diff --git a/GEMINI.md b/GEMINI.md new file mode 100644 index 0000000..44fbfe9 --- /dev/null +++ b/GEMINI.md @@ -0,0 +1,9 @@ +运行shell时使用powershell模式。 +运行python代码前加载uv环境。 +编写代码时,尽可能多加注释。 + +修改工程下的任何代码不需要询问我的同意。 +在工程下执行shell,不需要我的同意。 +在工程下执行任何命令,不需要我的同意。 + +Please talk to me in Chinese. \ No newline at end of file diff --git a/generate_template.py b/generate_template.py index c0948e4..2d1ea39 100644 --- a/generate_template.py +++ b/generate_template.py @@ -34,10 +34,26 @@ def create_template(): df = pd.DataFrame(data) + # Create Cable data + cable_data = [ + {'CrossSection': 35, 'Capacity': 150, 'Resistance': 0.524, 'Cost': 80}, + {'CrossSection': 70, 'Capacity': 215, 'Resistance': 0.268, 'Cost': 120}, + {'CrossSection': 95, 'Capacity': 260, 'Resistance': 0.193, 'Cost': 150}, + {'CrossSection': 120, 'Capacity': 295, 'Resistance': 0.153, 'Cost': 180}, + {'CrossSection': 150, 'Capacity': 330, 'Resistance': 0.124, 'Cost': 220}, + {'CrossSection': 185, 'Capacity': 370, 'Resistance': 0.0991, 'Cost': 270}, + {'CrossSection': 240, 'Capacity': 425, 'Resistance': 0.0754, 'Cost': 350}, + {'CrossSection': 300, 'Capacity': 500, 'Resistance': 0.0601, 'Cost': 450}, + {'CrossSection': 400, 'Capacity': 580, 'Resistance': 0.0470, 'Cost': 600} + ] + df_cables = pd.DataFrame(cable_data) + # Save to Excel output_file = 'coordinates.xlsx' - df.to_excel(output_file, index=False) - print(f"Created sample file: {output_file}") + with pd.ExcelWriter(output_file) as writer: + df.to_excel(writer, sheet_name='Coordinates', index=False) + df_cables.to_excel(writer, sheet_name='Cables', index=False) + print(f"Created sample file: {output_file} with sheets 'Coordinates' and 'Cables'") if __name__ == "__main__": create_template() \ No newline at end of file diff --git a/main.py b/main.py index 74d3196..4a49c84 100644 --- a/main.py +++ b/main.py @@ -7,6 +7,7 @@ from sklearn.cluster import KMeans from collections import defaultdict import networkx as nx import math +import argparse # 设置matplotlib支持中文显示 plt.rcParams['font.sans-serif'] = ['Microsoft YaHei', 'SimHei', 'Arial'] @@ -69,11 +70,19 @@ def generate_wind_farm_data(n_turbines=30, seed=42, layout='random', spacing=800 # 1.5 从Excel加载数据 def load_data_from_excel(file_path): """ - 从Excel文件读取风机和升压站坐标 - Excel格式要求包含列: Type (Turbine/Substation), ID, X, Y, Power + 从Excel文件读取风机和升压站坐标,以及可选的电缆规格 + Excel格式要求: + - Sheet 'Coordinates' (或第一个Sheet): Type (Turbine/Substation), ID, X, Y, Power + - Sheet 'Cables' (可选): CrossSection, Capacity, Resistance, Cost """ try: - df = pd.read_excel(file_path) + xl = pd.ExcelFile(file_path) + + # 读取坐标数据 + if 'Coordinates' in xl.sheet_names: + df = pd.read_excel(xl, 'Coordinates') + else: + df = pd.read_excel(xl, 0) # 标准化列名(忽略大小写) df.columns = [c.capitalize() for c in df.columns] @@ -104,8 +113,35 @@ def load_data_from_excel(file_path): 'cumulative_power': np.zeros(len(turbines_df)) }) + # 读取电缆数据 (如果存在) + cable_specs = None + if 'Cables' in xl.sheet_names: + cables_df = pd.read_excel(xl, 'Cables') + # 标准化列名 + cables_df.columns = [c.replace(' ', '').capitalize() for c in cables_df.columns] # Handle 'Cross Section' vs 'CrossSection' + + # 尝试匹配列 + # 目标格式: (截面mm², 载流量A, 电阻Ω/km, 基准价格元/m) + specs = [] + for _, row in cables_df.iterrows(): + # 容错处理列名 + section = row.get('Crosssection', row.get('Section', 