Thermal Margin Research Articles

Design Implementation and Parallel Operation of High-Current High-Power Multipulse Converters Feeding Nuclear Fuel Simulators

Nuclear reactors are designed to maintain a chain reaction producing a steady flow of neutrons generated by fission of heavy nuclei, such as uranium. They produce thermal energy, which is converted into mechanical energy and ultimately into electrical energy feeding to a grid network. In a nuclear reactor, fuel undergoes various power/temperature transients during normal and off -normal situations. One needs to simulate these transients in experimental facilities for performing variety of reactor engineering and safety related tasks. The facility consists of scaled thermal hydraulic test setup comprising process equipment, instrumented nuclear fuel channel simulator, and high current converters for feeding power equivalent to fission power to those simulators to handle the transients safely in controlled manner. The experimental results are used to generate database of various vital nuclear reactor process parameters under all types of operational transients and off -normal conditions that can be compared with predictions from computer codes thus validating ever-evolving and advanced software. Besides, simulation of severe accidental conditions of nuclear reactor in facility is also necessary for evaluation of thermal hydraulic design safety margin. A low-resistance fuel simulator of identical geometry with power scaling is directly heated by high dc current to simulate fission power for generating experimental database. The converters have capability to generate power/temperature transients for simulating nuclear reactor conditions. This article presents design, functional description, specifications, simulation, hardware implementation of 10 kA, 12-pulse, thyristorized converters powering fuel simulators. The successful implementation of parallel operation of four converters feeding 27 kA current is described in this article.

Critical Heat Flux on Curved Calandria Vessel of Indian PHWRs During Severe Accident Condition

Abstract In pressurized heavy water reactors (PHWRs), during an unmitigated severe accident, the absence of adequate cooling arising from multiple failures of the cooling system leads to the collapse of pressure tubes and calandria tubes, which may ultimately relocate to the lower portion of the calandria vessel (CV) forming a debris bed. Due to the continuous generation of decay heat in the debris, it will melt and form a molten pool at the bottom of the CV. The CV is surrounded by calandria vault water, which acts as a heat sink at this scenario. In-vessel corium retention (IVR) through the external reactor vessel cooling (ERVC) is conceived as an effective method for maintaining the integrity of a calandria vessel during a severe accident in a nuclear power plant. Under the IVR conditions, it is necessary to ensure that the imparted heat flux due to melt is less than the critical heat flux (CHF) at the bottom of the calandria vessel wall. To evaluate the thermal margin for IVR, experiments are performed in a prototypic curved section of calandria vessel (25o sector) of calandria vessel to determine the CHF, heat transfer coefficient, and its variation along with the curvature of calandria vessel. The effect of moderator drainpipe on CHF and the heat transfer coefficient has also been evaluated. It has been observed that the imparted heat flux is much less than the CHF at the bottom of the calandria vessel.

Evaluation of correlations for prediction of onset of heat transfer deterioration for vertically upward flow of supercritical water in pipe

Supercritical water has great potential as a coolant for nuclear reactor. Its use will lead to higher thermal efficiency of Rankine cycle. However, in certain conditions heat transfer may get deteriorated which may lead to undesirable high clad surface temperature. It is necessary to estimate the operating conditions in which heat transfer deterioration (HTD) will take place, so as to establish thermal margins for safe reactor operation. In the present work, the heat flux corresponding to onset of HTD for vertically upward flow of supercritical water in a pipe is obtained over a wide range of system parameters, namely pressure, mass flux, and pipe diameter. This is done by performing large number of simulations using an in-house CFD code, which is especially developed and validated for this purpose. The identification of HTD is based on observance of one or more peak/s in the computed wall temperature profile. The existing correlations for predicting the onset of HTD are compared against the results obtained by present simulations as well as available sets of experimental data. It is found that the prediction accuracy of the correlation proposed by Dongliang et al. is best among the existing correlations.

