multi-timescaleoptimaldispatchforac/dcdistribution...

Research ArticleMulti-Time Scale Optimal Dispatch for ACDC DistributionNetworks Based on a Markov Chain Dynamic ScenarioMethod and MPC

Jie Liu 1 Xingquan Ji 1 Kejun Li 2 and Kaiyuan Zhang 1

1College of Electrical Engineering and Automation Shandong University of Science and Technology Qingdao 266590 China2Institute of Renewable Energy and Smart Grid Shandong University Jinan 250061 China

Correspondence should be addressed to Xingquan Ji xqjisdusteducn

Received 20 July 2019 Revised 12 September 2019 Accepted 31 January 2020 Published 20 February 2020

Academic Editor Yagang Zhang

Copyright copy 2020 Jie Liu et al +is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A multi-time scale optimal dispatch model based on the scenario method and model predictive control (MPC) in the ACDCdistribution network is established due to the uncertainty of wind and load A Markov chain dynamic scenario method isproposed which generates scenarios by characterizing the forecast error via empirical distribution Considering the timecorrelation of the forecast error Markov chain is adopted in the Markov chain dynamic method to simulate the uncertainty andvariability in wind and load with time A multi-time scale optimal dispatch strategy based on MPC is proposed +e operationscheduling of operation units is solved in day-ahead and intraday optimal dispatch by minimizing the expected value of total costin each scenario In the real-time optimal dispatch the stability and robustness of system operation are considered MPC isadopted in the real-time optimal dispatch taking the intraday scheduling as reference and using the roll optimization method tocompute real-time optimal dispatch scheduling to smooth the output power +e simulation results in a 50-node system withuncontrollable distributed energy demonstrate that the proposed model and strategy can effectively eliminate fluctuations in windand load in ACDC distribution networks

1 Introduction

11 Motivation An active distribution network (ADN) hasadvantages in actively adjusting power flow managingvariable distributed energy and improving the efficiency ofdistributed energy [1ndash4] As an important part of the ADNthe ACDC distribution network is a significant develop-ment trend of future distribution networks and has betterefficiency in supplying the DC load [5ndash8] +e DC networkhas better energy quality and longer transmission distancethan the AC network +e energy storage system (ESS) andsome distributed generation (DG) must be connected to theAC distribution network by a voltage source converter(VSC) if the dc distribution network is used for powersupply a large number of converters will be saved andenergy loss will be reduced [9ndash11]

Distributed energy is a significant component of the ACDC distribution network +e output power of some types

such as wind and solar fluctuates and is uncontrollable andthe forecast accuracy decreases sharply with increasing timescale It is important to reasonably schedule the outputpower of controllable distributed energy to account foruncontrollable energy Methods based on stochastic pro-gramming have been widely adopted to address the un-certainty of uncontrollable energy output and scenario-based programming is the most commonly used stochasticprogramming method [12] +e main idea is to generatescenarios according to the character of the fluctuations ofuncertain factors making the decision variable meet therequirements in all scenarios In [13] a scenario method andchance-constrained programming were proposed to estab-lish a multi-time rolling dispatch model to optimize theconfiguration of variable resources In [14] a two-stagereactive power optimization of the distribution networkbased on extreme scenario was applied using extreme sce-nario constraints to deal with unknown variables In [15] a

HindawiJournal of Electrical and Computer EngineeringVolume 2020 Article ID 7516578 13 pageshttpsdoiorg10115520207516578

dynamic scenario method was proposed to generate a dy-namic scenario with correlation according to the analysis ofhistorical data

In [16] a multi-time scale optimal dispatch method wasapplied since the accuracy of wind turbine and load pre-diction gradually increased with time scale subdivision andthis method effectively increased the proportion of windturbine consumption In [17] a multi-time active powercoordination scheduling method was proposed based on theidea of level by level subdivision and mutual coordination tocorrect the error between the forecast value and the actualvalue in the next layer Unlike the traditional time scalesubdivision model predictive control (MPC) adopts the rolloptimization method to subdivide the time scale and con-siders the feedback correction of the control process whichcan address the fluctuation of controllable distributed energywell +e traditional multi-time scale optimal methods haveslow response speed which may lead to a large forecast errorIn [18] MPC was used for handling plug-and-play chargingrequests of flexible loads in a distribution system In [19]MPCwas applied to control voltage in the ADN according toroll optimization of unknown variables In [20] a methodbased on D-MPC was proposed to control the voltage ofwind farms which aimed to coordinate the wind turbine andthe static reactive power generator and optimize the processof reactive power adjustment to smooth the future voltagecurve In [21] a multi-time scale optimal dispatch methodbased on MPC was applied which using roll optimizationstrategy to replace the time scale subdivision optimal dis-patch method

12 Contribution In order to better deal with the uncer-tainty of wind power and improve the prediction precision amulti-time scale optimal dispatch model based on Markovchain dynamic scenario method and MPC for the ACDCdistribution network is proposed in this paper and the maincontributions are as follows

(1) +e distribution of the forecast error is generallyassumed as normal distribution and beta distribu-tion which is a relatively simple way to simulate theuncertainty of wind power without using historicalerror data However it is concluded that normaldistribution and beta distribution cannot be used tomodel the measured power for its given data setsbecause the great variety of the forecast methods andapplied locations would lead to different approxi-mate theoretical distributions or even no theoreticaldistribution [22] In order to better describe theuncertainty of wind power the Markov chains dy-namic scenario method is adopted to generate sce-narios which estimate the covariance matrix of themultivariate normal distribution to fit the distribu-tion of historical wind power fluctuations and adoptan inverse transform sampling method from amultivariate normal distribution to generate sce-narios Additionally considering the time correla-tion of the forecast error a Markov chain model isformulated to simulate the change process of the

forecast error probability distribution with timewhich can effectively ensure the reliability of gen-erated scenarios when the prediction time scale islong

(2) Traditional multi-time scale optimization methodsmainly focus on cost optimization without furtherconsideration of system stability In order to betterensure the stability of system an MPC-based multi-time scale optimal dispatch strategy is proposed Inthe day-ahead and intraday dispatch the scenario-based method is adopted to deal with the uncertaintyof wind power +e on-off state of device the gridpurchase decision the output power of regular de-vice and the expected power of the fast responsedevice are solved in day-ahead and intraday optimaldispatch by minimizing the expected value of totalcost in each scenario +e system stability is mainlyconsidered in real-time optimal dispatch since mostof the costs have been optimized +e expectedpower of the fast response device solved in the day-ahead and intraday dispatch is taken as the referenceto minimize the difference between the solvedcontrol variables and the expected value by rolloptimization and feedback correction +erefore inreal-time optimal dispatch it is only necessary toadjust the output power of fast response deviceappropriately based on the expected value accordingto the measured wind power which can not onlymeet the load power of system but also solve theproblem of volatility of DG power thus improvingthe stability of system

2 Markov Chain Dynamic Scenario Method

Markov chain dynamic scenario method characterizesforecast error via empirical distributions of a set of forecastbins using Markov chain to simulate the change process offorecast error distribution and the inverse transform isadopted to generate scenario according to the historicalforecast error distribution which ensure the reliability ofgenerated scenarios and the main steps are as follows

(1) Processing historical data collecting historical dataof wind and load to obtain the data pairs (measuredforecast) and transform the value of the data to per-unit values

(2) Generating the forecast bins choose 50 bins with002 pu bin widths in this case and every forecast hasa corresponding measurement which is assigned tothe same bin as the forecast +en sorting the datapairs (measured forecast) by the forecast values andassigned to the matching forecast power bins toobtain the forecast error distribution of each randomvariable in each forecast bin

(3) Discretizing the forecast error distribution of eachrandom variable into seven intervals centered on thezero mean with a width equal to the standard de-viation δ +e state of the corresponding interval i is