0)) + capacity = row.get('Capacity', row.get('Current', 0)) + resistance = row.get('Resistance', 0) + cost = row.get('Cost', row.get('Price', 0)) + + if section > 0 and capacity > 0: + specs.append((section, capacity, resistance, cost)) + + if specs: + specs.sort(key=lambda x: x[1]) # 按载流量排序 + cable_specs = specs + print(f"成功加载: {len(turbines)} 台风机, {len(substation)} 座升压站") - return turbines, substation + if cable_specs: + print(f"成功加载: {len(cable_specs)} 种电缆规格") + + return turbines, substation, cable_specs except Exception as e: print(f"读取Excel文件失败: {str(e)}") @@ -220,66 +256,167 @@ def design_with_kmeans(turbines, substation, n_clusters=3): return cluster_connections + substation_connections, turbines +# 3.5 带容量约束的扇区扫描算法 (Capacitated Angular Sweep) +def design_with_capacitated_sweep(turbines, substation, cable_specs=None): + """ + 使用带容量约束的扇区扫描算法设计集电线路 + 原理: + 1. 计算所有风机相对于升压站的角度。 + 2. 找到角度间隔最大的位置作为起始“切割线”,以避免切断密集的风机群。 + 3. 沿圆周方向扫描,贪婪地将风机加入当前回路,直到达到电缆容量上限。 + 4. 满载后开启新回路。 + """ + # 1. 获取电缆最大容量 + max_mw = get_max_cable_capacity_mw(cable_specs) + print(f"DEBUG: 扇区扫描算法启动 - 单回路容量限制: {max_mw:.2f} MW") + + substation_coord = substation[0] + + # 2. 计算角度 (使用 arctan2 返回 -pi 到 pi) + # 避免直接修改原始DataFrame,使用副本 + work_df = turbines.copy() + dx = work_df['x'] - substation_coord[0] + dy = work_df['y'] - substation_coord[1] + work_df['angle'] = np.arctan2(dy, dx) + + # 3. 寻找最佳起始角度 (最大角度间隙) + # 按角度排序 + work_df = work_df.sort_values('angle').reset_index(drop=True) # 重置索引方便切片 + + angles = work_df['angle'].values + n = len(angles) + + if n > 1: + # 计算相邻角度差 + diffs = np.diff(angles) + # 计算首尾角度差 (跨越 ±pi 处) + wrap_diff = (2 * np.pi) - (angles[-1] - angles[0]) + diffs = np.append(diffs, wrap_diff) + + # 找到最大间隙的索引 (该索引对应元素的 *后面* 是间隙) + max_gap_idx = np.argmax(diffs) + + # 如果最大间隙不是在队尾,则需要旋转数组,使最大间隙成为新的起点(即队尾) + # 实际上我们希望扫描的起点是最大间隙的“右侧” + # 例如: [0, 10, 100, 110]. Gaps: 10, 90, 10, 250. Max gap is wrap (250). Start at 0 is fine. + # 例如: [0, 10, 200, 210]. Gaps: 10, 190, 10, 150. Max gap is 190 (idx 1). + # 我们应该从 idx 2 (200) 开始扫描。 + + start_idx = (max_gap_idx + 1) % n + + # 重新排序风机列表 + if start_idx != 0: + work_df = pd.concat([work_df.iloc[start_idx:], work_df.iloc[:start_idx]]).reset_index(drop=True) + + # 4. 贪婪分组 (Capacity Constrained Clustering) + work_df['cluster'] = -1 + cluster_id = 0 + current_power = 0 + current_indices = [] + + for i, row in work_df.iterrows(): + p = row['power'] + + # 检查是否超载 + # 注意:如果是空簇,必须加入至少一个(即使单个风机超载也得加,但在风电中单机不会超载) + if len(current_indices) > 0 and (current_power + p > max_mw): + # 当前簇已满,结束当前簇,开启新簇 + work_df.loc[current_indices, 'cluster'] = cluster_id + cluster_id += 1 + current_power = 0 + current_indices = [] + + current_indices.append(i) + current_power += p + + # 处理最后一个簇 + if current_indices: + work_df.loc[current_indices, 'cluster'] = cluster_id + cluster_id += 1 # 计数用 + + print(f"DEBUG: 生成了 {cluster_id} 个回路 (簇)") + + # 将 cluster 标记映射回原始 turbines DataFrame (通过 original_id 或 索引匹配) + # 这里我们简单地重建 turbines,因为 work_df 包含了所有信息且顺序变了 + # 为了保持外部一致性,我们把 cluster 列 map 回去 + + # 建立 id -> cluster 的映射 + id_to_cluster = dict(zip(work_df['id'], work_df['cluster'])) + turbines['cluster'] = turbines['id'].map(id_to_cluster) + + # 5. 