Energy Supply Rate Research Articles

Optimizing energy consumption in smart homes using GA-LSTM

The need to optimize energy consumption arises from the inadequate energy supply many homes face. However, to optimize energy consumption in a home, one must be equipped with the knowledge of the energy consumption rate and energy supply rate in the home. This paper proposed the use of a Long Short-Term Memory (LSTM) model optimized by Genetic Algorithm (GA) to optimize the energy consumption in a smart home. The model was designed using 8 input variables, which were observed weather information of a given region over a span of 350 days. The data set was split into a training data set and a test data set in the ratio 4:1. Both the baseline LSTM model and our proposed GA-LSTM model was used to train and test the data. The results of the baseline LSTM model showed a Mean Average Percentage Error (MAPE) of 0.15 and a Root Mean Square Error (RMSE) of 0.0007, while our proposed GA-LSTM recorded an MAPE of 0.07 and RMSE of 0.0004. The implication of these results is a better performance of our proposed GA-LSTM model over the baseline LSTM model. This paper demonstrated how the Genetic Algorithm was able to optimize the baseline LSTM model by selecting the best weights during the LSTM training process. The findings of this paper are recommended for smart homes having the capability to monitor energy usage of installed electrical appliances and the ability to predict to weather condition of the region the home is sited.

한국 학령기 아동의 체중상태에 따른 식생활 특성 및 영양섭취 실태

Objectives This study aims to determine the status of obesity and underweight among school-age children in Korea and to compare and analyze dietary characteristics and nutrient intake status according to weight status.
 Methods Data from a total of 2,075 children aged 6 to 11 who participated in the 7th and 8th Korea National Health and Nutrition Examination Survey (KNHANES) conducted from 2016 to 2019 were used for analysis. The height and weight of participants were used to calculate body mass index (BMI). The participants were then classified into underweight, normal weight, and overweight/obese groups. Differences in socioeconomic and dietary characteristics for each weight group were analyzed. Energy, intake of the three main nutrients, rate of energy supply, nutrient intake ratio to dietary reference intake, and the ratio of those below the nutrient reference intake were calculated for each weight group.
 Results Results indicated that 9.45% of male children and 10.74% of female children were underweight, while 20.57% of male children and 18.10% of female children were overweight/obese. The lower the parents’ education level, the higher the rate of overweight/obesity in children. Children who skipped breakfast more than five times a week had a higher rate of overweight/obesity than children who skipped breakfast less than five times a week. Compared to the underweight group, the overweight/obese group consumed more vegetables, meat, fish, and seafood but less fruit. The intake ratio to the estimated energy requirements (EER) was 97% in the underweight group and 102 to 108% in the normal and overweight/obese groups. The intake ratio of protein to the recommended intake (RI) was 144 to 166%, exceeding the protein reference intakes for all weight groups. The intake ratios of vitamin A and calcium to the RI were low at 73 to 74% and 63 to 69% in all weight groups, respectively.
 Conclusions Thus, this study suggests that the government, community-related organizations, and schools should continue to cooperate to provide efficient intervention programs to manage the health and nutrition of obese and underweight children.

Multi-stage collaborative resilient enhancement strategy for coupling faults in distribution cyber physical systems

Due to the strong interdependence of cyber systems and physical systems, cyber-physical systems (CPS) often face serious coupling faults in case of extreme natural disasters. To improve the ability of the distribution CPS to withstand extreme events and rapidly resume normal operation, it is critical to consider effective recovery processes and formulate the collaborative resilience enhancement strategy of CPS. In this paper, a sequential multi-stage collaborative recovery strategy from CPS faults caused by natural disasters is proposed, considering the interdependence of the cyber system and physical system at the layers of facilities, topologies and functions, and the coupling relationship of power grid integration in the recovery process. In the implementation of this strategy, on the cyber side, based on the demand of power grid integration recovery, the communication optical fiber aims to be repaired as quickly as possible to control the power grid Remote Controlled Switches (RCS). On the physical side, the power grid is restored with the objective to reduce loss of load, considering the whole process of degradation, response and recovery during fault handling in coordination. Resilience metrics based on the proposed method are introduced to evaluate the resilience level, as the absorption rate, adaptation rate and energy supply rate. IEEE-33 system is used as an example to show that compared with the traditional recovery strategy that considers only the power grid, the proposed strategy can significantly improve the system's ability to face disasters at the early stage, maintain power supply after the disaster, and speed up the overall load recovery.