2 Journal of Electrical and Computer Engineering

denoted as xi(i 1 2 7) and the occurrenceprobability of this state interval is Si All the prob-ability Sikt(i 1 2 7) of the k-th forecast bin atmoment t constitutes the error state vector Pkt at thecurrent time +e expressions are as follows

Pkt S1kt S2kt S7kt1113858 1113859 (1)

1113944

7

i1Sikt 1 (2)

(4) Generating the probability density function Fkt(X)

in each forecast bin according to the error statevector in the forecast bins +e expression is asfollows

Fkt xj1113872 1113873 1113944

j

i1Sikt j 1 2 7 (3)

(5) Generating random vectors [15] generate Z randomvectors Y Y1 Y2 Yl1113864 1113865 with zero mean andstandard deviation which follows a multivariatenormal distribution +e structure of Σ is as follows

Σ

σ11 σ11 middot middot middot σ1l


⋮ ⋮ ⋱ ⋮

σl1 σl2 middot middot middot σll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

where l is the length of the generated scenario se-quence and σmn is the covariance of Ym and Ynwhich can be expressed as

σmn cov Ym Yn( 1113857 eminus ((|mminus n|)ε)

0le n mleΔt(5)

where ε is the range parameter controlling the strengthof the correlation of the random variable sequence

(6) Generating error scenarios [15] the inverse trans-form shown in (6) is used to transform a randomvector following a multivariate normal distributioninto an error vector with correlation to generate anerror scenario within the forecast time

Δωt Fminus 1ik Φ Yt( 1113857( 1113857 (6)

where Δωt is the generated forecast error at moment tandΦ(Yt) is the cumulative density function followinga normal distribution which is

Φ Yt( 1113857 1113946Yt

minus infin

exp minus x22( 11138572π

radic dx (7)

Following these steps above the multivariate normalrandom variable is converted into scenarios fol-lowing both the marginal distribution of wind powerforecast error among the forecast horizon But theprediction precision will decrease with the growth in

prediction time scale when the forecast horizon islong Wind and load power within a day need to bepredicated in the day-ahead dispatch so the timecorrelation of forecast error should be consideredFor the good performance of the Markov chainshown in the simulation of wind and load outputsequences [23 24] the Markov chain is incorporatedinto the traditional dynamic scenario method +echange process of the forecast error probabilitydistribution with time is regarded as a Markov chainwhich is a stochastic process of transition from onestate to another In this paper the state transitionmatrix is generated according to the historicalforecast error data +e state transition is utilized toupdate the forecast error probability distribution ineach forecast bin at set intervals when the predictiontime scale is long which can effectively ensure thereliability of generated scenarios +e main steps areas follows

(7) Forming the state transition matrix the state tran-sition matrix is the most important part in the wholeMarkov chain process and the expression is asfollows

Ekt

E11 E11 middot middot middot E1n


⋮ ⋮ ⋱ ⋮

En1 En2 middot middot middot Enn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ntimesn

(8)

where Ekt is the state transition matrix of the k-thforecast bin at moment t and Emn is the state transitionprobability from the state xm in the last moment to thestate xn in the next moment which is

Emn Nmn

1113936nj1 Nmj

(9)

where Nmn is the number at which the state xm in thelast moment transits to the state xn in the nextmoment through the statistics of historical data ofunknown variables

(8) Generating the error state of all forecast cases afterobtaining the state transition matrix the statetransition matrix is used to generate the error state ofall the forecast cases in the next period and thenreturn to Step (4) to continue scenario generation+e expression is as follows

Pkt+1 PktEkt (10)

3 Multi-Time Scale Optimal Strategy

+e uncertainty of wind turbines brought new challenges formulti-time scale optimal dispatch in the ACDC distributionnetwork Considering that the prediction precision willincrease with a shortened time scale a multi-time scaleoptimal coordinate dispatch strategy is adopted as shown in

Journal of Electrical and Computer Engineering 3

Figure 1 in which the dispatching process is divided intothree stages day-ahead intraday and real time [25]Microturbines are classified into regulation microturbines(RMTs) and quick-adjustment microturbines (QAMTs)according to the response speed

(1) Day-ahead scheduling the scheduling cycle is 24hours and the time interval is 1 hour +e Markovchain dynamic scenario method is adopted to gen-erate the scenario and the time interval of theMarkov chain process is 4 hours +e on-off state ofRMT and QAMT is solved in day-ahead optimaldispatch by minimizing the expected value of totalcost in each scenario

(2) Intraday scheduling the scheduling cycle is 1 hourand the time interval is set to 15 minutes +e dy-namic scenario method is adopted to generate theforecast scenario since the intraday time scale is notlong and the time correlation of forecast error can beignored +e RMT output power and the grid

purchase decision are solved in intraday optimaldispatch by minimizing the expected value of totalcost in each scenario

(3) Real-time scheduling the scheduling cycle is 15minutes and the time interval is 5 minutes Con-sidering the stability of system MPC is adopted tocompute output power of QAMT and ESS by takingthe intraday scheduling as reference and using rolloptimization method and feedback correction

4 Multi-Time Scale-CoordinatedOptimization Model

41 Day-Ahead Optimization Model

411 Objective Function +e objective function of day-ahead optimal dispatch is to minimize the expected value oftotal cost in each scenario which is

min

1113944

Nt

t1cgridt 1113944

Ns

s1πsPgridst + 1113944

Nt

t11113944

NDGF

i11113944

Ns

s1πsC

FDGist + U

FDGit + D

FDGit

⎛⎝ ⎞⎠+

1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist + U

RDGit + D

RDGit1113872 1113873+

1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

Δt (11)

where Nt is the dispatching cycle NDGF is the number ofQAMT NDGR is the number of RMT Ns is the number ofthe scenarios NESS is the number of ESSs Nwt is the numberof wind turbines cgridt is the electricity price at moment tPgridst is the exchange power between ADN and the uppergrid at moment t in scenario s CF

DGist is the power cost ofQAMT i at moment t in scenario s UF

DGit and DFDGit are the

cost of starting and stopping respectively QAMT i atmoment t CR

DGist is the power cost of RMT i at moment t inscenario s UR

DGit and DRDGit are the starting and stopping

costs respectively of RMT i at moment t CESSist is thepower cost of ESS i at moment t in scenario s Wcurt

ist is thecutting wind quantity of wind turbine i at moment t inscenario s λcurtist is the cutting wind cost of wind turbine i atmoment t in the scenario s πs is the probability of thescenario s and Δt is the time interval

412 Main Constraints

(1) Power balance constraints

1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

R

DGist+ 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS

i1PESSist + Pgridst minus Plossst minus Rst Ploadst

(12)

where PFDGist is the power of QAMT i at moment t in

scenario s PRDGist is the power of RMT i at moment t

in scenario s Pwtist is the power of wind turbine i atmoment t in scenario s PESSit is the power of ESS i atmoment t in scenario s Ploadst is the load power atmoment t in scenario s Plossst is the power loss in theACDC distribution network at moment t in sce-nario s and Rst is the spinning reserve in the sce-nario s at moment t [14]

