# A Cyber Physical Model Based on a Hybrid System for Flexible Load Control in an Active Distribution Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Power CPS Model and Its Application in ADN

#### 2.1. Control Model Based on Hybrid System

#### 2.2. CPS Model and Control in ADN

## 3. ADN Flexible Load Control Based on the Hybrid System Model

#### 3.1. Flexible Load Control Strategy

#### 3.2. Hybrid System Model of Flexible Load

**x**(t) = [x

_{1}(t), x

_{2}(t) … x

_{n}(t)] is the functional index which reflects the loads’ functional demand at time t.

**u**(t) = [u

_{1}(t), u

_{2}(t) … u

_{n}(t)]

^{T}is the control input, and the element u

_{n}(t) $\in $

**U**= {u

_{n}

_{1}, u

_{n}

_{2}… u

_{ni}} denotes that each load contains i kinds of input and can only chose one of these inputs to control the load at time t.

**A**,

**B**

_{2}are n × n coefficient matrixes of the

**x**(t) and

**u**(t), they are determined by load type.

**B**

_{1}(t) = [B

_{11}(t), B

_{12}(t) … B

_{1n}(t)]

^{T}is the outside disturbance which will affect the function index at time t + 1.

**D**= [p

_{1}(t), p

_{2}(t) … p

_{n}(t)] consists of the power of each load at time t, and p

_{n}(t) $\in $

**P**= {p

_{n}

_{1}, p

_{n}

_{2}… p

_{ni}}. The elements of P have a one-to-one correlation with U and denote the power of i-th control inputs of n flexible loads.

^{n}kinds of operation modes that

**u**(t) =

**u**

_{m}= [u

_{1}(t), u

_{2}(t) … u

_{n}(t)]

^{T}and m$\in \text{}${1, 2 … j}. According to Equation (3), set a logical variable for each of the j operation modes respectively, and make up a column vector

**δ**(t) = [δ

_{1}(t), δ

_{2}(t) … δ

_{m}(t) … δ

_{j}(t)]

^{T}, where

**δ**(t)$\text{}\in \text{}${0, 1}, m$\text{}\in \text{}${1, 2 … j}. Each element of

**δ**(t) means a state combination of the loads’ operation mode. When the loads work under this state combination, set the corresponding element of

**δ**(t) to 1, that is

**δ**(t) = 1 ⇔

**u**(t) =

**u**

_{m}.

**δ**(t), and then a n × j matrix

**B**

_{2t}= {B

_{2t}

_{1,}B

_{2t}

_{2}… B

_{2ti}} is deduced. The elements (they are all n-dimension column vectors) of

**B**

_{2t}is calculated by

**B**

_{1}(t) +

**B**

_{2}·

**u**

_{m}which represents the influence factors brought to a functional index which are caused by load disturbance or load control under the operation mode

**δ**

_{m}(t).

**u**(t) of Equation (2) with

**δ**(t), then the meaning of

**D**changes from the description of each load’s power to the description of n loads’ total power under j state combinations. So set a j-dimension row vector

**D**

_{2t}= [P

_{1}, P

_{2}… P

_{m}… P

_{j}] which consists of j possible total powers corresponding to j kinds of state combinations, where P

_{m}=

**D**·

**u**

_{m}.

**δ**(t) can be set to 1. This constrain is written as Equation (4), where

**1**is the n-dimension vector of only 1.

**x**(t) $\in \text{}$[

**a**,

**b**], a MLD based flexible load model Equation (5) is acquired, where

**0**is a n-dimension zero matrix and

_{n}**I**is a n-dimension identity matrix.

_{n}#### 3.3. MPC of Flexible Load

_{δ}, Q

_{x}, Q

_{y}in Equation (6) is weight factors of logical variable, functional index, and total power consumption.

_{1}) means the values of time t are predicted at time t − t

_{1}. So $\sum _{s=1}^{q}{P}_{max-DG-s}(t|t-{t}_{1})$ represents the predictive sum of q DGs’ maximum power of time t; P

_{threshold}(t|t − t

_{1}) is the total consumption of all the common load in the feeder at time t, and this is predicted at time t − t

_{1}too; P

_{f-ref}denotes target of the Feeder Power which is obtained by global EMS; $\sum _{m=1}^{n}{P}_{max-ctrlLoad-m}$ indicates the maximum consumption of n flexible loads.

