active load management strategy considering...

23rd International Conference on Electricity Distribution Lyon, 15-18 June 2015

Paper 1504

CIRED 2015 1/5

ACTIVE LOAD MANAGEMENT STRATEGY CONSIDERING FLUCTUATION CHARACTERISTICS OF INTERMITTENT ENERGY

Fei CHEN Dong LIU Qingsheng LI Shanghai Jiao Tong University– China Shanghai Jiao Tong University– China China Southern Power Grid - China [email protected] [email protected] [email protected]

ABSTRACT The penetration of distributed generations (DGs) in distribution network has been severely restricted as the power fluctuation caused by intermittent energy. Direct load control (DLC) offers an efficient resource for power fluctuation stabilizing and load shifting with the help of advanced metering infrastructure (AMI) in active distribution network (ADN). This paper proposes two quantified indexes for controllable loads to represent the configuration status of ADN. Then the control strategy of active load management for ADN is illustrated in details based on the model of thermostatically controlled loads (TCLs). The strategy makes full use of the controllable loads to realize optimal operation for ADN through multi-layer control. Finally, the demonstration application simulation of active load control in ADN in China sponsored by the National High-tech R&D Program is presented which validates the effectiveness of the proposed solutions.

INTRODUCTION The power fluctuation caused by renewable energy such as wind and solar has severely restricted the penetration of distributed generations in distribution network. Most researchers focus on the usage of energy storage systems to suppress the fluctuation caused by intermittent energy in order to improve the compatibility for intermittent energy in distribution network [1]. However, the large-scale application of energy storage system in distribution network has been restricted by the considerable construction cost. Demand response (DR) especially direct load control (DLC) offers an efficient and adjustable resource for distribution network and reduce investment at the same time [2-3]. ADN is a distribution network that can improve asset utilization and DGs’ penetration by effective management on distributed energy, controllable load and DFACTS equipment. In ADN, distribution system operators (DSO) can capture real-time load data by AMI and make the customer device work in a more proper way with the help of smart socket, controllable user terminal and intelligent infrared controller [4]. The active load control in ADN can optimize system operation by stabilizing power fluctuation and load shifting. This paper puts forward some quantified indexes for load interconnected to ADN to represent the configuration status of loads. Moreover, Multi-layer control strategy of

active load management is proposed based on respective model of thermostatically controlled loads (TCLs). The feasibility and effectiveness of the active load management strategy are verified with simulation results of the demonstration located in Qingzhen, China.

THE QUANTIFIED INDEXES FOR TCLS IN ADN DLC technology is suitable for thermostatically controlled loads (TCLs) as its good storage properties. Different characteristics and capacity configurations of TCLs will affect the performance of ADN operation significantly. Two quantified indexes are proposed in this paper, list as follows: index of penetration for TCLs，index of source-load percentage.

Index of penetration for TCLs Index of penetration for TCLs TCL is defined as:

,

1

,1

100%

nrate

TCL ii

TCL n

L avg ii

P

P

(1)

Here, n is the number of nodes. ,rate

TCL iP is the rated power for TCLs. If the node doesn’t have access to TCLs, its value is 0. ,L avg iP is the average value of the load at i -th node, which include both controllable and uncontrollable loads.

Index of Source-Load percentage Index of source-load percentage is defined as:

, , ,

, ,

,

/ 100%

( ) ( )100%

Inter rates l i DG i TCL i

Inter InterDG i DG i

rateTCL i

R P P

P T T P TP

(2)

Here, , ( )InterDG iP T is the power supplied by intermittent

energy at time T . ,Inter

DG iP is the power variation during

interval T . ,rate

TCL iP is the rated power for TCLs at the i -

th node. ,Inter

DG iP can be obtained by Fourier transformation and filtering. When there is no need for an accuracy result, formula (2) can be simplified as follow.

,,

,

100%rate

DG is l i rate

TCL i

PR

P (3)


Paper 1504

CIRED 2015 2/5

Here ,rate

DG iP is the rated capacity of DGs at i -th node.

MODELING METHODOLOGIES FOR TCLS

TCLs have become a new focus of research on demand response as its excellent storage characteristics. In this section, we will establish separate TCL model according to the multi-layer strategy. The short-term power fluctuation model is proposed for simulation and the average power model is for optimization.

Short-term power fluctuation model

The short-term power fluctuation model is used in regional control to reflect the dynamic response characteristic of the load. It is suitable for regional control as it cares about the power variation. This paper use the standard hybrid-system model for short-term power fluctuation model which can reflect the dynamic process of TCLs in a proper way [5].

