# Aggregation Dispatch and Control Strategies for Multi-Type Loads in Industrial Parks
## 2 Aggregated Dispatch and Control Framework for Multi-Type Loads in Industrial Parks
### Control Characteristics of Multi-Type Loads in Industrial Parks  
Curtailable loads, interruptible loads, and shiftable loads are all considered as one type of controllable load in this paper. These three types of loads all have three operational stages: start-up, operation, and shutdown. After receiving start-up, power regulation, and shut-down commands, multi-type loads in industrial parks need to determine whether to participate in control based on the current production plan requirements and load control constraints. Controllable loads often have start-up and shut-down delays, and there are response phases of power increase or decrease during start-up and shut-down. In the process of control response, their operating power can be regulated according to the control requirements based on the load operating rules. Therefore, most of the multi-type loads in industrial parks are restricted control objects. The control process for these restricted control objects can be abstracted into three stages: start-up, operation, and shut-down, each of which has different control response-time characteristics. Typical operational characteristics curves of controllable loads in industrial parks are shown in Figure 1.  
Controllable loads exhibit different control response characteristics during the stages of startup, operation, and shutdown. Non-parametric models are utilized separately to model the control response characteristics of these three stages. * Startup stage: After receiving a startup command, the controllable load starts from a shutdown state after a delay and operates under the specified conditions. The startup process can be regarded as zero initial-state step response with an invariant input, which is the inherent startup characteristic of controllable load, and can be described by a non-parametric model. Perform a unit step response experiment when the controllable load is in a shut-down state, measure the power output value of the controllable load, which is denoted as \(a_{k}=a(kT),k=1,2,\ldots\), and \(T(T=15\ min)\) presents the sampling period. Assuming that the controllable load is an asymptotically stable object, and its output reaches steady state after \(N\) steps of change, the unit step response sequence of the controllable load in startup stage is denoted as \(a_{k}=\{0,\ldots,0,a_{\theta+1},a_{\theta+2},\ldots,a_{N}\}\), \(\theta T\) is the startup response delay of the controllable load. Considering the controllable load as a linear object, by the homogeneity of a linear system, the output of the controllable load during the startup stage can be expressed as:  
\[p(k)=a_{k}u(k_{s}),\ k\in[k_{s},k_{s}+NT-1] \tag{1}\]  
\[\Delta u(k)=u(k)-u(k-1)=0,\ k\in[k_{s}+1,k_{s}+NT-1] \tag{2}\]  
Figure 1: Typical operational characteristics curves of controllable loads in industrial parks. * Operation stage: The output power of controllable load can be adjusted within a certain range. After receiving a control command, it responds after a delay, and the response process is regarded as a non-zero state response, described by a non-parametric model. Perform a unit step response experiment during operation stage when the controllable load is in a steady state, using the same method as in the startup stage. The unit step response sequence of the controllable load during operation is obtained as \(b_{k}=\{0,\ldots,0,a_{\tau+1},a_{\tau+2},\ldots,a_{V}\}\), and its output reaches steady state after \(V\) steps of change, \(\tau T\) is the control response delay of the controllable load during operation stage. According to the homogeneity and superposition of the linear system, the power output of the controllable load during the operation stage is:  
\[p(k)=b_{V}u(k-V)+\sum_{i=1}^{V-1}b_{i}\Delta u(k-i),\;k\in[k_{r},k_{r}+VT-1] \tag{3}\]  
The output of the controllable load during the operation stage at time \(k\) is related to the control action at time \(k-V\) and the change in the control action during the period from time \(k-V\) to time \(k\).