Polar wind farm micro-siting method based on complex terrain wake and icing characteristics

Abstract

The application relates to the field of wind power generation, and discloses a polar wind farm micro-siting method based on complex terrain wake and icing characteristics, which comprises the following steps: for each meteorological time zone, terrain scene modeling is carried out through spatial environment parameters, and meteorological environment parameters are initialized; a wind farm area is discretized into a grid, global optimization is carried out through a mixed integer linear programming, and a rough selection grid area where a wind turbine is located is determined; a multi-stage adaptive hybrid heuristic algorithm based on the fusion of a multi-population genetic algorithm and a particle swarm algorithm is used to search in a continuous coordinate space corresponding to the rough selection grid area, and a wind turbine layout scheme is optimized by solving an adaptability function. The polar energy system planning reliability is ensured by eliminating the overestimation of the real power generation of a wind farm under an extreme blizzard working condition by a traditional general model.

Description

Technical Field

[0001] This application relates to the field of wind power generation, specifically to a micro-site selection method for polar wind farms based on the wake and icing characteristics of complex terrain. Background Technology

[0002] Antarctica possesses abundant wind energy resources, particularly the prevailing high-speed and persistent descent winds along its coast. Currently, research stations in Antarctica primarily rely on fossil fuels for power, but this incurs high transportation costs and easily pollutes the fragile ecosystem. Therefore, developing Antarctic wind energy resources and constructing a multi-energy complementary system integrating wind, solar, hydrogen, and energy storage is crucial for achieving a green energy transition for research stations.

[0003] However, the harsh Antarctic environment, short construction window, and high construction difficulty mean that once the wind turbines are installed, they are almost impossible to move. Therefore, precise micro-site selection (referring to site selection within a relatively small, predetermined area) is crucial during the planning phase to maximize wind energy utilization and minimize wake losses. This is essential for ensuring the energy security of research stations. Traditional micro-site selection methods have the following limitations in polar applications: 1. Failure to consider the three-dimensional wake effect of polar descent winds coupled with topography: Traditional site selection often uses simplified 2D plain wake models. In reality, the Antarctic ice sheet has few obstacles and low roughness, resulting in slow wake attenuation from upstream wind turbines, which can easily cause wind speed loss downstream. Simultaneously, the height and shear force of the Antarctic core driving force—the descent wind layer—dynamically evolve with the ice sheet topography, leading to spatial heterogeneity in local turbulence intensity. The actual wake profile is more consistent with a three-dimensional bell-shaped distribution. Using a two-dimensional constant model typically leads to an overestimation of available downstream wind speeds.

[0004] 2. The reduction in wind power capacity due to drastic climate changes and severe icing in multiple time zones is ignored: Antarctic temperatures fluctuate dramatically with the alternation of polar day and night. Air density and dominant wind speed profiles (e.g., the Low-Level Jet (LLJ) phenomenon) vary significantly across time zones throughout the year, and blizzards easily lead to icing and reduced efficiency of wind turbine blades. Existing site selection typically uses uniform annual average parameters and does not incorporate icing power reduction mechanisms, resulting in inflated predictions of actual wind farm capacity under extreme low-temperature conditions.

[0005] 3. Traditional algorithms struggle to meet the high-precision optimization requirements of polar wind farms with "zero fault tolerance": Factors such as three-dimensional wake coupling and multi-stage icing losses in polar regions cause the objective function to exhibit high nonlinearity and multi-peak characteristics. Due to the high cost of trial and error in Antarctica, the requirements for site selection accuracy far exceed those of conventional wind farms. However, in the vast and continuous physical coordinate space, traditional Multiple Population Genetic Algorithm (MPGA) converges slowly in the later stages of optimization and is prone to getting stuck in local optima, making it difficult to output a refined layout with extremely safe collision avoidance spacing and high power generation efficiency. Summary of the Invention

[0006] To address the aforementioned issues, this application proposes a micro-site selection method for polar wind farms based on the wake and icing characteristics of complex terrain, including: The wind farm area is divided into multiple meteorological time zones, and for each meteorological time zone, terrain scene modeling is performed using spatial environmental parameters, and meteorological environmental parameters are initialized. Based on the terrain scene modeling, spatial heterogeneity input is provided, and based on the meteorological environment parameter initialization, time-varying dynamic input is provided. The wind farm area is discretized into a grid, and global optimization is performed through mixed integer linear programming to determine the coarse grid area where the wind turbine is located. A multi-stage adaptive hybrid heuristic algorithm that integrates multiple population genetic algorithms and particle swarm optimization algorithms is used to search in the continuous coordinate space corresponding to the coarsely selected grid area and optimize the wind turbine layout scheme by solving the fitness function; wherein, the fitness function is obtained based on the weighted expected total power generation.

[0007] The micro-site selection method for polar wind farms based on the wake and icing characteristics of complex terrain proposed in this application can bring the following benefits: Breaking away from conventional assumptions about annual average parameters, this approach achieves a realistic physical characterization of extreme climate and icing-induced power reduction in polar regions across multiple time periods. Traditional schemes often use uniform annual wind direction and speed, along with fixed air density, for wind farm site selection. This leads to significant power calculation errors in the Antarctic environment, characterized by alternating polar days and nights and drastic temperature fluctuations. By dividing the polar year into multiple meteorological time zones, this approach dynamically characterizes the time-zone-specific extreme cold air density and polar low-level jet stream profile characteristics, and directly embeds the power attenuation coefficient caused by blade icing into the micro-level site selection optimization model. This mechanism eliminates the overestimation of actual wind farm capacity under extreme blizzard conditions by traditional general models, ensuring the reliability of polar energy system planning.

[0008] This study reveals the coupling mechanism between polar descent winds and complex terrain, improving the accuracy of 3D wake assessment. Traditional methods often employ simplified 2D Jensen plain models for micro-site selection, neglecting elevation changes. This application not only introduces a 3D bell-shaped wake model that better reflects the physical laws of real flow fields, but also captures the key characteristic that "the height of the Antarctic descent wind layer dynamically evolves with the undulations of the ice sheet topography," defining local turbulence intensity as a dynamic mapping function of terrain elevation. This effectively avoids downstream wind speed prediction biases caused by traditional fixed-roughness models and allows for more scientific avoidance of strong wake interference zones in complex ice sheet undulations.

