## 2 Emergency State and Automatic Generation Control  
### Emergency State  
AGC not only aims to balance the active power between generators and system loads in a large-scale interconnected power system but is also designed to reduce the frequency deviation of the power system. That is to say, a high control performance of an AGC controller is significantly important for a control area to maintain the frequency deviation within normal levels.  
Generally, frequency control has three gradations, i.e., a primary control zone, a secondary control zone, and an emergency control zone (see Figure 1). The primary control zone, which is subject to primary frequency regulation (PFR), is automatically regulated by the generator in response to frequency changes. The secondary control zone, which leads to AGC or secondary frequency regulation (SFR), is regulated by a control algorithm. The emergency control zone or tertiary control zone results in the implementation of economical dispatch and unit commitment, which occur with longer timescales, e.g., 15 min for economical dispatch (ED) and 24 h for unit commitment (UC). In particular, the range of the area control error (ACE) for each gradation is dependent on the basic capacity of the power system. Each gradation has a different frequency deviation range and a different control performance standard (CPS) index range:  
* The range of the frequency deviation for the dead zone is from \((f_{0}-\Delta f_{1})\) to \((f_{0}+\Delta f_{1})\), where the frequency deviation \(\Delta f_{1}\) is set to 0.025 Hz; The range of the CPS index for the dead zone is from \(k_{\text{CPS(1)}}\) to 100%, where the CPS index \(k_{\text{CPS(1)}}\) is set to 99% in this paper.
* The range of the frequency deviation for primary control is from \((f_{0}-\Delta f_{2})\) to \((f_{0}+\Delta f_{2})\), where the frequency deviation \(\Delta f_{2}\) is set to 0.1 Hz; The range of the CPS index for primary control is from \(k_{\text{CPS(2)}}\) to \(k_{\text{CPS(1)}}\), where the CPS index \(k_{\text{CPS(2)}}\) is set to 95% in this paper.
* The range of the frequency deviation for secondary control is from \((f_{0}-\Delta f_{3})\) to \((f_{0}+\Delta f_{3})\), where the frequency deviation \(\Delta f_{3}\) is set to 0.5 Hz; The range of the CPS index for secondary control is from \(k_{\text{CPS(3)}}\) to \(k_{\text{CPS(2)}}\), where the CPS index \(k_{\text{CPS(3)}}\) is set to 85% in this paper.
* The range of the frequency deviation for emergency control is from \((f_{0}-\Delta f_{4})\) to \((f_{0}+\Delta f_{4})\), where the frequency deviation \(\Delta f_{4}\) is set to \(\infty\) Hz; The range of the CPS index for emergency control is from \(k_{\text{CPS(4)}}\) to \(k_{\text{CPS(3)}}\), where the CPS index \(k_{\text{CPS(4)}}\) is set to 0% in this paper.  
To minimize emergency situations for a power system when a large load suddenly occurs, a preventive strategy for AGC is described below. Frequency deviation ranges from \((f_{0}-\Delta f_{\rm e})\) to \((f_{0}-\Delta f_{\rm e})\) and from \((f_{0}+\Delta f_{\rm e})\) to \((f_{0}+\Delta f_{3})\) were selected as the ranges for the preventive strategy. The preventive strategy aims to maintain the system frequency deviation \(\Delta f\) at a minimum value, i.e., \(\Delta f\to 0\) and \(|\Delta f|<\Delta f_{\rm e}\). The frequency deviation for the preventive strategy \(\Delta f_{\rm e}\) was set to 0.2 Hz in this study.