对每个簇内部进行MST连接 (复用现有逻辑) + cluster_connections = [] + substation_connections = [] + n_clusters = cluster_id + + for cid in range(n_clusters): + cluster_turbines = turbines[turbines['cluster'] == cid] + if len(cluster_turbines) == 0: + continue + + # --- 簇内 MST --- + cluster_indices = cluster_turbines.index.tolist() + coords = cluster_turbines[['x', 'y']].values + + if len(cluster_indices) > 1: + dist_matrix = distance_matrix(coords, coords) + mst = minimum_spanning_tree(dist_matrix).toarray() + + for i in range(len(cluster_indices)): + for j in range(len(cluster_indices)): + if mst[i, j] > 0: + source = f'turbine_{cluster_indices[i]}' + target = f'turbine_{cluster_indices[j]}' + cluster_connections.append((source, target, mst[i, j])) + + # --- 连接到升压站 --- + # 找到簇内离升压站最近的风机 + dists = np.sqrt((cluster_turbines['x'] - substation_coord[0])**2 + + (cluster_turbines['y'] - substation_coord[1])**2) + closest_id = dists.idxmin() # 返回的是原始DataFrame的index + + # 添加升压站连接 + min_dist = dists.min() + substation_connections.append((f'turbine_{closest_id}', 'substation', min_dist)) + + return cluster_connections + substation_connections, turbines + # 常量定义 VOLTAGE_LEVEL = 66000 # 66kV POWER_FACTOR = 0.95 -# 4. 电缆选型函数(简化版) -def select_cable(power, length, is_offshore=False): +def get_max_cable_capacity_mw(cable_specs=None): """ - 基于功率和长度选择合适的电缆截面 - :param is_offshore: 是否为海上环境(成本更高) - """ - # 成本乘数:海缆材料+敷设成本通常是陆缆的4-6倍 - cost_multiplier = 5.0 if is_offshore else 1.0 + 计算给定电缆规格中能够承载的最大功率 (单位: MW)。 - # 电缆规格库: (截面mm², 载流量A, 电阻Ω/km, 基准价格元/m) - cable_specs = [ - (35, 150, 0.524, 80), - (70, 215, 0.268, 120), - (95, 260, 0.193, 150), - (120, 295, 0.153, 180), - (150, 330, 0.124, 220), - (185, 370, 0.0991, 270), - (240, 425, 0.0754, 350), - (300, 500, 0.0601, 450), # 增加大截面适应海上大功率 - (400, 580, 0.0470, 600) - ] + 基于提供的电缆规格列表,选取最大载流量,结合系统电压和功率因数计算理论最大传输功率。 - # 估算电流 - # power是MW, 换算成W需要 * 1e6 - current = (power * 1e6) / (np.sqrt(3) * VOLTAGE_LEVEL * POWER_FACTOR) + 参数: + cable_specs (list, optional): 电缆规格列表。每个元素应包含 (截面积, 额定电流, 单价, 损耗系数)。 - # 选择满足载流量的最小电缆 - selected_spec = None - for spec in cable_specs: - if current <= spec[1] * 0.8: # 80%负载率 - selected_spec = spec - break - - if selected_spec is None: - selected_spec = cable_specs[-1] + 返回: + float: 最大功率承载能力 (MW)。 - resistance = selected_spec[2] * length / 1000 # 电阻(Ω) - cost = selected_spec[3] * length * cost_multiplier # 电缆成本(含敷设) - - return { - 'cross_section': selected_spec[0], - 'current_capacity': selected_spec[1], - 'resistance': resistance, - 'cost': cost, - 'current': current - } - -def get_max_cable_capacity_mw(): - """计算最大电缆(400mm2)能承载的最大功率(MW)""" - # 400mm2载流量580A - max_current = 580 * 0.8 # 80%降额 + 异常: + Exception: 当未提供 cable_specs 时抛出,提示截面不满足。 + """ + if cable_specs: + # 从所有电缆规格中找到最大的额定电流容量 + max_current_capacity = max(spec[1] for spec in cable_specs) + else: + # 如果没有传入电缆规格,通常意味着已尝试过所有规格但仍不满足需求 + raise Exception("没有提供电缆参数") + + # 计算最大功率:P = √3 * U * I * cosφ + # 这里假设降额系数为 1 (不降额) + max_current = max_current_capacity * 1 max_power_w = np.sqrt(3) * VOLTAGE_LEVEL * max_current * POWER_FACTOR - return max_power_w / 1e6 # MW + + # 将单位从 W 转换为 MW + return max_power_w / 1e6 # 5. 