Reaction-Induced Molecular Dancing and Boosted Diffusion of Enzymes

A novel mechanism of reaction-induced active molecular motion, not involving any kind of self-propulsion, is proposed and analyzed. Because of the momentum exchange with the surrounding solvent, conformational transitions in mechano-chemical enzymes are accompanied by motions of their centers of mass. As we show, in combination with rotational diffusion, such repeated reciprocal motions generate an additional random walk - or molecular dancing - and hence boost translational diffusion of an enzyme. A systematic theory of this phenomenon is developed, using as an example a simple enzyme model of a rigid two-state dumbbell. To support the analysis, numerical simulations are performed. Our conclusion is that the phenomenon of molecular dancing could underlie the observations of reaction-induced diffusion enhancement in enzymes. Major experimental findings, such as the occurrence of leaps, the anti-chemotaxis, the linear dependence on the reaction turnover rate and on the rate of energy supply, become thus explained. Moreover, the dancing behavior is possible in other systems, natural and synthetic, too. In the future, interesting biotechnology applications may be developed using such effects.

Regional collaborative planning equipped with shared energy storage under multi-time scale rolling optimisation method

Integrated energy systems (IES) have become a popular direction in the field of energy research due to their economic, efficient and environmental friendly advantages. Among them, multi-region integrated energy systems (M-RIES) are more valuable than single-region integrated energy systems (S-RIES) due to their low energy loss, high economy and reliability. At present, there is a lack of an optimisation method that integrates station-network synergy, inter-station interaction, shared energy storage configuration, overall planning of equipment configuration and multi-timescale rolling for the multi-faceted performance enhancement of M-RIES. Therefore, this paper proposes an M-RIES with station-storage interaction and inter-station interaction under the consideration of station-network synergy, and conducts a study on the optimal configuration of M-RIES from the viewpoint of economy and environmental protection. The final analysis is based on a northern region. The results show that the system achieves an energy efficiency of 1.07, a 16.9% reduction in total station equipment configuration, a 3.87% reduction in cost and a 0.76% increase in new energy consumption rate compared to a stand-alone operating system. Taking one of the energy stations as an example, under the operating conditions of 10% intra-day and 5% real-time error, the multi-timescale rolling optimisation method significantly improves the energy supply rate compared to the day-ahead dispatching method, where the error rates for the three typical days of transition, winter and summer are only 0.43%, 2.56% and 0.06%, corresponding to a reduction of 5.02%, 2.49% and 5.06%, and a smaller cost error than the ideal solution The cost error rates for the three typical days are only 1.99%, 3.60% and 3.46%. In summary, the collaborative autonomous planning and operation method proposed in this paper has great advantages in terms of economy, reliability, energy efficiency and environmental protection.

Simulation Research on Energy Evolution and Supply Law of Rock–Coal System under the Influence of Stiffness

The energy supply effect caused by the stiffness difference between roofs and sidewalls is an important factor that induces strain coal bursts. In order to quantitatively reveal the energy supply mechanism of strain coal bursts, this paper first establishes a coal burst energy model of the rock–coal system and proposes the calculation formula of coal burst kinetic energy considering supply energy and the stiffness ratio of rock to coal. Then the whole energy evolution law of the rock–coal system with different stiffness ratios is researched by using the numerical simulation method, and the whole process is divided into three stages. With the decrease in the stiffness ratio, the elastic strain energy of the coal changes little, while its kinetic energy is negatively correlated with the stiffness ratio in a power function. Meanwhile, the elastic strain energy and kinetic energy of the rock have power function relations with the stiffness ratio, too. When the rock–coal system is fractured, the kinetic energy of the coal comes from the release of elastic strain energy from the coal and the energy supplied from the rock. The energy supply rate is between 22% and 35% when the stiffness ratio changes from 3.0 to 0.5, and they show a linear relationship, while the supplied energy has a negative power function relationship with the stiffness ratio.

