutinizing the electronic structure, magnetic, mechanical, thermodynamic, optical and thermoelectric properties of lead-free hafnium based Hf2VP (P = Si, Sn) full Heusler alloys

The study of energy harvesting and thermoelectric materials has drawn more attention in the last several years. The great thermal stability of these materials is advantageous for thermoelectric devices, in addition to their structural capacity for showcasing and incorporating diverse novel concepts to augment the thermoelectric figure of merit. In the current study, we have predicted the physical properties of Hf2VP (P = Si, Sn) Heuslers using density functional theory in conjunction with the Boltzmann transport scheme. The strength and ductility of these materials are ascertained by simulating elastic characteristics The exchange correlation potential is handled via the modified Becke–Johnson potential (mBJ) and the generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA-PBE). Near the Fermi level, the band profiles for Hf2VSi and Hf2VSn Heuslers were found to be n-type indirect band-gap respectively. The thermodynamic stability of these materials is approved by the formation and cohesive energy. The relationships between different transport parameters are predicted using the band occupation and density of states in the post DFT treatment. Slack’s equation has identified the most significant lattice component of heat conductivity with great precision. These materials are likely to find use in the design of memory devices and future thermoelectric and energy harvesting materials due to their half-metallic nature and efficient thermoelectric parameters, such as electrical conductivity, Seebeck coefficient, thermal conductivity, power factor, and ZT.

Charge transport optimisation in SnO2 nanoparticles via Zn doping to achieve a power factor of 83 μW/m.K2

Charge transport optimisation in SnO2 nanoparticles via Zn doping to achieve a power factor of 83 μW/m.K2

Improvement of a Magnus VAWT Based on Numerical Simulation using a Fixed Blade

Magnus wind turbines have a wide range of advantages ranging from generating energy at low wind speeds to adapting to any wind direction. However, the cylindrical blades themselves have high drag and low lift. The aim of the work is to study the addition of a fixed blade to the cylindrical blades of a wind turbine to improve the efficiency of the entire wind turbine. The paper presents a numerical study of the lifting force and drag force of a wind turbine, as well as the blades themselves, averaged over time from the air flow velocity and the number of revolutions. Using the averaging method of the Navier-Stokes equations RANS (Reynolds-averaged Navier–Stokes), numerical results were obtained showing the efficiency of the installation starting from 3 m/s, i.e. low wind speeds. It is determined that the use of adding a fixed blade to a rotating cylinder gives an increase in the value of the lifting force from 40-55% and power factor of the wind turbine by almost 1.5-1.7 times due to the regulation and reduction of the disruption of vortices behind the rotating cylinder. The effect of the plate on the velocity and pressure field is illustrated. The results obtained are useful when designing real experimental installations.

EFFECT OF ANNEALING TEMPERATURE ON THE STRUCTURAL AND THERMOELECTRIC PROPERTIES OF CuFeS2 NANOPARTICLES PREPARED BY THE HYDROTHERMAL METHOD

The current study described precise and simple hydrothermal method used to synthesize CuFeS2 nanoparticles. The thermoelectric properties of CuFeS2 nanoparticles were studied under different conditions of annealing treatment. The phase structure, functional groups, and thermal stability of the CuFeS2 nanoparticles samples were analyzed via X-ray diffractometer (XRD), Fourier transform infrared spectroscopy (FT-IR), and thermogravimetric analysis (TGA). The X-ray diffraction (XRD) results of the synthesized nanoparticles closely matched the CuFeS2 chalcopyrite patterns. FT-IR measurements confirmed the presence of the characteristic S-O, Fe-S, and O-H groups in the structure of the prepared nanoparticles. The TGA results indicate that the CuFeS2 nanoparticles are thermally stable below 650°C. The scan electron microscope (SEM) measurements revealed that the particle size of all the samples was less than 100 nm after the annealing treatment. The optical measurements showed that the absorbance edges of the CuFeS2 samples shifted to longer wavelengths after the annealing treatment. The thermoelectric measurements indicated that the annealing treatment modulated the electrical conductivity, Seebeck coefficient, power factor, and thermal conductivity of the CuFeS2 samples.

Linearization of Photovoltaic Cell Single Diode Equivalent Circuit Model Using Piecewise Linear Parallel Branches Model and Findin Fill Factor

In this article, the linearization and analysis of the Photovoltaic (PV) cell single diode equivalent circuit model have been performed. The diode element in the PV cell equivalent circuit model is a nonlinear component. The nonlinear PV cell single diode model has been linearized using the piecewise linear parallel branches model. In addition, the maximum power and fill factor (FF) of the PV cell have been determined based on the equivalent circuit parameters. Thevenin theorem was used in this analysis process. For this theorem to apply, the circuit must have a linear characteristic. The linearization of the nonlinear diode element has been achieved through the piecewise linear parallel branches model (PLPBM). In practice, the aim is to transfer the maximum power (Pmax) from the PV cell. Another important parameter of the PV solar cell is the FF. The FF is used to describe the general behavior of a solar PV cell. This factor is used to determine the quality of the solar PV cell. The FF provides information about the quality and efficiency of the solar cell. In a low FF scenario, the value of the series resistance is high, while the value of the parallel resistance is low. The FF of typical PV cells ranges between 50% and 82%. In the analysis conducted in the article, the FF of the PV solar cell was found to be 74%.