[0009] This paper proposes an innovative, precise convex relaxation method for nonlinear power and wake models, balancing global optimization accuracy and solution stability. The superposition effect of the sum of squares of wakes throughout the entire lifecycle of polar wind farms, along with the cubic power curve considering icing, exhibits high nonlinearity and nonconvexity. This application abandons the Big M method, which easily leads to spurious expansion of the feasible region and numerical instability, and employs a piecewise linear approximation combined with SOS2 constraint variables to rigorously transform the complex nonlinear relationships into a mixed-integer linear programming problem. This approach can approximate the complex real power surface of Antarctic wind turbines with high mathematical accuracy, giving the initially selected grid region absolute global optimum potential.

[0010] This paper utilizes a three-stage adaptive hybrid algorithm, MPGA-PSO, to overcome the convergence bottleneck of high-dimensional optimization in continuous space under complex polar constraints. Addressing the highly nonlinear and multi-peak characteristics of the objective function caused by factors such as three-dimensional wake coupling and multi-stage icing losses in polar regions, traditional genetic algorithms often converge slowly and are prone to local deadlocks in the later stages of the vast continuous coordinate space. In the second stage of coordinate refinement, this application innovatively designs a three-stage control architecture: "MPGA pure genetic exploration, MPGA-PSO hybrid, and PSO pure particle swarm optimization fine-tuning." Combined with a mutation rate that decreases linearly with the number of generations and an adaptive particle perturbation mechanism triggered by a diversity threshold, this perfectly integrates the global escape capability of MPGA in the early stages and the rapid local deep-mining capability of PSO in the later stages, ensuring high power generation efficiency of polar wind farms under extreme conditions. Attached Figure Description

[0011] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the micro-site selection method for polar wind farms based on the wake and icing characteristics of complex terrain in this application embodiment. Figure 2 This is a flowchart illustrating the overall process of two-stage micro-location in one scenario of this application. Figure 3This is a schematic diagram illustrating the spatial principle of the coupling between complex terrain elevation and 3D bell-shaped wake driven by polar descent winds in one scenario of this application embodiment; Figure 4 This is a schematic diagram of the mode switching logic and execution flow of the MPGA-PSO three-stage adaptive hybrid algorithm in one scenario of this application embodiment. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0013] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0014] like Figure 1 As shown, embodiments of this application provide a micro-site selection method for polar wind farms based on the wake and icing characteristics of complex terrain, including: S101: Divide the wind farm area into multiple meteorological time zones, and for each meteorological time zone, perform terrain scene modeling through spatial environmental parameters, and initialize meteorological environmental parameters.

[0015] First, multi-period environmental parameters in the polar region were initialized and complex terrain scenarios were modeled. Wind conditions and terrain elevation data around the research station built in Antarctica were collected. Considering the dramatic climate changes caused by the alternation of polar day and night, the year was divided into four meteorological time zones. Taking into account the low polar temperatures, wind turbine icing characteristics, and complex terrain undulations, standard air density and icing power loss coefficients for each time zone were extracted, and a spatial turbulence intensity grid that dynamically changes with the terrain was constructed (reflected by local turbulence intensity).

[0016] Specifically, the process mainly includes three parts: the first part is to model the terrain scene using the absolute elevation of the terrain to obtain the corresponding dynamic mapping function; the second part is to correct the profile of the polar low-altitude jet stream; and the third part is to dynamically assign the icing power loss coefficient corresponding to the polar multi-time period icing and the standard air density.

[0017] For the first part, the spatial environment parameters mainly include elevation data. A terrain fitting polynomial is constructed based on the measured elevation data of the wind farm area to determine the corresponding absolute terrain elevation. The absolute terrain elevation Z(X,Y) at any coordinate point (X,Y) is calculated using the same polynomial, as shown in Formula 1. Formula 1; Where (X,Y) are the horizontal reference coordinates after transformation based on the polar grid coordinate system. Let (X,Y) be the absolute elevation of the terrain at coordinate point (X,Y). , , , , , These are the pre-fitted terrain feature coefficients.

[0018] The intensity of local turbulence driven by the descent wind is defined as a dynamic mapping function with respect to the absolute elevation of the terrain. Considering that the descent wind, unique to Antarctica, is the core driving force of polar wind fields, the intensity of local turbulence in wind farms dynamically evolves due to the height of the descent wind layer varying with the ice sheet topography. Therefore, the intensity of local turbulence driven by the descent wind is defined as... Defined as a dynamic mapping function with respect to terrain height (corresponding to absolute terrain elevation), it can be expressed as shown in Formula 2: Formula 2; in, The basic turbulence intensity for flat polar ice surfaces, , , , represent the minimum and maximum values ​​of the total terrain height in the wind farm area, respectively, and k is the sensitivity adjustment coefficient of the descent wind height to terrain undulation. for The local turbulence intensity corresponding to the location.

[0019] The second and third parts mainly focus on meteorological environmental parameters, which may include corrections to the polar low-level jet (LLJ) wind profile, dynamic assignment of polar multi-period icing and air density.

[0020] To correct the LLJ wind profile, a core transfer function is constructed using the characteristic height of the polar low-level jet stream and the jet stream core height. Based on the core transfer function, as well as the reference wind speed coefficient and scale constant, the actual incoming wind speed corresponding to the actual hub height of the wind turbine is obtained.

[0021] Instead of the conventional power-law model for onshore wind shear, a polar-specific LLJ vertical wind speed profile model is adopted. The target height z (i.e., the actual hub height of the wind turbine) is... The actual incoming wind speed v(z) at point () is calculated as shown in Formulas 3 and 4: Formula 3; in, Let z be the core transfer function corresponding to the target height (corresponding to the actual hub height of the wind turbine), and h be the LLJ characteristic height. , This is the core height of the jet stream.

[0022] Formula 4; Where v(z) is the actual incoming wind speed at the target height. , These are the reference wind speed coefficient and the scale constant, respectively. , Reference altitude observed from polar weather towers wind speed at the location The result was obtained by solving a system of equations simultaneously with the maximum wind speed ratio at the core.