Review of the microheterogeneous thoria‐urania fuel for micro‐sized high temperature reactors

This paper presents a systematic review of the micro-modular thorium-fueled high temperature reactors (HTR) loaded with duplex fuel pellet design. Specifically, each unique criterion of the design is discussed separately in an attempt to understand the combined advantages of the proposed reactor. Micro modular HTRs have great potential as a source of electricity or industrial heat in the future. The use of thorium not only improves its economic performance and safety, but also prolongs its operation. Nevertheless, the traditional seed-and-blanket configuration would not be able to maximize the thorium fuel burnup. As such, a new tristructural-isotopic (TRISO) fuel based on duplex pellet designs were proposed instead. It should be noted that these duplex pellets were not practical for pressurized water reactor (PWR) technology due to its uneven power distribution which possibly leads to a very high local pellet temperature. However, this unorthodox inherent characteristics of the duplex pellets may actually suit the HTR burnup profile better due to its substantially higher thermal margin - thus possibly enabling a relatively long operation of the HTR. The paper shall thereby provide a reasonably sound justification for the detailed technical investigations of the proposed reactor design.

Preliminary Study of the High Temperature Superconducting Solution for 2 GeV CW FFAG Magnet

Proton beam with an average power of 5 MW-10 MW have important applications in particle physics towards the intensity frontier, as well as in the advanced energy, and material science. The fixed field alternating gradient (FFAG) accelerator combines the advantages of existing accelerators, which has a higher limitation of beam energy than high power cyclotron and has a higher beam-to-grid efficiency than existing high power linac and synchrotron, thus is considered as a good candidate for high power proton machine. By utilizing the strong focusing and large acceptance features of FFAG in the theoretical framework of the fixed field and fixed frequency of isochronous cyclotron, a continue wave FFAG capable of producing 2 GeV/3 mA protons (with an beam power of 6 MW) has been proposed in China Institute of Atomic Energy (CIAE). Due to the beam loss of high power proton beams, the resulting high radiation will deposit a large amount of radiation dose and heat load on the superconducting (SC) magnet. As the high temperature superconductors (HTS) have a much larger thermal margin due to high critical temperature (> 90 K) and high upper critical field (>100 T) than the traditional low temperature superconductors, and have been also considered have the lower overall construction costs and power consumption than the conventional magnet, currently the HTS magnet is the favorable solution for the 2 GeV FFAG magnet design. In this paper, the lattice design along with the requirements on the F-D-F magnet of the 2 GeV FFAG design is briefly introduced first. Then, the design of the F-D-F magnet is outlined. The details of the HTS coil design utilizing ReBCO conductor and operating at ~30 K is also included.

Conceptual design of small modular reactor driven by natural circulation and study of design characteristics using CFD & RELAP5 code

A detailed computational fluid dynamics (CFD) simulation analysis model was developed using ANSYS CFX 16.1 and analyzed to simulate the basic design and internal flow characteristics of a 180 MW small modular reactor (SMR) with a natural circulation flow system. To analyze the natural circulation phenomena without a pump for the initial flow generation inside the reactor, the flow characteristics were evaluated for each output assuming various initial powers relative to the critical condition. The eddy phenomenon and the flow imbalance phenomenon at each output were confirmed, and a flow leveling structure under the core was proposed for an optimization of the internal natural circulation flow. In the steady-state analysis, the temperature distribution and heat transfer speed at each position considering an increase in the output power of the core were calculated, and the conceptual design of the SMR had a sufficient thermal margin (31.4 K). A transient model with the output ranging from 0% to 100% was analyzed, and the obtained values were close to the Thot and Tcold temperature difference value estimated in the conceptual design of the SMR. The K-factor was calculated from the flow analysis data of the CFX model and applied to an analysis model in RELAP5/MOD3.3, the optimal analysis system code for nuclear power plants. The CFX analysis results and RELAP analysis results were evaluated in terms of the internal flow characteristics per core output. The two codes, which model the same nuclear power plant, have different flow analysis schemes but can be used complementarily. In particular, it will be useful to carry out detailed studies of the timing of the steam generator intervention when an SMR is activated. The thermal and hydraulic characteristics of the models that applied porous media to the core & steam generators and the models that embodied the entire detail shape were compared and analyzed. Although there were differences in the ability to analyze detailed flow characteristics at some low powers, it was confirmed that there was no significant difference in the thermal hydraulic characteristics' analysis of the SMR system's conceptual design.