Effects of voluntary hypoventilation on exercise duration and physiological responses during continuous exercise

Introduction: Elite endurance runners often demonstrate lower VE and higher PETCO2 than normal during exercise testing, indicative of diminished sensitivity to CO2. This is thought to be advantageous since the ventilatory work can be reduced during the race, with the rate of aerobic energy supply potentially increased due to the concomitant hypercapnia. If such a breathing pattern (hypoventilation) is voluntarily mimicked during endurance training, trainees may adapt to hypercapnia, the mimicked breathing volume may become natural, and their endurance performance may improve more than after a normal breathing training.

Energy consumption inequality in China: What can an agent-based model tell us?

China is a major energy consumer, however, related empirical research on China's unequal energy consumption is very limited. Therefore, according to the data from 30 provinces and cities, this study aims to establish a simulation model to analyse the Gini coefficient (the Lorenz curve) of China's energy consumption, and identify the main factors affecting the Gini coefficient through dynamic scenario analysis. During the simulation cycle (from 2022 to 2081), the average Gini coefficient of energy consumption fluctuates between 0.30 and 0.41, which indicates the inequality is slightly high. But the maximum value fluctuation ranges from 0.40 to 0.50, which indicates the inequality is high. The author also found that three factors—technological level, government subsidies, and growth rate of energy supply—can significantly affect the Gini coefficient of energy consumption. It is necessary to promote the technological level, increase subsidies for energy production, and promote the growth of total energy supply to significantly reduce inequity in energy consumption.

Ecoenzymatic stoichiometry can reflect microbial resource limitation, substrate quality, or both in forest soils

Many studies have used the relative activities of extracellular enzymes associated with microbial carbon (C), nitrogen (N) and phosphorus (P) acquisition to infer the relative C vs. nutrient limitation of the microbial community. However, recent experimental and theoretical evidence has shown that the use of ecoenzymatic ratio to infer limiting microbial resources may be invalid. We added the two contrasting leaf litters ash (Fraxinus excelsior L., relatively more labile and nutrient rich) and oak (Quercus robur L.), into samples of mineral soils to validate the use of ecoenzymatic stoichiometry to reflect microbial resource limitation. The litter treatments were also combined with N and P addition treatments to push microbial communities toward stronger C limitation. The microbial resource limitations were examined in all treatments by the responses in microbial respiration, bacterial and fungal growth, microbial community composition, and by detecting the responses of microbial growth to factorial C and nutrient additions in short-term limiting factor assays (LFAs). High ratios of β-1,4-glucosidase (BG) to β-1,4-N-acetylglucosaminidase (NAG) + leucine aminopeptidase (LAP) (>2:1) contrasted with the expected reduction in C limitation after initial litter inputs. The high ratio was mainly driven by an increase in BG activity associated with high energy supply and high microbial rates of metabolism induced by added labile C substrates. During the later incubation period (7–56 days), decreasing respiration and bacterial and fungal growth rates reflected increased microbial C limitation in all treatments. An increasing BG/(NAG + LAP) ratio was in line with increasing microbial C limitation in the ash treatment where cellulose dominated as microbial C source, but a decreasing BG/(NAG + LAP) ratio was inconsistent with the temporal dynamics in microbial C limitation in the oak treatment where substrates other than cellulose (i.e., microbial necromass and lignin) dominated as C source late in the incubation. The increased BG/(NAG + LAP) ratio was in line with intensified microbial C limitation by NP addition, which was mainly due to the stimulated BG activity. In the oak and litter plus NP treatments, fungal growth was stimulated and NAG - an enzyme targeting amino sugars - was increased, presumably to meet the fungal C demand by utilizing microbial necromass - partly consisting of amino sugar polymers. Taken together, these results suggest that variation in substrate quality, availability and how these matched the present microbial energy allocation strategy and resource allocation to enzyme production caused a substantial variation in the BG/(NAG + LAP) ratio, thereby disconnecting the ratio from unambiguously reflecting the microbial resource limitation.

