Abstract
In a cyber-physical power system, active distribution network (ADN) facilitates the energy control through hierarchical and distributed control system (HDCS). Various researches have dedicated to develop the control strategies of primary devices of ADN. However, an ADN demonstration project shows that the information transmission of HDCS may cause time delay and response lag, and little model can describe both the ADN primary device and HDCS as a cyber-physical system (CPS). In this paper, a hybrid system based CPS model is proposed to describe ADN primary devices, control information flow, and HDCS. Using the CPS model, the energy process of primary devices and the information process of HDCS are optimized by model predictive control (MPC) methodology to seamlessly integrate the energy flow and the information flow. The case study demonstrates that the proposed CPS model can accurately reflect main features of HDCS, and the control technique can effectively achieve the operation targets on primary devices despite the fact that HDCS brings adverse effects to control process.
Keywords
Active distribution network (ADN); cyber-physical system (CPS); hybrid system; hierarchical and distributed control system
WITH the rapid development of information technology, how to properly integrate the information system with the traditional industrial control system has become a major research challenge in various application domains. This spawns the new concept of cyber-physical system (CPS), aiming at handling the close interaction between the information system and real physical system [
A smart grid possesses all the essential characteristics of a CPS [
As an advanced form of smart grid, active distribution network (ADN) [
However, the existing control method and model are idealized, and only consider the primary system of ADN. The typical design of HDCS consists of three levels of controllers and stretches across several power supply areas. Thus, the time delay is a key problem which may affect control effect. In the debugging stage of an ADN demonstration project in Guangdong province, China, the time delay leads to severe response lag of distributed generators (DGs). Although the control results have been promoted in the demonstration project by adjusting proportional-integral (PI) parameters, the essential principal is still unknown.
There are two reasons for the problems above: ① the controlled objective mainly focuses on the energy flow (physical system), while the HDCS and the control information flow are not considered; ② the existing control model and strategy mainly focus on continuous dynamic process (physical process), while the discrete state switching (information process) is not included.
Just like the adverse phenomenon in the demonstration project, time delay is difficult to be avoided even if the communication infrastructure and the performance of controllers are all improved. The most feasible way is to consider the time delay in the control input, and build a control model integrating with CPSs.
This paper aims to design such an integration model which considers time delay caused by HDCS. Each control input computed by this model will include relevant attribution of time delay, thus the adverse influence can be reduced as much as possible. Firstly, the HDCS of ADN and the information flow are analyzed, and the impact of HDCS on primary system is studied. Then, taking the control of ADN flexible load as an example, a hybrid system based CPS model is built which integrates the primary device, the control information flow, and the HDCS structure. According to the integration model, a model predictive control (MPC) strategy is designed to optimize the load operation. Finally, the model and strategy are verified with extensive simulations.
The HDCS completes all the measurement, data transmission, computation and control in ADN, and it is the most important tool to realize ADN function. The control system of ADN is shown in

Fig. 1 Control system of ADN.
In HDCS, the controlled primary devices are connected to different SNCCs according to the category or performance of devices. SNCCs of each control area receive and execute the control commands from ACC. All SNCCs and ACCs are managed and coordinated by GEMS.
The controllers of HDCS exchange information with each other through communication network. Taking the control of ADN flexible load under power shortage condition as an example [
As shown in

Fig. 2 Control information route of MPC for ADN flexible load.
The control information of HDCS depends on diverse control function. It could induce different information processing modes, which leads to different device control effects. These need to be considered in the control target computation.
As mentioned above, the control target of ADN primary system can eventually be achieved by changing the control parameters. However, it is not clear how the control information affects the primary process . Thus, in order to achieve a more effective control, the working process of HDCS needs to be carefully studied and significantly improved.
Different from the primary system, the dynamic characteristic and the spatio-temporal feature of control system are unable to be completely represented by differential-algebraic equations which need to be replaced by logical description. Therefore, as shown in