위성용 영상처리장치 구조 및 열해석

In this study, we performed structural and thermal analyses on the image processing units of satellites. The image processing unit is a major satellite payload weighing 15 kgf with an aluminum frame structure. Owing to modal analysis, the first mode of the structure was 393 Hz, and it met the payload design requirement of exceeding 100 Hz. Quasi-static analysis was conducted by applying a gravitational acceleration of 28 g. The maximum stress of the structure was 14.9 MPa, and all the parts of structure had a safety margin of 12.9-18.9 compared to the ultimate strength of Al6061 and FR4. Additionally, the highest temperature of the IC Chip was 85.7℃ and all the components of the payload had thermal margins based on temperature derating.

Investigation of a best oxidation model and thermal margin analysis at high temperature under design extension conditions using SPACE

Abstract Zircaloy cladding oxidation is an important phenomenon for both design basis accident and severe accidents, because it results in cladding embrittlement and rapid fuel temperature escalation. For this reason during the last decade, many experts have been conducting experiments to identify the oxidation phenomena that occur under design basis accidents and to develop mathematical analysis models. However, since the study of design extension conditions (DEC) is relatively insufficient, it is essential to develop and validate a physical and mathematical model simulating the oxidation of the cladding material at high temperatures. In this study, the QUENCH-05 and -06 experiments were utilized to develop the best-fitted oxidation model and to validate the SPACE code modified with it under the design extension condition. It is found out that the cladding temperature and oxidation thickness predicted by the Cathcart-Pawel oxidation model at low temperature (T 1853 K) were in excellent agreement with the data of the QUENCH experiments. For ‘LOCA without SI’ (Safety Injection) accidents, which should be considered in design extension conditions, it has been performed the evaluation of the operator action time to prevent core melting for the APR1400 plant using the modified SPACE. For the ‘LBLOCA without SI’ and ‘SBLOCA without SI’ accidents, it has been performed that sensitivity analysis for the operator action time in terms of the number of SIT (Safety Injection Tank), the recovery number of the SIP (Safety Injection Pump), and the break sizes for the SBLOCA. Also, with the extended acceptance criteria, it has been evaluated the available operator action time margin and the power margin. It is confirmed that the power can be enabled to uprate about 12% through best-estimate calculations.

Thermal margin evaluation for the stratified molten pool in SMR-IP200

In this paper, a simple model for stratified corium pool is built based on the concept of FIBS, to estimate the IVR thermal load of IP200 reactor (which is a small modular reactor with thermal power 220 MW). For the model validation, the IVR benchmark of AP600 reactor is calculated, and the results are compared with that of UCSB and INEEL. Then, the molten pool of IP200 with two-layer, three-layer and water-layer configurations are calculated respectively. The thermal load distributions with the effects of internal power and metal mass are analyzed. Besides, the changes of peak heat flux, which are caused by the heavy metal’s appearance and the water layer’s boiling, are discussed by the comparison of local CHF. The specific results show that, in two-layer configuration, the peak heat flux is within 279.9–667.8 kW/m2, and the thermal margin is within 0.31–0.74. In three-layer configuration, the bottom heat flux of molten pool will be enlarged. The internal heat of heavy metal can be the dominant factor for the thermal load fluctuation, when the mass composition is changed. In water-layer configuration, considering the heat transfer of film boiling can keep in a same magnitude as that of radiation, the heat dissipation of pool’s upper face will be enhanced to mitigate the peak heat flux. The present work gives out some key values of steady-state IVR under different configurations, which can provide some references for the safety evaluation of SMR.

Enhanced heat transfer and reduced pressure loss with U-pattern of helical wire spacer arrangement for liquid metal cooled-fast reactor fuel assembly

This paper proposes the new pattern of wire wrap spacer, called U-pattern to enhance coolant mixing and reduce pressure drop for liquid metal cooled reactor fuel assembly. It is designed by designating its winding direction and pin arrangement without any additional structures for fuel assembly. To evaluate its thermal-hydraulic performance, both experimental and numerical approaches are performed; flow visualization experiments using a combined particle image velocimetry (PIV) and matching index-of-refraction (MIR) technique and CFD simulation. The visualized flow field in both axial and lateral planes shows that U-pattern wire wrap spacer has a stronger swirl flow in center subchannel compared to the conventional case. To extend the application ranges to the normal LMFR operation condition, CFD analysis is conducted using ANSYS-CFX. Simulation results indicate 8.60 °C decrease of peak cladding temperature and 5.2% reduced pressure drop respectively. Rod bundle with U-pattern wire spacer has a similar range of bundle loss coefficient at Re < 8500, and a smaller than the conventional one at Re > 10,000. Measurement and calculation results for the U-pattern exhibit that flow is re-distributed to have flatter temperature profile and larger flow channel with the removal of the wire wrap spacer at the center pin brings a lower flow resistance. Therefore, the U-pattern wire wrap spacer for LMFR can enhance the thermal margin and improve economics by promoting thermal mixing and reduction in pressure loss.