0( ) 1 ( ( ) ( ) ( ) )

1,2...

roomroom i i i

i i

T tT t T t s t PR

t C R

i N

，

(4)

Here, 0 ( )T t is outdoor temperature, ( )room

T t is indoor temperature,

iC is thermal capacitance,

iR is thermal

resistance and i

P is the rated power for i

TCL . It is positive for heating device and negative for cooling device. The binary signal ( )

is t is the state of

iTCL . The

unit is in the ON state at time t if ( )=1i

s t , and in the OFF state if ( )=0

is t . And ( )

is t can be expressed as:

min,i

max,i

1 ( - ) 0, ( ) ( )

( ) 0 ( - ) 1, ( ) ( )

( - )

i t room

i i t room

i t

when s t T t T t

s t when s t T t T t

s t when other

(5)

min,i ,

max,i ,

( ) ( )

( ) ( )set i db

set i db

T t T t T

T t T t T

(6)

Here ( )set

T t is the set point, db

T is the dead-band, which

means max,i ( )T t and min,i ( )T t is the upper limit and lower

limit for i

TCL . t is infinitesimal delay, it can also be the

time step in discrete-time simulation.

Average power model

The foregoing proposed short-term power fluctuation model is too cumbersome which will lead to two problems. Firstly, the model contains both continuous variables (e.g. temperature) and discrete ‘on/ off’ binary variables. Secondly, each TCL in the grid is modelled in separate, which will cause the curse of dimensionality when solving dynamic response for global optimization. The only thing we care about is the average power during a period when taking global optimization. So the average power model is proposed in this paper as a more

convenient abstraction of accurate TCL model. The model is mainly used to optimize the operation depends on the forecasting data. The dynamics of TCLs is described in eq.4. As can be seen from the equation, we can choose an appropriate

,avg iP that will maintain the temperature at the set-point

,set iT , which can be described as:

0 , ,( ) 1 ( ) 0room

set i avg i i

i i

T tT T P R

t C R

(7)

In this paper, we will define the power ,avg iP as the average

power, which can be given by: , 0

, ,

( ) ( )( , ) set i

avg i set i

i

T t T tP t T

R

(8)

ACTIVE LOAD MANAGEMENT STRATEGY

In this section, a multi-layer active load management strategy is proposed on the basis of the foregoing models. The strategy takes TCLs as main controllable devices. A control method based on incentives is applied to the strategy considering both users’ comfort and load adjustment. The framework for the strategy is shown in fig.1.

Fig.1 Framework for Active Load Management Strategy

The active load management strategy is combined by regional control and global optimization. The global optimization will calculate the optimum set temperature

, ( )set i

T t and regional target power ( )Tar

P t depends on global information of ADN. It will realize the load shifting during a long period. The regional control strategy will suppress the regional power fluctuation during a relatively short period based on the local measurements and load management.

Strategy for regional control

The strategy for regional control is to track the dynamic behaviour of TCLs by controlling the statement (ON/OFF) of the device. This control method has good real-time performance and scalability. Besides, it requires relatively less controllable resources for power fluctuation stabilizing. Before details of the control strategy, the regional load regulation margin index is to be introduced. This index changes over time and describes the adjustment range of loads. It plays an important role in the strategy.

SCADA

Bus Bar

TCL TCL

intelligent infrared controller

Control error

Advanced Distribution Management System

Measurements for power exchange Control

Signal

Original data: Network topology for ADN; Forecasts for Loads and Renewable energy; Parameters For TCL

MV

110kV/10kVOLTC

Uncontrollable Loads

Renewable Energy

Uncontrollable Loads

Renewable Energy

Temperature set-point for TCLTarget for power exchange

Control error+-

intelligent infrared controller

ControlSignalTCL

state

Controllable user terminal

TCLstate

Customer Requirement

global optimization

regional control

errP

,set optT

TarP

*region

P

,set cstmT

errP

,set optT


Paper 1504

CIRED 2015 3/5

Regional load regulation margin index The regional load regulation margin index will be used to guide local load adjustment. Taking into account that the devices for regional load regulation are microcontrollers or PCs, the control index will be calculated by a relatively simple logic. Depends on former short-term power fluctuation model, if the temperature in the house min,i max,i[ , ]roomT T T and the state of the TCL is ON, it means that this TCL can be turned off. Vice versa, if the temperature in the house

min,i max,i[ , ]roomT T T and the state of the TCL is OFF, it means that this TCL can be turned on. In order to avoid the frequent switching when a TCL is under control we add a control interval. Any TCLs in that interval cannot be controlled. The states of a TCL and its switching conditions are shown in fig.2 described as state machine.