(2) Power limit constraints

uFistP

FDGimin leP

FDGist le u

FistP

FDGimax (13)

uRistP

RDGimin leP

RDGist le u

RistP

RDGimax (14)

where PFDGimax and PF

DGimin are the upper limit andlower limit of the power of QAMT i respectively uF

it

is the on-off state of QAMT i at moment t PRDGimax

and PRDGimin are the upper limit and lower limit of

the power of RMT i respectively and uRit is the on-off

state of RMT i at moment t(3) On-off state constraints

xFit + y

Fit le 1 (15)

xFit minus y

Fit u

Fit minus u

Fitminus 1 (16)


xRit + y

Rit le 1 (17)

xRit minus y

Rit u

Rit minus u

Ritminus 1 (18)

where xFit and yF

it are the starting and stoppingaction respectively of QAMT i and xR

it and yRit are

the starting and stopping action respectively ofRMT i

(4) Climbing constraints

PRDGist minus PR

DGistminus 11113868111386811138681113868

1113868111386811138681113868le uRit minus uR

itminus 11113868111386811138681113868

1113868111386811138681113868PRDGimin + ΔR

i

PFDGist minus PF

DGistminus 1

11138681113868111386811138681113868111386811138681113868le uF

it minus uFitminus 1

11138681113868111386811138681113868111386811138681113868PF

DGimin + ΔFi

⎧⎨

⎩

(19)

where ΔRi and ΔF

i are the climbing rate of RMT andQAMT respectively

(5) VSC converter station constraints+e AC part and the DC part are connectedthrough the VSC and the connecting point can be

assumed as a virtual node [26] as shown inFigure 2 In Figure 2 Pacijst Qacijst and Pdcjkst

are the active power in the AC part reactivepower in the AC part and active power in the DCpart in scenario s at moment t respectivelyQvscjst is the reactive power of VSC in scenario sat moment t Rvscij is the equivalent resistance ofthe loss in the converter station Xvscij is theequivalent reactance of the filter in the converterstation Uacist is the voltage at the AC side inscenario s at moment t Udckst is the voltage at theDC side in scenario s at moment t and Uvscjst isthe voltage of the VSC virtual node in scenario s atmoment tAccording to the equivalent circuit in Figure 2 weobtain

Pacijst minusPacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875

Uacsi( 11138572 Rvscij Pdcjkst

(20)

0800

0900 0910 09150905

Real-timeoptimal dispatch

0900 1000

15min

5min

Intraday optimaldispatch

On-off state ofQAMT

On-off state ofRMT

RMT output powerGrid purchase

decision

QAMT output power ESS output power

0000 0600 18001200 2400

1h

Day-aheadoptimal dispatch

Figure 1 Multi-time scale optimization process


Qacijst minusPacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875

Uacsi( 11138572 Xvscij minus Qvscjst

(21)

minus Qvscjmax leQvscjst leQvscjmax (22)

Uvscsj Uacsi minus 2 PacijstRvscij + QacijstXvscij1113872 1113873

+Pacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875 Rvscij1113872 1113873

2+ Xvscij1113872 1113873

21113874 1113875

Uacsi( 11138572

(23)

Uvscsj

3

radic

3μMiUdcsk (24)

where Qvscjmax and minus Qvscjmax are the upper limitand lower limits respectively of the power of VSC jμ is the efficiency of dc voltage (0le μle 1 μ is set to0866 when the modulation mode is SPWM) and Mi

is the modulation of VSC i (0leMi le 1)(6) ESS operation constraints

SESSist SESSistminus 1 1 minus εESS( 1113857 minusPESSistΔt

Esiηd

PESSist gt 0

SESSist SESSistminus 1 1 minus εESS( 1113857 minusηcPESSistΔt

Esi

PESSist lt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(25)

SESSimin le SESSist le SESSimax (26)

minus PESSimax lePESSist lePESSimax (27)

SESSisT SESSis1 (28)

where SESSist is the energy of ESS i atmoment t in scenariosPESSist is the power of ESS i atmoment t in scenario s ηd

and ηc are the efficiency of discharge and charge respec-tivelyEsi is the capacity of ESS i in scenario s SESSimax andSESSimin are the upper limit and lower limits respectively ofthe capacity of ESS i εESS is the ESS self-discharge andPESSimax is the upper limit of the power of ESS i

413 Day-Ahead Optimal Dispatch Result +e starting andstopping plan of QAMT uR

ist and the starting and stoppingplans of RMT uF

ist in the next day are determined throughday-ahead optimal dispatch which are taken as input datain the intraday optimal dispatch model to compute otherunknown variables in the intraday optimal dispatchmodel

42 Intraday Optimal Model

421 Objective Function +e objective function of intradayoptimal dispatch is to minimize the expected value of totalcost in each scenario which is

min1113944

Nt

t11113944

NDGF

i1C

FDGit + 1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist1113872 1113873

+ 1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

(29)



1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

RDGit + 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS

i1PESSist + Pgridt minus Plossst minus Rst Ploadst

(30)

where PRDGit is the power of RMT i at moment t and

Pgridt is the exchange power between ADN and theupper grid at moment t

+e remaining constraints of the intraday optimizationmodel are the same as the constraints of the day-aheadoptimal dispatch and the operation states of QAMT andRMT are obtained by the day-ahead optimal dispatch

423 Intraday Optimal Dispatch Result +e powerscheduling of RMT and the grid purchase decision theexpected value of QAMT and ESS are determined throughintraday optimal dispatch these values are taken as inputs inthe real-time optimal dispatch model to compute otherunknown variables

43 Real-Time Optimal Dispatch Model

431 MPC Model predictive control is a finite domainclosed-loop optimal control algorithm based on the pre-diction model +e main idea is as follows in each samplemoment the prediction model is established to computeoptimal control variable according to objective function andconstraints and the control variable at the current momentis issued +en the feedback correction is adopted for theissued control variable to modify the control variable [27]

VSC

Pacijst + jQacijst ndashQvscjst Pdcjkst

Uacsi

Rvscij Xvscij

Uvscsj

Udcsk

Figure 2 VSC converter station model


+e MPC-based optimal dispatch method is utilized tominimize the difference between the solved control variables inthe future and the expected value of the control variables solved inthe day-ahead optimal dispatch considering the network con-straints by using roll optimization and feedback correction whichsamples every 5 minutes and the process is shown in Figure 3+e actual values of QAMTand ESS at the current sampling timeare taken as the original state to compute the control commandsequence in the next 15minutes and issue the control instructionsin the first 5 minutes and the process is repeated at the nextsampling time which can not only meet the load demand of thesystembut also keep the issued adjustment value fromgetting toohigh Additionally the closed-loop control is formed due to thefeedback correction part which can further increase the pre-diction precision to ensure the stability of system

432 Establishing Prediction Model +e prediction modelis adopted to predict output power of QAMT ESS and thegrid in the next period to compute the control variablewhich are as follows [19]

PDG(k + i | k) PDG0(k) + 1113936i

t1ΔuDG(k + t | k) i 1 2 N

PESS(k + i | k) PESS0(k) + 1113936i

t1ΔuESS(k + t | k) i 1 2 N

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(31)

where N is the prediction step and PDG0(k) and PESS0(k) arethe original value of QAMT and ESS measured in thesampling time respectively ΔuDG(k + t | k) and ΔuESS(k +

t | k) are the power increments of QAMTand ESS in the nextperiod predicted at moment k respectively PDG(k + i | k)

and PESS(k + i | k) are the power of QAMT and ESS in thenext period predicted at moment k respectively

433 Objective Function +e objective is to minimize thedeviation between the issued control command sequenceand the expected value of intraday optimal dispatch which is

min PDGpre minus PDGref1113872 1113873TW PDGpre minus PDGref1113872 1113873

+ PESSpre minus PESSref1113872 1113873TQ PESSpre minus PESSref1113872 1113873

(32)

whereW is the weight coefficient matrix of QAMT Q is theweight matrix of ESS PDGpre is the power of QAMT in thefuture k + i times predicted in the sampling time and PESSpreis the power of ESS in the future k + i times predicted in thesampling time which is

PDGpre PDG(k + 1 | k)PDG(k + 2 | k) PDG(k + N | k)1113858 1113859T

PESSpre PESS(k + 1 | k)PESS(k + 2 | k) PESS(k + N | k)1113858 1113859T

⎧⎪⎨

⎪⎩

(33)

PDG(k + i | k) PDG1(k + i | k) PDG2(k + i | k) 1113858

middot PDGNDG(k + i | k)1113961

(34)

PESS(k + i | k) PESS1(k + i | k) PESS2(k + i | k) 1113858

middot PESSNESS(k + i | k)1113961

(35)where PDGref is the expected value of QAMT in intradayoptimal dispatch from sampling time to time k + N andPgridref is the expected value of ESS in intraday optimaldispatch from sampling time to time k + N which is