Fabrication of Sodium/Inconel 718 Heat Pipes for Combustor Cooling

Cooling channel involved heat pipes, which synergistically combined the high conductivity of heat pipe and thermal efficiency of regenerative cooling, were considered for combustor cooling. In this study, cooling channels were fabricated in sodium/Inconel 718 heat pipes in China Academy of Aerospace Aerodynamics (CAAA). And their startup properties and thermal response were investigated systematically. It was found that the frozen startup limit of fabricated heat pipes were 2.60 and 2.76, satisfying the criterion for frozen startup. During startup tests, the sodium/Inconel 718 heat pipes startup successfully, displaying uniform temperatures of about 900 K and 830 K, respectively. Moreover, sodium/Inconel 718 heat pipes decreased operating temperatures and alleviated thermal stresses in combustor sidewalls. Under simulated Ma6 aerothermal environment, the operating temperature of sodium/Inconel 718 heat pipe was 1007 K, being 224 K lower than that of regenerative cooling model. Therefore, it was concluded that heat pipes could increase the thermal margin of regenerative cooling system, being suitable for applications in combustor cooling.

Core neutronics and safety characteristics of a boron-free core for Small Modular Reactors

This work presents the safety-related neutronics and thermal-hydraulics features of a reactor core designed to fit into a Small Modular Reactor (SMR) moderated and cooled by light water. The core design process is conducted in an iterative manner to optimize its performance from safety perspective. The optimized core is operated without boron in the moderator and is characterized by enhanced safety features as a result of (1) avoiding concerns related to boric acid induced corrosion of a reactor pressure vessels internals; and (2) eliminating the probability of boron dilution accidents. The optimization studies are performed with an advanced multi-physics simulation tools including both neutronics (deterministic, Monte Carlo) coupled with a subchannel thermal-hydraulics code. With an intensive core design iteration process and through using such multi-physics tools, a reactor core with sufficient thermal margins, a cold shutdown margin, and a reduced power peaking factor is obtained. In this paper, the core design approach, core features, and the verification of the core analysis method are discussed in details. Finally, it has been concluded that the developed and optimized core fulfills all safety requirements and design objectives.

Optimal line flows based on voltage profile, power loss, cost and conductor temperature using coordinated controlled UPFC

In the context of flexible operation and bidirectional line flows in modern transmission systems, suitable line flows are essential for safe, secure and stable power systems. Improper line flows may deteriorate stability and longevity of transmission lines. To avoid line outage and faults, improvement in thermal margin of conductors by regulating line flows is a practical consideration. To maintain and control the line flows, the unified power flow controller (UPFC) is the most appropriate compensating device. Thus, in this study, line flows are considered as state variables to optimise several functions, like, voltage deviation index, active and reactive power losses, temperature of conductors and cost of UPFC. The UPFC is modelled with practical losses like switching, coupling and internal transmission losses. Suitable line flows are obtained for the 30-bus and 57-bus test systems by applying an adaptive-version of the wind-driven optimisation (AWDO) algorithm. The AWDO is designed using two innovative tuning parameters: a decaying friction coefficient to reduce the probability of stagnation, and an adaptive velocity function to maintain diversity. The results are compared among different cases of line flows, validating the necessity of the technical challenge. The performance of AWDO is compared with other techniques, suggesting its superiority over other methods.

Progress in understanding and modelling of annular two-phase flows with heat transfer

Annular two-phase flows with heat transfer play important role in many industrial applications. In particular, thermal margins of Boiling Water Reactors (BWR) are entirely determined by this type of flow and heat transfer conditions. To avoid dryout, a liquid film must be present on heated rods of BWR fuel assemblies during normal operation. The present paper describes the recent progress in understanding and modelling of the governing phenomena of annular two-phase flow and heat transfer. A special attention has been devoted to experimental observations that have the most significant influence on the adopted modelling approach. The primary goal is to pave a path to mechanistic modelling of dryout and post-dryout heat transfer applicable to nuclear fuel assemblies. Current Computational Fluid Dynamics (CFD) approaches to model the governing phenomena are presented and their further improvements are suggested.