[0023] To address the dynamic assignment of air density and multi-period icing in the polar regions, and considering the diurnal temperature range in Antarctica, the year is divided into T meteorological time zones (e.g., four zones as shown above). Each time zone t is assigned an independent standard air density. and the icing power loss coefficient characterizing the degree of extreme cold ,and, .

[0024] S102: Based on the terrain scene modeling, spatial heterogeneity input is provided, and based on the meteorological environment parameter initialization, time-varying dynamic input is provided. The wind farm area is discretized into a grid, and global optimization is performed through mixed integer linear programming to determine the coarse grid area where the wind turbine is located.

[0025] like Figure 2 As shown, in the first stage, the initial grid selection is based on mixed-integer linear programming. The wind farm area is discretized into a grid, and the three-dimensional wind speed loss between grids is calculated using a 3D bell-shaped wake model that incorporates topographic factors. The icing power loss coefficient is embedded into the power curve corresponding to the wind turbine, and convex relaxation is performed on the nonlinear wake superposition and power model using piecewise linear approximation and SOS2 constraints. The optimal grid region that maximizes the annual weighted power generation is then locked through a global optimization solver.

[0026] Specifically, the absolute elevation of the terrain and the local turbulence intensity are used as terrain enhancements and integrated into the 3D bell-shaped wake model. The wind farm area is discretized into a grid, and the wind speed loss between each grid is determined by the 3D bell-shaped wake model to obtain the effective wind speed after the superposition of multiple wakes.

[0027] Specifically, for both upstream and downstream wind turbines, the tower structure height of the turbines was corrected using their respective absolute terrain elevations, resulting in their respective actual hub absolute elevations. Considering the impact of terrain elevation differences on the wake propagation trajectory, the upstream wind turbine (coordinates...) ) and downstream wind turbines (coordinates) The actual absolute height of the wheel hub and The corrections are made using Formula 5 and Formula 6 respectively: Formula 5; Formula Six; in, , These are the actual absolute hub elevations for the upstream and downstream wind turbines, respectively. , These are the absolute elevations of the terrain corresponding to the upstream and downstream wind turbines, respectively. , These represent the horizontal and vertical coordinates corresponding to the upstream and downstream wind turbines, respectively. This refers to the height of the wind turbine's tower structure.

[0028] Based on the local turbulence intensity corresponding to the upstream wind turbine and the turbine impeller diameter, the additional turbulence intensity induced by the turbine rotor rotation in the wake is obtained. Since the local turbulence intensity varies with the terrain, the wake turbulence intensity at a downstream propagation distance x is thus determined. and wake attenuation constant The corresponding calculations need to be performed. At this point, as shown in Formula 7, the additional turbulence intensity should be calculated first: Formula 7; in, denoted as , where is the additional turbulence intensity induced in the wake by the fan rotor rotation; 'a' is the fan axial induction factor; 'x' is the downstream propagation distance; and 'D' is the fan impeller diameter. This represents the local turbulence intensity at the upstream wind turbine location.

[0029] Based on the additional turbulence intensity and the local turbulence intensity corresponding to the upstream wind turbine, the wake turbulence intensity as the wake propagates downstream can be obtained, as shown in Formula 8: Formula 8; in, Let x be the turbulence intensity of the wake as it propagates downstream. The local turbulence intensity at the upstream wind turbine location. To add turbulence intensity.

[0030] Based on the wake turbulence intensity, the initial wake expansion rate, and the local turbulence intensity corresponding to the upstream wind turbine, the wake attenuation constant as the wake propagates downstream is obtained, as shown in Equation 9: Formula Nine; in, Let x be the wake attenuation constant as the wake propagates downstream a distance x. The initial wake expansion rate, Let x be the turbulence intensity of the wake as it propagates downstream. This represents the local turbulence intensity at the upstream wind turbine location.

[0031] like Figure 3 As shown, the three-dimensional wind speed loss (also known as wake velocity loss) experienced by the downstream wind turbine is described by the wake cross-sectional characteristic parameters and the Gaussian bell distribution. The Gaussian bell distribution is obtained by the Gaussian standard deviation, the crosswind horizontal distance of the downstream wind turbine from the wake centerline of the upstream wind turbine, and the actual absolute hub elevations of the downstream and upstream wind turbines. The Gaussian standard deviation is based on the wake attenuation constant, the Gaussian distribution constant, and the rotor radius, as shown in Formula 10. Formula 10; in, This represents the three-dimensional wind speed loss at the coordinates of the downstream wind turbine. , These are the characteristic parameters of the wake section derived from mass conservation. Let C be the Gaussian standard deviation (where C is the Gaussian distribution constant). The rotor radius is... (Wake attenuation constant as the wake propagates downstream a distance x) The horizontal distance in the crosswind direction from the centerline of the upstream wind turbine's wake is represented by z, where z is replaced by the actual absolute elevation of the downstream wind turbine's hub. .

[0032] Based on the three-dimensional wind speed deficit corresponding to each upstream wind turbine, and the initial incoming wind speed at the actual hub height of the wind turbine without wake interference, the effective wind speed after multiple wake superposition is obtained; the initial incoming wind speed is represented by the actual incoming wind speed. The wake superposition effect of multiple wind turbines in the entire field can be calculated using the square sum root method, as shown in Formula 11: Formula 11; in, The effective wind speed after the superposition of multiple wakes. The initial incoming wind speed at the actual hub height of the wind turbine without wake interference. This represents the independent three-dimensional wind speed loss caused by the i-th upstream wind turbine.

[0033] At this point, the effective wind speed after the superposition of multiple wakes is obtained, which is then used to continue the coarse selection of the grid.

[0034] By using piecewise linear approximation, the nonlinear power model including icing power loss is transformed into a mixed-integer linear programming model. For the mixed-integer linear programming model, a global solver is used to select the wind turbine deployment grid area that maximizes the weighted expected total power generation for multiple meteorological time zones, which is then used as the coarse grid area for the wind turbines. Icing power loss is obtained through the icing power loss coefficient, and the weighted expected total power generation is obtained through the icing power loss coefficient, standard air density, and effective wind speed corresponding to each meteorological time zone.

