## 3 Hierarchical Frequency Control Scheme
### Coordinated Control Strategy  
Traditionally, the power balance of a power system is maintained by AGC in real-time. The available reserve of regulation generators account for a large proportion of the available capacity. The positive deviation from the frequency benchmark incurs the reduction of the power output of generators. Otherwise the negative deviation from the frequency benchmark incurs the increase of power output. Considering the participation of flexible load in supplementing frequency, the allocation methods of control signals is the key of the coordination control scheme. Based on a conventional  
Figure 1: Hierarchical frequency control scheme. AGC—automatic generation control; ACE—area control error; PI—proportional integral; UPCE—an adjustable control error based on unit capacity; AC—air conditioning. ACE calculated by system frequency deviation and tie-line power, the widely utilized approach for frequency allocation is a distribution factor predefined by the operator. The traditional allocation methods are incapable of handling the inadequacy of regulation reserve capacities and the deterioration of frequency control performance. A modified control strategy is partitioned into multiple control zones based on absolute value of ACE, which overcomes the deficiency of traditional distribution factors in a certain sense but the distribution factor in the same control area remains constant. That requires an adjustable frequency control performance and the corresponding allocation strategy. In the tie-line bias control, \(ACE\) can be calculated as follows:  
\[ACE(t)=B\Delta f(t)+\Delta P_{tie}(t) \tag{16}\]  
where \(B\) refers to frequency bias factor, \(\Delta f(t)\) denotes frequency deviation at \(t\)th period, \(\Delta P_{tie}(t)\) refers to tie-line power fluctuation at \(t\)th period. As the common frequency control strategy, the PI control method is employed to mitigate the frequency deviation. The total regulation power of secondary frequency control can be obtained as follows:  
\[\Delta P_{c}(t)=-K_{Pro}ACE(t)-K_{I}\int ACE(t) \tag{17}\]  
where \(\Delta P_{c}(t)\) is total regulation power at \(t\)th period, \(K_{Pro}\), \(K_{I}\) denotes proportional gain and integral gain of PI Controller, respectively. Considering the participation of demand-side resources, the traditional allocation method of fixed distribution factor can be modelled as follows:  
\[\left\{ \begin{array}{c}\Delta P_{G}(t)=\alpha_{G}\cdot\Delta P_{c}(t)\\ \Delta P_{AC}(t)=\alpha_{AC}\cdot\Delta P_{c}(t)\\ \alpha_{G}+\alpha_{AC}=1\end{array} \right. \tag{18}\]  
where \(\Delta P_{G}(t)\) refers to regulation power of generators at \(t\)th period, \(\Delta P_{AC}(t)\) is regulation power of inverter ACs at \(t\)th period, \(\alpha_{G},\alpha_{AC}\) denotes allocation factor of generators and ACs. Taking the regulation capacity of generators into consideration, UPCE can define the deviation between the absolute value of the allocated regulated power and total available reserve capacity of generators instead of the ACE:  
\[UPCE(t)=|\alpha_{G}\Delta P_{c}|-\sum_{i=1}^{N_{G}}\Delta P_{G,i}^{\max} \tag{19}\]  
where \(P_{G,i}^{max}\) is maximum power of the \(i\)th generator. The UPCE focuses on the evaluation of generator reserve adequacy instead of frequency deviation and tie-line power of the system, which represents the operation characteristics of power system more accurately. Derived from the mechanism of the divisional control, coordinated control methods are categorized into three control levels to cover certain rare albeit high-risk scenarios. Given \(E_{set}\) refers to the threshold value of ACE, the dynamic allocation method based on UPCE is formulated as per Figure 2.  
When \(UPCE(t)\leq 0\), the total available reserve capacity of generators is adequate to compensate the frequency fluctuations and the allocation factor is predefined as the traditional allocation methods, which are formulated as the Equation (20):  
\[\left\{