Larvae of Caribbean Echinoids Have Small Warming Tolerances for Chronic Stress in Panama.

In species with complex life cycles, early developmental stages are often less thermally tolerant than adults, suggesting that they are key to predicting organismal response to environmental warming. Here we document the optimal and lethal temperatures of larval sea urchins, and we use those to calculate the warming tolerance and the thermal safety margin of early larval stages of seven tropical species. Larvae of Echinometra viridis, Echinometra lucunter, Lytechinus williamsi, Eucidaris tribuloides, Tripneustes ventricosus, Clypeaster rosaceus, and Clypeaster subdepressus were reared at 26, 28, 30, 32, and 34 °C for 6 days. The temperatures at which statistically significant reductions in larval performance are evident are generally the same temperatures at which statistically significant reductions in larval survival were detected, showing that the optimal temperature is very close to the lethal temperature. The two Echinometra species had significantly higher thermal tolerance than the other species, with some surviving culture temperatures of 34 °C and showing minimal impacts on growth and survival at 32 °C. In the other species, larval growth and survival were depressed at and above 30 or 32 °C. Overall, these larvae have lower warming tolerances (1 to 5 °C) and smaller thermal safety margins (-3 to 3 °C) than adults. Survival differences among treatments were evident by the first sampling on day 2, and survival at the highest temperatures increased when embryos were exposed to warming after spending the first 24 hours at ambient temperature. This suggests that the first days of development are more sensitive to thermal stress than are later larval stages.

Coupled neutronic/thermal-hydraulic hot channel analysis of high power density civil marine SMR cores

Core average power density of standard small modular reactors (SMR) are generally limited to 60–65 MW/m3, which is 40% lower than for a standard civil PWR in order to accommodate better thermal margins. While designing a SMR core for civil marine propulsion systems, it is required to increase its power density to make more attractive for future deployment. However, there are obvious thermal-hydraulic (TH) concerns regarding a high power density (HPD) core, which needs to be satisfied in order to ensure safe operation through accurate prediction of the TH parameters.This paper presents a coupled neutronic/thermal-hydraulic (TH) hot channel analysis of a HPD 375 MWth soluble-boron-free PWR core using 19.25% 235U enriched micro–heterogeneous ThO2-UO2 duplex fuel and 16% 235U enriched homogeneously mixed all-UO2 fuel with a 15 effective full-power-years (EFPY) core life. To perform this analysis the hybrid Monte Carlo reactor physics code MONK is coupled with sub-channel analysis TH code COBRA-EN. This approach is used to investigate the feasibility of different HPD marine PWR concepts and to identify the main TH challenges characterising these designs. To design HPD cores of between 82 and 111 MW/m3, three cases were chosen by optimizing the fuel pin diameter, pin pitch and pitch-to-diameter ratio. These cases have been studied to determine whether TH safety limits are satisfied by evaluating key parameters, such as minimum departure from nucleate boiling ratio, surface heat flux, critical heat flux, cladding inner surface and fuel centreline temperatures, and pressure drop. The results show that it is possible to achieve a core power density of 100 MW/m3 for both the candidate fuels, a ∼50% improvement on the reference design (63 MW/m3), while meeting the target core lifetime of 15 EFPY and remaining within TH limits. The size of the pressure vessel can therefore be reduced substantially and the economic competitiveness of the proposed civil marine PWR reactor core significantly improved.

Thermo-mechanical behavior of all the metallic fuel rods in a sodium-cooled fast reactor

Abstract A detailed analysis of neutronics, core thermal-hydraulics, and fuel performance has been developed to predict the thermo-mechanical failures of all the metallic fuel rods in a sodium-cooled fast reactor. The neutronics analysis provides a reload pattern for fuel assemblies and power/flux spatial distributions for each fuel rod. The core thermal-hydraulics allows the calculation of the cladding temperatures via subchannel analysis. The fuel performance analysis evaluates the thermo-mechanical integrity of all the fuel rods by considering the detailed spatial and temporal variations of the thermal power, neutron flux, and cladding temperature during the in-core lifetime of each fuel assembly. This analysis leads to improved computational accuracy and provides more comprehensive physical information for each code than a conventional one-dimensional fuel performance calculation. It is evident that, compared with a simple conservative one-dimensional analysis, the present method will improve plant performance while maintaining the thermal margin. The developed analysis has been applied to evaluate the fuel performance of a Prototype Gen IV sodium-cooled fast reactor candidate core by considering the uncertainties of the design parameters.

