Longer Blades Research Articles

Gradient-based structural optimization of a wind turbine blade root section including high-cycle fatigue constraints

Under the modern design paradigm of wind turbines, the continuous drive towards lower costs through longer blades is raising serious challenges in design, and structural optimization is key to solving the problems effectively. This article focuses on the challenging structural optimization of wind turbine blade root sections, which is scarcely treated in the literature owing to the complex and computationally expensive critical criteria, i.e. buckling, static failure and fatigue damage. The root is parametrized with 1894 thickness design variables and, to solve such an optimization problem efficiently, an adjoint gradient-based framework is proposed, which includes all the criteria mentioned for twelve load cases. Fatigue is notoriously difficult owing to its highly nonlinear behaviour, and its inclusion in the adjoint optimization framework for wind turbine blade optimization is a novelty. The resulting optimization behaviour, laminate layup and structural response are all illustrated, showing many active constraints at convergence, and a significant reduction in mass.

Research on semi-active vibration reduction of offshore wind turbine structure combined eddy current theory with tuned mass dampers

At present, the offshore wind power gradually shows a development trend towards the profound ocean with characteristic of larger capacity, higher tower and longer blades. Therefore, the offshore wind turbine (OWT) is more vulnerable to extreme loads and may lead to the negative influence of structural vibration safety. In this research, a new semi-active eddy current tuned mass damper (SEC-TMD) was proposed for the vibration control of OWT structures and its vibration reduction effect under multiple kinds of dynamic loads was also discussed. Firstly, taking one actual 3.0 MW OWT supported by bucket foundation as object, the SEC-TMD was designed based on the linear quadratic optimal control (LQR) algorithm and bounded Hrovat optimal control algorithm in order to obtain the optimal control force of structural vibration systems. The relationship between damping coefficient and magnetic conductivity spacing was further fitted to achieve variable damping control of SEC-TMD. Secondly, the theoretical model of 3.0 MW OWT structure installed with SEC-TMD was established and the effectiveness of the established theoretical model was verified through the comparison on modal analysis between the theoretical calculations and measured data identification. Finally, the vibration reduction effect of SEC-TMD on the measured OWT structure under wind-wave, seismic and vibration amplification conditions was analyzed and compared with the results calculated from the other passive dampers including EC-TMD and TLCD. It is shown that the maximum reduction percentage of peak value for vibration displacement and acceleration on the tower top can respectively reach 31.93 %, 44.11 %, 30.20 % and 54.57 %, 33.94 %, 31.75 % under three above conditions. Comparing with EC-TMD and TLCD, the better vibration reduction effect indicates that the proposed SEC-TMD has good engineering application value for the vibration suppression of OWT.

Incorporating visibility information into multi-criteria decision making (MCDM) for wind turbine deployment

Wind turbines with taller hubs and longer blades are more feasible and cost-effective than their predecessors since they reduce the unit cost of energy production. However, the larger size of these structures makes them more visible and dominant features in the landscape. Higher visibility of wind turbines generally raises economic and environmental concerns in communities. The increasing size of wind turbines, therefore, poses a dilemma between lower costs of wind energy and higher visibility impacts. Most MCDM applications highlight the importance of wind turbine visibility and conceptualize this factor as the distance from settlements, coastal areas, etc. They assume that the higher distance from a potential turbine site lowers the impact of visibility or vice versa. This assumption helps introduce visibility impacts into the MCDM to some degree. However, calculating visibility can provide more reliable and realistic geospatial information to be used as a decision variable. This paper conceptualizes turbine visibility as quantitative visibility scores derived from multiple viewshed calculations. Geospatial information on visibility, capacity factor, land cover, topographic ruggedness, slope, and eight other distance criteria (e.g., distance from settlements) were processed in a GIS environment. Fuzzy standardization and the analytic hierarchy process (AHP) were used to standardize the maps and calculate criteria weights. A suitability map was produced by combining the weighted maps. Policy recommendations were made for wind power deployment.