PDGref PTDGref(k + 1 | k)PT

DGref(k + 2 | k) 1113858

PTDGref(k + N | k)1113859

T

PESSref PTESSref(k + 1 | k)PT

ESSref(k + 2 | k) 1113858

PTESSref(k + N | k)1113859

T

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(36)

434 Issuing Instruction +e control command sequence ofQAMTand ESS in the futureNmoment is solved by the real-time optimization model

ΔuT(k + 1 | k)ΔuT

(k + 2 | k) ΔuT(k + N | k)1113966 1113967

(37)

Begin

Adopt actual active power asoriginal value

Establish rolling optimisationmodel

Solve control variable

Issued first control variablesequence

Feedback correction

Is the optimization periodover

End

Yes

No

Figure 3 Real-time optimal dispatch process


+e first command is issued in the control incrementsequence to compute the power of QAMT and ESS in theACDC distribution network in the next period

P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)

435 Feedback Correction +e measured value at currentsampling time is taken as the original value of the new rolloptimization before the next roll optimization to avoid theinterference caused by the uncertainty of the wind turbine+e feedback formula is as follows [19]

P0(k + 1) Preal(k + 1) + δ (39)

where P0(k + 1) is the original power in the time k + iPreal(k + 1) is the actual measured power in the time k + iand δ is the measured error

+e remaining constraints of the real-time optimizationmodel are the same as those of the day-ahead optimaldispatch and the expected value of QAMT and ESS theRMT power and the grid purchase decision is obtained byintraday optimal dispatch

436 Real-Time Optimal Dispatch Result +e controlcommand sequence of QAMTand ESS the output power ofQAMTand ESS and the storage state of ESS are determinedthrough real-time optimal dispatch

5 Case Study

+e Yalmip and Cplex solvers are used for modeling andsolving the optimal dispatch model+e test is performed ona PC with an Intel Core (TM) i5-3340s CPU28 GHzprocessor and 8GB of memory

+e simulation is conducted on a 50-node ACDCdistribution network as shown in Figure 4 [28] WT is thewind turbine unit DG_F is the QAMT DG_R is the RMTand ESS is the energy storage system +e RMT with anupper limit of power of 300 kW is connected to nodes 10 and37 and the QAMTwith an upper limit of power of 300 kW isconnected to nodes 18 and 46 with a power factor of 09 ESSwith an upper limit of power of 300 kW and energy storageof 1800 kWh is connected to nodes 36 and 49 and ESS withan upper limit of power of 240 kW and energy storage of1400 kWh is connected to nodes 41 and 45 +e time-of-useelectricity price is adopted which is shown in Figure 5

One thousand scenarios for wind and load are generatedin intraday dispatch and day-ahead dispatch respectivelyand then these original scenarios are reduced to 5 scenariosfor wind and load by the K-means clusteringmethod [29] sothe number of total scenarios is 25+e generated scenario isapplied to the wind and load data of EirGrid in 2017 and2018 Figures 6 and 7 are the reduced wind scenario and thereduced load scenario respectively generated in the day-ahead dispatch +e wind and load scenarios are generatedby the forecast value and forecast error sampled from theempirical cumulative distribution function using thetransformation in (6) It is observed that the load scenarios

have lower volatility than the wind scenarios and this isbecause the forecast error of load is much smaller than thatof wind power in the historical data Additionally it is shownthat the wind output power is low from 200 to 600 so thedemand of microturbine output power and exchange poweris high From 700 to 1200 with the sharp increase in windoutput power and the growth of load power is relatively lowthe demand of microturbine output power and exchangepower begins to decrease In the later stage the load powerdecreases slowly while the wind power output shows asubstantial decline which lead to a constant increase in thedemand of microturbine output power and exchange power

51 Optimization Result Discussion +e intraday optimaldispatch results of RMTand the grid purchase decision from0800 to 1000 are given with an interval of 15 minutes whichis shown in Figure 8 It is observed that the rise in electricityprice begins at 800 leading to an increase in the cost of ex-change power so the exchange power is decreased and theRMTpower is used as the main output power When the loadpower rises gradually the ACDC distribution network systemproperly reduces the output power of RMT and increases theexchange power because the RMT cost increases sharply withthe rise in power and the RMT output power is limited +ereal-time optimal dispatch results of the power of ESS and theQAMT from 0800 to 0900 are given with an interval of5minutes which is shown in Figure 9 It is observed that whenthe load power is low at the starting optimal stage the storage ismainly charged for the growth of load power in the futureWith the constant increase in the load power the state ofstorage is transformed to discharge and the power of QAMTalso increases rapidly which realizes peak shaving maximallyand ensures safe operation of the ACDC distribution network+e state of charge is shown in Figure 10 It is observed that thestate of charge is optimized according to the ESS constraints inthe multi-time scale optimal model the curve of state of chargebecomes smoother and there are no large fluctuations in-creasing the ESS usage life and the economy of the ACDCdistribution network

52 Markov Chain Dynamic Scenario Analysis To verify theeffectiveness of the proposed method the total adjustmentvalue G of the multi-time scale optimal dispatch is analyzedas shown in (40) +e total adjustment value in the intradayoptimal dispatch of the Markov chain dynamic scenariomodel dynamic scenario model and Monte Carlo model isshown in Figure 11 It is observed that there is little forecasterror observed between the generated scenario and theactual scenario at the beginning due to the high predictionprecision +e prediction precision decreases sharply andthe forecast error between the generated scenario and theactual scenario becomes increasingly larger with the growthin the prediction time scale Scenarios generated by theMonte Carlo method are obtained only by superimposingthe perturbation of the normal distribution on the actualload and wind curve and the total adjustment value in-creases considerably with the growth in the prediction timescale Considering the correlation of the original scenario


with time the Markov chain is adopted in the Markovchain dynamic scenario method to simulate the change inforecast error with time through the state transfer matrixso the deviation between the generated scenario and theactual scenario and the adjustment value is relativelysmall +e total adjustment value of the dynamic scenariomethod is between the two +e multi-time scale optimal

dispatch based on the Markov chain dynamic scenariomethod can effectively reduce the pressure of the intradayoptimal dispatch verifying the feasibility of the proposedmodel

WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS

Figure 4 Test system with 50 nodes

Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132

Figure 5 Time-of-use electricity price

Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022

Wind power scenario 1Wind power scenario 2Wind power scenario 3

Wind power scenario 4Wind power scenario 5

Figure 6 Wind scenario in day-ahead dispatch

Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3

Load scenario 1Load scenario 2


Figure 7 Load scenario in day-ahead dispatch

Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5

RMT1RMT2Exchange power

Figure 8 Intraday optimal dispatch result


G 1113944T

t11113944

kc

k1

Pdayaheadtk minus Pintradaytk

11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)

where Pdayaheadtk is the power of output unit k at moment tin the day-ahead optimal dispatch Pintradaytk is the power of

output unit k at moment t in the intraday optimal dispatchkc is the number of operation units and T is the optimal timescale

To further illustrate the effectiveness of the methodproposed in this paper the coverage ratio of the scenario setover the actual valueΠ is analyzed as shown in the followingequations

Π 1T

1113944

T

t1g Pt( 1113857 (41)

g Pt( 1113857 1 Ptmin lePt lePtmax

0 Pt gtPtmax Pt ltPtmin

1113896 (42)

where g(Pt) is the probability of covering the actual valuefor the scenario set at moment t T is the optimal time scalePt is the actual value at moment t Ptmin is the minimumvalue of the scenario set and Ptmax is the maximum value ofthe scenario set +e range of Π is 0 to 1 +e larger thecalculation result is the higher the coverage ratio of thescenario set to the actual value is the higher the reliability ofthe solved dispatch schedule is and the lower the possibilityof a failure occurring in the ACDC distribution networkoperation is