Consistency of von Karman Decay Rate with the Energy Supply Rate and Heating Rate Observed by Parker Solar Probe

Abstract The von Kármán-Howarth equations give a starting basis for the classical turbulence theory. The formula for the magnetohydrodynamics von Kármán decay rate represents an energy source in many solar wind models with turbulence as the driver. However, it still lacks the radial trend comparison between the von Kármán decay rate, the energy supply rate, and the perpendicular heating rate based on direct observations of the solar wind. Here we carry out this kind of comparison for the first time using Parker Solar Probe measurements from its first three orbits. We find that the radial variation of the von Kármán decay rate is consistent with that of both the energy supply rate and the heating rate in the slow solar wind. These results support the idea that the von Kármán decay law is an active process responsible for solar wind heating. These results also suggest a new idea that both the von Kármán decay law and the low-frequency break sweeping may be controlled by the same nonlinear process. Some limitations of the present study are also addressed.

Injection-production optimization of fault-karst reservoir\u2014considering high-speed non-Darcy effect

Fault-karst reservoirs are featured by complex geological characteristics, and accurate and fast simulation of such kind of reservoirs using traditional simulator and simulation methods is pretty hard. Herein, we tried to discrete the complex fault-karst structures into one-dimensional connected units connecting the well, fracture and cave based on reservoir static physical parameters and injection-production dynamics. Two characteristic parameters, conductivity and connected volume, are proposed to characterize the inter-well connectivity and material basis. Meanwhile, the high-speed non-Darcy seepage term is introduced into the material balance equations for well-fracture-cave connected units to describe the actual seepage characteristics within the fault-karst reservoirs, and to better simulate the oil/water production dynamics. Based on this method, a fracture reservoir model of 1 injection-3 production was established. The change of oil–water action law in different injection and extraction systems under two production regimes of fixed production rate and fixed pressure is analyzed. A case study was conducted on S fault zone, where the flow of oil and gas did not follow the Darcy seepage rule and with a β value of 103–104, the single well flow pressure and oil production were perfectly matched with the real data. In addition, connected units with more prominent high-speed non-Darcy features were found to have better connectivity, which might shed light on the more accurate prediction of inter-well connectivity. Moreover, an improved injection-production well pattern and was proposed based on connectivity prediction model and reservoir engineering method to solve the problems of insufficient natural energy supply and overhigh oil production rate in Block S. Furthermore, the injection/production rate as well as the timing and cycle of water injection was predicted and optimized so as to better guide to site operations.