_{threshold}. If ΔP(t) ≤ P

_{threshold}, the feeder is in the Normal Condition. All the flexible loads run independently to reduce power consumption in a control period T, and Equation (5) should set target points as

**δ**

_{f}=

**δ**

_{min},

**δ**

_{min}→ (P

_{min}= 0) or y

_{f}= P

_{min}= 0.

_{threshold}, the area coordination control will be closed at once. All the flexible loads, DGs in the feeder are controlled to mitigate fluctuation and diminish deviation of the Feeder Power. Then choose a consumption target P

_{m}from the flexible loads’ achievable power set

**D**

_{2t}. The chosen P

_{m}makes $|{P}_{m}-({\displaystyle \sum _{m=1}^{n}{P}_{max-ctrlLoad-m}}-\Delta P(t))|$ to be minimal, and it means that the flexible loads try their best to counteract the power shortage.

**x**(t), and this will lead to a negotiation mechanism between the two sides.

#### 3.4. Case Study

**x**(t) is inner temperature at time t;

**B**

_{1}(t) indicates temperature disturbance caused by outside heat, and it is invariant in this example;

**B**

_{2}denotes the refrigeration effect coefficient matrix; the control input

**u**(t) has two states including Stop and Start, the two states represented by 0 and 1 respectively, that is u

_{n}(t) $\in $ U = {0, 1}, n $\in $ {1, 2, 3}; set the control step Δt = 2 s. Table 4 lists the typical parameters of the three types of cold storages.

**x**(t), and this contributes to the stability.

**x**(t) exceeds the limit. Moreover, by this mode,

**x**(t) always occupies the whole range of the limit and leads to sharp fluctuation.

## 4. Distributed Load Control in the Underpowered Condition

- (1)
- Complex control model of the large scale system. When all loads are controlled together, there are too many possible state switching and combinations, this leads to a huge model for Equation (5). After the model is transformed to MIQP, the scale and complexity of the calculation model expand with the increase of the control period T.
- (2)
- Non-convergence caused by a distinction of model objects. There are always some differences between different kinds of objects like the model parameter and the control period. If these objects are modeled together, the control problem may last too long or even be unsolvable.
- (3)
- The interaction between area coordination controllers is insufficient. The modeling and controlling mostly rely on global EMS, and do not take full advantage of the ability of lower-level controllers.

#### 4.1. Distributed MPC in ADN

#### 4.2. Distributed Control Model and Method of Flexible Load

_{I}(i,j) = 1, i = 1,…,s, j = 1,…,n, the j-th load belongs to the i-th class LCO

_{i}.

_{q}and other s − 1 LCOs. If the q-th LCO

_{q}couples with the p-th LCO

_{p}, the vector’s elements A

_{II-q}(1,p) = 1, p = 1,…,s, p ≠ q, and A

_{II-q}(1,q) = 0.

_{1}(t) + $\cdots $ + y

_{q}(t) + $\cdots $ + y

_{s}(t).

_{q}knows the model of q-th LCO

_{q}including the state model (Equation (1)) and the power consumption model (Equation (2)). Moreover, the Ctrl

_{q}does not consider the rest of s − 1 LCOs. Because of this, other controllers such as the p-th controller Ctrl

_{p}must offer power information at time t to the Ctrl

_{q}, that is y(t) = y

_{1|t}(t) + $\cdots $ + y

_{q|t}(t) + $\cdots $ + y

_{s|t}(t), where y

_{p|t}is the knowable coupling variable, p = 1, …, s, and p ≠ q.

_{p|t}is unable to be obtained. As shown in Figure 12, the coupling information can be replaced by the predictive control results of [t

_{1}− 1, t

_{1}− 1 + T] which are calculated at time t = t

_{1}− 1, and T is the control period.

_{q}operates at time t = t − 1, it predicts the LCO

_{q}’s functional index of t = [t

_{1}, t

_{1}− 1 + T], that is

**x**

_{q}(t

_{1}|t

_{1}− 1)~

**x**

_{q}(t

_{1}– 1 + T|t

_{1}− 1). Then the control input

**u**

_{q}(t

_{1}− 1|t

_{1}− 1)~

**u**

_{q}(t

_{1}− 1 + T − 1|t

_{1}− 1) and the power y

_{q}(t

_{1}− 1|t

_{1}− 1)~y

_{q}(t

_{1}− 1 + T − 1|t

_{1}− 1) also can be obtained. Other controllers like Ctrl

_{p}get the power y

_{p}(t

_{1}− 1|t

_{1}− 1)~

**y**

_{p}(t

_{1}− 1 + T − 1|t

_{1}− 1) too.