Accurate Stall Prediction for Thick Airfoil by Delayed Detached-Eddy Simulations

The continuous increase in wind turbine blade length raises a serious question about how to effectively reduce the blade mass. As one of the solutions, recently, some wind turbine manufacturers are moving towards longer blades with thicker airfoils. As most of the numerical simulation experiences are based on thin airfoils, the present paper focused on airfoils with thickness to chord ratios of 30% and specifically focused on the influence of spanwise length on the numerical results. Airfoils with a spanwise length of 0.1 to 5 chords were simulated utilizing the Delayed Detached-Eddy Simulations (DDES) approach. One of the important objectives was to identify the necessary grid resolution and configuration while still maintaining accuracy under a deep stall situation. It was found that the spanwise length of the computational domain had a crucial influence on the prediction of lift and drag. At a stall angle of attack, the aerodynamic force could not be accurately predicted when the airfoil span was reduced to 0.3 chords, even with a high grid density. The periodicity of the spanwise flow was clearly visible when the airfoil span was extended to 5 chords.

Effect of wind turbine size on load reduction with active flow control

Decades of wind turbine research, development and installation have demonstrated reductions in levelized cost of energy (LCOE) resulting from turbines with larger rotor diameters and increased hub heights. Further reductions in LCOE by up-scaling turbine size can be challenged by practical limitations due to a mass increase trend. On-blade, active flow control devices have the potential to disrupt this trend by allowing longer blades with less mass through an active load control system. Typically, these load control systems are developed for specific wind turbines, making it difficult to study load reduction trends with turbine size to gain further insights into the benefits and risks of this control technology. This paper quantifies the variation in load reduction, complexity, and robustness of load control systems with flow control actuators for three turbines of increasing size. It is shown that, under limited control authority, load reduction can increase with turbine size provided more elaborate control algorithms are used to preserve the bandwidth and robustness of the control system.

Effect of nano phase change materials on the cooling process of a triangular lithium battery pack

This paper simulates a nano-PCM (NPCM) in a circular enclosure where an inverted triangle is placed in its middle. Inside the barrier is a li-ion battery pack (LIIBP) with a triangular arrangement. The desired NPCM is made by adding graphene nanoparticles (NPs) in PCM, CaCl2.6H2O. There are 12 blades (BLs) on the middle LIIBP. The unsteady simulations are performed in two modes of melting and freezing of NPCM using the finite element method. The charging and discharging process of the PCM is investigated while the LIIBP temperature is kept constant. Simulations are done by employing COMSOL Multiphysics software. The percentages of molten material, average Nu, TAve, and local temperature are studied by altering the blade length (LBL) during the melting and freezing of NPCM. The results demonstrate that under the identical circumstances, the melting time of NPCM is longer than the freezing period. An enhancement in the LBL intensifies the TAve of the NPCM in the melting process and reduces the TAve in the freezing process. Enhancing the LBL increases the amount of NPCM at constant times from the beginning of the melting and freezing processes. The complete melting time of NPCM in a longer BL is less than that in bladeless mode. The same behavior is observed for freezing time.

Impact of blade structural and aerodynamic uncertainties on wind turbine loads

AbstractOffshore wind power has been in the spotlight among renewable energy sources. The current trends of increased power ratings and longer blades come together with the aim to reduce energy costs by design optimisation. The standard approach to deal with uncertainties in wind‐turbine design has been by the use of characteristic values and safety factors. This paper focusses on modelling the effect of structural and aerodynamic uncertainties in blades. First, the uncertainties in laminate properties are characterised and propagated in a blade structural model by means of a Monte Carlo simulation. Wind tunnel measurement data are then used to define the variability in lift and drag coefficients for both clean and rough aerofoil behaviour, which is then used to extrapolate rough behaviours throughout the blade. A stochastic spatial interpolation parameter is used to define the evolution of the degradation level. The combined effect and the variance contribution of these two uncertainty sources in turbine loads is finally defined by aeroelastic turbine simulation. This research aims to provide a framework to deal with uncertainties in wind‐turbine blade design and understand their effects in turbine behaviour.

At the Turn: Flint Mining as an Element of Social Changes in the Second Half of the Fifth Millennium BC in Western Lesser Poland

In the second half of the fifth millennium BC, a new model of supply and processing of siliceous rocks appeared in western Lesser Poland (Małopolska). The existing methods of production of blades and flakes from small cores obtained at a short distance from the settlement were supplemented by those enabling the production of much longer blades from cores made from raw material obtained by mining. The significant increase in the size of lithics meant that this moment was referred to as “the metric change” (Polish: przełom metryczny). It was assumed that this was due to internal technological development within the early Neolithic communities of the Lengyel-Polgár cycle. This paper introduces a different explanation for this phenomenon. It is argued that the new model of supply appeared as an already developed model that was implemented by experienced outsiders. A thesis that the indicated technological caesura is not categorical and new patterns in a relatively small area could co-exist with previous ones.