Late Endovascular Treatment for Ischemic Stroke with Moderate to Large Infarct Volume is Associated with a Better Clinical Prognosis.

The concept of "time is brain" is crucial for the reperfusion therapy of ischemic stroke. However, the Infarct Growth Rate (IGR) varies among individuals, which is regarded as a more powerful factor than the time when determining infarct volume and its association with clinical outcomes. For stroke patients with a similar infarct volume, a longer time from stroke Onset to Imaging (OTI) correlates with a lower IGR, which may indicate a better prognosis. This study aimed to compare the prognoses of patients with anterior circulation stroke who received Endovascular Treatment (EVT), specifically comparing early EVT vs. late EVT. We analyzed 255 patients with acute anterior circulation stroke due to large vessel occlusion and who have successfully undergone recanalization after EVT. All patients were divided into the late (OTI≥6 hours) and early (<6 hours) time window groups and compared. The primary outcome was moderate functional prognosis, defined as a modified Rankin Scale (mRS) ≤3 at 90 days. The secondary outcome was No Significant Infarct Expansion (NSIE), defined as a reduction of less than 2 points on the Alberta Stroke Program Early CT Score (ASPECTS). In the moderate to large infarct subgroup, the late time window EVT was independently associated with a higher rate of moderate functional outcome (P =0.007) and NSIE (P =0.001); mediation analysis showed that NSIE partially mediated the effects of the late time window EVT on moderate functional outcome (coefficient: 0.112, 95% CI: 0.051 to 0.239, P =0.011); however, these associations were not consistent in the small infarct group. For anterior circulation stroke patients who received EVT according to current guidelines, those with moderate to large infarct volume and having a longer OTI had better clinical outcomes than those who had a shorter OTI and were more suitable for EVT.

Screening of Coulombic Interactions To Achieve a Higher Power Factor in Conjugated Polymers.

Thermoelectric properties of conducting polymers typically suffer from molecular chain disordering, as charge transport is predominantly controlled by morphology. This is especially more problematic when counterions are introduced to tune the carrier concentration for optimal thermoelectric performance, which disturbs the morphology further. In this work, we introduce a new avenue for enhancing thermoelectric properties without needing to regulate the morphology, namely, by controlling the coulombic interaction between polarons and counterions. We perform in situ de-doping thermoelectric experiments over 3 orders of magnitude change in electrical conductivity of three distinct thermoelectric polymers, namely, poly(3-hexylthiophene-2,5-diyl) (P3HT), poly[2,5-bis(3-dodecylthiophen-2-yl)thieno[3,2-b]thiophene] (PBTTT-C12), and poly[2,5-(2-octyldodecyl)-3,6-diketopyrrolopyrrole-alt-5,5-(2,5-di(thien-2-yl)thieno[3,2-b]thiophene)] (OD-PDPP2T-TT) conjugated polymers, followed by grazing-incidence wide-angle X-ray scattering (GIWAXS) to study their respective morphologies. We demonstrate a 9-fold enhancement in the thermoelectric power factor in OD-PDPP2T-TT compared to PBTTT-C12 and link it to the coulombic screening of charge carriers, including in the optimally doped regime. We support this hypothesis using Boltzmann transport equations and show that, in both P3HT and PBTTT-C12, as the polymer is doped, impurity scattering remains the dominant scattering mechanism, while in OD-PDPP2T-TT, the scattering mechanism changes from impurity to acoustic phonon limited, resulting in more effective screening of ionized counterions. Our results provide an additional knob to enhance the fundamental understanding of thermoelectric physics of conducting polymers and provide a pathway to achieve higher performance in the field of organic thermoelectrics.

Exploring Factors Driving Consumer’s Purchase Intention Towards Electric Two-Wheelers

This study investigates the consumer purchase intentions towards electric two-wheelers in Kathmandu Valley. The research examines the roles of environmental concerns, perceived economic benefits, social influence, and charging infrastructure. Data were collected from 400 respondents through a structured questionnaire survey, and hierarchical multiple regression was used for the causal analysis. Results indicate that environmental concerns are a strong motivator for adopting e-bikes, highlighting the potential for leveraging environmental benefits in marketing strategies. Perceived economic benefits also play a crucial role, suggesting that financial incentives could enhance e-bike appeal. Social influence emerged as a powerful factor, indicating that endorsements from peers and social networks can significantly shape purchase intentions. Despite these positive influences, high initial costs and inadequate charging infrastructure remain significant barriers. The study suggests that addressing these barriers through targeted interventions such as subsidies, improved charging infrastructure, and public awareness campaigns, is essential for promoting e-bike adoption. The findings provide valuable insights for policymakers and industry stakeholders to design strategies that support the transition to sustainable transportation, contributing to a cleaner environment and improved public health in Kathmandu Valley.