Five hundred wind turbine scenarios are generated bythe Markov chain dynamic scenario method the dynamicscenario method and theMonte Carlo method respectively+e coverage ratios of these generated scenarios are ana-lyzed which is shown in Table 1 +e coverage ratio of thescenario generated by the Monte Carlo method is lower thanthose of the other two methods and the coverage ratiodecreases significantly with an increase in the predictiontime scale +e scenario generated by the dynamic scenariomethod has the same high coverage ratio as the Markovchain dynamic scenario method when the prediction timescale is low but with the continuous growth of the pre-diction time scale the coverage ratio of the scenario gen-erated by the dynamic scenario method starts to decreasegradually while the scenarios generated by the Markov chaindynamic scenario method still have high coverage rates

53 MPC Analysis +e result of the intraday optimal dis-patch based on MPC and the intraday optimal dispatchwithout using the MPC method is shown in Figure 12 +eintraday optimal dispatch results based on MPC have thesame output power trend as the intraday optimal dispatchresults without MPC while the intraday optimal dispatchresults without using MPC have large fluctuations Feedbackcorrection and roll optimization are adopted in the optimaldispatch based on MPC so the result is relatively smoothwhich is more beneficial to the operation of the ACDCdistribution network

To better compare the results of different optimizationmethods the stability of the power of QAMT is analyzed+e output volatility of QAMT is defined as follows

Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2

Figure 9 Real-time optimal dispatch result

Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4

Figure 10 State of charge of ESS

Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18

Markov-chain dynamic scenario methodDynamic scenario methodMonte Carlo

Figure 11 +e total adjustment in each optimization model


where PmaxDGi and Pmin

DGi are the maximum and minimumpower of QAMT i in the entire optimal period respectivelyand PDGi is the average power value of QAMT i in the wholeoptimal period

+e results of these three different optimizationmethods arecompared as shown in Table 2 MPC1 represents the opti-mization method that only utilizes roll optimization withoutfeedback correction MPC2 represents an optimization methodutilizing both roll optimization and feedback correction

Table 2 shows that these three methods have almost thesame optimal results However as the MPC1 optimizationmethod adopts the roll optimization the output volatility is597 which shows a better stability than that of the traditionaloptimal flow MPC2 has a lower volatility than MPC1 duefeedback correction which is 561 As a result MPC2 canensure that the large power fluctuations in QAMTand ESS willnot occur when dealing with the uncertainty and volatility ofuncontrollable energy which is beneficial to maintain thebalance of active power in the ACDC distribution networkimproving the stability of system operation

6 Conclusions

A multi-time scale optimal dispatch model of an ACDCdistribution network based on the Markov chain dynamic

scenario method and MPC is proposed +e Markov chaindynamic method is proposed to generate a scenario toaddress with the fluctuation of uncontrollable energy andthe output power of the unit is solved by adopting rolloptimization in intraday optimal dispatch based on MPCrealizing the coordination of day-ahead intraday and real-time optimization and the consumption of wind turbine

(1) As the correlation of the forecast error state withtime is considered the scenario generated by theMarkov chain dynamic scenario method has a highercoverage ratio than the scenario generated by thedynamic scenario method when the time scale is longand the solved dispatch schedule using the Markovchain dynamic method has less fluctuations whichimproves the stability of the ACDC distributionnetwork and ensures the safe operation of thesystem

(2) All operating units with different adjusting times isused in the power system dispatch by adopting amulti-time scale optimal dispatch model +e op-eration units with long adjusting times are used inthe consumption of uncontrollable distributed en-ergy in the ACDC distribution network while theoperation units with short start adjusting times are

Table 1 Comparative result of the coverage ratio

Π Markov chain dynamic scenario method Dynamic scenario method Monte Carlo method

Time

100ndash600 09981 09975 09471700ndash1200 09896 09795 089951300ndash1800 09744 09452 084511900ndash2400 09611 08997 08071

QAMT1 MPCQAMT1 non-MPC


005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time

Figure 12 Comparison of real-time dispatch results

Table 2 Results of different optimization methods

Optimization method Volatility () Cost ($)Non-MPC 663 1841232MPC1 597 1863425MPC2 561 1878747


used to suppress the short-term fluctuation of un-controllable distributed energy

(3) As the roll optimization method and feedback cor-rection are used in the process of optimization MPChas better stability than traditional optimal flowwhich can ensure that the output power of QAMTand ESS fluctuates within a certain range therebyimproving the stability and robustness of systemoperation

Data Availability

+e rawprocessed data required to reproduce these findingscannot be shared at this time as the data also form part of anongoing study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] X Xu N Tai Y Hu W Wang F Zheng and W HeldquoReliability calculation of ACDC hybrid distribution networkwith a solid-state transformerrdquo gte Journal of Engineeringvol 2019 no 16 pp 3067ndash3071 2019

[2] Y Wang N Zhang H Li et al ldquoLinear three-phase powerflow for unbalanced active distribution networks with PVnodesrdquo CSEE Journal of Power and Energy Systems vol 3no 3 pp 321ndash324 2017

[3] X Zhu H Han S Gao Q Shi H Cui and G Zu ldquoA multi-stage optimization approach for active distribution networkscheduling considering coordinated electrical vehicle charg-ing strategyrdquo IEEE Access vol 6 pp 50117ndash50130 2018

[4] J Barr and R Majumder ldquoIntegration of distributed gener-ation in the voltVAR management system for active distri-bution networksrdquo IEEE Transactions on Smart Grid vol 6no 2 pp 576ndash586 2015

[5] F Salvadori C S Gehrke A C de Oliveira M de Camposand P S Sausen ldquoSmart grid infrastructure using a hybridnetwork architecturerdquo IEEE Transactions on Smart Gridvol 4 no 3 pp 1630ndash1639 2013

[6] A A Eajal M F Shaaban K Ponnambalam and E F El-Saadany ldquoStochastic centralized dispatch scheme for ACDChybrid smart distribution systemsrdquo IEEE Transactions onSustainable Energy vol 7 no 3 pp 1046ndash1059 2016

[7] M A Allam A A Hamad M Kazerani and E F El-SaadanyldquoA novel dynamic power routing scheme to maximizeloadability of islanded hybrid ACDC microgrids underunbalanced AC loadingrdquo IEEE Transactions on Smart Gridvol 9 no 6 pp 5798ndash5809 2018

[8] H W D Hettiarachchi K T M U Hemapala andA G B P Jayasekara ldquoReview of applications of fuzzy logic inmulti-agent-based control system of AC-DC hybrid micro-gridrdquo IEEE Access vol 7 pp 1284ndash1299 2019

[9] X Kong Z Yan R Guo X Xu and C Fang ldquo+ree-stagedistributed state estimation for AC-DC hybrid distributionnetwork under mixed measurement environmentrdquo IEEEAccess vol 6 pp 39027ndash39036 2018

[10] H Peng M Su S Li and C Li ldquoStatic security risk assessmentfor islanded hybrid ACDC microgridrdquo IEEE Access vol 7pp 37545ndash37554 2019

[11] D Chen X Ji Y Yu X Bai and J Liu ldquoUnbalanced powerflow algorithm for ACampDC hybrid distribution network withdiverse-controlled VSC-MTDC convertsrdquo gte Journal ofEngineering vol 2019 no 16 pp 1918ndash1925 2019

[12] J Wang A Botterud R Bessa et al ldquoWind power forecastinguncertainty and unit commitmentrdquo Applied Energy vol 88no 11 pp 4014ndash4023 2011

[13] Y Q Bao B B Wang Y Li et al ldquoRolling dispatch modelconsidering wind penetration and multi-scale demand re-sponse resourcesrdquo Proceedings of the CSEE vol 36 no 17pp 4589ndash4600 2016

[14] T Ding S Liu W Yuan Z Bie and B Zeng ldquoA two-stagerobust reactive power optimization considering uncertainwind power integration in active distribution networksrdquo IEEETransactions on Sustainable Energy vol 7 no 1 pp 301ndash3112016