Computationally efficient model predictive control of complex wind turbine models

AbstractAs wind turbines are designed with longer blades and towers, it becomes increasingly important to factor structural modes into the design of the controller. In classical turbine controllers, where pitch‐speed, torque‐speed, drivetrain and tower dampers are designed separately, it has for years been commonplace to base that design on a linearisation of the existing high‐fidelity aeroelastic model. Furthermore, any measurement filters that are required at run‐time are included in the control loop shaping process. In contrast, most previous work on model predictive control (MPC) for wind turbines uses simplified models and ignores the need or effect of measurement filters. In this work, we demonstrate a mostly automatic design process that takes a detailed linearised model from an aeroelastic simulation package and adds linear filters and feedback, to produce a model predictive controller with low run‐time computational complexity. The tuning process is substantially simpler than classical control, making it an attractive tool in industrial applications.

The effect of salinity on aspects of the early development of the kelp species Undaria pinnatifida and Saccorhiza polyschides

Abstract It is likely that the introduction of the brown macroalga Undaria pinnatfida from the Pacific into the North Atlantic will impact competitively on the native species Saccorhiza polyschides; both are large kelps occupying the same subtidal zone with very similar life histories. The present study examines their tolerance to changes in salinity, under laboratory conditions, in order to provide a better understanding of their respective competitiveness in an estuarine environment. Experiments were carried out over a full range of salinity values, from 35 to 0, with respect to zoospore settlement and attachment, germination, post-germination progression to form gametophytes, gametophyte sex ratio, sporophyte production and blade length. Undaria zoospores settled and attached over the salinity range from 35 to 14 and germinated between 35 and 3.5. Post-germination progression occurred over the range from 35 to 14 whilst only small differences in the male/female ratio were recorded. Sporophyte blade production and development occurred over the range from 35 to 17.5 and peak production and longest blade length was recorded at 21. Saccorhiza zoospores settled and attached at and above 24.5 and germinated between 35 and 21. Sporophyte production and blade development occurred over the range from 35 to 24.5. In general, Undaria was shown to be much more tolerant of reductions in salinity compared to Saccorhiza and is more likely to penetrate further into estuarine environments.

High-resolution numerical simulation of the performance of vertical axis wind turbines in urban area: Part I, wind turbines on the side of single building

In urban areas, vertical axis wind turbines have been installed on both sides of the road and rooftop. Compared with rooftop, vertical axis wind turbines mounted on the side of a building have a larger swept area with longer blades, and the effect of tip vortices can be reduced at the same time. Around the building, there are several high wind speed regions that can provide more wind energy. In this paper, a high-resolution numerical method composed of overset grid and adaptive mesh refinement techniques is adopted to verify the feasibility of vertical axis wind turbines mounted on the side of the building. Firstly, the complex flow field around the building is simplified into the flow field around the cylindrical building. Five typical flow regions with different flow conditions are determined: windward zone, crosswind zone, tailwind zone, recirculation zone and leeward zone. Secondly, wind turbines are installed evenly around the building. The simulation results show that the energy output of wind turbines in tailwind zone can be increased by 120% compared with the reference value. Thirdly, multiple wind turbines are coupled with the building. In order to get the optimal arrangement, power outputs of four arrangements are compared for the best choice. The results indicate that the arrangement with six wind turbines in crosswind zone and tailwind zone can achieve the best performance. Through changing the rotational directions, the forward blades of wind turbines can be close to the wall, and the energy output of all the wind turbines around the building can be improved.

Lattice and Tubular Steel Wind Turbine Towers. Comparative Structural Investigation

Renewable energy is expected to experience epic growth in the coming decade, which is reflected in the record new installations since 2010. Wind energy, in particular, has proved its leading role among sustainable energy production means, by the accelerating rise in total installed capacity and by its consistently increasing trend. Taking a closer look at the history of wind power development, it is obvious that it has always been a matter of engineering taller turbines with longer blades. An increase in the tower height means an increase in the material used, thereby, impacting the initial construction cost and the total energy consumed. In the present study, a numerical investigation is carried out in order to actively compare conventional cylindrical shell towers with lattice towers in terms of material use, robustness and environmental impact. Lattice structures are proved to be equivalently competitive to conventional cylindrical solutions since they can be designed to be robust enough while being a much lighter tower in terms of material use. With detailed design, lattice wind turbine towers can constitute the new generation of wind turbine towers.