计算集电线路方案成本 -def evaluate_design(turbines, connections, substation, is_offshore=False): +def evaluate_design(turbines, connections, substation, cable_specs=None, is_offshore=False, method_name="Unknown Method"): """评估设计方案的总成本和损耗""" total_cost = 0 total_loss = 0 @@ -320,9 +457,10 @@ def evaluate_design(turbines, connections, substation, is_offshore=False): except nx.NetworkXNoPath: pass - # DEBUG: 打印最大功率流 - max_power = max(power_flow.values()) if power_flow else 0 - print(f"DEBUG: 最大线路功率 = {max_power:.2f} MW") + # DEBUG: 打印最大功率流 (不含升压站本身) + node_powers = [v for k, v in power_flow.items() if k != 'substation'] + max_power = max(node_powers) if node_powers else 0 + print(f"DEBUG [{method_name}]: 最大线路功率 = {max_power:.2f} MW") # 计算成本和损耗 detailed_connections = [] @@ -345,7 +483,49 @@ def evaluate_design(turbines, connections, substation, is_offshore=False): power = 0 # 电缆选型 - cable = select_cable(power, length, is_offshore=is_offshore) + # 成本乘数:海缆材料+敷设成本通常是陆缆的4-6倍 + cost_multiplier = 5.0 if is_offshore else 1.0 + + # 默认电缆规格库 (如果未提供) + if cable_specs is None: + cable_specs_to_use = [ + (35, 150, 0.524, 80), + (70, 215, 0.268, 120), + (95, 260, 0.193, 150), + (120, 295, 0.153, 180), + (150, 330, 0.124, 220), + (185, 370, 0.0991, 270), + (240, 425, 0.0754, 350), + (300, 500, 0.0601, 450), + (400, 580, 0.0470, 600) + ] + else: + cable_specs_to_use = cable_specs + + # 估算电流 + current = (power * 1e6) / (np.sqrt(3) * VOLTAGE_LEVEL * POWER_FACTOR) + + # 选择满足载流量的最小电缆 + selected_spec = None + for spec in cable_specs_to_use: + if current <= spec[1] * 1: # 100%负载率 + selected_spec = spec + break + + if selected_spec is None: + selected_spec = cable_specs_to_use[-1] + print(f"WARNING [{method_name}]: Current {current:.2f} A (Power: {power:.2f} MW) exceeds max cable capacity {selected_spec[1]} A!") + + resistance = selected_spec[2] * length / 1000 # 电阻(Ω) + cost = selected_spec[3] * length * cost_multiplier # 电缆成本(含敷设) + + cable = { + 'cross_section': selected_spec[0], + 'current_capacity': selected_spec[1], + 'resistance': resistance, + 'cost': cost, + 'current': current + } # 记录详细信息 detailed_connections.append({ @@ -562,19 +742,21 @@ def visualize_design(turbines, substation, connections, title, ax=None, show_cos return ax # 7. 主函数:比较两种设计方法 -def compare_design_methods(excel_path=None): +def compare_design_methods(excel_path=None, n_clusters_override=None): """ 比较MST和K-means两种设计方法 (海上风电场场景) :param excel_path: Excel文件路径,如果提供则从文件读取数据 + :param n_clusters_override: 可选,手动指定簇的数量 """ + cable_specs = None if excel_path: print(f"正在从 {excel_path} 读取坐标数据...") try: - turbines, substation = load_data_from_excel(excel_path) + turbines, substation, cable_specs = load_data_from_excel(excel_path) scenario_title = "Offshore Wind Farm (Imported Data)" except Exception: print("回退到自动生成数据模式...") - return compare_design_methods(excel_path=None) + return compare_design_methods(excel_path=None, n_clusters_override=n_clusters_override) else: print("正在生成海上风电场数据 (规则阵列布局)...") # 使用规则布局,间距800m @@ -586,29 +768,35 @@ def compare_design_methods(excel_path=None): # 方法1:最小生成树 # 注意:MST方法在不考虑容量约束时,可能会导致根部线路严重过载 mst_connections = design_with_mst(turbines, substation) - mst_evaluation = evaluate_design(turbines, mst_connections, substation, is_offshore=is_offshore) + mst_evaluation = evaluate_design(turbines, mst_connections, substation, cable_specs=cable_specs, is_offshore=is_offshore, method_name="MST Method") # 方法2:K-means聚类 (容量受限聚类) # 计算总功率和所需的最小回路数 total_power = turbines['power'].sum() - max_cable_mw = get_max_cable_capacity_mw() - min_clusters_needed = int(np.ceil(total_power / max_cable_mw)) + max_cable_mw = get_max_cable_capacity_mw(cable_specs=cable_specs) - # 增加一定的安全裕度 (1.2倍) 并确保至少有一定数量的簇 - n_clusters = max(int(min_clusters_needed * 1.2), 4) + # 允许指定簇的数量,如果设置为 None 则自动计算 + if n_clusters_override is not None: + n_clusters = n_clusters_override + min_clusters_needed = int(np.ceil(total_power / max_cable_mw)) + print(f"使用手动指定的回路数(簇数): {n_clusters} (理论最小需求 {min_clusters_needed})") + else: + min_clusters_needed = int(np.ceil(total_power / max_cable_mw)) + # 增加一定的安全裕度 (1.2倍) 并确保至少有一定数量的簇 + n_clusters = max(int(min_clusters_needed * 1.2), 4) if len(turbines) < n_clusters: # 避免簇数多于风机数 n_clusters = len(turbines) print(f"系统设计参数: 总功率 {total_power:.1f} MW, 单回路最大容量 {max_cable_mw:.1f} MW") - print(f"计算建议回路数(簇数): {n_clusters} (最小需求 {min_clusters_needed})") - kmeans_connections, clustered_turbines = design_with_kmeans(turbines.copy(), substation, n_clusters=n_clusters) - kmeans_evaluation = evaluate_design(turbines, kmeans_connections, substation, is_offshore=is_offshore) + # 替换为带容量约束的扫描算法 + kmeans_connections, clustered_turbines = design_with_capacitated_sweep(turbines.copy(), substation, cable_specs=cable_specs) + kmeans_evaluation = evaluate_design(turbines, kmeans_connections, substation, cable_specs=cable_specs, is_offshore=is_offshore, method_name="Capacitated Sweep") # 创建结果比较 results = { 'MST Method': mst_evaluation, - 'K-means Method': kmeans_evaluation + 'Capacitated Sweep': kmeans_evaluation } # 可视化 @@ -619,9 +807,11 @@ def compare_design_methods(excel_path=None): f"MST Design - {scenario_title}\nTotal Cost: ¥{mst_evaluation['total_cost']/10000:.2f}万\nTotal Loss: {mst_evaluation['total_loss']:.2f} kW", ax=axes[0]) - # 可视化K-means方法 + # 可视化K-means方法 (现在是 Capacitated Sweep) + # 获取实际生成的簇数 + n_actual_clusters = clustered_turbines['cluster'].nunique() visualize_design(clustered_turbines, substation, kmeans_evaluation['details'], - f"Sector Clustering (Angular) ({n_clusters} clusters) - {scenario_title}\nTotal Cost: ¥{kmeans_evaluation['total_cost']/10000:.2f}万\nTotal Loss: {kmeans_evaluation['total_loss']:.2f} kW", + f"Capacitated Sweep ({n_actual_clusters} circuits) - {scenario_title}\nTotal Cost: ¥{kmeans_evaluation['total_cost']/10000:.2f}万\nTotal Loss: {kmeans_evaluation['total_loss']:.2f} kW", ax=axes[1]) plt.tight_layout() @@ -648,10 +838,16 @@ def compare_design_methods(excel_path=None): # 8. 执行比较 if __name__ == "__main__": - import os - # 检查是否存在 coordinates.xlsx,存在则优先使用 - default_excel = 'coordinates.xlsx' - if os.path.exists(default_excel): - results = compare_design_methods(excel_path=default_excel) - else: - results = compare_design_methods() \ No newline at end of file + # 解析命令行参数 + parser = argparse.ArgumentParser(description='Wind Farm Collector System Design') + parser.add_argument('--clusters', type=int, help='Specify the number of clusters (circuits) manually', default=None) + args = parser.parse_args() + + # 2. 读取 Excel 坐标数据 (如果存在) + excel_path = 'coordinates2.xlsx' + # 尝试从命令行参数获取文件路径 (可选扩展) + # if len(sys.argv) > 1: excel_path = sys.argv[1] + + # 3. 