[0035] The system is constructed based on nonlinear power relaxation considering icing losses and mixed-integer linear programming (MILP). The wind turbine is at an effective wind speed in meteorological time zone t. Actual output power Based on the effective wind speed, wind energy utilization coefficient, swept area, and standard air density corresponding to the height nonlinearity of the wind turbine, the theoretical output power of the wind turbine unaffected by icing is obtained, as shown in Formula Twelve: Formula 12; in, This represents the theoretical output power of the wind turbine unaffected by icing. The wind energy utilization coefficient, For the area swept, Effective wind speed.

[0036] After correcting the theoretical output power and rated power of the wind turbine using the icing power loss coefficient, the minimum value is taken as the actual output power of the wind turbine at the effective wind speed, as shown in Formula Thirteen: Formula Thirteen; in, This represents the actual output power. This represents the theoretical output power of the wind turbine. Rated power, This represents the power loss coefficient due to icing.

[0037] To achieve a globally optimal solution, a piecewise linear approximation strategy is adopted, setting several breakpoints within the wind speed domain and introducing the SOS2 set of continuous variables. SOS2 stands for Special Ordered Set of type 2 (SOS2). The convex combination property of the SOS2 set... ), which will result in highly nonlinear effective wind speed With the sum of squares of the wake, strict relaxation is a linear constraint in a mixed-integer linear programming (MILP) model.

[0038] The objective function is set to maximize the weighted expected total power generation across multiple weather time zones. The weighted expected total power generation is obtained based on the expected power at each grid, and the expected power is the actual output power.

[0039] The objective function is set to maximize the weighted expected total power generation across multiple time zones, as shown in Formula 14: Formula Fourteen; in, Let be the objective function. To maximize the objective function, T represents the total number of weather time zones, which can be set to 4 in this embodiment. Let M be the set of wind condition scenarios within time zone t; M and N are the number of rows and columns of the discretized grid matrix of the wind farm, respectively. The comprehensive annual weight of the downwind scenario s for the meteorological time zone t; For those located in the grid Expected power at the location; For binary decision variables, it is whether to deploy wind turbines in the grid.

[0040] S103: A multi-stage adaptive hybrid heuristic algorithm based on the fusion of multi-population genetic algorithm and particle swarm algorithm is used to search in the continuous coordinate space corresponding to the coarsely selected grid area and optimize the wind turbine layout scheme by solving the fitness function; wherein, the fitness function is obtained based on the weighted expected total power generation.

[0041] The multi-stage adaptive hybrid heuristic algorithm refers to the combination of the global exploration capability of multi-population genetic algorithms and the local development advantage of particle swarm optimization algorithms, and dynamically adjusts the role weights and search parameters of the two algorithms through an adaptive strategy.

[0042] like Figure 2 As shown, in the second stage, continuous coordinate refinement is based on a three-stage hybrid algorithm of MPGA-PSO. Within the grid area locked in stage 1, a three-stage adaptive hybrid heuristic algorithm integrating Multiple Population Genetic Algorithm (MPGA) and Particle Swarm Optimization (PSO) is introduced. The wind turbine position is dynamically adjusted in continuous coordinate space. The algorithm sequentially goes through the "MPGA pure genetic exploration stage", the "MPGA-PSO hybrid stage", and the "PSO pure particle swarm fine adjustment stage", and combines a mutation rate mechanism that decreases linearly with the number of generations, a population diversity perturbation strategy, and a polar physical safety distance penalty function for efficient optimization.

[0043] Specifically, for the fitness function, a dynamic fitness evaluation and a three-dimensional safety distance penalty are set: the precise coordinate set of the wind turbine in continuous space. The fitness function is set as the total power generation of the entire field minus the penalty function for the polar physical safety distance.

[0044] The physical safety distance penalty function value is obtained based on the positive part of the difference between the preset minimum safety distance and the distance between each wind turbine, and the preset penalty factor.

[0045] Precise coordinate set of the wind turbine in continuous space The fitness function is set as the total power generation of the entire field minus the penalty function for polar physical safety distance, as shown in Formulas 15 and 16: Formula 15; in, , Let be the horizontal coordinates of the i-th wind turbine. , These are the horizontal coordinates of the j-th wind turbine. Let be the three-dimensional Euclidean distance between the i-th wind turbine and the j-th wind turbine.

[0046] Formula Sixteen; in, The physical safety distance penalty function value. The preset minimum safe distance, Let be the three-dimensional Euclidean distance between the i-th wind turbine and the j-th wind turbine. A very large penalty factor ensures that solutions that violate physical constraints are eliminated. This refers to the total number of wind turbines planned to be installed within the wind farm.

[0047] Based on the weighted expected total power generation of the wind farm and the physical safety distance penalty function value, the fitness function used to describe the precise coordinates of each area in the coarsely selected grid region is obtained, as shown in Formula 17: Formula 17; in, Let be the fitness function for each precise coordinate in the precise coordinate set. This represents the weighted expected total power generation of the wind farm. This is the penalty function value for physical safety distance.

[0048] At this point, a multi-stage adaptive hybrid heuristic algorithm is executed. The algorithm is divided into three execution stages according to the number of generations gen, which deeply integrates the global scalability of the genetic algorithm and the local convergence of the particle swarm algorithm.

[0049] For each precise coordinate, when the evolutionary generation is lower than the first preset generation, multi-population genetic operations are performed based on a mutation rate that decreases linearly with the evolutionary generation. Phase 1 is the exploration period, during which the evolutionary generation gen is lower than the first preset generation. Meanwhile, to balance the diversity in the early stages with the stability in the later stages, a mutation rate that decreases linearly with the number of generations is introduced. As shown in Formula 18: Formula 18; in, Let be the mutation rate in the gen-th generation. , These are the initial maximum mutation rate and the final minimum mutation rate, respectively. The maximum number of generations to be evolved for the algorithm.

[0050] When the number of generations is higher than the first preset number of generations but lower than the second preset number of generations, multi-population genetic operations and particle swarm operations are executed sequentially and alternately, and the new individuals generated in the multi-population genetic operations are used as the initial particles for the particle swarm operations. Phase 2 is the mixing period, at which time the number of generations... Greater than the first preset algebra And less than the second preset algebra The new individuals generated in the MPGA operation are directly used as the initial particles in the PSO operation. The velocity of the i-th particle in the PSO operation... and location The updates are shown in Formula 19 and Formula 20 respectively: Formula 19; Formula 20; Where t is the current iteration number, , Let be the velocity and position of the i-th particle at iteration number t, respectively. For adaptive inertia weights, , These are self-awareness and social-awareness learning factors, respectively. , Independent random numbers uniformly distributed in the interval [0,1]. Let be the set of the individual historical optimal coordinates of the i-th particle. This is the globally optimal coordinate set.