Preface

Proceedings of the 41st Risø International Symposium on Materials Science: Materials and Design for Next Generation Wind Turbine Blades L P Mikkelsen, B Madsen, S FæsterThe 41st Risø Symposium aims to address new requirements for materials and design for next generation wind turbine blades. Over the last 40 years, wind turbine blades have grown an order of magnitude. Today, the longest blades are exceeding 100 meters and weighing 50 tons. Because of this growth in blade size, the cost of wind energy can now compete with fossil-based energy sources on market terms. Together with a wish in society for a zero-emission future, the wind energy sector is foreseen to further expand. This will require new solutions and approaches for next generation wind turbine blades, such as improved mechanical performance and structural reliability, coupled to more sustainable solutions including end-of-life considerations.These new requirements for next generation wind turbine blades will be addressed at the symposium by covering the themes of manufacturing, mechanical properties and performance, experimental characterization and testing, polymer matrices and coatings, and sustainability, life-time extension and end-of-life.The Proceedings contain 5 invited papers, and 40 contributed papers. The 41st Risø International Symposium is organised by the Division of Materials and Components, Department of Wind Energy, Technical University of Denmark (DTU), at the Risø Campus. We would like to thank all those at DTU Wind Energy who assisted in the preparation of the Symposium. We appreciate additionally the support from the international advisory committee consisting of: Kristofer Gamstedt, SE; Roberts Joffe, SE; Hiroyuki Kawada, JP; Marino Quaresimin, IT; Michael Sutcliffe, UK; Ramesh Talreja, US; Michael Wisnom, UK.

Flow structure and convective heat transfer in a bladed structure under wind conditions

Bladed receivers have been proposed as an alternative to conventional external receivers for high-temperature concentrating solar power systems. Instead of flat banks of tubes arranged on the receiver surface, the tube-banks are oriented into the form of blades protruding from the back-wall of the receiver. This modified arrangement improves light-trapping, without the size and cost implications of a large cavity receiver, and also acts to trap hot air between the blades, hence reducing convective transfer per-tube-area. The present paper investigates the convective heat transfer from a scaled model of a bladed receiver and its correlation with the flow behavior between the blades. Wind tunnel measurements were undertaken to investigate the effects of the wind speed, the blade length and the receiver orientation on the convective heat transfer. It was observed that increasing the pitch angle from 26° to 70°, measured downwards from the vertical in a headwind configuration, leads to a significant reduction in the convective heat transfer coefficient of up to 60%, for the investigated blade lengths. To identify the effect of flow structure on the rate of the convective heat transfer at low Richardson umbers, a second experimental study with isothermal conditions was conducted in a water channel matching the Reynolds number of the wind tunnel experiment. The mean velocity fields and the associate streamline topologies within an open cavity with different pitch angles and blade length to spacing ratios (RBS) were also investigated through Particle Image Velocimetry (PIV) measurements. The streamlines revealed that the shear layer at a pitch angle of 70° for the receiver with the longest blade,RBS = 3, bridges the cavity opening without a strong interaction with the counter-rotating vortices inside the cavity, which resulted in an enlargement of the stagnation zone close to the cavity back-wall. This stagnation zone was identified to be the cause of the convective heat transfer reduction observed in the earlier wind tunnel experiments. It was also found that the Reynolds number has a strong impact on the heat transfer rate, as increasing the wind speed from 3 m/s to 6 m/s enhanced the heat transfer coefficient by up to 50%. As the corresponding Reynolds number in the water channel increased from 1.4 × 104 to 2.8 × 104, PIV data showed that the shear layer was drawn into the cavity and consequently, the velocity magnitude near the back-wall of the cavity reached up to 90% of the freestream velocity. The results provide a good understanding of flow behavior in the vicinity of the blades and its impacts on the convective heat transfer from the receiver.