ANALYSIS OF DIRECTIONS OF ENERGY SAVING POTENTIAL MANAGEMENT IN INDUSTRIAL PRODUCTION OF UKRAINE

Annotation. The aim of the work is to substantiate the areas of energy saving potential management of the industrial sector of the national economy. To achieve this goal, the methods of economic and mathematical modeling were used and a function was obtained that reflects the relationship of structural changes with the energy intensity of Ukraine's GDP. The assessment of the energy saving potential in Ukrainian industry by structural and technical factors allowed to prove a positive impact not only on the energy efficiency of industrial production, but also to determine the potential reduction of energy intensity of the country's GDP by supply of primary energy resources. Thus, structural shifts in the economy of Ukraine towards reducing the share of industrial production and increasing the share of services in the field of information technology, scientific and technical activities, lower rates of primary energy supply compared to GDP, it is possible to achieve target energy efficiency targets by 2030. The result of the research is to determine the potential reduction of energy intensity of the country's GDP by the supply of primary energy resources as a result of structural and technical changes (reduction of industrial production and increasing the share of services in information technology, science and technology, lower primary energy supply GDP, modernization of electricity, gas, steam and air conditioning technologies by reducing coal consumption). The scientific novelty of the study is to improve methods of analysis and forecasting of energy saving potential in industrial production of Ukraine. Improving the technical characteristics of industrial production will significantly reduce the share of coal and natural gas savings. In the sectoral context, the greatest potential for energy savings in industry is to modernize technologies for the supply of electricity, gas, steam and air conditioning by reducing coal consumption. A significant share of potential energy saving technologies is made by the processing industry mainly due to the reduction of natural gas consumption at metallurgical enterprises. The practical significance of the study is determined by further development of appropriate management measures that can affect energy efficiency of Ukraine's industrial sector.

Study on unsteady seepage characteristics and production decline of tight channel sandstone gas reservoirs

Tight channel sandstone gas reservoirs are mainly characterized by low porosity and permeability to ultra-low porosity and permeability, strong heterogeneity, and slow energy supply rate in the later stage, resulting in small gas well control reserves, and fast decline rate of gas well pressure and production. Therefore, it is urgent to carry out targeted research on production decline. In this paper, from the perspective of percolation mechanics, a mathematical model of low-velocity non-Darcy unstable percolation in tight channel sandstone gas reservoir is established, a diagram of the relationship between non-Darcy effect, flow boundary characteristics, and dynamic bottom-hole flow is established, and the dynamic influencing factors of bottom hole flow are analyzed. From a seepage mechanics point of view, this paper establishes a tight sandstone gas reservoir river unstable low-speed non-darcy seepage flow mathematical model of non-darcy effect and flow boundary characteristics and the relationship between the bottom hole flow dynamic chart and analysis of bottom hole flow dynamic influence factors, research shows that start-up pressure gradient, skin factor, the closed boundary of tight sandstone gas reservoir river bottom hole flow dynamic effect is bigger, The research content of this paper has certain guiding significance for realizing the effective development of tight channel sandstone gas reservoir.

Stuttering: A Disorder of Energy Supply to Neurons?

Stuttering is a disorder characterized by intermittent loss of volitional control of speech movements. This hypothesis and theory article focuses on the proposal that stuttering may be related to an impairment of the energy supply to neurons. Findings from electroencephalography (EEG), brain imaging, genetics, and biochemistry are reviewed: (1) Analyses of the EEG spectra at rest have repeatedly reported reduced power in the beta band, which is compatible with indications of reduced metabolism. (2) Studies of the absolute level of regional cerebral blood flow (rCBF) show conflicting findings, with two studies reporting reduced rCBF in the frontal lobe, and two studies, based on a different method, reporting no group differences. This contradiction has not yet been resolved. (3) The pattern of reduction in the studies reporting reduced rCBF corresponds to the regional pattern of the glycolytic index (GI; Vaishnavi et al., 2010). High regional GI indicates high reliance on non-oxidative metabolism, i.e., glycolysis. (4) Variants of the gene ARNT2 have been associated with stuttering. This gene is primarily expressed in the brain, with a pattern roughly corresponding to the pattern of regional GI. A central function of the ARNT2 protein is to act as one part of a sensor system indicating low levels of oxygen in brain tissue and to activate appropriate responses, including activation of glycolysis. (5) It has been established that genes related to the functions of the lysosomes are implicated in some cases of stuttering. It is possible that these gene variants result in a reduced peak rate of energy supply to neurons. (6) Lastly, there are indications of interactions between the metabolic system and the dopamine system: for example, it is known that acute hypoxia results in an elevated tonic level of dopamine in the synapses. Will mild chronic limitations of energy supply also result in elevated levels of dopamine? The indications of such interaction effects suggest that the metabolic theory of stuttering should be explored in parallel with the exploration of the dopaminergic theory.