Fig. 3 Influence factor of information flow for ADN control. (a) HDCS of chain structure. (b) HDCS structure with branch.
1) Aspect 1: transition logic of information flow. It describes the transition rules of control information by logical form which reflects information process structure of different control functions. Similar to the two structures in
2) Aspect 2: structure of action objects. Even if the same control functions act on the same controlled objects, the computation and action of control information are determined by the structure of objects. In
3) Aspect 3: information transition time. There is time consumption in the processing and communication procedure of controllers.
4) Aspect 4: information processing capacity. When controllers and communication devices process the control information, it is impossible to execute unlimited threads, thus the limited processing capacity leads to stagnation. If the ACC in
Four aspects reflect the main features of HDCS and its impact on control effect. That is, aspects 1 and 2 are associated with the spatial factor; aspect 3 is about time effect; and aspect 4 is the attribute of HDCS itself.
In order to combine these four aspects of impacts with the ADN primary system, a logic based constraint model can be used to represent the impact and merged into the primary control model. Subsequently, the impacts of HDCS can be considered in the control problem.
In this subsection, the control of ADN flexible load is used as an example to illustrate the CPS model which integrates energy and control information flow.
1) Hybrid System Based Primary Device Model
The hybrid system gives the integration of information and physical process, which is an ideal tool to describe continuous and discrete characteristics of the system. Some literatures define the physical laws of controlled object including continuous dynamic and event-driven state as hybrid system [
The recursive
(1) |
where x(t) is the state variable matrix; and A and B are the parameter matrices.
Unlike the time step in [
If there are j control states in (1), the logical variable vector needs to meet the equality constraint of (2) to ensure that there is only one control mode at a time.
(2) |
After flexible load is controlled by at time t, the logical variable vector switches to . The switching follows a certain state transition principle which is made according to the finite state machine (FSM) of controlled device. For flexible load, there are always j equivalent states for choosing at any time.
2) Control Information Model
In order to model and control the information processing, it is necessary to set the number of control information of a primary device in a control period. The reason is that even through the same processing steps, the time consumption of different control information may not be the same due to the processing capacity and the stagnation time of HDCS. Therefore, when the effect of HDCS is taken into account, the primary device will not receive and execute control information by a fixed time interval in a control period but by a fixed number.

Fig. 4 Comparison of control information.
From
(3) |
(4) |
Since the primary device can only execute one group of control information at a time, (5) can be obtained.
(5) |
Besides, the control information state determines the logical variable (t) at which time can be executed. Thus, the in (1) should be written as the sum of .
3) HDCS Model
In HDCS, the location of control information at time is determined by its location of time t and the processing capability of controller. Define as a state target set for the switching target of controller at time t. At time t, the control information is processed in controller n, and it may be transferred to controller or stay at the controller n at time . The switching targets of controllers n and are 2 elements of .
(6) |
(7) |
Considering the processing capacity of every control node, if the controller n (except the GEMS and the actor) can process no more than w control information at the same time, (8) can be obtained.
(8) |
Moreover, the logical relationship between control information and HDCS should be described as (9), which means that: ① when the
(9) |
(10) |
Based on (1) to (10), MPC can be used to optimize flexible loads of ADN. The control problem is to compute the values of all the 0-1 variables at each time interval, which makes the power of loads follow a target to ensure the output of load function in a limited range. The target function is as:
(11) |
where pm is the power of the control state of load m; and Pf is the power target of load. Then, the optimal state switching mode of flexible loads and the processing procedure of control information are obtained.
The MPC method of ADN flexible load is realized by receding horizon optimization (RHO) in [

Fig. 5 Block diagram of MPC for ADN flexible load considering information flow.
According to the prediction of power output of DGs in ADN, the power target of flexible loads and the target function can be obtained at first. Then, the MLD of flexible load, control information transition and HDCS process can be modeled. After transforming MLD to MIQP problem, all the 0-1 variables are solved and the control information can be executed on the loads. Finally, the model for next control period is updated.
In this section, the flexible load model of ADN for refrigerator in [
(12) |
where B1(t) = [B11(t), B12(t), …, B1n(t)
The initial operation states of three loads are [

Fig. 6 HDCS structure of flexible loads in different control areas.
Assume that the controllers and the transmission nodes 2, 3, 4, 6, 7, 9, 10 can process only one control information at the same moment, thus the variable in (8) is set as 1. Set the control step , and the control period . It means that there are 60 steps in one period. Since the control information from GEMS to each load goes through at least 4 HDCS nodes, and spends , the number of control information switching is set as .

