# -*- coding: utf-8 -*- """ DGCUP 2021 A —— 高铁牵引供电系统运行数据分析及等值建模 ===================================================== 确定性真源模型（纯标准库，random.seed(2021) 锚定，零外部依赖）。 赛题背景：牵引变电所将 220 kV 三相电压降为 27.5 kV 单相，经牵引网向动车组供电。 动车组的非线性、单相性、冲击性负荷带来电压/电流不平衡与谐波等电能质量问题； 同时牵引网可抽象为戴维南（Thevenin）等效，用于短路/潮流/谐波阻抗分析。 本题练习数据集为**合成测量数据**（仅用于跑通方法，非官方原题实测）： 24 小时、5 分钟分辨率、共 288 个采样点； 3 个供电臂（区段 A/B/C）的牵引电流，及其在供电侧合成的 3 相电流； 母线馈线电压 U（标称 27.5 kV，列车通过时跌落至约 22 kV）、总有功 P、无功 Q、功率因数。 四路数字一致：本文件为唯一真源；fig_*.py 与 papers/*.md 均引用此处产出的数值。 子问题映射（与真实赛题主题一致，数据为本站合成）： 问题1 数据预处理与运行工况特征：缺失/异常清洗、日负荷曲线、区段负荷分布； 问题2 电能质量评估：对称分量（正/负/零序）求电流不平衡度、功率因数； 问题3 谐波与异常检测：FFT 求电流谐波频谱与 THD、基于残差的异常检测（电压暂降/电流冲击）； 问题4 等值建模：由 (P,Q)-(U,I) 散点最小二乘拟合戴维南 E0、Zeq；谐波阻抗模型 Z_h=R+jhX。 用法：cd tools/ && python3 gen_dgcup2021a.py """ import os import csv import math import random SEED = 2021 HERE = os.path.dirname(os.path.abspath(__file__)) OUT_DIR = os.path.normpath(os.path.join(HERE, "..", "assets", "problems", "data")) # ---------------- 物理 / 系统常数（合成、量级贴近真实牵引网） ---------------- UNOM = 27.5 # 牵引网标称电压 (kV) E0_TRUE = 28.5 # 戴维南等效电势幅值 (kV)，角度 0 ZR_TRUE = 1.2 # 等效电阻 (Ω) ZX_TRUE = 3.5 # 等效电抗 (Ω) N = 288 # 24h * 12 步/h = 288 DT_MIN = 5 # 采样间隔（分钟） SECTIONS = ["A", "B", "C"] # ---------------- 工具：迭代 FFT（radix-2，纯标准库） ---------------- def _fft(x): n = len(x) # 位反转置换 j = 0 out = list(x) for i in range(1, n): bit = n >> 1 while j & bit: j ^= bit bit >>= 1 j ^= bit if i < j: out[i], out[j] = out[j], out[i] L = 2 while L <= n: ang = -2.0 * math.pi / L wr, wi = math.cos(ang), math.sin(ang) for i in range(0, n, L): r, im = 1.0, 0.0 half = L // 2 for k in range(half): a = out[i + k] b = out[i + k + half] tr = b.real * r - b.imag * im ti = b.real * im + b.imag * r out[i + k] = complex(a.real + tr, a.imag + ti) out[i + k + half] = complex(a.real - tr, a.imag - ti) nr = r * wr - im * wi ni = r * wi + im * wr r, im = nr, ni L <<= 1 return out # ---------------- 日负荷需求轮廓（驱动列车运行密度） ---------------- def _demand(hour): """返回 0..1 的负荷强度系数：夜间低、早晚高峰高。""" if 0 <= hour < 5: return 0.15 if 5 <= hour < 7: return 0.35 + 0.10 * (hour - 5) if 7 <= hour < 9.5: return 1.0 if 9.5 <= hour < 16: return 0.55 if 16 <= hour < 19.5: return 0.95 if 19.5 <= hour < 22: return 0.5 return 0.25 # ---------------- 生成各供电臂的列车牵引电流 ---------------- def _train_currents(rng): """按日负荷轮廓生成 3 个供电臂的牵引电流序列（A），含基线负荷与梯形脉冲。""" I = {s: [0.0] * N for s in SECTIONS} for s in SECTIONS: base = 120.0 + rng.uniform(0, 80) # 基线（无车）电流 A t = 0 while t < N: hour = t * DT_MIN / 60.0 p = _demand(hour) if rng.random() < 0.55 * p + 0.04: dur = rng.randint(2, 6) # 持续 10~30 min peak = rng.uniform(800, 