从刚性到绝热：基于作用-角变量的交流网络正则化
From Rigid to Adiabatic: Canonical Regularization of AC Networks via Action-Angle Variables
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中文总结 AI 辅助
本文针对传统电力系统刚性网络假设的局限，采用作用-角变量正则化交流网络，建立端口-哈密顿标准形式，通过两机系统揭示纬向不稳定通道，统一功角与电压稳定分析框架。
中文摘要 AI 辅助
传统电力系统分析依赖时间尺度分离与刚性网络假设，通过斯坦梅茨相量理论将电磁暂态冻结为代数潮流方程。随着网侧变流器渗透率提升，输电线路上的磁能动态与变流器控制环路在相近时间尺度上相互作用，对该刚性网络假设构成挑战。本文回到旋转磁场驱动的法拉第电磁感应定律，在作用-角正则坐标下建模输电线路的旋转磁场，将潮流方程的刚性代数约束正则化为绝热辛流形上的正则方程，建立交流电网的端口-哈密顿标准形式。基于最小反例原理并采用等面积准则的经典两机系统，本文通过布洛赫球坐标揭示了一种纬向不稳定通道：Q-V控制释放电压幅值自由度，将稳定边界从赤道不稳定平衡点（UEP）转移至鞍点，从而统一电力系统分析中P-δ功角稳定与Q-V电压稳定的分析框架。
英文摘要
Traditional power system analysis relies on timescale separation and the rigid-network assumption, freezing electromagnetic transients into algebraic power-flow equations via Steinmetz's phasor theory. As grid-forming converter penetration increases, magnetic energy dynamics on transmission lines interact with converter control loops on comparable timescales, challenging this rigid-network assumption. Returning to Faraday's law of electromagnetic induction driven by rotating magnetic fields, this paper models the transmission lines' rotating magnetic fields in action-angle canonical coordinates, regularizes the rigid algebraic constraints of power-flow equations into canonical equations on adiabatic symplectic manifolds, and establishes a port-Hamiltonian standard form for AC power grids. Based on the minimal-counterexample principle and using the equal-area criterion's classical two-machine system, this paper reveals a latitudinal instability channel via Bloch-sphere coordinates: Q-V control releases voltage-amplitude freedom, shifting the stability boundary from the equatorial UEP (unstable equilibrium point) to a saddle point, thereby unifying the analytical frameworks of P-delta angle stability and Q-V voltage stability in power system analysis.
发表机构
- School of Electrical Engineering, Xi’an Jiaotong University（西安交通大学电气工程学院）
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