输电线路电压电流的相位角测量方法

摘要

本发明公开了一种输电线路电压电流的相位角测量方法，它首先采集输电线路保护安装处各采样时刻的三相电压、三相电流瞬时值，计算起始时间的三相电压的相位角和三相电流的相位角，然后起始时间以采样间隔时间递增，采用递推算法依次计算各采样时刻的三相电压的相位角和各采样时刻的三相电流的相位角。本发明利用递推算法计算各采样时刻的三相电压的相位角和各采样时刻的三相电流的相位角，每次运算只需用到两个电压采样值或两个电流采样值，所需计算数据少，算法原理简单，运算量少，计算速度快，可极大提高继电保护动作速度。

主权项

输电线路电压电流的相位角测量方法，其特征在于，包括如下依序步骤：步骤1，保护装置实时采集输电线路保护安装处各t采样时刻的A、B、C三相电压瞬时值u_A(t)、u_B(t)、u_C(t)和各t采样时刻的A、B、C三相电流瞬时值i_A(t)、i_B(t)、i_C(t)；步骤2，保护装置计算第t_k采样时刻的A、B、C三相电压的虚部和第t_k采样时刻的A、B、C三相电流的虚部$\mathrm{Im}\left({\stackrel{·}{U}}_A\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{u}_A\left(t\right)\sin \left(\omega t\right)dt,\mathrm{Im}\left({\stackrel{·}{U}}_B\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{u}_B\left(t\right)\sin \left(\omega t\right)dt,\mathrm{Im}\left({\stackrel{·}{U}}_C\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{u}_C\left(t\right)\sin \left(\omega t\right)dt$$\mathrm{Im}\left({\stackrel{·}{I}}_A\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{i}_A\left(t\right)\sin \left(\omega t\right)dt,\mathrm{Im}\left({\stackrel{·}{I}}_B\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{i}_B\left(t\right)\sin \left(\omega t\right)dt,\mathrm{Im}\left({\stackrel{·}{I}}_C\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{i}_C\left(t\right)\sin \left(\omega t\right)dt$其中：T为基波周期时间；步骤3，保护装置计算第t_k采样时刻的A、B、C三相电压的实部和第t_k采样时刻的A、B、C三相电流的实部$\mathrm{Re}\left({\stackrel{·}{U}}_A\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{u}_A\left(t\right)\cos \left(\omega t\right)dt,\mathrm{Re}\left({\stackrel{·}{U}}_B\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{u}_B\left(t\right)\cos \left(\omega t\right)dt,\mathrm{Re}\left({\stackrel{·}{U}}_C\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{u}_C\left(t\right)\cos \left(\omega t\right)dt$$\mathrm{Re}\left({\stackrel{·}{I}}_A\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{i}_A\left(t\right)\cos \left(\omega t\right)dt,\mathrm{Re}\left({\stackrel{·}{I}}_B\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{i}_B\left(t\right)\cos \left(\omega t\right)dt,\mathrm{Re}\left({\stackrel{·}{I}}_C\right(t_k\left)\right)=\frac{\sqrt{2}}{T}\underset{t_k-T}{\overset{t_k}{\int }}{i}_C\left(t\right)\cos \left(\omega t\right)dt;$步骤4，保护装置计算第t_k采样时刻的A、B、C三相电压的相位角和第t_k采样时刻的A、B、C三相电流的相位角${\theta }_{t_k}\left({\stackrel{·}{U}}_A\right(t_k\left)\right)=arctan\frac{\mathrm{Im}\left({\stackrel{·}{U}}_A\right(t_k\left)\right)}{\mathrm{Re}\left({\stackrel{·}{U}}_A\right(t_k\left)\right)},{\theta }_{t_k}\left({\stackrel{·}{U}}_B\right(t_k\left)\right)=arctan\frac{\mathrm{Im}\left({\stackrel{·}{U}}_B\right(t_k\left)\right)}{\mathrm{Re}\left({\stackrel{·}{U}}_B\right(t_k\left)\right)},{\theta }_{t_k}\left({\stackrel{·}{U}}_C\right(t_k\left)\right)=arctan\frac{\mathrm{Im}\left({\stackrel{·}{U}}_C\right(t_k\left)\right)}{\mathrm{Re}\left({\stackrel{·}{U}}_C\right(t_k\left)\right)}$${\theta }_{t_k}\left({\stackrel{·}{I}}_A\right(t_k\left)\right)=arctan\frac{\mathrm{Im}\left({\stackrel{·}{I}}_A\right(t_k\left)\right)}{\mathrm{Re}\left({\stackrel{·}{I}}_A\right(t_k\left)\right)},{\theta }_{t_k}\left({\stackrel{·}{I}}_B\right(t_k\left)\right)=arctan\frac{\mathrm{Im}\left({\stackrel{·}{I}}_B\right(t_k\left)\right)}{\mathrm{Re}\left({\stackrel{·}{I}}_B\right(t_k\left)\right)},{\theta }_{t_k}\left({\stackrel{·}{I}}_C\right(t_k\left)\right)=arctan\frac{\mathrm{Im}\left({\stackrel{·}{I}}_C\right(t_k\left)\right)}{\mathrm{Re}\left({\stackrel{·}{I}}_C\right(t_k\left)\right)};$步骤5，保护装置以第t_k采样时刻为起始时间，计算第t_k+1采样时刻的A、B、C三相电压的相位角和第t_k+1采样时刻的A、B、C三相电流的相位角${\theta }_{t_{k+1}}\left({\stackrel{·}{U}}_A\right(t_{k+1}\left)\right)=\frac{{\theta }_{t_k}\left({\stackrel{·}{U}}_A\right(t_k\left)\right)+\frac{2}{\mathrm{Re}\left({\stackrel{·}{U}}_A\left(t_k\right)\right)N}[u_A\left(t_k\right)-u_A(t_k-T)]sin\frac{2k\pi }{N}}{1+\frac{2}{\mathrm{Re}\left({\stackrel{·}{U}}_A\right(t_k\left)\right)N}[u_A\left(t_k\right)-u_A(t_k-T)]cos\frac{2k\pi }{N}}$${\theta }_{t_{k+1}}\left({\stackrel{·}{U}}_B\right(t_{k+1}\left)\right)=\frac{{\theta }_{t_k}\left({\stackrel{·}{U}}_B\right(t_k\left)\right)+\frac{2}{\mathrm{Re}\left({\stackrel{·}{U}}_B\left(t_k\right)\right)N}[u_B\left(t_k\right)-u_B(t_k-T)]sin\frac{2k\pi }{N}}{1+\frac{2}{\mathrm{Re}\left({\stackrel{·}{U}}_B\right(t_k\left)\right)N}[u_B\left(t_k\right)-u_B(t_k-T)]cos\frac{2k\pi }{N}}$${\theta }_{t_{k+1}}\left({\stackrel{·}{U}}_C\right(t_{k+1}\left)\right)=\frac{{\theta }_{t_k}\left({\stackrel{·}{U}}_C\right(t_k\left)\right)+\frac{2}{\mathrm{Re}\left({\stackrel{·}{U}}_C\left(t_k\right)\right)N}[u_C\left(t_k\right)-u_C(t_k-T)]sin\frac{2k\pi }{N}}{1+\frac{2}{\mathrm{Re}\left({\stackrel{·}{U}}_C\right(t_k\left)\right)N}[u_C\left(t_k\right)-u_C(t_k-T)]cos\frac{2k\pi }{N}}$${\theta }_{t_{k+1}}\left({\stackrel{·}{I}}_A\right(t_{k+1}\left)\right)=\frac{{\theta }_{t_k}\left({\stackrel{·}{I}}_A\right(t_k\left)\right)+\frac{2}{\mathrm{Re}\left({\stackrel{·}{I}}_A\left(t_k\right)\right)N}[i_A\left(t_k\right)-i_A(t_k-T)]sin\frac{2k\pi }{N}}{1+\frac{2}{\mathrm{Re}\left({\stackrel{·}{I}}_A\left(t_k\right)\right)N}[i_A\left(t_k\right)-i_A(t_k-T)]cos\frac{2k\pi }{N}}$${\theta }_{t_{k+1}}\left({\stackrel{·}{I}}_B\right(t_{k+1}\left)\right)=\frac{{\theta }_{t_k}\left({\stackrel{·}{I}}_B\right(t_k\left)\right)+\frac{2}{\mathrm{Re}\left({\stackrel{·}{I}}_B\left(t_k\right)\right)N}[i_B\left(t_k\right)-i_B(t_k-T)]sin\frac{2k\pi }{N}}{1+\frac{2}{\mathrm{Re}\left({\stackrel{·}{I}}_B\right(t_k\left)\right)N}[i_B\left(t_k\right)-i_B(t_k-T)]cos\frac{2k\pi }{N}}$${\theta }_{t_{k+1}}\left({\stackrel{·}{I}}_C\right(t_{k+1}\left)\right)=\frac{{\theta }_{t_k}\left({\stackrel{·}{I}}_C\right(t_k\left)\right)+\frac{2}{\mathrm{Re}\left({\stackrel{·}{I}}_C\left(t_k\right)\right)N}[i_C\left(t_k\right)-i_C(t_k-T)]sin\frac{2k\pi }{N}}{1+\frac{2}{\mathrm{Re}\left({\stackrel{·}{I}}_C\right(t_k\left)\right)N}[i_C\left(t_k\right)-i_C(t_k-T)]cos\frac{2k\pi }{N}}$其中：u_A(t_k)、u_B(t_k)、u_C(t_k)分别为第t_k采样时刻的A、B、C三相电压瞬时值，i_A(t_k)、i_B(t_k)、i_C(t_k)分别为第t_k采样时刻的A、B、C三相电流瞬时值，u_A(t_k‑T)、u_B(t_k‑T)、u_C(t_k‑T)分别为第t_k‑T采样时刻的A、B、C三相电压瞬时值，i_A(t_k‑T)、i_B(t_k‑T)、i_C(t_k‑T)分别为第t_k‑T采样时刻的A、B、C三相电流瞬时值，T为基波周期时间，N为每周波采样点数量，k为第t_k采样时刻对应的采样点数值；步骤6，起始时间t_k以采样间隔时间Δt递增，返回步骤5，在前一个采样时刻计算的A、B、C三相电压的相位角和A、B、C三相电流的相位角的基础上依次递推计算下一个采样时刻的A、B、C三相电压的相位角和下一个采样时刻的A、B、C三相电流的相位角。