CHF correlation development under ERVC conditions by using the local liquid velocity from PIV measurements

In-vessel retention through external reactor vessel cooling (IVR-ERVC) is a severe accident management strategy that removes the decay heat from the molten corium in the reactor vessel by flooding the reactor cavity. In ERVC conditions, the critical heat flux (CHF) on the outer wall of the vessel is a crucial factor that indicates a thermal margin of the system. Previous studies used averaged mass flux to predict CHF (Haramura and Katto, 1983; Lee and Mudawwar, 1988, Katto, 1990; Jeong et al., 2005; Park et al., 2013). The averaged value cannot indicate the degree of liquid supply which is the most critical factor in the CHF model. Local liquid velocity near the heated surface is one of the most crucial factors that should be quantified to develop a CHF model. In this study, the local liquid velocity near the surface has been measured. A curved rectangular flow channel was devised to simulate the gap between the external reactor vessel wall and the insulation. The boiling heat transfer and CHF were simulated with air injection at the inner wall of the test section. In the experiment, the flow field under the simulated ERVC conditions was measured using the particle image velocimetry (PIV) technique. The PIV measurement was validated by comparing the measured velocity data and the analytic solution under circular pipe flow. The liquid velocity profile at the middle plane of the curved rectangular test section was obtained in the multiple mass flux and inclination angle conditions. Based on the velocity data, a local velocity correlation was developed. The local velocity correlation was applied to improve the CHF prediction model.

Analysis of magnetic field harmonics change due to manufacturing error in air-core HTS quadruple magnet

An high temperature superconducting (HTS) quadruple magnet used to focus and defocus beams in particle accelerator has been studied for overcoming the disadvantages of low temperature superconducting (LTS) quadruple magnet. LTS quadruple magnet is hard to withstand radiation and heat load at hot cell because of small thermal margin of LTS, and has a nonlinear magnetic characteristic due to iron-core. The thermal margin is improved by changing the LTS to HTS. The magnetic field components are linear according to the operation current by removing the iron-core. Therefore, the air-core HTS quadruple magnet was designed in the past research. Field qualities that determine the performance of the quadruple magnet are composed of field gradient, field uniformity and effective length, and those of air-core HTS quadruple magnet can be achieved using harmonic matching (HM) method. However, when the quadruple magnet is fabricated, parameters of the fabricated magnet are different from designed parameters due to the manufacturing errors. This manufacturing error, REBCO conductor’s dimensional variation of thickness and width, and human errors during winding and assembling, could crucially influence to the field qualities of the quadruple magnet. In this paper, we present a draft design of air-core HTS quadruple magnet and describes an analytical method to predict change of field gradient, uniformity and effective length caused by manufacturing errors and (3) an evaluation of the permissible manufacturing error for an air-core HTS quadruple magnet.

Transient analysis of MOX-3600 and MET-1000 sodium-cooled fast reactor using SARAX code system

The capability of transient analysis has been implemented in the SARAX code system recently. Alternatively, two calculation schemes using the point-kinetics model and 3-D transport-based spatially-dependent model have been developed. Based on these, two transient benchmarks of sodium fast reactor (SFR) suggested by the Working Party on Reactor and System (WPRS) were calculated, which include the large size core loaded with oxide fuel (MOX-3600) and the medium size core loaded with metallic fuel (MET-1000). Two typical states including the state of begin-of-cycle (BOC) and state of end-of-cycle (EOC) were considered. The unprotected loss of flow (ULOF) transient, unprotected transient over power (UTOP) transient, and unprotected control rod withdrawal (UCRW) were calculated. For the large size MOX-fueled SFR, the ULOF transient is the most severe accident, which leads to the core damage in a very short time. At the EOC state, the thermal margin is smaller because of the change of fuel compositions due to the depletion. Besides, the comparisons show that it is very important to use the spatially-dependent model in predicting the power level in the UCRW transient, where the point-kinetics model significantly underestimates the power level by 7–17%.