Fig.2 States and Switching Conditions for TCLs

The change of states depends on short-term power fluctuation model proposed by eq.4-6. The regional load regulation margin index describes the adjustment capability for TCLs. It can be described as:

0

1

( , ) ( , )

( , ) ( , )i

i

positive is t

negative is t

P g t P g t

P g t P g t

( )

( )

(9)

S.T. ,min ,now ,max 1...i i i iU U U U i N (10)

Here, positiveP is the maximum power that can be increased

and negativeP is the maximum power that can be decreased.

g is the network topology constraints. Assume G is the set for solution space that satisfies the network topology constraints, then any ( )P g requires g G . is the vector addition considering flow constraints. When all TCLs are connected to the same bus or the topology can be neglected, formula (9) can be simplified as:

0

1

( ) ( )

( ) ( )i

i

positive is t

negative is t

P t P t

P t P t

( )

( )

(11)

,miniU and ,maxiU in eq.10 is the minimum and maximum voltage that is allowed at i -th node. ,nowiU is the voltage at i -th node before adjustment, iU is the change for

voltage after adjustment. iU can be approximated by:

(12)

Here, C is the collection of wires between AP for TCLs and the balance node. Finally, we can get the regional load regulation margin index considering constrains as:

( ) [ max( ( )),max( ( ))]RLRM negative positiveIdex t P t P t (13)

Here, max( ( ))negativeP t describes the maximum power

can be decreased, and max( ( ))positiveP t describes the maximum power can be increased. Control Strategy When the penetration of distributed generations become larger, the power fluctuation along the feeder caused by intermittent energy will increase at the same time. The usage of DLC technology can replace energy storage to stabilize the devices power fluctuation by reasonable regulation on TCLs. The payload within a region when TCLs are under control can be described as:

* ( ) ( + )i j m nregion TCL NL W V

i j m nP P P P P (14)

Here, iTCLP is the average power for iTCL .

jNLP is the

active power of uncontrollable loads andmWP ,

nVP are the active power offered by wind turbine and photovoltaic. The goal of the strategy is to stabilize the fluctuation in the region. It also means that keep the payload *

regionP at

TarP during a short period sT . sT can be set from 15min to 1hour according to the control accuracy requirements.

TarP is gotten by global optimization, which will be discussed in next section. The control target for TCLs can be described as:

* *

*

*

( )

( ) ( ) ( ) ( ) ( )

max( ( )) max( ( ))

max( ( )) max( ( ))

err

Tar region Tar region RLRM

negative Tar region negative

positive Tar region positive

P t

P t P t P t P t Idex t

P t P P P t

P t P P P t

(15)

The number of devices involved in load control is: ( )/ rateN ceil P t P ( ) (16)

rateP is the rated power for each TCL. The control order for TCLs is first-in-first-out in order to avoid frequent switching for device status, as shown in fig.3.

Fig.3 Control Order for TCLs

Can be turned on Can be turned off

Uncontrollable

ON OFF

*( )/( ) )i i

i

U S U R jX

C

(

first infirst out

first infirst out

TCLoff-1

TCLoff-2

TCLoff-3

TCLoff-4

TCLoff-5 TCLon-5

TCLon-4

TCLon-3

TCLon-2

TCLon-1

out

in

out

in

QUEUE

QUEUE

TCLuc-1TCLuc-2TCLuc-3TCLuc-4

max,i( ) ( )( - ) 1

room

i t

T t T ts t

min,i max,i[ , ]( 2)

room

i

T T TState unctrl s

min,i max,i[ , ]( ) 1( - ) 0

room

i

i inv

T T Ts ts t T

min,i max,i[ , ]( ) 0( - ) 1

room

i

i inv

T T Ts ts t T

min,i( ) ( )( - ) 0

room

i t

T t T ts t

min,i max,i[ , ]( 0)

room

i

T T TState OFF s

min,i max,i[ , ]

( 1)room

i

T T TState ON s

invT invT

( 0)i

State OFFs ( 1)i

State ONs

( 2)i

State uncontrollables Uncon or

CIRED 2015

Thefig.2regulation margin regional control

Strategy for globalAglobal during a longfollowsStep1P tStepon the forecasting

Stepthrough controllable pStep4.maximum

change to

Here,limitedStep

CIRED 2015

The state of all TCLfig.2, which will also influence the rregulation margin regional control