2000) # 牵引脉冲峰值电流 A ramp = 1 # 1 步爬升，平滑 for k in range(t, min(t + dur, N)): dk = k - t if dk < ramp: val = base + (peak - base) * (dk + 1) / (ramp + 1) elif dk >= dur - ramp: val = base + (peak - base) * (dur - dk) / (ramp + 1) else: val = peak I[s][k] = max(I[s][k], val) t += dur + rng.randint(2, 5) else: t += 1 for k in range(N): I[s][k] += base return I # ---------------- 对称分量（正/负/零序） ---------------- def _sym_components(ia, ib, ic): a = complex(-0.5, math.sqrt(3) / 2.0) # e^{j120°} a2 = a * a v0 = (ia + ib + ic) / 3.0 v1 = (ia + a * ib + a2 * ic) / 3.0 v2 = (ia + a2 * ib + a * ic) / 3.0 return v0, v1, v2 # ---------------- 合成运行工况电流波形（用于 FFT / THD） ---------------- def _synth_wave(amps, rng, N=1024, noise=0.0): y = [0.0] * N for h, A in amps: ph = h * 0.3 for k in range(N): y[k] += A * math.sin(2.0 * math.pi * h * k / N + ph) if noise > 0: for k in range(N): y[k] += rng.gauss(0.0, noise) return y def _thd_of(amps_dict, rng): """amps_dict: {工况: [(h, A), ...]}；返回 THD(%) 与各工况 top5 谐波。""" out = {} for cond, amps in amps_dict.items(): y = _synth_wave(amps, rng, noise=0.004 * amps[0][1]) Y = _fft([complex(v) for v in y]) A = [2.0 * abs(Y[h]) / len(Y) for h in range(len(Y))] A1 = A[1] s = 0.0 for h in range(2, len(A) // 2): s += A[h] ** 2 thd = math.sqrt(s) / A1 * 100.0 if A1 > 0 else 0.0 harmonics = sorted(((h, 50.0 * h, A[h]) for h in range(2, len(A) // 2)), key=lambda z: -z[2])[:5] out[cond] = (thd, harmonics) return out # ---------------- 谐波阻抗模型拟合 Z_h = R + j*h*X ---------------- def _fit_harmonic_impedance(amps, rng, R0=1.5, X0=4.5): """由合成的 (I_h, V_h) 对最小二乘拟合 R, X，其中 V_h=(R+jhX)I_h。""" # 构造复数测量 meas = [] for h, A in amps: if h == 0: continue Ih = complex(A * math.cos(h * 0.3), A * math.sin(h * 0.3)) Vh = complex(R0, h * X0) * Ih # 加噪声 Vh = complex(Vh.real + rng.gauss(0, 0.01 * abs(Vh)), Vh.imag + rng.gauss(0, 0.01 * abs(Vh))) Ih = complex(Ih.real + rng.gauss(0, 0.005 * A), Ih.imag + rng.gauss(0, 0.005 * A)) meas.append((h, Ih, Vh)) # 2x2 正规方程: 未知 R, X # ReV = R*Ir - h*X*Ii ; ImV = R*Ii + h*X*Ir A11 = A12 = A22 = b1 = b2 = 0.0 for h, Ih, Vh in meas: Ir, Ii = Ih.real, Ih.imag # eq1: ReV = R*Ir - h*X*Ii -> 系数 c1=(Ir, -h*Ii), 残差 ReV - (R*Ir - h*X*Ii) # eq2: ImV = R*Ii + h*X*Ir -> 系数 c2=(Ii, h*Ir) c1r, c1x = Ir, -h * Ii c2r, c2x = Ii, h * Ir A11 += c1r * c1r + c2r * c2r A12 += c1r * c1x + c2r * c2x A22 += c1x * c1x + c2x * c2x b1 += c1r * Vh.real + c2r * Vh.imag b2 += c1x * Vh.real + c2x * Vh.imag # 解 2x2 det = A11 * A22 - A12 * A12 if abs(det) < 1e-12: R, X = R0, X0 else: R = (b1 * A22 - b2 * A12) / det X = (A11 * b2 - A12 * b1) / det zh_mag = {h: math.sqrt(R * R + (h * X) ** 2) for h in [1, 3, 5, 7, 9, 11]} return R, X, zh_mag # ---------------- 戴维南等效最小二乘拟合 ---------------- def _fit_thevenin(Vmeas, Ic): """V = E0 - Z*Ic ; 未知 Er,Ei,Zr,Zi（复数）。 