[15] X-Y Ma Y-Z Sun and H-L Fang ldquoScenario generation ofwind power based on statistical uncertainty and variabilityrdquoIEEE Transactions on Sustainable Energy vol 4 no 4pp 894ndash904 2013

[16] X Lei T Huang Y Yang Y Fang and P Wang ldquoA bi-layermulti-time coordination method for optimal generation andreserve schedule and dispatch of a grid-connected microgridrdquoIEEE Access vol 7 pp 44010ndash44020 2019

[17] L Guanqun F Yongshen Q Dagong S Guangmin andS Xiaoqing ldquoResearch on multi-objective optimal joint dis-patching of wind-thermal-hydro power in multi time scalesrdquoin Proceedings of the 2016 IEEE PES Asia-Pacific Power andEnergy Engineering Conference (APPEEC) pp 1832ndash1839Xirsquoan China October 2016

[18] C L Floch S Bansal C J Tomlin S J Moura andM N Zeilinger ldquoPlug-and-play model predictive control forload shaping and voltage control in smart gridsrdquo IEEETransactions on Smart Grid vol 10 no 3 pp 2334ndash23442019

[19] G Valverde and T Van Cutsem ldquoModel predictive control ofvoltages in active distribution networksrdquo IEEE Transactionson Smart Grid vol 4 no 4 pp 2152ndash2161 2013

[20] H Zhao Q Wu Q Guo H Sun and Y Xue ldquoDistributedmodel predictive control of a wind farm for optimal activepower controlmdashpart II implementation with clustering-basedpiece-wise affine wind turbine modelrdquo IEEE Transactions onSustainable Energy vol 6 no 3 pp 840ndash849 2015

[21] L Dong H Chen T J Pu et al ldquoMulti-time scale dynamicoptimal dispatch in active distribution network based onmodel predictive controlrdquo Proceedings of the CSEE vol 36no 17 pp 4609ndash4617 2016

[22] S Tewari C J Geyer and N Mohan ldquoA statistical model forwind power forecast error and its application to the estimationof penalties in liberalized marketsrdquo IEEE Transactions onPower Systems vol 26 no 4 pp 2031ndash2039 2011

[23] A Shamshad M Bawadi W Wanhussin T Majid andS Sanusi ldquoFirst and second order Markov chain models forsynthetic generation of wind speed time seriesrdquo Energyvol 30 no 5 pp 693ndash708 2005

[24] M I Garcia-Planas and T Gongadze ldquoWind profile pre-diction using linear Markov chains a linear algebra ap-proachrdquo IEEE Latin America Transactions vol 16 no 2pp 536ndash541 2018

[25] B M Zhang W C Wu T Y Zheng et al ldquoDesign of a multi-time scale coordinated active power dispatching system foraccommodating large scale wind power penetrationrdquo Auto-mation of Electric Power Systems vol 35 no 1 pp 1ndash6 2011


[26] X Ma R P Guo L Wang et al ldquoDay-ahead optimal dispatchmodel of ACDC active distribution network based on sec-ond-order cone programmingrdquo Automation of Electric PowerSystem vol 42 no 22 pp 144ndash150 2018

[27] E F Camacho and C Bordons Model Predictive Controlvol 204 pp 14ndash31 Springer-Verlag New York NY USA2004

[28] S X Wang S J Chen and S G Xie ldquoSecurity-constrainedcoordinated economic dispatch of energy storage systems andconverter stations for ACDC distribution networksrdquo Auto-mation of Electric Power Systems vol 41 no 11 pp 85ndash912017

[29] L Wu M Shahidehpour and Z Li ldquoComparison of scenario-based and interval optimization approaches to stochasticSCUCrdquo IEEE Transactions on Power Systems vol 27 no 2pp 913ndash921 2012


dynamic scenario method was proposed to generate a dy-namic scenario with correlation according to the analysis ofhistorical data

In [16] a multi-time scale optimal dispatch method wasapplied since the accuracy of wind turbine and load pre-diction gradually increased with time scale subdivision andthis method effectively increased the proportion of windturbine consumption In [17] a multi-time active powercoordination scheduling method was proposed based on theidea of level by level subdivision and mutual coordination tocorrect the error between the forecast value and the actualvalue in the next layer Unlike the traditional time scalesubdivision model predictive control (MPC) adopts the rolloptimization method to subdivide the time scale and con-siders the feedback correction of the control process whichcan address the fluctuation of controllable distributed energywell +e traditional multi-time scale optimal methods haveslow response speed which may lead to a large forecast errorIn [18] MPC was used for handling plug-and-play chargingrequests of flexible loads in a distribution system In [19]MPCwas applied to control voltage in the ADN according toroll optimization of unknown variables In [20] a methodbased on D-MPC was proposed to control the voltage ofwind farms which aimed to coordinate the wind turbine andthe static reactive power generator and optimize the processof reactive power adjustment to smooth the future voltagecurve In [21] a multi-time scale optimal dispatch methodbased on MPC was applied which using roll optimizationstrategy to replace the time scale subdivision optimal dis-patch method

12 Contribution In order to better deal with the uncer-tainty of wind power and improve the prediction precision amulti-time scale optimal dispatch model based on Markovchain dynamic scenario method and MPC for the ACDCdistribution network is proposed in this paper and the maincontributions are as follows

(1) +e distribution of the forecast error is generallyassumed as normal distribution and beta distribu-tion which is a relatively simple way to simulate theuncertainty of wind power without using historicalerror data However it is concluded that normaldistribution and beta distribution cannot be used tomodel the measured power for its given data setsbecause the great variety of the forecast methods andapplied locations would lead to different approxi-mate theoretical distributions or even no theoreticaldistribution [22] In order to better describe theuncertainty of wind power the Markov chains dy-namic scenario method is adopted to generate sce-narios which estimate the covariance matrix of themultivariate normal distribution to fit the distribu-tion of historical wind power fluctuations and adoptan inverse transform sampling method from amultivariate normal distribution to generate sce-narios Additionally considering the time correla-tion of the forecast error a Markov chain model isformulated to simulate the change process of the

forecast error probability distribution with timewhich can effectively ensure the reliability of gen-erated scenarios when the prediction time scale islong

(2) Traditional multi-time scale optimization methodsmainly focus on cost optimization without furtherconsideration of system stability In order to betterensure the stability of system an MPC-based multi-time scale optimal dispatch strategy is proposed Inthe day-ahead and intraday dispatch the scenario-based method is adopted to deal with the uncertaintyof wind power +e on-off state of device the gridpurchase decision the output power of regular de-vice and the expected power of the fast responsedevice are solved in day-ahead and intraday optimaldispatch by minimizing the expected value of totalcost in each scenario +e system stability is mainlyconsidered in real-time optimal dispatch since mostof the costs have been optimized +e expectedpower of the fast response device solved in the day-ahead and intraday dispatch is taken as the referenceto minimize the difference between the solvedcontrol variables and the expected value by rolloptimization and feedback correction +erefore inreal-time optimal dispatch it is only necessary toadjust the output power of fast response deviceappropriately based on the expected value accordingto the measured wind power which can not onlymeet the load power of system but also solve theproblem of volatility of DG power thus improvingthe stability of system

2 Markov Chain Dynamic Scenario Method

Markov chain dynamic scenario method characterizesforecast error via empirical distributions of a set of forecastbins using Markov chain to simulate the change process offorecast error distribution and the inverse transform isadopted to generate scenario according to the historicalforecast error distribution which ensure the reliability ofgenerated scenarios and the main steps are as follows

(1) Processing historical data collecting historical dataof wind and load to obtain the data pairs (measuredforecast) and transform the value of the data to per-unit values

(2) Generating the forecast bins choose 50 bins with002 pu bin widths in this case and every forecast hasa corresponding measurement which is assigned tothe same bin as the forecast +en sorting the datapairs (measured forecast) by the forecast values andassigned to the matching forecast power bins toobtain the forecast error distribution of each randomvariable in each forecast bin