**u**(t

_{q}_{1}|t

_{1}− 1), Ctrl

_{q}moves to time t = t

_{1}, and a new control loop begins. At this time, set y

_{p|t}= y

_{p}(t|t

_{1}− 1) for every step of t = [t

_{1}, t

_{1}− 1 + T − 1].

_{1}+ T − 1, there is no y

_{p}(t

_{1}+ T − 1|t

_{1}− 1) that can be assigned to y

_{p|t}

_{1+T-1}. Define constants y

_{f-q}and y

_{f-p}, p = 1, …, s, and p ≠ q. y

_{f-q}and y

_{f-p}consist of a power combination of all the LCOs. The power combination corresponds to a kind of load operation mode

**δ**

_{m}and satisfies ${y}_{f-q}+{\displaystyle \sum _{p=1,p\ne q}^{s}{y}_{f-p}}={P}_{m}$, where the meaning of

**δ**

_{m}and P

_{m}can be found in 3.3. Let y

_{p|t}

_{1+T-1}= y

_{f-p}, in other words, the unknown coupling variable y

_{p|t}

_{1+T -1}is set artificially based on P

_{m}. Besides, in the first loop of control, for time t = [0, T − 1], set y

_{p|t}= y

_{f-p}.

_{p}may not follow the y

_{p|t}which has been sent to Ctrl

_{q}. So, there should be some restrictions in optimal function or constraint to keep the actual trajectory of LCO consistent with the coupling variables of the coupled controllers.

_{1}, t

_{1}+ T], minimizing the deviation between y

_{q}(t) and y

_{q|t}, gives Equation (8).

_{q}(t) and y

_{q|t}of any step during the control period t = [t

_{1}, t

_{1}+ T] not larger than the maximal deviation in the last control period t = [t

_{1}− 1, t

_{1}− 1 + T]. That is Equation (9).

_{q}includes the functional index deviation J

_{x}, load consumption deviation J

_{y}, and coupling variable deviation J

_{y}.

_{x}keeps x

_{q}(t) tracing the target x

_{f-q}in the control period t = [t

_{1}, t

_{1}+ T], that is Equation (10).

_{y}contains coupling relationship of LCO

_{q}and LCO

_{p}, and reflects the difference of total consumption and its target. Define matrix $\mathit{Y}\in {\mathbb{R}}^{s\times 1}$, $\mathit{Y}={[{y}_{1|t},{y}_{2|t},\cdots ,{y}_{s|t}]}^{\text{'}}$ is the coupling information set of time t which should have been sent by s controllers to each other. Also the load consumption deviation of LCO

_{q}is shown as Equation (11).

_{yq}has been presented in Equation (8). So the optimal function is Equation (12).

#### 4.3. Case Study

_{1}, Load

_{2}, Load

_{3}are classified to three LOCs of LOC

_{1}, LOC

_{2}, LOC

_{3}. Based on Table 3 and Equations (5) and (9), three MLD models of LOCs are built. Set the total power consumption target P

_{m}= 356 kW, then the three optimal functions can be obtained by Equation (12). The models and optimal function are controlled 100 times according to the procedure in Figure 13.

_{3}, it not only operates steadily, but also works at a lower temperature.

_{3}is the largest load, and the centralized mode considers the optimization from the overall model, so the action of Load

_{3}should be diminished and the lower loads work more to counteract disturbance. However, in the distributed mode, the controller manages only one load, and does not need to consider other problems.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CPS | Cyber Physical Systems |

