# Dispatching Strategy for Low-Carbon Flexible Operation of Park-Level Integrated Energy System
## 2 Flexible Supply of PIES  
There is no consensus on the definition of flexibility in power systems. According to a vast amount of the existing literature, the flexibility of system dispatching should be subject to the shortage of real-time system power due to the system's adjustability and uncertainty factor [21]. In PIES, the system's adjustability mainly comes from the available power of the flexibility resources, whereas the uncertainty factor is primarily manifested in the difficulty of accurately predicting the wind-solar access power. In this paper, the flexibility of the dispatching process is defined as the system's ability to leave a flexibility margin during the period of day-ahead dispatching through rational planning of flexibly controllable resources, and to quickly adapt to fluctuating changes to guarantee balanced power in real-time in the event of wind-solar power fluctuations. Flexibility resources include all means of coping with random variations in power. The access to flexibility resources allows PIES to promptly and accurately regulate energy [22]. In addition, the variation in the output power of the flexibility resources is directional, and so is the corresponding flexibility, which is divided into upward and downward flexibility, and is defined as Equation (1):  
\[\left\{ \begin{array}{l}f_{mup,t}=\min\Bigl{(}P_{\max}^{m}-P_{t}^{m},\Delta P _{m}^{\text{up}}\,\Delta t\Bigr{)}\\ f_{mdown,t}=\min\Bigl{(}P_{t}^{m}-P_{\min}^{m},\Delta P_{m}^{\text{down}}\, \Delta t\Bigr{)}\end{array} \right. \tag{1}\]  
where \(m\) is a collection of flexibility resources, \(P_{t}^{m}\) is the power of flexible resource, \(f_{mup,t}\) and \(f_{mdown,t}\) are the upward and downward flexibility, \(\Delta P_{m}^{\text{up}}\) and \(\Delta P_{m}^{\text{down}}\) are the climbing upper and lower power of the flexibility resource, and \(\Delta t\) is the time interval for dispatching. For a more concrete analysis of the flexibility of each controllable resource, PFI is adopted to evaluate the flexibility level of controllable resources. PFI refers to the ratio of the range of adjustable power output of the equipment to its rated power at a certain moment, which provides flexible resources with the ability to cope with power variations. In PIES, the adjustability of the system primarily comes from the micro-turbine (_MT_), energy storage system (_ESS_), load-side flexibility resources (LFRs), etc. The following indicator is used to evaluate the upward and downward flexibility supply of Equation (1) as Equation (2):  
\[\left\{ \begin{array}{l}F_{MT,p,t}=(P_{\max}^{MT}-P_{ef}^{MT})/P_{N}^{MT}\\ F_{MTdown,t}=(P_{\max}^{MT}-P_{\min}^{MT})/P_{N}^{MT}\\ F_{LFR,p,t}=(P_{\max}^{IL}+P_{\max}^{HL}-P_{t}^{EL}-P_{t}^{HL})/(\frac{P_{ \max}^{IL}}{P_{\max}^{IL}})\\ F_{ESS_{up,t}}=\min[P_{\max}^{ES_{\text{SM}}c}-P_{t}^{ES_{\text{SM}}c},\frac{ ESS_{N}(S_{t}^{ES_{\text{SM}}}-S_{t}^{ES_{\text{SM}}})^{ES_{\text{SM}}c}}{ \frac{ES_{N}}{S_{t}^{ES_{\text{SM}}}}}]/ES_{N}\\ F_{ESS_{down,t}}=\min[P_{\max}^{ES_{\text{SM}}}-P_{t}^{ES_{\text{SM}}},\frac{ ESS_{N}(S_{\max}^{ES_{\text{SM}}}-S_{t}^{ES_{\text{SS}}})}{\frac{TS_{N}}{TS_{N}} \Delta t}]/ES_{N}\end{array} \right.