(3) Discretizing the forecast error distribution of eachrandom variable into seven intervals centered on thezero mean with a width equal to the standard de-viation δ +e state of the corresponding interval i is



Pkt S1kt S2kt S7kt1113858 1113859 (1)

1113944

7

i1Sikt 1 (2)



Fkt xj1113872 1113873 1113944

j

i1Sikt j 1 2 7 (3)


Σ



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)



0le n mleΔt(5)



Δωt Fminus 1ik Φ Yt( 1113857( 1113857 (6)


Φ Yt( 1113857 1113946Yt

minus infin


radic dx (7)




Ekt



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ntimesn

(8)


Emn Nmn

1113936nj1 Nmj

(9)



Pkt+1 PktEkt (10)












min

1113944

Nt

t1cgridt 1113944

Ns


Nt

t11113944

NDGF

i11113944

Ns

s1πsC

FDGist + U

FDGit + D

FDGit

⎛⎝ ⎞⎠+

1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist + U

RDGit + D

RDGit1113872 1113873+

1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

Δt (11)











1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

R

DGist+ 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(12)





uFistP

FDGimin leP

FDGist le u

FistP

FDGimax (13)

uRistP

RDGimin leP

RDGist le u

RistP

RDGimax (14)



it





xFit + y

Fit le 1 (15)

xFit minus y

Fit u

Fit minus u

Fitminus 1 (16)


xRit + y

Rit le 1 (17)

xRit minus y

Rit u

Rit minus u

Ritminus 1 (18)

where xFit and yF


it and yRit are



PRDGist minus PR

DGistminus 11113868111386811138681113868

1113868111386811138681113868le uRit minus uR

itminus 11113868111386811138681113868

1113868111386811138681113868PRDGimin + ΔR

i

PFDGist minus PF

DGistminus 1

11138681113868111386811138681113868111386811138681113868le uF


11138681113868111386811138681113868111386811138681113868PF

DGimin + ΔFi

⎧⎨

⎩

(19)

where ΔRi and ΔF






2+ Qacijst1113872 1113873

21113874 1113875


(20)

0800

0900 0910 09150905


0900 1000

15min

5min


On-off state ofQAMT

On-off state ofRMT


decision


0000 0600 18001200 2400

1h





2+ Qacijst1113872 1113873

21113874 1113875


(21)



+Pacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875 Rvscij1113872 1113873

2+ Xvscij1113872 1113873

21113874 1113875

Uacsi( 11138572

(23)

Uvscsj

3

radic

3μMiUdcsk (24)




Esiηd

PESSist gt 0


Esi

PESSist lt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(25)











min1113944

Nt

t11113944

NDGF

i1C

FDGit + 1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist1113872 1113873

+ 1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

(29)



1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

RDGit + 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(30)







VSC


Uacsi

Rvscij Xvscij

Uvscsj

Udcsk





PDG(k + i | k) PDG0(k) + 1113936i


PESS(k + i | k) PESS0(k) + 1113936i


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(31)







(32)




⎧⎪⎨

⎪⎩

(33)



(34)





DGref(k + 2 | k) 1113858


T


ESSref(k + 2 | k) 1113858


T

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(36)


ΔuT(k + 1 | k)ΔuT

(k + 2 | k) ΔuT(k + N | k)1113966 1113967

(37)

Begin





Feedback correction


End

Yes

No




P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)


P0(k + 1) Preal(k + 1) + δ (39)




5 Case Study










WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References

































Pkt S1kt S2kt S7kt1113858 1113859 (1)

1113944

7

i1Sikt 1 (2)



Fkt xj1113872 1113873 1113944

j

i1Sikt j 1 2 7 (3)


Σ



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)



0le n mleΔt(5)



Δωt Fminus 1ik Φ Yt( 1113857( 1113857 (6)


Φ Yt( 1113857 1113946Yt

minus infin


radic dx (7)




Ekt



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ntimesn

(8)


Emn Nmn

1113936nj1 Nmj

(9)



Pkt+1 PktEkt (10)












min

1113944

Nt

t1cgridt 1113944

Ns


Nt

t11113944

NDGF

i11113944

Ns

s1πsC

FDGist + U

FDGit + D

FDGit

⎛⎝ ⎞⎠+

1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist + U

RDGit + D

RDGit1113872 1113873+

1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

Δt (11)











1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

R

DGist+ 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(12)





uFistP

FDGimin leP

FDGist le u

FistP

FDGimax (13)

uRistP

RDGimin leP

RDGist le u

RistP

RDGimax (14)



it





xFit + y

Fit le 1 (15)

xFit minus y

Fit u

Fit minus u

Fitminus 1 (16)


xRit + y

Rit le 1 (17)

xRit minus y

Rit u

Rit minus u

Ritminus 1 (18)

where xFit and yF


it and yRit are



PRDGist minus PR

DGistminus 11113868111386811138681113868

1113868111386811138681113868le uRit minus uR

itminus 11113868111386811138681113868

1113868111386811138681113868PRDGimin + ΔR

i

PFDGist minus PF

DGistminus 1

11138681113868111386811138681113868111386811138681113868le uF


11138681113868111386811138681113868111386811138681113868PF

DGimin + ΔFi

⎧⎨

⎩

(19)

where ΔRi and ΔF






2+ Qacijst1113872 1113873

21113874 1113875


(20)

0800

0900 0910 09150905


0900 1000

15min

5min


On-off state ofQAMT

On-off state ofRMT


decision


0000 0600 18001200 2400

1h





2+ Qacijst1113872 1113873

21113874 1113875


(21)



+Pacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875 Rvscij1113872 1113873

2+ Xvscij1113872 1113873

21113874 1113875

Uacsi( 11138572

(23)

Uvscsj

3

radic

3μMiUdcsk (24)




Esiηd

PESSist gt 0


Esi

PESSist lt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(25)











min1113944

Nt

t11113944

NDGF

i1C

FDGit + 1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist1113872 1113873

+ 1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

(29)



1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

RDGit + 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(30)







VSC


Uacsi

Rvscij Xvscij

Uvscsj

Udcsk





PDG(k + i | k) PDG0(k) + 1113936i


PESS(k + i | k) PESS0(k) + 1113936i


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(31)







(32)




⎧⎪⎨

⎪⎩

(33)



(34)





DGref(k + 2 | k) 1113858


T


ESSref(k + 2 | k) 1113858


T

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(36)


ΔuT(k + 1 | k)ΔuT

(k + 2 | k) ΔuT(k + N | k)1113966 1113967

(37)

Begin





Feedback correction


End

Yes

No




P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)


P0(k + 1) Preal(k + 1) + δ (39)




5 Case Study










WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References








































min

1113944

Nt

t1cgridt 1113944

Ns


Nt

t11113944

NDGF

i11113944

Ns

s1πsC

FDGist + U

FDGit + D

FDGit

⎛⎝ ⎞⎠+

1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist + U

RDGit + D

RDGit1113872 1113873+

1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

Δt (11)











1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

R

DGist+ 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(12)





uFistP

FDGimin leP

FDGist le u

FistP

FDGimax (13)

uRistP

RDGimin leP

RDGist le u

RistP

RDGimax (14)



it





xFit + y

Fit le 1 (15)

xFit minus y

Fit u

Fit minus u

Fitminus 1 (16)


xRit + y

Rit le 1 (17)

xRit minus y

Rit u

Rit minus u

Ritminus 1 (18)

where xFit and yF


it and yRit are



PRDGist minus PR

DGistminus 11113868111386811138681113868

1113868111386811138681113868le uRit minus uR

itminus 11113868111386811138681113868

1113868111386811138681113868PRDGimin + ΔR

i

PFDGist minus PF

DGistminus 1

11138681113868111386811138681113868111386811138681113868le uF


11138681113868111386811138681113868111386811138681113868PF

DGimin + ΔFi

⎧⎨

⎩

(19)

where ΔRi and ΔF






2+ Qacijst1113872 1113873

21113874 1113875


(20)