Power CPS | CPS in Power Systems |

ADN | Active Distribution Network |

DG | Distributed Generation |

MPC | Model Predictive Control |

EMS | Energy Management System |

RHO | Receding Horizon Optimization |

MLD | Mixed Logical Dynamical |

MIQP | Mixed Integer Quadratic Programming |

RMS | Root Mean Square |

LCO | Load Controlled Object |

Ctrl_{q} | The q-th Controller |

## References

- Kyoung, D.K.; Kumar, P.R. Cyber-physical systems: A perspective at the centennial. Proc. IEEE
**2012**, 100, 1287–1380. [Google Scholar] [CrossRef] - Edward, A.L.; Sanjit, A.S. Introduction to Embedded Systems: A Cyber-Physical Systems Approach; China Machine Press: Beijing, China, 2012. [Google Scholar]
- Eidson, J.; Edward, A.L.; Matic, S. Time-Centric Models for Designing Embedded Cyber-Physical Systems; University of California, Berkeley, Technical Memorandum: Berkeley, CA, USA, 2009. [Google Scholar]
- Radha, P. Cyber-Physical Systems: Close encounters between two parallel worlds. Proc. IEEE
**2010**, 98, 1363–1366. [Google Scholar] - Derler, P.; Edward, A.L.; Vincentelli, A.S. Modeling cyber-physical systems. Proc. IEEE
**2011**, 100, 13–28. [Google Scholar] [CrossRef] - Krishna, S.; Radha, P. Cyber-physical system framework for future aircraft and air traffic control. In Proceedings of the 2012 IEEE Aerospace Conference, Big Sky, MT, USA, 3–10 March 2012; pp. 1–9.
- Du, S.; Wang, X.; Xie, G.; Cai, T.; Zhang, Q. Reliability evaluation of substation automation system based on IEC61850. Power Syst. Prot. Control
**2012**, 5, 32–41. [Google Scholar] - Yu, B.; Guo, C.; Wang, Y.; Zhang, L. Research on the reliability of the power system considering impacts of the information system. Power Syst. Prot. Control
**2013**, 7, 7–13. [Google Scholar] - Li, H.; Qiu, R.C.; Wu, Z. Routing in cyber physical systems with application for voltage control in microgrids: A hybrid system approach. In Proceedings of the 32nd International Conference on Distributed Computing Systems Workshops, Macau, China, 18–21 June 2012; pp. 254–259.
- Yoshihiko, S.; Koo, T.J.; Hiroaki, E.; Takuya, Y.; Takashi, O.; Takuji, U.; Takashi, H. A hybrid system approach to the analysis and design of power grid dynamic performance. Proc. IEEE
**2012**, 1, 225–239. [Google Scholar] - Hiskens, I.A. Power system modeling for inverse problems. IEEE Trans. Circuits Syst.
**2004**, 3, 539–551. [Google Scholar] [CrossRef] - Davis, C.M.; Tate, J.E.; Okhravi, H.; Grier, C.; Overbye, T.J.; Nicol, D. SCADA cyber security testbed development. In Proceedings of the 38th North American Power Symposium, Carbondale, IL, USA, 17–19 September 2006; pp. 483–488.
- Sun, C.-C.; Hong, J.; Liu, C.-C. A co-simulation environment for integrated cyber and power systems. In Proceedings of the IEEE International Conference on Smart Grid Communications, Miami, FL, USA, 1–5 November 2015; pp. 133–138.
- Georg, H.; Muller, S.C.; Dorsch, N.; Rehtanz, C.; Wietfeld, C. INSPIRE: Integrated co-simulation of power and ICT systems for real-time evaluation. In Proceedings of the IEEE International Conference on Smart Grid Communications, Vancouver, BC, Canada, 21–24 October 2013; pp. 576–581.
- Lin, H.; Veda, S.S.; Shukla, S.S.; Mili, L.; Thorp, J. GECO: Global event-driven co-simulation framework for interconnected power system and communication network. IEEE Trans. Smart Grid
