AI 中文总结
本文针对限电流型网侧电压支撑逆变器，构建分析框架预测圆形电流限制器激活时的电网电压边界，通过分段光滑系统建模与延拓公式，经仿真验证其可预测电压崩溃的不同情形。
AI 中文摘要
网侧电压支撑（GFM）逆变器的过流能力有限，因此在大扰动期间电流限制至关重要。圆形电流限制器（CCL）的激活并不总是导致运行平衡点消失。本文开发了一个分析框架，用于预测CCL激活时的电网电压边界，确定运行平衡点是否作为饱和稳定平衡点（satSEP）持续存在，并识别其消失时的电压。将带有冻结抗积分饱和的基于CCL的GFM逆变器建模为分段光滑系统，包含正常控制和电流限制两种模式，因此限制器激活被解释为边界平衡分岔（BEB）。引入了一种延拓公式，当CCL激活时切换到简化的电流限制模型，以避免由冻结积分器状态引起的秩亏问题。包含滤波电容的等效电路得出了CCL激活时的上下边界电压的闭式表达式。正的下边界斜率表明satSEP在电流限制模式下持续存在，并在后续的鞍结处分歧消失，而非正斜率则表明非光滑折叠分岔及平衡点在BEB处消失。在假设的参数条件下，上边界斜率始终为负。在单逆变器和改进9节点系统中进行的功角分析、动态模型延拓以及时域仿真验证了这些预测，结果表明CCL激活既可以通过非光滑折叠分岔立即导致平衡点消失，也可以允许satSEP持续存在直至其在后续鞍结处分歧消失。
英文摘要
The limited overcurrent capability of grid-forming (GFM) inverters makes current limiting essential during large disturbances. Activation of a circular current limiter (CCL) does not always cause the operating equilibrium to disappear. This paper develops an analytical framework to predict the grid-voltage boundaries at which the CCL is activated, determine whether the operating equilibrium persists as a saturated stable equilibrium point (satSEP), and identify the voltage at which it is lost. The CCL-based GFM inverter with frozen anti-windup is formulated as a piecewise-smooth system comprising normal-control and current-limited modes, so limiter activation is interpreted as a boundary-equilibrium bifurcation (BEB). A continuation formulation that switches to a reduced current-limited model when the CCL is activated is introduced to avoid the rank deficiency caused by frozen integrator states. An equivalent circuit that includes the filter capacitor yields closed-form expressions for the lower and upper boundary voltages at which the CCL is activated. A positive lower-boundary slope predicts that a satSEP persists in the current-limited mode and is lost at a later saddle-node, whereas a nonpositive slope predicts a non-smooth fold and equilibrium loss at the BEB. The upper-boundary slope is always negative under the assumed parameter conditions. Power-angle analysis, dynamic-model continuation in single-inverter and modified 9-bus systems, and time-domain simulations validate these predictions, showing that CCL activation can either cause immediate equilibrium loss through a non-smooth fold or allow a satSEP to persist until it is lost at a later saddle-node.