Fig.4 The

Strategy for globalA relatively simpleglobal optimizationduring a longfollows: Step1. Obtained the

, ( )iLoad fcP t and renewable energ

Step2. Calculate the average poweron the forecasting forecasting data

95 95

0 0t Load Rgn t DG RgnavgP

Step3. Get customer through controllable payload *

regionPStep4. Calculate the maximum power

change to ,set cstm xT T

ccP

Here, nowt is the time limited by considering

P is positive, and negative when Step5. Calculate

, xset optT

where P

Collect payload within the region

Calculate control target for TCLs

Decided

23

state of all TCLs will keep updating as shown in , which will also influence the r

regulation margin index. regional control strategy is shown in

The Flowchart for

Strategy for global optimizationsimple heuristic

optimization in order to during a long period. Calculation process is

Obtained the forecasting( ) and renewable energ

Calculate the average powerforecasting data, in this paper there will be one

data every 15 minutes95 95

, ,0 0

i j

i k j k

Load fc DG fct Load Rgn t DG Rgn

P t P t

Get customer requirementthrough controllable user

regionP within the regionCalculate the power

power can be changed

, xset cstm xT T based on *

region now avgP P t P

x k

set now set cstm xcc

TCL Rgn

T T TP

is the time whenconsidering users

is positive, and negative when Calculate the target set point

,,

,

x

x

x

x k

set cstm x ccset opt

set cstm x cc

TCL Rgn

T T when P P

T T when P P

where P

Begin



t=1

Calculate the number of deviceinvolved in load control

Decided the control signal sequence

Send control commands

Time delay

end

?st T

23rd International Conference on Electricity Distribution

will keep updating as shown in , which will also influence the r

. The algorithm flowchart for is shown in fig.4.

lowchart for Regional Control

optimization heuristic algorithm in order to realize the load shifting

Calculation process is

forecasting data for and renewable energy , ( )

jDG fcP tCalculate the average power in region

, in this paper there will be one minutes:

95 95

, ,0 0

( ) ( )

24

i j

i k j k


P t P t

hour

requirement ,set cstmT terminal. And get current

region kRgn throughpower want to be changed

can be changed Pbased on formula (

( )region now avgP P t P

, ,x xset now set cstm x

x

T T TR

when step3 begins.users’ comfort. It is positive

is positive, and negative when P isset point ,set optT

x k

set cstm x cc

Ltset cstm x cc

Ltx

TCL Rgn x

T T when P P

T T when P P

TR


Read

optimization


number of devices involved in load control

the control signal sequence

Send control commands

Read

Update

keep updating

*regionP

( )P t

International Conference on Electricity Distribution

will keep updating as shown in , which will also influence the regional load

lgorithm flowchart for ig.4.

ontrol Strategy

is proposed forrealize the load shifting

Calculation process is shown

data for both loads, ( )DG fcP t during a day

in region kRgn based , in this paper there will be one

, ,( ) ( )i j

i k j k


P t P t

(1

xset cstm in region RgnAnd get current

Rgn through AMR. want to be changed P

ccP when ,set nowTformula (8).

region now avgP P t P (

x xset now set cstm xT T T (

step3 begins. xT will be It is positive when

P is negative. , xset optT

set cstm x cc

set cstm x cc

T T when P P

T T when P P

(

Read

global optimization

Update

keep updating

( )RLRMIdex t

( )RLRMIdex t

TarP


will keep updating as shown in egional load

lgorithm flowchart for

is proposed for realize the load shifting

shown as

loadsduring a day.

Rgn ased , in this paper there will be one

( ) ( )P t P t(17)

kRgnAnd get current

P and , xset nowT

(18)

(19)

will be when

(20)

Step6

P P t P t

Step1 and Step2 can the temperature being set by is unpredictable,intervals offoregoing

DEMONSTRATIONThe demonstration application of management with is electric school campus can realize DLC smart infrared controllerthe process of active load managein figcollected by ADMS is for pinformation collected by ALMS is for r

FigSeveral simulation results proposed by the scalepaperschool holidaysis relatively small. turbinesparameters for TCLs

1) Case1: Before the simulation for the strategiesinfluences on direct with the i

(a)

110

110kVOLTC


Step6. Calculate

( ( , ) ( , ))

k i j

i k j k

x k

Tar Load fc now DG fc nowLoad Rgn DG Rgn

avg x now set opt avg x now set nowTCL Rgn

P P t P t

P t T P t T

Step1 and Step2 can the temperature being set by is unpredictable,intervals of sTforegoing one.