Fig. 7 Temperature of refrigerator loads in ADN without information flow in case 1.

Fig. 8 Power consumption of ADN flexible loads without information flow in case 1.
When the information flow of HDCS is added, the inner temperatures of 3 refrigerators are shown in

Fig. 9 Temperature of refrigerator loads in ADN considering information flow in case 1.
Compared with

Fig. 10 Power consumption of ADN flexible loads considering information flow in case 1.
Compared with
Tables III-V list the procedure of 15 control information for three loads in HDCS. It can be seen that: ① all the control information is processed by corresponding controllers and allocated to loads; ② information of three loads all stays in node 2, for example, s6 of Load 1 stays at node 2 when , and it is not sent to node 6 immediately; ③ except the GEMS and load, other HDCS nodes process only one control information; ④ the information does not stay at the ACC and SNCC more than one step. Hence, the information procedure satisfies all constraints.
In HDCS as shown in

Fig. 11 Control system structure of flexible loads in the same control area.
Set to restrict the capability of nodes 2, 3, and 4. The control step and control period are still set as and s, respectively. Assume that the switching number of control information is 15. The inner temperature variation is shown in

Fig. 12 Temperature of refrigerator loads in ADN without information flow in case 2.
This phenomenon is concerned with different HDCS structures. In this case, control information of each moment includes operation states of the three loads, and is sent to each load at the same time. Therefore, only when the information of different values is executed on loads, the operation state of loads may change. In Section IV-A, the temperature changes when any load changes its state.

Fig. 13 Power consumption of ADN flexible loads considering information flow in case 2.
Table VI lists the procedure of 15 control information of HDCS in a control period. The 3 loads are treated together, thus only a group of information is obtained. Compared with Tables IV and V, ① the information process in this HDCS structure is more incompact and the time difference of information arrival and execution is more abundant; ② the control information stays at node 2 for more time, moreover, the information s10 is not transmitted to node 2 immediately after s9 is handled in ACC, and it stays at node 1 for longer time. The reason for this phenomenon is that the demand for control information of loads is reduced. In Section IV-A, any load may change state independently at any time which causes state switching of other loads. Thus, the HDCS structure of Section IV-A has a higher requirement to the proceeding speed and frequency of information, and the situation of staying at the cycle nodes like GEMS and node 2 is infrequent.
Table VII lists the power consumption of three study cases.
If information process is not considered, the control effect is obviously the best no matter what the HDCS structure is. However, HDCS and its information process truly bring negative influence to the primary device, and the best way is to optimize the control problem and dilute the influence. It can also be found from Table VII that loads in one control area operate better than loads in different areas, and the more complex the structure is, the greater the influence is.
ADN control function is based on HDCS. The existing researches mostly focus on the control of the primary system, and seldom pay attention to the influence brought by HDCS to primary devices.
To solve this problem, a CPS model for HDCS is studied. The information flow of ADN control process is analyzed, and the impact of HDCS is concluded from several aspects. The hybrid system based ADN model is built considering information flow, which includes primary device model, control information model, and HDCS model. An MPC method for ADN control is also formed based on this model.
After considering HDCS information flow in modeling and control of ADN, the energy flow of power system and information process of HDCS are integrated. The ADN control process not only optimizes the operation of primary devices, but also optimizes the working modes and time sequences of HDCS.
The modeling and control methods are tested in a case study of ADN flexible load. The simulation result shows that:
1) HDCS not only helps the primary system to realize control target but also brings adverse influence, and different HDCS structures lead to different influences. This indicates that the model of this paper represents the main properties of HDCS correctly.
2) Although HDCS has adverse effects on the primary system, the control target can still be optimized as far as possible. This indicates that the control method of this paper can eliminate the disadvantages of HDCS to an extent.
It can be seen from the test example that the models of this paper successfully integrate the information and physical performance of ADN control process. However, some operation details of ADN are still not contained, and models should be refined to fit more complex scenarios and devices, which will be considered in the future work.
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