[0051] When the number of generations exceeds the second preset number of generations, the population diversity evaluation index is defined as the average Euclidean distance between all particles in the population, and particle swarm optimization is performed. If the diversity evaluation index falls below a preset threshold, the population is deemed to have prematurely matured and stagnated, triggering a high-frequency random perturbation operation. Stage 3 is the fine-tuning period, during which the number of generations gen exceeds the second preset number of generations. The process then shifts entirely to local depth development of PSO. To prevent particle velocity decay to zero and subsequent local extrema during the final optimization phase, the population diversity evaluation index "Diversity" is defined as the average Euclidean distance between all particles in the population, as shown in Formula 21: Formula 21; in, As an indicator for evaluating population diversity, This represents the population size of the particle swarm (i.e., the total number of individuals). Let be the Euclidean distance between the position vectors of the two particles.

[0052] Establish an adaptive perturbation mechanism when Below the preset threshold When premature maturation stagnation is detected in the population, a high-frequency random perturbation operation is triggered, as shown in Formula 22: Formula 22; in, With a mean of 0 and a variance of The normal distribution perturbation term is used to force particles out of local optima, ultimately locking in the efficient and precise two-dimensional coordinates of the wind field. , These are the particle space coordinate vectors before and after the perturbation, respectively.

[0053] After completing the micro-site selection process, the scheme output and performance evaluation are carried out. The layout of the wind turbines with precise coordinates is output, and the energy efficiency evaluation is performed. The actual expected annual power generation and wake loss rate of the polar wind farm are calculated after considering the weighted average of multiple time periods throughout the year, the 3D wake effect, and the efficiency reduction due to icing.

[0054] Breaking away from conventional assumptions about annual average parameters, this approach achieves a realistic physical characterization of extreme climate and icing-induced power reduction in polar regions across multiple time periods. Traditional schemes often use uniform annual wind direction and speed, along with fixed air density, for wind farm site selection. This leads to significant power calculation errors in the Antarctic environment, characterized by alternating polar days and nights and drastic temperature fluctuations. By dividing the polar year into multiple meteorological time zones, this approach dynamically characterizes the time-zone-specific extreme cold air density and polar low-level jet stream profile characteristics, and directly embeds the power attenuation coefficient caused by blade icing into the micro-level site selection optimization model. This mechanism eliminates the overestimation of actual wind farm capacity under extreme blizzard conditions by traditional general models, ensuring the reliability of polar energy system planning.

[0055] This study reveals the coupling mechanism between polar descent winds and complex terrain, improving the accuracy of 3D wake assessment. Traditional methods often employ simplified 2D Jensen plain models for micro-site selection, neglecting elevation changes. This application not only introduces a 3D bell-shaped wake model that better reflects the physical laws of real flow fields, but also captures the key characteristic that "the height of the Antarctic descent wind layer dynamically evolves with the undulations of the ice sheet topography," defining local turbulence intensity as a dynamic mapping function of terrain elevation. This effectively avoids downstream wind speed prediction biases caused by traditional fixed-roughness models and allows for more scientific avoidance of strong wake interference zones in complex ice sheet undulations.

[0056] This paper proposes an innovative, precise convex relaxation method for nonlinear power and wake models, balancing global optimization accuracy and solution stability. The superposition effect of the sum of squares of wakes throughout the entire lifecycle of polar wind farms, along with the cubic power curve considering icing, exhibits high nonlinearity and nonconvexity. This application abandons the Big M method, which easily leads to spurious expansion of the feasible region and numerical instability, and employs a piecewise linear approximation combined with SOS2 constraint variables to rigorously transform the complex nonlinear relationships into a mixed-integer linear programming problem. This approach can approximate the complex real power surface of Antarctic wind turbines with high mathematical accuracy, giving the initially selected grid region absolute global optimum potential.

[0057] This paper utilizes a three-stage adaptive hybrid algorithm, MPGA-PSO, to overcome the convergence bottleneck of high-dimensional optimization in continuous space under complex polar constraints. Addressing the highly nonlinear and multi-peak characteristics of the objective function caused by factors such as three-dimensional wake coupling and multi-stage icing losses in polar regions, traditional genetic algorithms often converge slowly and are prone to local deadlocks in the later stages of the vast continuous coordinate space. In the second stage of coordinate refinement, this application innovatively designs a three-stage control architecture: "MPGA pure genetic exploration, MPGA-PSO hybrid, and PSO pure particle swarm optimization fine-tuning." Combined with a mutation rate that decreases linearly with the number of generations and an adaptive particle perturbation mechanism triggered by a diversity threshold, this perfectly integrates the global escape capability of MPGA in the early stages and the rapid local deep-mining capability of PSO in the later stages, ensuring high power generation efficiency of polar wind farms under extreme conditions.

[0058] In one embodiment, an example from a real-world scenario is provided.

[0059] This embodiment selects a flat ice sheet and its undulating edge region in Antarctica as the planning target, and plans to construct a polar micro wind farm. The planned area is [area missing]. The plan is to install 30 polar-type wind turbine generators. The base rated power of a single unit is 110kW, the rotor radius is 6.5m, the hub height is 15m, and the safety collision avoidance physical distance threshold is [not specified]. Set at 65m. The two-stage micro-location optimization specifically includes the following steps: Step (1): Initialization of polar environmental parameters over multiple time periods and modeling of complex terrain scenarios.

[0060] 1) Extraction and dynamic assignment of meteorological and environmental parameters across multiple time zones: Given the dramatic climate changes caused by the polar day and night in Antarctica, this study breaks with the traditional assumption of average annual wind conditions and strictly divides the year into four meteorological time zones, each with its own time weight. Corresponding polar low-temperature air density Ice power loss coefficient, which characterizes the degree of icing during extreme cold blizzards. : December-February: Time Weighting Standard air density The icing attenuation is relatively mild. ; March-April: Time Weighting Standard air density moderate icing attenuation ; May-September: Time Weighting Extreme cold and blizzards occur frequently, with the highest air density. Icing attenuation is the most severe. ; October-November: Time Weighting Standard air density Ice attenuation is minimal .