A novel rotor blade fatigue test setup with elliptical biaxial resonant excitation

Abstract. The full-scale fatigue test of rotor blades is an important and complex part of the development of new wind turbines. It is often done for certification according to the current IEC (2014) and DNV GL AS (2015) standards. Typically, a new blade design is tested by separate uniaxial fatigue tests in both main directions of the blade, i.e. flapwise and lead lag. These tests are time-consuming and rather expensive due to the high number of load cycles required, up to 5 million. Therefore, it is important to run the test as efficiently as possible. During fatigue testing, the rotor blade is excited at or near its resonant frequency. The trend for new rotor blade designs is toward longer blades, leading to a significant drop in their natural frequencies and a corresponding increase in test time. To reduce the total test time, a novel test method aims to combine the two consecutive uniaxial fatigue tests into one biaxial test. The biaxial test excites the blade in both directions at the same time and at the same frequency, resulting in an elliptical deflection path of the blade axis. Using elliptical loading, the counting of damage equivalent load cycles is simplified in comparison to biaxial tests with multiple frequencies. In addition, the maximum loads in both main directions remain separated, while off-axis loading is introduced. To achieve such a test, specific load elements need to be arranged so as to equalize the natural frequencies of the test setup for both test directions. This is accomplished by adding stiffness or inertial effects in a specific direction. This work describes a new method to design suitable test setups. A parameterized finite element (FE) model of the test with beam elements for the blade represents the test setup. A harmonic analysis on the FE model can identify the load distribution and the test conditions of a specific test setup within seconds. An optimization algorithm that varies parameters of the model and searches for the optimal setup is then applied to the analysis. This approach allows the efficient determination of a test setup, suited to the predefined requirements. The method is validated by applying it to three different test scenarios for a modern rotor blade: (a) state-of-the-art uniaxial setups, (b) uniaxial setups including springs and (c) a biaxial setup. In conclusion, the resulting setups are evaluated in terms of test quality and efficiency.

Investigations of aerodynamic drag forces during structural blade testing using high-fidelity fluid–structure interaction

Abstract. Aerodynamic loads need to be known for planning and defining test loads beforehand for wind turbine blades that are tested for fatigue certifications. It is known that the aerodynamic forces, especially drag, are different for tests and operation, due to the entirely different flow conditions. In test facilities, a vibrating blade will move in and out of its own wake, increasing the drag forces on the blade. This is not the case in operation. To study this special aerodynamic condition present during experimental tests, numerical simulations of a wind turbine blade during pull–release tests were conducted. High-fidelity three-dimensional computational fluid dynamics methods were used throughout the simulations. In this way, the fluid mechanisms and their impact on the moving blade are clarified, and through the coupling with a structural solver, the fluid–structure interaction is studied. Results are compared to actual measurements from experimental tests, verifying the approach. It is found that the blade experiences a high drag due to its motion towards its own whirling wake, resulting in an effective drag coefficient of approximately 5.3 for the 90∘ angle of attack. This large drag coefficient was implemented in a fatigue test load simulation, resulting in a significant decrease in bending moment along the blade, leading to less load being applied than intended. The confinement from the test facility did not impact this specific test setup, but simulations with longer blades could possibly yield different conclusions. To the knowledge of the authors, this investigation, including three-dimensional effects, structural coupling and confinement, is the first of its kind.

Influence of Structural Configurations on the Shear Fatigue Damage of the Blade Trailing-Edge Adhesive Joint

Wind turbines are under continuous development for large-scale deployment and oceanization, leading to the requirement of longer blades. The economic losses caused by blade replacement and shutdown have increased. The downtime caused by blade issues in a wind turbine is 8–20% of the total downtime. Many of these blade issues originate from the cracking of the blade trailing edge. The edge is more susceptible to damage due to the complex geometry, manufacturing technique, and operation conditions. The traditional design method and the expensive experimental research are not suitable for the accurate damage analysis of the trailing-edge adhesive because of simplifying assumptions and costs. This study aimed to investigate the influence of trailing-edge structural configurations on the shear fatigue life of the trailing-edge adhesive joint using finite element and stress transformation matrix (STM) methods. The structural configurations of the blade trailing edge included the position of unidirectional fiber layer (UD), chamfer of bonding line, prefabricated components, and outer over-lamination of the trailing edge. In this study, the finite element method was used to simulate the blade structure. The shell element was used for laminates, and the solid element was used for the trailing-edge adhesive joint. The basic shear fatigue properties of the adhesive were obtained by standard component tests. The shear fatigue life of the blade trailing-edge adhesive joint under given load conditions was calculated using the fatigue properties of the adhesive and STM method. The results showed that the angle of chamfering, location of UD, rigidity of the preform, and outer over-lamination all had an obvious influence on the fatigue damage of trailing-edge adhesive. The findings of this study can be used to guide blade structure design and blade production and maintenance.