DEMONSTRATIONhe demonstration application of anagement located in Qinzhen, Guiyang

with 300kW photovoltaic presented as

electric school campus can realize DLC mart sockets, controllable user terminal

infrared controllerthe process of active load managein fig.5. It should be noticed that the information collected by ADMS is for pinformation collected by ALMS is for r

Fig.5 Demonstration Project of ADN Several simulation results proposed voltageby the scale of the demonstrationpaper mainly concentratschool holidays.s relatively small.

turbines and 100kparameters for TCLs

3600 / 0.024 /C J C R C W

i dbP W T C) Case1: Before the simulation for the strategies

influences on direct with the index of

Control Effect Fig.6 Active Power of

Bran-ch box

110kV Substation ShuiTang

ShuiPei FeederkV/10kVOLTC

WTP(250kW)

L1

L10L11

L

TCL1

intelligent infrared

controller

controllable user terminal

Smart socket

TCL120

Smart socket

… …

Calculate the target payload in the region

, ,

, , , ,

( ) ( )

( ( , ) ( , ))

k i j

i k j k


avg x now set opt avg x now set now

P P t P t

P t T P t T

Step1 and Step2 can be in operationthe temperature being set by is unpredictable, Step3-Step6 will be activate

sT . The definition of

DEMONSTRATION he demonstration application of

ocated in Qinzhen, GuiyangW photovoltaic, 250kW

presented as fig.5. The dormitory area in Hongfeng electric school campus can realize DLC

controllable user terminalinfrared controllers. The informationthe process of active load manage

It should be noticed that the information collected by ADMS is for pinformation collected by ALMS is for r

Demonstration Project of ADN Several simulation results are

voltage control strategyof the demonstration

concentrates . By that time

s relatively small. There are00kW photovoltaic

parameters for TCLs can be listed 3600 / 0.024 /C J C R C W

1000 0.5i dbP W T C ) Case1: Before the simulation for the strategies

influences on direct load control ndex of source-load percentage

for TCLs (b) DifferenActive Power of Feeder u

(5

Hongfeng electrical school campus

Branch box

Branch box

Branch box

PV1(100kW)

L2

L3

L4 L5 L6 L7

L12L13

L14 L15 L16controllable user

terminal

ALMS

Lyon, 15-

payload in the region

, ,

, , , ,

( ) ( )

( ( , ) ( , ))

k i j

i k j k

x x



P P t P t

P t T P t T

operation once a day. the temperature being set by the i -th TCL

Step6 will be activateThe definition of sT is the same as

he demonstration application of ocated in Qinzhen, Guiyang

250kW wind turbinesThe dormitory area in Hongfeng

electric school campus can realize DLC controllable user terminals

The information and control signal in the process of active load management are

It should be noticed that the information collected by ADMS is for power forecastinginformation collected by ALMS is for real-

Demonstration Project of ADN Active Load are reported to validate the

control strategy in this sectionof the demonstration, the simulation

on ShuiPei feederBy that time the load of

are 120 TCLs, W photovoltaic in the region. The

listed as: 3600 / 0.024 /C J C R C W

1000 0.5i dbP W T C

) Case1: Before the simulation for the strategiescontrol was discussed combine oad percentage.

Different Disturbance Feeder under Different

…

PV3(5*20kW)

…

PV25*20kW)

Hongfeng electrical school campus

…

…

HongPei FeederL8 L9

L11L11

L11

-18 June 2015

Paper 1504

4

payload in the regionkTarP

, ,

, , , ,

( ) ( )

( ( , ) ( , ))

k i j

x x

Tar Load fc now DG fc now


P P t P t

P t T P t T (21

once a day. But ath TCL at future time

Step6 will be activated asT is the same as

he demonstration application of active load ocated in Qinzhen, Guiyang is involve

ind turbines, which The dormitory area in Hongfeng

electric school campus can realize DLC with help of and intelligent

and control signal in are also presented

It should be noticed that the information forecasting and the

-time control.