[0061] Rated power in each meteorological time zone The correction is proportional to the air density, as shown in Formula 23: Formula 23; in, This is the basic rated power of the wind turbine. The rated power is 1.225, and the air density is 1.225 under standard atmospheric conditions. ).

[0062] 2) Nonlinear correction of vertical wind profile for the polar low jet stream (LLJ): The descent winds unique to Antarctica do not conform to conventional logarithmic or power-law distributions. This embodiment uses the polar LLJ physical model, given the reference height of the weather tower. wind speed at the location Calculate the actual effective wind speed of the incoming flow at a hub height of 15m. .

[0063] Set the core height of the jet stream Core wind speed to ground wind speed ratio Constructing height feature parameters And define the dimensionless core transfer function as shown in Formula 24: Formula 24; Analytical solution of the scale constant C and the reference wind speed using simultaneous extreme boundary conditions As shown in formulas 25, 26 and 27: Formula 25; Formula 26; Formula 27; in, This represents the maximum wind speed at the core of the jet stream. The ratio of the core wind speed of the jet stream to the reference wind speed at the ground is given by C, where C is the scale constant. As the reference wind speed, For the observed wind speed, For reference height.

[0064] The wind speed at any spatial point at height z is finally obtained as shown in Formula 28: Formula 28; in, Let z be the actual incoming wind speed at the target height. Where C is the reference wind speed and C is the scale constant. This is the core transfer function corresponding to the target height.

[0065] 3) Generation of terrain elevation and dynamic spatial turbulence grid: Will The wind farm planning area is discretized into Grid matrix (single grid scale) Based on polar elevation sampling data, a continuous surface elevation surface Z(X,Y) is generated using a bivariate quadratic polynomial: Formula 29; Because the height and shear force of the Antarctic descending air layer undergo significant dynamic evolution with the topographic relief of the ice sheet, the local spatial turbulence intensity is defined. This is a nonlinear mapping of elevation. The turbulence intensity is based on a flat ice surface. Based on this, with a terrain sensitivity adjustment coefficient k=0.1, the result is as shown in Formula 30: Formula 30; in, For local spatial turbulence intensity, The basic turbulence intensity is for a flat ice surface.

[0066] Step (2): First stage, grid selection based on mixed integer linear programming.

[0067] 1) Construct a terrain-enhanced 3D bell-shaped (Gaussian) wake physics model: Calculate the grid where any upstream wind turbine is located. For downstream grid The resulting wind speed loss. After taking into account the terrain elevation difference, the actual absolute elevation corrections for both are shown in Formulas 31 and 32: Formula 31; Formula 32; in, , These are the actual absolute hub elevations for the upstream and downstream wind turbines, respectively. , These represent the absolute elevations of the terrain corresponding to the upstream and downstream wind turbines, respectively, and 15.0 represents the hub structure height of the wind turbine in this embodiment. , unit m.

[0068] Calculate the wake attenuation constant based on the evolution of local turbulence intensity. As shown in formulas 33 and 34: Formula 33; Formula 34; in, The additional turbulence intensity induced in the wake by the rotation of the wind turbine rotor. Let be the wake attenuation constant. Here are the values ​​for the axial induction factor of the wind turbine, where x is the horizontal distance in the downwind direction relative to the upstream wind turbine. The local turbulence intensity at the upstream wind turbine location. Where is the impeller diameter and 0.075 is the initial wake expansion ratio. The value of .

[0069] Gaussian wind speed loss at downstream three-dimensional spatial coordinates The calculations are shown in Formulas 35 and 36: Formula thirty-five; Formula Thirty-Six; Where 1.98 is the value of the Gaussian distribution constant C. This represents the three-dimensional wind speed loss at the coordinates of the downstream wind turbine. , These are the characteristic parameters of the wake section derived from mass conservation. The standard deviation of Gaussians is 1.98, which is the Gaussian distribution constant. The rotor radius is... (Wake attenuation constant as the wake propagates downstream a distance x) The horizontal distance in the crosswind direction from the centerline of the upstream wind turbine's wake is represented by z, where z is replaced by the actual absolute elevation of the downstream wind turbine's hub. .

[0070] The superposition effect of the wakes from multiple wind turbines across the entire field is calculated using the nonlinear sum-of-squares method, as shown in Formula 37: Formula thirty-seven; in, The effective wind speed after the superposition of multiple wakes. The initial incoming wind speed at the actual hub height of the wind turbine without wake interference. This represents the independent three-dimensional wind speed loss caused by the i-th upstream wind turbine.

[0071] 2) Construction of a nonlinear power convex relaxation and MILP constraint system considering icing loss.

[0072] In any meteorological time zone t, a single wind turbine at an effective wind speed Actual output power Defined as shown in Formulas 38 and 39: Formula 38; Formula 39; in, This represents the theoretical output power of the wind turbine unaffected by icing. The wind energy utilization coefficient, The effective wind speed is given by constant 6.5, which represents the radius (m) of the wind turbine impeller. This represents the actual output power. Rated power, This represents the power loss coefficient due to icing.

[0073] Due to the square root term of the wake superposition and the power equation The term possesses high non-convexity; in this embodiment... to Within the wind speed domain, 35 segmented interpolation breakpoints were precisely defined. The SOS2 continuous variable set from Gurobi was introduced. (satisfy (and at most two adjacent non-zero elements).

[0074] The properties of convex combinations are shown in Equations 40 and 41: Formula 40; Formula 41; in, For continuous combination variables that satisfy the SOS2 constraint, To finely divide the cut-in and cut-out wind velocities into 35 wind speed interpolation breakpoints. Effective wind speed.

[0075] In this way, the highly nonlinear problem is strictly and equivalently transformed into a set of MILP constraint equations.

[0076] 3) Initial global mesh selection solution: The linearized model is then imported into the Gurobi global solver. The first-stage optimization objective function... The goal is to maximize the weighted total power generation across all four seasons and scenarios throughout the entire lifecycle, as shown in Formula 42: Formula 42; in, Let be the objective function. To maximize the objective function, the upper limits of 4 and 10 represent the four meteorological time zones divided in this embodiment, respectively. Discrete grid matrix, The comprehensive annual weight (weighted probability of occurrence) of downwind scenario s in meteorological time zone t. For those located in the grid Expected power at the location; For binary decision variables, it is whether to deploy wind turbines in the grid.