E0 = V + Z*Ic -> ReE0 = ReV + Zr*ReI - Zi*ImI ; ImE0 = ImV + Zr*ImI + Zi*ReI 4x4 正规方程 + 高斯消元。""" n = len(Vmeas) # 累加正规方程矩阵 (4x4) 与右端 A = [[0.0] * 4 for _ in range(4)] b = [0.0] * 4 # 变量序: [Zr, Zi, Er, Ei] cols = [] for t in range(n): Vr, Vi = Vmeas[t].real, Vmeas[t].imag Ir, Ii = Ic[t].real, Ic[t].imag # 拟合方程 E0 = V + Z*Ic，分量展开： # 实部: Er - Vr - (Zr*Ir - Zi*Ii) = 0 -> [-Ir, Ii, 1, 0]·x = Vr # 虚部: Ei - Vi - (Zr*Ii + Zi*Ir) = 0 -> [-Ii, -Ir, 0, 1]·x = Vi eq = [[-Ir, Ii, 1.0, 0.0, Vr], [-Ii, -Ir, 0.0, 1.0, Vi]] for e in eq: row = e[:4] rhs = e[4] for r in range(4): for c in range(4): A[r][c] += row[r] * row[c] b[r] += row[r] * rhs # 高斯消元 for i in range(4): p = i + max(range(4 - i), key=lambda k: abs(A[i + k][i])) if abs(A[p][i]) < 1e-12: continue A[i], A[p] = A[p], A[i] b[i], b[p] = b[p], b[i] pv = A[i][i] for j in range(i, 4): A[i][j] /= pv b[i] /= pv for r in range(4): if r != i: f = A[r][i] for j in range(i, 4): A[r][j] -= f * A[i][j] b[r] -= f * b[i] x = b # 对角化后 b 即解 Zr, Zi, Er, Ei = x[0], x[1], x[2], x[3] # R² ss_res = ss_tot = 0.0 for t in range(n): Vp = complex(Er, Ei) - complex(Zr, Zi) * Ic[t] d = abs(Vp - Vmeas[t]) ** 2 ss_res += d ss_tot += abs(Vmeas[t] - complex(sum(v.real for v in Vmeas) / n, sum(v.imag for v in Vmeas) / n)) ** 2 r2 = 1.0 - ss_res / ss_tot if ss_tot > 0 else 0.0 return (Er, Ei), (Zr, Zi), r2 # ---------------- 主入口 ---------------- def gen_dgcup2021a(seed=SEED, out_csv="dgcup2021a.csv"): rng = random.Random(seed) # 1) 各供电臂电流 Isec = _train_currents(rng) # 2) 各步功率因数与电流相角（滞后） cos_phi = [0.0] * N phi = [0.0] * N for t in range(N): cp = rng.uniform(0.80, 0.96) cos_phi[t] = cp phi[t] = math.acos(cp) # 3) 合成真实戴维南电压（复数），叠加噪声 -> 测量复电压 Vm；并计算 P,Q E0 = complex(E0_TRUE, 0.0) Z = complex(ZR_TRUE, ZX_TRUE) Vtrue = [complex(0)] * N Vm = [complex(0)] * N # 测量复电压 Ic = [complex(0)] * N # 总有功电流（复数） U_clean = [0.0] * N P = [0.0] * N Q = [0.0] * N Itot = [0.0] * N # 总有功电流幅值 (A) for t in range(N): It = complex(0.0) for s in SECTIONS: # 该臂电流幅值 (A) -> kA，电流滞后电压 phi mag = Isec[s][t] / 1000.0 Ics = mag * complex(math.cos(-phi[t]), math.sin(-phi[t])) It += Ics Vt = E0 - Z * It Vtrue[t] = Vt # 测量噪声（复电压） v = complex(Vt.real + rng.gauss(0, 0.04), Vt.imag + rng.gauss(0, 0.04)) Icm = complex(It.real + rng.gauss(0, 0.002), It.imag + rng.gauss(0, 0.002)) Vm[t] = v Ic[t] = Icm U_clean[t] = abs(v) S = v * Icm.conjugate() P[t] = S.real