Energy Supply by Low-frequency Break Sweeping for Heating the Fast Solar Wind from 0.3 to 4.8 au

Abstract Solar wind protons undergo significant heating during the expansion of the solar wind and turbulence plays an important role in this process. It is believed that the energy is injected from the energy-containing range into the inertial range and then transferred to dissipate into heat eventually. However, the energy injection process in the heliosphere remains unclear. Here we analyze this process. We utilize Helios 2 and Ulysses measurements of the fast solar wind at different radial distances from 0.29 to 4.8 au. We obtain the perpendicular heating rate based on the gradient of the magnetic moment. We estimate for the first time the energy supply rate due to the sweeping of low-frequency break based on the identification of low-frequency break and the corresponding power spectra density profile. We find that the energy supply rate is comparable to the perpendicular heating rate of protons, which support the idea that low-frequency range becomes part of the inertial range as the solar wind turbulence ages. These results help us understand the energy supply process from the energy-containing range and the heating process of solar wind protons.

Developing solar energy in household scale at Tan Binh District, Ho Chi Minh City, Vietnam

In 2019, Ho Chi Minh City has a total population of 8.99 million with GRDP around 6.021 USD/year [1]. Given the population size and the above GDP level, the electricity consumption demand for production and living purposes in the City was 83 million kWh per day in 2019 [2]. With high electricity demand, it must have developed the rate of renewable energy supply. And in Tan Binh district area, the population is considered quite high and is one of the economic development areas of the city. In Ho Chi Minh City, the sufficient supply of electricity is the top concern. And Tan Binh district is one of 24 districts belong to Ho Chi Minh City with crowded residential and industrial parks, that also has 1-2 houses applying solar energy. In there, solar energy is developing with industrial scale in many enterprises. So, this research was initial survey the potential using solar energy for household and the challenges of resident in Tan Binh district about applying solar energy for their home. According this study, now there is 1 house using and rating positively about solar energy combine national power grid. Around 92% people (1,500 interviewers in 15 wards) think that using solar energy is potential applying in their home because it gains the economic efficiency for reducing electricity fee. But it’s only 23% household interested in using solar energy in their house, when 50% citizens unsure about that. As the results, the factors effective their decision are the policies support from national government about using solar energy and the increasing of electricity bill. It’s a point for encounrage the applying solar energy in household scale in Ho Chi Minh.

Modeling and performance analysis of energy harvesting wireless communication systems with reliable energy backup

SummaryEnergy harvesting wireless communication system (EH‐WCS) has the capability of harvesting energy for system operations from the surrounding renewable energy sources. However, the randomness and instability of the harvested energy will result in the depletion of the energy consumption. To provide reliable communication services with the quality of service (QoS) guarantee, it is necessary for the EH‐WCS to use a reliable energy backup (REB) for supplying energy to the system during the failure of its primary energy source. In this paper, a novel stochastic model, i.e., the extended Markov fluid flow model, is proposed to describe the EH‐WCS with REB. The Kolmogorov forward equations of the system model are derived. By solving the corresponding equations, we obtain the stationary distributions of the key performance metrics for the EH‐WCS with REB, including the average energy consumption rate of the EH‐WCS, the residual energy distribution, the average energy supply rate by REB, the packet queue length in data buffer, the data queue delay, and the packet blocking probability. A numerical example is provided to investigate the theoretical results, and the effects of the system parameters on the performance are further studied numerically. Both the theoretical insights and the numerical analyses are believed to be important for the design of EH‐WCSs.