0800

0900 0910 09150905


0900 1000

15min

5min


On-off state ofQAMT

On-off state ofRMT


decision


0000 0600 18001200 2400

1h





2+ Qacijst1113872 1113873

21113874 1113875


(21)



+Pacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875 Rvscij1113872 1113873

2+ Xvscij1113872 1113873

21113874 1113875

Uacsi( 11138572

(23)

Uvscsj

3

radic

3μMiUdcsk (24)




Esiηd

PESSist gt 0


Esi

PESSist lt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(25)











min1113944

Nt

t11113944

NDGF

i1C

FDGit + 1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist1113872 1113873

+ 1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

(29)



1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

RDGit + 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(30)







VSC


Uacsi

Rvscij Xvscij

Uvscsj

Udcsk





PDG(k + i | k) PDG0(k) + 1113936i


PESS(k + i | k) PESS0(k) + 1113936i


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(31)







(32)




⎧⎪⎨

⎪⎩

(33)



(34)





DGref(k + 2 | k) 1113858


T


ESSref(k + 2 | k) 1113858


T

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(36)


ΔuT(k + 1 | k)ΔuT

(k + 2 | k) ΔuT(k + N | k)1113966 1113967

(37)

Begin





Feedback correction


End

Yes

No




P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)


P0(k + 1) Preal(k + 1) + δ (39)




5 Case Study










WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References
































xRit + y

Rit le 1 (17)

xRit minus y

Rit u

Rit minus u

Ritminus 1 (18)

where xFit and yF


it and yRit are



PRDGist minus PR

DGistminus 11113868111386811138681113868

1113868111386811138681113868le uRit minus uR

itminus 11113868111386811138681113868

1113868111386811138681113868PRDGimin + ΔR

i

PFDGist minus PF

DGistminus 1

11138681113868111386811138681113868111386811138681113868le uF


11138681113868111386811138681113868111386811138681113868PF

DGimin + ΔFi

⎧⎨

⎩

(19)

where ΔRi and ΔF






2+ Qacijst1113872 1113873

21113874 1113875


(20)

0800

0900 0910 09150905


0900 1000

15min

5min


On-off state ofQAMT

On-off state ofRMT


decision


0000 0600 18001200 2400

1h





2+ Qacijst1113872 1113873

21113874 1113875


(21)



+Pacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875 Rvscij1113872 1113873

2+ Xvscij1113872 1113873

21113874 1113875

Uacsi( 11138572

(23)

Uvscsj

3

radic

3μMiUdcsk (24)




Esiηd

PESSist gt 0


Esi

PESSist lt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(25)











min1113944

Nt

t11113944

NDGF

i1C

FDGit + 1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist1113872 1113873

+ 1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

(29)



1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

RDGit + 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(30)







VSC


Uacsi

Rvscij Xvscij

Uvscsj

Udcsk





PDG(k + i | k) PDG0(k) + 1113936i


PESS(k + i | k) PESS0(k) + 1113936i


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(31)







(32)




⎧⎪⎨

⎪⎩

(33)



(34)





DGref(k + 2 | k) 1113858


T


ESSref(k + 2 | k) 1113858


T

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(36)


ΔuT(k + 1 | k)ΔuT

(k + 2 | k) ΔuT(k + N | k)1113966 1113967

(37)

Begin





Feedback correction


End

Yes

No




P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)


P0(k + 1) Preal(k + 1) + δ (39)




5 Case Study










WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References

































2+ Qacijst1113872 1113873

21113874 1113875


(21)



+Pacijst1113872 1113873

2+ Qacijst1113872 1113873

21113874 1113875 Rvscij1113872 1113873

2+ Xvscij1113872 1113873

21113874 1113875

Uacsi( 11138572

(23)

Uvscsj

3

radic

3μMiUdcsk (24)




Esiηd

PESSist gt 0


Esi

PESSist lt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(25)











min1113944

Nt

t11113944

NDGF

i1C

FDGit + 1113944

Nt

t11113944

NDGR

i11113944

Ns

s1πsC

RDGist1113872 1113873

+ 1113944

Nt

t11113944

NESS

i11113944

Ns

s1πsCESSist( 1113857 + 1113944

Nt

t11113944

Nwt

i11113944

Ns

s1πsλ

curtist W

curtist1113872 1113873

(29)



1113944

NDGF

i1P

FDGist + 1113944

NDGR

i1P

RDGit + 1113944

Nwt

i1Pwtist minus W

curtist1113872 1113873

+ 1113944

NESS


(30)







VSC


Uacsi

Rvscij Xvscij

Uvscsj

Udcsk





PDG(k + i | k) PDG0(k) + 1113936i


PESS(k + i | k) PESS0(k) + 1113936i


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(31)







(32)




⎧⎪⎨

⎪⎩

(33)



(34)





DGref(k + 2 | k) 1113858


T


ESSref(k + 2 | k) 1113858


T

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(36)


ΔuT(k + 1 | k)ΔuT

(k + 2 | k) ΔuT(k + N | k)1113966 1113967

(37)

Begin





Feedback correction


End

Yes

No




P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)


P0(k + 1) Preal(k + 1) + δ (39)




5 Case Study










WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References


































PDG(k + i | k) PDG0(k) + 1113936i


PESS(k + i | k) PESS0(k) + 1113936i


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(31)







(32)




⎧⎪⎨

⎪⎩

(33)



(34)





DGref(k + 2 | k) 1113858


T


ESSref(k + 2 | k) 1113858


T

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(36)


ΔuT(k + 1 | k)ΔuT

(k + 2 | k) ΔuT(k + N | k)1113966 1113967

(37)

Begin





Feedback correction


End

Yes

No




P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)


P0(k + 1) Preal(k + 1) + δ (39)




5 Case Study










WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References

































P(k + 1 | k) P0(k) + ΔuT(k + 1 | k) (38)


P0(k + 1) Preal(k + 1) + δ (39)




5 Case Study










WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References


































WT

DG_F

DG_R

7

22

11 13

21

1 2 5 6 8

23 24

20

9 10 124

4443

30

4039

1814 15 16 17

45

34

31

42 35

32

4625

5049

364138DCAC

DCAC

2826 27 3329 47 48

37

DCAC

DCAC

3

DG_R

WT

WT

DG_F

WT

ESS

ESS

ESS19

ESS


Time (h)0 6 12 18 24

Elec

tric

ity p

rices

($k

Wh)

0

0034

0048

0062

0076

009

0104

0118

0132


Time (h)0 6 12 18 24

Pow

er (M

W)

004006008

01012014016018

02022




Time (h)0 6 12 18 24

Pow

er (M

W)

0123456789

10

Load scenario 3




Time800 815 830 845 900 915 930 945 1000

RMT

(MW

)

005

01

015

02

025

03

Exch

ange

pow

er (M

W)

25

3

35

4

45

5




G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References
































G 1113944T

t11113944

kc

k1


11138681113868111386811138681113868

11138681113868111386811138681113868

Pdayaheadtk

(40)




Π 1T

1113944

T

t1g Pt( 1113857 (41)



1113896 (42)





Γ 1113944

NDG

i1

PmaxDGi minus Pmin

DGi

PDGi

times 100 (43)

Time

800

805

810

815

820

825

830

835

840

845

850

855

900

Pow

er (M

W)

ndash0050

00501

01502

02503

035

ESS2

ESS4ESS3

QAMT1

ESS1QAMT2


Time800 810 820 830 840 850 900

Stat

e of c

harg

e

0

01

02

03

04

05

06

07

ESS1ESS2

ESS3ESS4


Time (h)0 6 12 18 24

Pow

er (K

W)

02

6

10

14

18








6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References




































6 Conclusions







Time




005

01

015

02

025

03

035

Pow

er (M

W)

815 830 845 900800Time







Data Availability




References


































Data Availability




References
































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