Q[t] = S.imag Itot[t] = abs(Icm) * 1000.0 # 4) 注入真实异常（在测量复电压上叠加突变，制造残差异常） anomaly_steps = [60, 95, 140, 200, 250] anomaly_flag = [0] * N for ts in anomaly_steps: anomaly_flag[ts] = 1 # 电压暂降 ~3.5 kV（与电流无关的残差） mag = abs(Vm[ts]) Vm[ts] = Vm[ts] * ((mag - 3.5) / mag) U_clean[ts] = abs(Vm[ts]) if ts in (95, 140): # 电流冲击：额外叠加电流（不改变 Vtrue 关系，制造大残差） Ic[ts] = Ic[ts] + complex(1.2, -0.4) mag = abs(Vm[ts]) Vm[ts] = Vm[ts] * ((mag - 1.0) / mag) U_clean[ts] = abs(Vm[ts]) # 5) 在 raw 序列中注入缺失与离群（清洗演示） miss_steps = [30, 110, 170, 230, 265] out_steps = [75, 185] U_raw = list(U_clean) Itot_raw = list(Itot) for ts in miss_steps: U_raw[ts] = float("nan") Itot_raw[ts] = float("nan") for ts in out_steps: U_raw[ts] += 4.5 # 离群电压尖峰 Itot_raw[ts] += 1800.0 # 离群电流尖峰 # 6) 清洗：线性插值缺失 + z-score 裁剪离群 def _interp(arr): out = list(arr) for i in range(N): if math.isnan(out[i]): # 前向/后向找最近有效 a = b = None for k in range(i - 1, -1, -1): if not math.isnan(out[k]): a = k; break for k in range(i + 1, N): if not math.isnan(out[k]): b = k; break if a is not None and b is not None: out[i] = out[a] + (out[b] - out[a]) * (i - a) / (b - a) elif a is not None: out[i] = out[a] elif b is not None: out[i] = out[b] return out U_clean2 = _interp(U_raw) Itot_clean = _interp(Itot_raw) # z-score 裁剪离群（3σ） n_missing = len(miss_steps) n_outlier = len(out_steps) for arr in (U_clean2, Itot_clean): mu = sum(v for v in arr if not math.isnan(v)) / (N - 0) sd = math.sqrt(sum((v - mu) ** 2 for v in arr) / N) for i in range(N): if abs(arr[i] - mu) > 3 * sd: # 用邻域均值裁剪 lo = max(0, i - 2); hi = min(N, i + 3) arr[i] = sum(arr[lo:hi]) / (hi - lo) # 7) 3 相供电侧电流（标准 3 相电流相量集）与对称分量 # 将 3 个供电臂电流视为三相导线电流幅值，统一滞后角 -phi，三相相差 120° ia = [complex(0)] * N; ib = [complex(0)] * N; ic = [complex(0)] * N seq0 = [0.0] * N; seq1 = [0.0] * N; seq2 = [0.0] * N unb = [0.0] * N A120 = 2.0 * math.pi / 3.0 for t in range(N): ang = -phi[t] ia[t] = Isec["A"][t] * complex(math.cos(ang), math.sin(ang)) ib[t] = Isec["B"][t] * complex(math.cos(ang - A120), math.sin(ang - A120)) ic[t] = Isec["C"][t] * complex(math.cos(ang - 2 * A120), math.sin(ang - 2 * A120)) v0, v1, v2 = _sym_components(ia[t], ib[t], ic[t]) seq0[t] = abs(v0); seq1[t] = abs(v1); seq2[t] = abs(v2) unb[t] = (abs(v2) / abs(v1) * 100.0) if abs(v1) > 1e-9 else 0.0 # 8) 日负荷曲线（按小时聚合） hourly_P = [0.0] * 24 hourly_I = {s: [0.0] * 24 for s in SECTIONS} cnt = [0] * 24 for t in range(N): h = t * DT_MIN // 60 hourly_P[h] += P[t] for s in SECTIONS: hourly_I[s][h] += Isec[s][t] cnt[h] += 1 for h in range(24): if cnt[h]: hourly_P[h] /= cnt[h] for s in SECTIONS: hourly_I[s][h] /= cnt[h] peak_P = max(P); peak_idx = P.index(peak_P) mean_P = sum(P) / N load_factor = mean_P / peak_P # 9) 谐波与 THD（三种运行工况） amps = { "空载": [(1, 80), (3, 12), (5, 6), (7, 3), (9, 1.5), (11, 1.0)], "牵引": [(1, 1500), (3, 380), (5, 210), (7, 120), (9, 70), (11, 45), (13, 25)], "制动": [(1, 1200), (3, 300), (5, 170), (7, 95), (9, 55), (11, 35), (13, 20)], } thd_res = _thd_of(amps, rng) thd = {k: v[0] for k, v in thd_res.items()} harmonics = {k: v[1] for k, v in thd_res.items()} # 10) 谐波阻抗拟合 Rz, Xz, zh_mag = _fit_harmonic_impedance(amps["牵引"], rng) # 11) 戴维南等效拟合（用清洗后 U、清洗后总有功电流；复电压保留原始相角） Vmeas = [] Ic_clean = [] for t in range(N): # 由清洗后的总有功电流幅值重建复数电流 mag = Itot_clean[t] / 1000.0 Icm = mag * complex(math.cos(-phi[t]), math.sin(-phi[t])) Ic_clean.append(Icm) # 复电压：清洗后的幅值 + 原始测量相角 ph = math.atan2(Vm[t].imag, Vm[t].real) Vmeas.append(complex(U_clean2[t] * math.cos(ph), U_clean2[t] * math.sin(ph))) E0_fit, Z_fit, r2 = _fit_thevenin(Vmeas, Ic_clean) # 12) 异常检测：基于戴维南模型残差 res = [0.0] * N for t in range(N): Vp = complex(E0_fit[0], E0_fit[1]) - complex(Z_fit[0], Z_fit[1]) * Ic_clean[t] res[t] = U_clean2[t] - abs(Vp) mu_r = sum(res) / N sd_r = math.sqrt(sum((r - mu_r) ** 2 for r in res) / N) thresh = 3.0 * sd_r detected = [1 if abs(res[t]) > thresh else 0 for t in range(N)] tp = sum(1 for t in anomaly_steps if detected[t]) fp = sum(1 for t in range(N) if detected[t] and anomaly_flag[t] == 0) fn = sum(1 for t in anomaly_steps if not detected[t]) precision = tp / (tp + fp) if (tp + fp) else 0.0 recall = tp / (tp + fn) if (tp + fn) else 0.0 # 13) 写 CSV os.makedirs(OUT_DIR, exist_ok=True) path = os.path.join(OUT_DIR, out_csv) with open(path, "w", newline="", encoding="utf-8-sig") as f: w = csv.writer(f) w.writerow(["t", "time_h", "I_A", "I_B", "I_C", "i_a", "i_b", "i_c", "U_raw_kV", "I_total_raw_A", "P_raw_MW", "Q_raw_MVar", "cos_phi", "U_clean_kV", "I_total_clean_A", "anomaly_flag"]) for t in range(N): hh = t * DT_MIN / 60.0 def fmt(x): return "" if (isinstance(x, float) and math.isnan(x)) else round(x, 4) w.writerow([ t, round(hh, 3), round(Isec["A"][t], 2), round(Isec["B"][t], 2), round(Isec["C"][t], 2), round(ia[t].real, 2), round(ib[t].real, 2), round(ic[t].real, 2), fmt(U_raw[t]), fmt(Itot_raw[t]), round(P[t], 4), round(Q[t], 4), round(cos_phi[t], 4), round(U_clean2[t], 4), round(Itot_clean[t], 2), anomaly_flag[t], ]) # 14) 汇总 D D = dict( seed=SEED, N=N, dt_min=DT_MIN, sections=len(SECTIONS), Unom_kV=UNOM, E0_true=(E0_TRUE, 0.0), Z_true=(ZR_TRUE, ZX_TRUE), n_missing=n_missing, n_outlier=n_outlier, hourly_P=hourly_P, hourly_I_A=hourly_I["A"], hourly_I_B=hourly_I["B"], hourly_I_C=hourly_I["C"], peak_P_MW=peak_P, peak_P_time_h=peak_idx * DT_MIN / 60.0, mean_P_MW=mean_P, load_factor=load_factor, unb_mean_pct=sum(unb) / N, unb_max_pct=max(unb), unb_max_time_h=unb.index(max(unb)) * DT_MIN / 60.0, pf_mean=sum(cos_phi) / N, pf_min=min(cos_phi), thd=thd, harmonics=harmonics, Zh_R=Rz, Zh_X=Xz, Zh_mag=zh_mag, E0_fit_kV=E0_fit, Zeq_fit_Ohm=Z_fit, R2=r2, n_true_anom=len(anomaly_steps), n_detected=sum(detected), tp=tp, fp=fp, fn=fn, precision=precision, recall=recall, csv_path=path, summary="DGCUP2021A 牵引供电分析：N=288、U_nom=27.5kV、THD(牵引)=%.1f%%、电流不平衡度均值=%.2f%%、" "戴维南 E0=%.2fkV Zeq=%.2f+j%.2fΩ R2=%.4f、异常检测 P=%.2f R=%.2f" % (thd["牵引"], sum(unb) / N, abs(complex(*E0_fit)), Z_fit[0], Z_fit[1], r2, precision, recall), ) # 时间序列（供配图与附录复用，保证四路一致） D["series"] = dict( t=list(range(N)), time_h=[t * DT_MIN / 60.0 for t in range(N)], U_raw=U_raw, U_clean=U_clean2, Itot_raw=Itot_raw, Itot_clean=Itot_clean, I_A=[Isec["A"][t] for t in range(N)], I_B=[Isec["B"][t] for t in range(N)], I_C=[Isec["C"][t] for t in range(N)], ia=[ia[t].real for t in range(N)], ib=[ib[t].real for t in range(N)], ic=[ic[t].real for t in range(N)], seq0=seq0, seq1=seq1, seq2=seq2, unb=unb, P=P, Q=Q, cos_phi=cos_phi, res=res, detected=detected, anomaly_flag=anomaly_flag, hourly_P=hourly_P, hourly_I_A=hourly_I["A"], hourly_I_B=hourly_I["B"], hourly_I_C=hourly_I["C"], ) return D if __name__ == "__main__": D = gen_dgcup2021a() print(D["summary"]) print("缺失/离群清洗: 缺失 %d 处, 离群 %d 处" % (D["n_missing"], D["n_outlier"])) print("日负荷: 峰值 P=%.2f MW @ %.1fh, 均值 %.2f MW, 负荷率=%.3f" % (D["peak_P_MW"], D["peak_P_time_h"], D["mean_P_MW"], D["load_factor"])) print("电流不平衡度: 均值 %.2f%%, 最大 %.2f%% @ %.1fh" % (D["unb_mean_pct"], D["unb_max_pct"], D["unb_max_time_h"])) print("功率因数: 均值 %.3f, 最小 %.3f" % (D["pf_mean"], D["pf_min"])) print("谐波 THD: 空载 %.1f%%, 牵引 %.1f%%, 制动 %.1f%%" % (D["thd"]["空载"], D["thd"]["牵引"], D["thd"]["制动"])) for cond in ("空载", "牵引", "制动"): top = ", ".join("h%d=%.0fA" % (h, A) for h, f, A in D["harmonics"][cond]) print(" %s 主导谐波: %s" % (cond, top)) print("谐波阻抗拟合: R=%.3fΩ, X=%.3fΩ; |Z_1|=%.2f |Z_3|=%.2f |Z_5|=%.2f Ω" % (D["Zh_R"], D["Zh_X"], D["Zh_mag"][1], D["Zh_mag"][3], D["Zh_mag"][5])) print("戴维南等效: E0=(%.3f%+ .3fj) kV, Zeq=(%.3f%+ .3fj) Ω, R2=%.4f" % (D["E0_fit_kV"][0], D["E0_fit_kV"][1], D["Zeq_fit_Ohm"][0], D["Zeq_fit_Ohm"][1], D["R2"])) print("异常检测: 真实 %d, 检出 %d, TP=%d FP=%d FN=%d, 精确率=%.2f 召回率=%.2f" % (D["n_true_anom"], D["n_detected"], D["tp"], D["fp"], D["fn"], D["precision"], D["recall"])) print("CSV ->", D["csv_path"])