Energy Supply for Heating the Slow Solar Wind Observed by Parker Solar Probe between 0.17 and 0.7 au

Abstract Energy supply sources for the heating process in the slow solar wind remain unknown. The Parker Solar Probe (PSP) mission provides a good opportunity to study this issue. Recently, PSP observations have found that the slow solar wind experiences stronger heating inside 0.24 au. Here for the first time we measure in the slow solar wind the radial gradient of the low-frequency breaks on the magnetic trace power spectra and evaluate the associated energy supply rate. We find that the energy supply rate is consistent with the observed perpendicular heating rate calculated based on the gradient of the magnetic moment. Based on this finding, one could explain why the slow solar wind is strongly heated inside 0.25 au but expands nearly adiabatically outside 0.25 au. This finding supports the concept that the energy added from the energy-containing range is transferred by an energy cascade process to the dissipation range, and then dissipates to heat the slow solar wind. The related issues for further study are discussed.

They do change after all: 25 yr of GONG data reveal variation of p-mode energy supply rates

ABSTRACT It has been shown over and over again that the parameters of solar p modes vary through the solar activity cycle: frequencies, amplitudes, lifetimes, energies. However, so far, the rates at which energy is supplied to the p modes have not been detected to be sensitive to the level of magnetic activity. We set out to re-inspect their temporal behaviour over the course of the last two Schwabe cycles. For this, we use Global Oscillation Network Group (GONG) p-mode parameter tables. We analyse the energy supply rates for modes of harmonic degrees l = 0–150 and average over the azimuthal orders and, subsequently, over modes in different parameter ranges. This averaging greatly helps in reducing the noise in the data. We find that energy supply rates are anticorrelated with the level of solar activity, for which we use the F10.7 index as a proxy. Modes of different mode frequency and harmonic degrees show varying strengths of anticorrelation with the F10.7 index, reaching as low as r = −0.82 for low frequency modes with l = 101–150. In this first dedicated study of solar p-mode energy supply rates in GONG data, we find that they do indeed vary through the solar cycle. Earlier investigations with data from other instruments were hindered by being limited to low harmonic degrees or by the data sets being too short. We provide tables of time-averaged energy supply rates for individual modes as well as for averages over disjunct frequency bins.

Energy Expenditure of Dynamic Submaximal Human Plantarflexion Movements: Model Prediction and Validation by in-vivo Magnetic Resonance Spectroscopy

To understand the organization and efficiency of biological movement, it is important to evaluate the energy requirements on the level of individual muscles. To this end, predicting energy expenditure with musculoskeletal models in forward-dynamic computer simulations is currently the most promising approach. However, it is challenging to validate muscle models in-vivo in humans, because access to the energy expenditure of single muscles is difficult. Previous approaches focused on whole body energy expenditure, e.g., oxygen consumption (VO2), or on thermal measurements of individual muscles by tracking blood flow and heat release (through measurements of the skin temperature). This study proposes to validate models of muscular energy expenditure by using functional phosphorus magnetic resonance spectroscopy (31P-MRS). 31P-MRS allows to measure phosphocreatine (PCr) concentration which changes in relation to energy expenditure. In the first 25 s of an exercise, PCr breakdown rate reflects ATP hydrolysis, and is therefore a direct measure of muscular enthalpy rate. This method was applied to the gastrocnemius medialis muscle of one healthy subject during repetitive dynamic plantarflexion movements at submaximal contraction, i.e., 20% of the maximum plantarflexion force using a MR compatible ergometer. Furthermore, muscle activity was measured by surface electromyography (EMG). A model (provided as open source) that combines previous models for muscle contraction dynamics and energy expenditure was used to reproduce the experiment in simulation. All parameters (e.g., muscle length and volume, pennation angle) in the model were determined from magnetic resonance imaging or literature (e.g., fiber composition), leaving no free parameters to fit the experimental data. Model prediction and experimental data on the energy supply rates are in good agreement with the validation phase (<25 s) of the dynamic movements. After 25 s, the experimental data differs from the model prediction as the change in PCr does not reflect all metabolic contributions to the energy expenditure anymore and therefore underestimates the energy consumption. This shows that this new approach allows to validate models of muscular energy expenditure in dynamic movements in vivo.