**2012**, 3, 1444–1456. [Google Scholar] [CrossRef] - Mallouhi, M.; Al-Nashif, Y.; Cox, D.; Chadaga, T.; Hariri, S. A testbed for analyzing security of SCADA control systems (TASSCS). In Proceedings of the IEEE PES Innovative Smart Grid Technologies, Anaheim, CA, USA, 17–19 January 2011; pp. 1–7.
- Zhao, H. Hybrid Modeling and Analysis of Power Systems. Ph.D. Thesis, North China Electric Power University, Baoding, China, 2004. [Google Scholar]
- Sayak, B. Cyber-Physical Modeling, Analysis, and Optimization—A Shipboard Smart Grid Reconfiguration Case Study. Ph.D. Thesis, Kansas State University, Manhattan, Kansas, 2004. [Google Scholar]
- You, Y.; Liu, D.; Yu, W.; Chen, F.; Pan, F. Technology and its trends of active distribution network. Autom. Electr. Power Syst.
**2012**, 18, 10–16. [Google Scholar] - Yu, W.; Liu, D.; Yu, N. Feeder control error and its application in coordinate control of active distribution network. Proc. CSEE
**2013**, 33, 108–115. [Google Scholar] - Jia, H.; Qi, Y.; Mu, Y. Frequency response of autonomous micro grid based on family-friendly controllable loads. Sci. China Technol. Sci.
**2013**, 56, 693–702. [Google Scholar] [CrossRef] - Faran, A.; Tomasz, T.; Colin, N. Model predictive control for market-based demand response participation. IFAC Proc. Vol.
**2014**, 3, 11153–11158. [Google Scholar] - Tullio, F.; Marco, L.; Della, V. Real-time modeling for direct load control in cyber-physical power systems. IEEE Trans. Ind. Inform.
**2011**, 4, 689–698. [Google Scholar] - Liu, D.; Sheng, W.; Wang, Y.; Lu, Y.; Sun, C. Key technologies and trends of cyber physical system for power grid. Proc. CSEE
**2015**, 14, 3522–3531. [Google Scholar] - Zheng, H.; Jian, J.; Yang, L.; Quan, R. A deterministic method for the unit commitment problem in power systems. Comput. Oper. Res.
**2016**, 66, 241–247. [Google Scholar] [CrossRef] - Marcovecchio, M.G.; Novais, A.Q.; Grossmann, I.E. Deterministic optimization of the thermal Unit Commitment problem: A Branch and Cut search. Comput. Aided Chem. Eng.
**2014**, 67, 53–68. [Google Scholar] [CrossRef] - Zaman, F.; Elsayed, S.M.; Ray, T.; Sarker, R.A. Evolutionary algorithms for power generation planning with uncertain renewable energy. Energy
**2016**, 112, 408–419. [Google Scholar] [CrossRef] - Khodr, H.; Halabi, N.; García-Gracia, M. Intelligent renewable microgrid scheduling controlled by a virtual power producer: A laboratory experience. Renew. Energy
**2012**, 48, 269–275. [Google Scholar] [CrossRef] - Yu, W.; Liu, D.; Huang, Y. Operation optimization based on the power Supply and storage capacity of an active distribution network. Energies
**2013**, 6, 6423–6438. [Google Scholar] [CrossRef] - You, Y.; Liu, D.; Zhong, Q.; Yu, N. Multi-time scale coordinated control of distributed generators based on active distribution network. Autom. Electr. Power Syst.
**2014**, 9, 192–198. [Google Scholar] - Chen, F.; Liu, D.; Chen, Y. Hierarchically Distributed Voltage Control Strategy for Active Distribution Network. Autom. Electr. Power Syst.
**2015**, 39, 61–67. [Google Scholar] - Weng, J.; Liu, D.; Luo, N. Distributed processing based fault location, isolation, and service restoration method for active distribution network. J. Mod. Power Syst. Clean Energy
**2015**, 3, 494–503. [Google Scholar] [CrossRef] - Alberto, B.; Manfred, M.; Della, V. Control of systems integrating logic, dynamics, and constraints. Automatica
**1999**, 35, 407–427. [Google Scholar] - William, B.D. Distributed Receding Horizon Control of Multi-Agent Systems. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, USA, 2004. [Google Scholar]