[0077] Simultaneously set a safety distance exclusion constraint: if the mesh and Spacing less than Then additional constraints are applied. After the solution is completed, a two-dimensional index set of 30 mesh layouts is output as the hard boundary wall for the second stage of local search.

[0078] Step (3): Second stage, continuous coordinate refinement based on MPGA-PSO three-stage hybrid algorithm.

[0079] Within the continuous physical boundaries of the 30 grids locked in the first phase, fine-tuning of continuous two-dimensional coordinates is initiated.

[0080] like Figure 4 As shown, the basic parameters of the algorithm are configured as follows: maximum number of generations. Parallel subpopulation number Number of individuals in a single population The fitness is calculated using the absolute penalty function for the three-dimensional safety distance in polar regions, as shown in Equation 43. Formula 43; in, Let be the fitness function for each precise coordinate in the precise coordinate set. 65 represents the weighted expected total power generation of the wind farm, and 65 is the physical safety distance threshold set in this embodiment. , Let be the spatial three-dimensional Euclidean distance between the i-th wind turbine and the j-th wind turbine, and 1000.0 be a very large penalty factor constant.

[0081] A three-stage control architecture that evolves with algebra was designed: 1) First stage (exploration period, generations 1 to 69): A highly exploratory pure multi-population genetic algorithm (MPGA) is executed. Large-scale tournament selection (TournamentSize=5) is utilized with an arithmetic crossover operator (crossover rate 0.9). An adaptive linearly decreasing mutation rate is employed to maximize search breadth in the early stages. During this stage, individuals are in a high-priority region and are superimposed with a 1.5-fold enhanced mutation exploration bias, which prompts them to make large-scale jumps within their respective grid envelopes, maintaining the extreme diversity of the population.

[0082] 2) Second stage (mixed period, generations 70-179): MPGA and PSO are executed sequentially and alternately. MPGA variability rate. The following formula (forty-four) shows a continuous linear decay: Formula 44; Where gen is the current generation number. denoted as the mutation rate of the gen generation, and 200 is the maximum number of generations set in this embodiment; constants 0.08 and 0.04 are the initial and final mutation rates, respectively.

[0083] At this point, the new individual coordinate array evolved from MPGA is seamlessly transformed into the position vector of the PSO particles. The coordinates of the i-th particle in PSO... The update incorporates individual memory (cognitive factors) ) and group information (social factors) As shown in Formula 45: Formula 45; Where t is the current iteration number, , Let be the velocity and position of the i-th particle at iteration number t, respectively. 0.8, 1.8, and 1.2 represent the inertia weight, individual cognitive factor, and social learning factor during the fine-tuning phase, respectively. , Independent random numbers uniformly distributed in the interval [0,1].

[0084] This stage enables a smooth transition of the algorithm from "divergent global exploration" to "convergent local exploration".

[0085] 3) The third stage (fine-tuning period, generations 180-200): Stop MPGA crossover and mutation operations, and switch to pure PSO local depth fine-tuning. The number of internal iterations of PSO is increased from 4 to 6, and the inertia weight is adjusted. As the algebraic number decreased sharply from 0.7 to 0.4, the cognitive factor increased to .

[0086] To eliminate the "local optimum deadlock" problem caused by the particle swarm's velocity approaching zero at the end of the optimization phase, the average Euclidean distance (Diversity) between individuals in the population is calculated in real time. When it is detected... At that time, an adaptive perturbation mechanism based on Gaussian random distribution is triggered, as shown in Equation 46: Formula 46; in, , These are the particle space coordinate vectors before and after the perturbation, respectively. N is a Gaussian normal distribution, the constant 650 is the physical side length reference (m) of the wind farm in this embodiment, and 0.03 is the perturbation basis strength coefficient.

[0087] This perturbation forces a spatial offset into the stationary particles and resets their velocity vectors. This allows for a strong breakthrough in breaking the deadlock.

[0088] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the device and medium embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the description of the method embodiments.