oad Management reported to validate the

in this section. Limited , the simulation in this ShuiPei feeder during

ShuiPei feeder 120 TCLs, 250kW wind

in the region. The

3600 / 0.024 /C J C R C W

1000 0.5P W T C ) Case1: Before the simulation for the strategies

s discussed combine

isturbance Values ifferent Conditions

Hydropower Station

（10000kW

…

…

110kV Substation QingZhen

ZhenWu Feeder

HongPei Feeder

L11

L11

Control Signal From Active Distribution Management System (ADMS)

Information Collection

Control Signal From Active Load Management System (ALMS)

Customer Requirement

ADMS

18 June 2015

Paper 1504

4/5

( ( , ) ( , ))1)

But as time

at is the same as

oad is involved

which The dormitory area in Hongfeng

help of and intelligent

and control signal in also presented

It should be noticed that the information and the

anagement

reported to validate the . Limited

in this uring

ShuiPei feeder ind

in the region. The

) Case1: Before the simulation for the strategies, s discussed combine

Hydropower Station

kW）

Control Signal From Active Distribution


Paper 1504

CIRED 2015 5/5

Fig.6(a) shows the effect for TCLs’ control. At 10t s ,

TarP was set to the average power 2.09MW. At 15t s the power supplied by intermittent energy increased by 30kW, which means ,

InterDG iP was 30kW and the source-

load percentage was 25.25%. The active power with and without control are shown in fig6(a) as the red and black line. The red line in fig6(a) suggests that TCLs have good response characteristics for power fluctuation. Fig6(b) shows different control effects when the source-load percentage is 15.15%, 25.25% and 50.5%. When the fluctuation is relatively small, TCLs can realize power fluctuation in a proper way shown as the red and black line. The blue line in fig.6 shows that when the fluctuation for DGs is relatively large, TCLs only stabilize part of the fluctuation. But when the power recovered, TCLs can restore the control effect. 2) Case2: In this case, we aimed to test the effectiveness of regional control strategy while using the more accurate short-term power fluctuation model for each TCL.

Fig.7 Result for Regional Control of TCLs during 15mins

Fig.7 shows the result for regional control during 15mins. By comparing both active power with and without regional control, the fluctuation caused by load and intermittent energy can be depressed to 56.14%, which illustrated the effectiveness of regional control strategy. 3) Case3: In this case, we aimed to test the influence when global optimization strategy added to regional control strategy.

Fig.8 Optimization for Different TCLs Penetration

Fig.8 shows that with a higher penetration for TCLs, the load shifting effects can be more pronounced. But the penetration for the demonstration was only 5.28%, so a period from 20:00 to 20:15 was amplified to analyze the effect for optimization as shown in fig.9.

kTarP before the

optimization was gotten by , ,=x xset opt set cstmT T .

From the simulation, we can get the average power has been declined by 12kW. Considering the penetrations for

TCLs is rather small, the result can still prove the realization for load shifting.

Fig9. Active Power of Feeder under Different Conditions

CONCLUSION AND FUTURE WORK A multi-layer control strategy of active load management is proposed for power fluctuation stabilizing and load shifting in this paper based on respective model. The strategy for regional control suppresses the regional power fluctuation caused by intermittent energy based on power fluctuation model. The strategy for global optimization realizes load shifting by resetting the set-point for TCLs based on average power model. Simulation analysis of different scenarios verified the effectiveness of the strategy. This strategy points out a new way to increase the penetration of distributed generation through active management in ADN. However, a more detailed modeling for TCLs or a more efficient algorithm for global optimization can improve the control strategy for better control effect, which will worth a further research.

Acknowledgments This paper was supported by the National High-tech R&D Program of China (863 Program): 2014AA051902. REFERENCES [1] YU W., LIU D., YU N., 2013, "Feeder Control Error

and Its Application in Coordinate Control of Active Distribution Network"(in Chinese), Proceedings of the CSEE, vol.33, 108-115.

[2] Sánchez-Martín P., Sánchez G., Morales-España G., 2012, "Direct load control decision model for aggregated EV charging points", IEEE Transactions on Power Systems, vol.27, 1577-1584.

[3] Facchinetti T., Della Vedova M. L., 2011,"Real-time modeling for direct load control in cyber-physical power systems", IEEE Transactions on Industrial Informatics vol.7, 689-698.

[4] Grenard S., Pudjianto D., Strbac G., 2005, "Benefits of active management of distribution network in the UK." Electricity Distribution, CIRED 2005. 18th International Conference and Exhibition on. IET.

[5] Lu N., Chassin D P., 2004, "A state-queueing model of thermostatically controlled appliances", IEEE Transactions on Power Systems, vol.19, 1666-1673.

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