**Figure 6.**The function indexes comparison of refrigerator loads under normal condition; (

**a**) flexible group; (

**b**) traditional group.

**Figure 8.**The exchange power of ADN feeder and control areas under normal condition; (

**a**) feeder and external system; (

**b**) feeder and areas.

**Figure 9.**The total power consumption comparison of ADN flexible loads in the underpowered condition; (

**a**) flexible group; (

**b**) traditional group.

**Figure 10.**The comparison of the ADN Feeder Power in underpowered condition; (

**a**) state switching; (

**b**) power consumption.

**Figure 11.**Comparison of centralized and distributed ADN load control in underpowered condition; (

**a**) centralized control; (

**b**) distributed control.

**Figure 14.**The function indexes comparison of centralized and distributed control; (

**a**) centralized control; (

**b**) distributed control.

**Figure 15.**The state switching and power consumption of distributed control; (

**a**) state switching; (

**b**) power consumption.

**Table 1.**The problems of Active Distribution Network and solution based on Cyber Physical Systems (CPS).

Problem | Solution | ||
---|---|---|---|

1 | Lack of the optimization of state switching which occurs in the primary system; | Discrete Model | Mixed Logical Dynamical Model |

2 | The influence of information flow is not considered in the power system operation; | Logical Model | |

3 | The optimization model is not predictive and cannot be updated in real time; | Model Predictive Control (Receding Horizon Optimization) |

Condition | Control Level | Controlled Load | Load Target | Feeder Target |
---|---|---|---|---|

Normal | Area coordination controller | Flexible loads of each control area | Minimum consumption | Sustain Area Power |

Underpowered | Global Energy Manage System (EMS) | All the flexible loads in feeder | Sustain total consumption | Sustain Feeder Power |

Name | Type | Location | Max Power | Target Power | Note |
---|---|---|---|---|---|

DG1 | Green energy | Node 14 | 350 kW | 350 kW | Make full use of clean energy |

DG2 | Energy storage | Node 12 | 300 kW | 265 kW | |

DG3 | Green energy | Node 7 | 400 kW | 365 kW | |

DG4 | Green energy | Node 11 | 500 kW | 500 kW | |

DG5 | Energy storage | Node 8 | 600 kW | 570 kW | |

Load_{1} | Flexible load | Node 13 | 122 kW | - | Controllable loads |

Load_{2} | Flexible load | Node 6 | 234 kW | - | |

Load_{3} | Flexible load | Node 10 | 370 | - | |

P_{feeder} | Exchange power | 10 kV Bus | - | 300 kW | From outside to feeder |

P_{area}_{1} | Exchange power | Node 13 | - | 15 kW | From feeder to Area1 |

P_{area}_{2} | Exchange power | Node 4 | - | 15 kW | From feeder to Area2 |

P_{area}_{3} | Exchange power | Node 2 | - | 20 kW | From feeder to Area3 |

Name | Type | A | B_{1} | B_{2} | D | x(t) |
---|---|---|---|---|---|---|

Load_{1} | 1000 ton | 0.99 | 0.1 °C | −0.24 | 122 kW | [−1, 1] °C |

Load_{2} | 2000 ton | 0.98 | 0.2 °C | −0.36 | 234 kW | [−5, −3] °C |

Load_{3} | 2500 ton | 0.97 | 0.3 °C | −0.5 | 370 kW | [−1.5, 0.5] °C |

Name | Group | Power | Working Time | RMS/kW | Energy Conservation |
---|---|---|---|---|---|

Load_{1} | flexible | 2.71 kW·h | 80 s | 77.16 kW | 11.15% |

traditional | 3.05 kW·h | 90 s | 81.84 kW | ||

Load_{2} | flexible | 9.88 kW·h | 152 s | 203.99 kW | 5% |

traditional | 10.4 kW·h | 160 s | 209.30 kW | ||

Load_{3} | flexible | 12.54 kW·h | 122 s | 288.98 kW | 1.6% |

traditional | 12.75 kW·h | 124 s | 290.44 kW |

Group | Power Consumption | Max Load Difference | RMS | RMS Deviation |
---|---|---|---|---|

flexible | 24.81 kW·h | 370 kW | 462.81 kW | 30% |

traditional | 25.99 kW·h | 604 kW | 520.18 kW | 46% |

Control | Power Consumption | Max Load Difference | RMS | Target Deviation | Computing Time |
---|---|---|---|---|---|

Centralized | 24.81 kW·h | 370 kW | 462.81 kW | 30% | 1.847 s |

Distributed | 25.17 kW·h | 726 kW | 486.98 kW | 37% | 1.053 s |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Liu, D.; Sun, C.
A Cyber Physical Model Based on a Hybrid System for Flexible Load Control in an Active Distribution Network. *Energies* **2017**, *10*, 267.
https://doi.org/10.3390/en10030267

**AMA Style**

Wang Y, Liu D, Sun C.
A Cyber Physical Model Based on a Hybrid System for Flexible Load Control in an Active Distribution Network. *Energies*. 2017; 10(3):267.
https://doi.org/10.3390/en10030267

**Chicago/Turabian Style**

Wang, Yun, Dong Liu, and Chen Sun.
2017. "A Cyber Physical Model Based on a Hybrid System for Flexible Load Control in an Active Distribution Network" *Energies* 10, no. 3: 267.
https://doi.org/10.3390/en10030267