In this paper fast-scale instability boundary in power converters loaded by a constant power load is addressed using an analytical approach. From a piecewise linearized model of the converter, the discrete-time steady-state values of the electrical variables are first determined. Based on justified and realistic approximations of the voltage and current ripples, simple and accurate expressions for these steady-state values are derived and validated. Starting from a matrix-based analytical expression representing the fast-scale instability boundary, a simple design-oriented approximate expression is derived showing insight into how the different system parameters influence this boundary. We highlight its dependency on ripple and slope quantities of the electrical variables of the converter and we explore the impact of variation of parameters in different projections of the multi-dimensional parameter space. An important parameter is the outer voltage controller gain which we demonstrate mathematically that it could have an either stabilizing or destabilizing effect depending whether the steady-state duty cycle is smaller or larger than 1/2. Experimental measurements from a laboratory prototype are in correlation with the theoretical predictions.

中文翻译：

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具有CPL和闭环电压的电流模式控制DC-DC转换器快速尺度不稳定性边界的解析确定

在本文中，使用解析方法解决了由恒定功率负载加载的功率转换器中的快速尺度不稳定性边界。从转换器的分段线性模型中，首先确定电变量的离散时间稳态值。基于电压和电流纹波的合理逼真的近似值，可以得出并验证这些稳态值的简单准确的表达式。从代表快速尺度不稳定性边界的基于矩阵的分析表达式开始，可以导出一个简单的面向设计的近似表达式，以了解不同系统参数如何影响该边界。我们突出显示了其对转换器电变量的纹波和斜率量的依赖性，并探讨了多维参数空间的不同投影中参数变化的影响。一个重要的参数是外部电压控制器的增益，我们通过数学方法证明其增益可能具有稳定或不稳定的作用，这取决于稳态占空比是小于还是大于1/2。实验室原型的实验测量值与理论预测值相关。一个重要的参数是外部电压控制器的增益，我们可以通过数学方法证明其增益可能具有稳定或不稳定的作用，这取决于稳态占空比是小于还是大于1/2。实验室原型的实验测量值与理论预测值相关。一个重要的参数是外部电压控制器的增益，我们通过数学方法证明其增益可能具有稳定或不稳定的作用，这取决于稳态占空比是小于还是大于1/2。实验室原型的实验测量值与理论预测值相关。