Structural design and analysis of a redesigned wind turbine blade

Wind turbine power is on the rise due to increased energy extraction made possible by longer blades, higher tower heights, and improved electronics. As wind turbine blades get larger, structural compliance is necessary to ensure reliable operation and maintenance. In this paper, structural design and analysis of a redesigned 5MW wind turbine blade was conducted. To ensure that the blade was structurally compliant, the blade tip deflection and engineering strains were not allowed to exceed permissible limits of 5.56 m and .562% respectively. Moreover, the goal was to avoid blade resonance conditions. Structural analysis was conducted and after several iterations, it was observed that mass of the redesigned blade was 7.2% less when compared to the traditional 5MW blade. The maximum flap wise deflection of the blade was 3.31 m, the maximum material strain was .394%, and resonance was avoided ensuring blade structural compliance.

Morphological variability in a red seaweed: confirmation of co-occurring f. lessonii and f. chauvinii in Chondracanthus chamissoi (Rhodophyta, Gigartinales).

Variability in thallus morphology is common in red seaweeds. Two co-occurring forms have been described for Chondracanthus chamissoi based mainly on blade width. To determine whether two distinct forms or a range of intermediate morphologies occur in C. chamissoi, thalli were collected from three localities in southern Chile in autumn-winter, repeating the sampling in one locality in spring and in summer. In each occasion, individual sporophytic and male and female gametophytic clumps were collected, and the longest blade with intact apex from each clump was evaluated. Blade length, width, density of spines, axis curvature and thickness, and pinnule length and width were evaluated in each blade. Principal components analyses separated two groups of thalli, one group with narrow, thick, and curved (concavo-convex) blades, with few spines consistent with f. lessonii, and another with broad, thin, and flat blades, with many spines consistent with f. chauvinii. These variables also had bimodal frequency distributions. Pinnule measurements were mainly associated with differences among sporophytes and gametophytes. Age (length), phase of the life cycle, and sex were not related to the forms. Furthermore, thalli of both forms were collected side by side in the study sites and throughout the year so the occurrence of the two forms was not attributable to local environmental conditions. In this species, secondary basal disks are produced after attachment of apexes to the substratum. These disks may produce blades with a modified morphology in a way similar to proliferations and regenerations described for Schottera nicaeensis.

The Application of the Baumann Stage in the Low-Pressure Cylinders of Condensing Turbines

Among the characteristics of the power-generating steam turbines, the specific metal intensity ranks very high. Low-pressure cylinders (LPCs) that use a two-tier Baumann stage have the lowest value of this parameter. The Baumann stage allows a 50% increase in the limit steam passage rate to the condenser without increasing the last-stage blade length and the weight of the turbine. In Russia, such a solution was implemented in the most widely used K-200-12.8 (K-200-130) turbine manufactured by LMZ. However, the experience from operating the turbine and results of investigations into the economic efficiency of the K-200-12.8 turbine have shown that these turbines equipped with the Baumann stage have lower efficiency than similar turbines without the Baumann stage. In the course of subsequent modernization of the K-200-12.8 turbine, the Baumann stage was replaced by a new last stage with longer rotor blades. The design solutions employed by different turbine manufacturers to modernize the K-200-12.8 turbine have been analyzed. It is pointed out that the LPC of this turbine was modernized without analyzing the causes of the low economic efficiency of the basic LPC. An investigation into the real causes of the reduced efficiency of the K-200-12.8 turbine has shown that the LPCs modernized by different companies preserved the drawbacks intrinsic to the basic design. In view of this, a simple variant for modernization of the LPC preserving the Baumann stage is proposed. Its efficiency should not be inferior to the efficiency of modern LPCs whose last stage is equipped with longer blades; a conclusion that is supported by the results of mathematical modeling of the flows in the penultimate- and last-stage nozzle diaphragms of the new LPC.