[0089] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A polar wind farm micro-siting method based on complex terrain wake and icing characteristics, characterized in that, include: The wind farm area is divided into multiple meteorological time zones, and for each meteorological time zone, terrain scene modeling is performed using spatial environmental parameters, and meteorological environmental parameters are initialized. Based on the terrain scene modeling, spatial heterogeneity input is provided, and based on the meteorological environment parameter initialization, time-varying dynamic input is provided. The wind farm area is discretized into a grid, and global optimization is performed through mixed integer linear programming to determine the coarse grid area where the wind turbine is located. A multi-stage adaptive hybrid heuristic algorithm, which integrates multiple population genetic algorithms and particle swarm optimization algorithms, is used to search in the continuous coordinate space corresponding to the coarsely selected grid area. The wind turbine layout scheme is optimized by solving the fitness function. The fitness function is based on the weighted expected total power generation. Terrain scene modeling is performed using spatial environmental parameters, and meteorological environmental parameters are initialized, specifically including: Terrain scene modeling is performed using absolute terrain elevation to obtain dynamic mapping functions corresponding to local turbulence intensity. Polar low-level jet stream profile correction is performed, as well as dynamic assignment of icing power loss coefficient and standard air density for multi-period polar icing. Terrain scene modeling is performed using absolute terrain elevation to obtain a dynamic mapping function corresponding to local turbulence intensity, specifically including: Based on the measured elevation data of the wind farm area, a terrain fitting polynomial is constructed to determine the corresponding absolute terrain elevation; and the local turbulence intensity driven by the root source of the downwind is defined as a dynamic mapping function with respect to the absolute terrain elevation. Based on the terrain scene modeling, spatial heterogeneity input is provided, and based on the initialization of the meteorological environment parameters, time-varying dynamic input is provided. The wind farm area is discretized into a grid, and global optimization is performed through mixed-integer linear programming to determine the coarse grid area where the wind turbine is located. Specifically, this includes: The absolute elevation of the terrain and the local turbulence intensity are used as terrain enhancements and incorporated into a 3D bell-shaped wake model. The wind farm area is discretized into a grid, and the wind speed deficit between each grid is determined through the 3D bell-shaped wake model to obtain the effective wind speed after the superposition of multiple wakes. By using piecewise linear approximation, the nonlinear power model including icing power loss is transformed into a mixed-integer linear programming model. For the mixed-integer linear programming model, a global solver is used to select the wind turbine deployment grid area that maximizes the weighted expected total power generation for multiple meteorological time zones, which is then used as the coarse-selected grid area for the wind turbines. The icing power loss is obtained through the icing power loss coefficient, and the weighted expected total power generation is obtained through the icing power loss coefficient, standard air density, and effective wind speed corresponding to each meteorological time zone. The absolute elevation of the terrain and the local turbulence intensity are used as terrain enhancements and incorporated into a 3D bell-shaped wake model. The wind farm area is discretized into a grid, and the wind speed deficit between each grid is determined using the 3D bell-shaped wake model to obtain the effective wind speed after multiple wake superpositions. Specifically, this includes: For upstream and downstream wind turbines, the tower structure height of the wind turbines is corrected by using their respective corresponding absolute terrain elevations, and the actual absolute hub elevations are obtained for each turbine. Based on the local turbulence intensity corresponding to the upstream wind turbine and the wind turbine impeller diameter, the additional turbulence intensity caused by the rotation of the wind turbine rotor in the wake is obtained; and based on the additional turbulence intensity and the local turbulence intensity corresponding to the upstream wind turbine, the wake turbulence intensity when the wake propagates downstream is obtained; and based on the wake turbulence intensity, the initial wake expansion rate, and the local turbulence intensity corresponding to the upstream wind turbine, the wake attenuation constant when the wake propagates downstream is obtained. The three-dimensional wind speed deficit experienced by the downstream wind turbine is described by wake cross-sectional characteristic parameters and a Gaussian bell-shaped distribution. The Gaussian bell-shaped distribution is obtained by the Gaussian standard deviation, the crosswind horizontal distance of the downstream wind turbine from the wake centerline of the upstream wind turbine, and the actual absolute hub elevations of the downstream and upstream wind turbines. The Gaussian standard deviation is based on the wake attenuation constant, the Gaussian distribution constant, and the rotor radius. Based on the three-dimensional wind speed deficit corresponding to each upstream wind turbine, and the initial incoming wind speed without wake interference at the actual hub height of the wind turbine, the effective wind speed after the superposition of multiple wakes is obtained; the initial incoming wind speed is represented by the actual incoming wind speed.

2. The polar wind farm micro-site selection method based on complex terrain wake and icing characteristics as described in claim 1, characterized in that, The process includes correcting the profile of the polar low-level jet stream and dynamically assigning values ​​to the icing power loss coefficient corresponding to multi-period polar icing and standard air density. Specifically, this includes: A core transfer function is constructed by using the characteristic height of the polar low-altitude jet stream and the core height of the jet stream; and based on the core transfer function, as well as the reference wind speed coefficient and scale constant, the actual incoming wind speed corresponding to the actual hub height of the wind turbine is obtained. Each meteorological time zone is assigned an independent standard air density, as well as an icing power loss coefficient characterizing the degree of extreme cold.

3. The polar wind farm micro-site selection method based on complex terrain wake and icing characteristics as described in claim 1, characterized in that, By using piecewise linear approximation, the nonlinear power model including icing power loss is transformed into a mixed-integer linear programming model. For this mixed-integer linear programming model, a global solver is used to select the wind turbine deployment grid region that maximizes the weighted expected total power generation across multiple weather time zones. This grid region is then used as the coarsely selected grid region for the wind turbines, specifically including: Based on the effective wind speed, wind energy utilization coefficient, swept area, and standard air density corresponding to the wind turbine, the theoretical output power of the wind turbine unaffected by icing is obtained. The theoretical output power and rated power of the wind turbine are corrected by the icing power loss coefficient, and the minimum value is taken as the actual output power of the wind turbine at the effective wind speed. By employing a piecewise linear approximation strategy, several breakpoints are set within the wind speed domain, and a set of continuous variables, SOS2, is introduced. Through the convex combination property of the SOS2 set, the highly nonlinear effective wind speed and the sum of squares of the wake are strictly relaxed into linear constraints in a mixed-integer linear programming model. The objective function is set to maximize the weighted expected total power generation across multiple weather time zones, where the weighted expected total power generation is obtained based on the expected power at each grid, and the expected power is the actual output power.

4. The polar wind farm micro-site selection method based on complex terrain wake and icing characteristics according to claim 1, characterized in that, Before optimizing the wind turbine layout scheme by solving the fitness function, the method further includes: The physical safety distance penalty function value is obtained based on the positive part of the difference between the preset minimum safety distance and the distance between each wind turbine, and the preset penalty factor. Based on the weighted expected total power generation of the wind farm and the physical safety distance penalty function value, a fitness function is obtained to describe the precise coordinates of each area in the coarsely selected grid region.

5. The polar wind farm micro-site selection method based on complex terrain wake and icing characteristics according to claim 4, characterized in that, A multi-stage adaptive hybrid heuristic algorithm, integrating multiple population genetic algorithms and particle swarm optimization, searches the continuous coordinate space corresponding to the coarsely selected grid region. The wind turbine layout scheme is optimized by solving the fitness function. Specifically, this includes: For each precise coordinate, when the number of generations is lower than the first preset number of generations, multi-population genetic operations are performed based on the mutation rate, which decreases linearly with the number of generations. When the number of generations is higher than the first preset number of generations but lower than the second preset number of generations, multi-population genetic operations and particle swarm operations are executed sequentially and alternately, and the new individuals generated in the multi-population genetic operations are used as the initial particles for the particle swarm operations. When the number of generations of evolution is higher than the second preset number of generations, the population diversity evaluation index is defined as the average Euclidean distance between all particles in the population, and particle swarm optimization is performed; wherein, if the diversity evaluation index is lower than the preset threshold, it is determined that the population has premature stagnation, and a high-frequency random perturbation operation is triggered.

6. The polar wind farm micro-site selection method based on complex terrain wake and icing characteristics according to claim 4, characterized in that, The method further includes: Output the layout of the wind turbine with precise coordinates and perform an energy efficiency assessment.

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