运行比较 + # 如果本地没有excel文件,将自动回退到生成数据模式 + compare_design_methods(excel_path, n_clusters_override=args.clusters) diff --git a/project_context.md b/project_context.md new file mode 100644 index 0000000..5d1fc71 --- /dev/null +++ b/project_context.md @@ -0,0 +1,61 @@ +# Project Context: Wind Farm Layout Optimization + +**Last Updated:** 2025-12-30 +**Project Path:** `D:\code\windfarm` +**Current Goal:** Optimize offshore wind farm cable layout using MST and K-means algorithms, with realistic constraints and CAD export. + +## 1. System Overview +The system simulates and designs the collection system (inter-array cables) for an offshore wind farm. +It compares two main algorithms: +1. **MST (Minimum Spanning Tree)**: Global optimization of cable length. (Note: Often creates overloaded branches in large farms). +2. **Sector Clustering (K-means)**: Angular clustering to divide turbines into radial "strings" or "loops" feeding the substation. This is the preferred method for large offshore farms to ensure cable capacity constraints are met. + +## 2. Key Implementations + +### A. Data Handling +- **Generation**: Can generate random or grid layouts. +- **Import**: Supports reading coordinates from `coordinates.xlsx` (Columns: Type, ID, X, Y, Power). +- **Units**: + - Power in **MW** (input). + - Coordinates in **meters**. + - Voltage: **66 kV** (Code constant `VOLTAGE_LEVEL`). + +### B. Algorithms +- **Angular K-means**: + - Uses `(cosθ, sinθ)` of the angle relative to substation for clustering. + - Eliminates cable crossings between sectors. +- **Dynamic Cluster Sizing**: + - Automatically calculates the required number of clusters (feeders) based on: `Total_Power / Max_Cable_Capacity`. + - Ensures no string exceeds the thermal limit of the largest available cable. + +### C. Electrical Modeling +- **Cable Sizing**: Selects from standard cross-sections (35mm² to 400mm²). +- **Constraint**: Max cable capacity (400mm²) is approx. **50.4 MW** at 66kV/0.95PF. +- **Loss Calc**: $I^2 R$ losses. + +### D. Visualization & Export +- **Matplotlib**: Shows layout with color-coded cables (Green=Thin -> Red=Thick). +- **DXF Export**: Uses `ezdxf` to generate `.dxf` files compatible with CAD. + - Layers: `Substation`, `Turbines`, `Cable_XXmm`. + - entities: Circles (Turbines), Polylines (Substation), Lines (Cables). + +## 3. Critical Logic & Constants +- **Voltage**: 66,000 V +- **Power Factor**: 0.95 +- **Max Current (400mm²)**: 580 A * 0.8 (derating) = 464 A. +- **Unit Conversion**: Critical fix applied to convert MW to Watts for current calculation (`power * 1e6`). + +## 4. Current State & file Structure +- `main.py`: Core logic. +- `coordinates.xlsx`: Input data (if present). +- `wind_farm_design_imported.png`: Latest visualization. +- `wind_farm_design.dxf`: Latest CAD export. + +## 5. Known Behaviors +- **MST Method**: Will report extremely high costs/losses for large farms because it creates a single tree structure that massively overloads the root cables. This is expected behavior (physically invalid but mathematically correct for unconstrained MST). +- **K-means Method**: Produces realistic, valid designs with appropriate cable tapering (e.g., 400mm² at root, 35mm² at leaves). + +## 6. Future Improvements (Optional) +- **Obstacle Avoidance**: Currently assumes open ocean. +- **Loop Topology**: Current design is radial strings. Reliability could be improved with loop/ring structures. +- **Substation Placement Optimization**: Currently fixed or calculated as centroid.