finite control set model predictive control for complex...

Research ArticleFinite Control Set Model Predictive Control for Complex EnergySystem with Large-Scale Wind Power

Yang-Wu Shen 1 Jin-Rong Yuan2 Fei-Fan Shen3 Jia-Zhu Xu4

Chen-Kun Li1 and Ding Wang1

1State Grid Hunan Electric Power Company Limited Research Institute Changsha Hunan China2State Grid Changde Power Supply Company China3Technical University of Denmark Lyngby Denmark4Hunan University Changsha Hunan China

Correspondence should be addressed to Yang-Wu Shen shenyangwu126com

Received 9 April 2019 Accepted 23 June 2019 Published 28 July 2019

Guest Editor Xiaoqing Bai

Copyright copy 2019 Yang-Wu Shen et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Complex energy systems can effectively integrate renewable energy sources such as wind and solar power into the informationnetwork and coordinate the operation of renewable energy sources to ensure its reliability In the voltage source converter-based high voltage direct current system the traditional vector control strategy faces some challenges such as difficulty in PIparameters tuning and multiobjective optimizations To overcome these issues a finite control set model predictive control-based advanced control strategy is proposed Based on the discrete mathematical model of the grid-side voltage source converterthe proposed strategy optimizes a value function with errors of current magnitudes to predict switching status of the grid-sideconverter Moreover the abilities of the system in resisting disturbances and fault recovery are enhanced by compensating delay andintroducing weight coefficients The complex energy system in which the wind power is delivered by the voltage source converter-based high voltage direct current system is modeled by Simulink and simulation results show that the proposed strategy is superiorto the tradition PI control strategy under various situations such as wind power fluctuation and fault occurrences

1 Introduction

To deal with energy shortage and environment pollutionissues the development of complex energy systems whichcan effectively coordinate the operation with various renew-able energy sources such as wind and solar power toensure its reliability has drawn much attention from manycountries The focus is on the wind farm due to its highefficiency of wind power utilization and no occupation ofland resources [1ndash4] With the increasing capacity of thewind farm and innovations of power electronic technologiesmany researchers focus on applications of the voltage sourceconverter-based high voltage direct current (VSC-HVDC)technique and require better operational performance of theconverter of the VSC-HVDC system

The model predictive control (MPC) [5ndash9] has beenextensively applied in the control of modular multilevel

inverters [10] uninterruptible power systems [11] andneutral-point clamped converters [12] due to its advantagessuch as control flexibility and being free of modulators TheMPC strategies used for the control of the converter canbe classified as the continuous control set MPC and thefinite control set (FCS) MPC For the continuous control setMPC a modulator generates switching states based on thecontinuous output of the predictive controller However theFCS-MPC considers the limited number of switching statesof the converter for solving optimization problems

In [13] the MPC was applied to the low voltage ride-through (LVRT) of photovoltaic (PV) power plants toimprove the transient stability of PV power plants Theproposed MPC based strategy is able to control the outputcurrent of the inverters quickly based on the referencecurrent After a fault in the grid the proposed strategy cancontrol the reactive power output of the PV power plant to

HindawiComplexityVolume 2019 Article ID 4358958 13 pageshttpsdoiorg10115520194358958

2 Complexity

support the system voltage and improve the transient stabilityof the systemThe simulation results show that the PV powerplant is able to support the voltage with the proposed strategyin the low voltage situation

In [14ndash17] the FCS MPC strategy was used to optimizethe control of inverters A mixed logical dynamical (MLD)model for inverters was proposed in [15] By treating theMLD model as a predictive model a FCS-MPC strategy forinverters was developed The proposed strategy considersthe discreteness of inverters and selects the switch statecorresponding to the optimal objective value as the controlsignal for inverters to control the output voltage The simu-lation and test results validate that the proposed FCS-MPCstrategy can improve the output voltage quality of invertersTo improve the conventional FCS-MPC strategy a multistepprediction FCS-MPC strategy for converters is proposed in[15] in which the optimal and suboptimal control actions areconsidered in one control cycleThe optimal control action isdetermined in a fashion that the control action is optimal intwo control cycles Simulation results show that the proposedmultistep FCS-MPC scheme can improve the quality of theoutput voltage of the three-phase inverter and reduces thetracking error of the reference voltage as compared withthe conventional FCS-MPC In [16] the authors proposeda FCS-MPC strategy for a four-level converter to controloutput currents and voltages of flying capacitors A discretemodel of the converter is developed to obtain switchingstates During each sampling period the predicted variablesare evaluated by an evaluation function and the optimalswitching state with the minimum cost value is selected andapplied to the converter In [17] the authors proposed asimplified FCS-MPC with extended voltage vectors for two-level three-phase grid-connected converters The proposedalgorithm uses multiple voltage vectors for the predictionprocess to reduce the ripple in the grid currentMoreover theproposed approach utilizes a preselection scheme along witha simplified MPC approach to reduce the number of voltagevectors used in the proposed strategy Simulations show thatthe proposed strategy retains the effectiveness obtained inthe case where all the voltage vectors are used and at thesame time the current ripple is not adversely affected and thecontrol delay is effectively reduced

Improved MPC strategies were proposed for the STAT-COM and multilevel converters in [18 19] A novel controldelay elimination for the MPC strategy was proposed in[18] for the control of the cascaded STATCOM The MPCbased optimization problem was proposed and simplified forthe possible switching states Based on the further recursionof the simplified MPC based model the effect of controldelay on the control performance is reduced The simulationresults show that the proposed delay elimination for theMPC strategy can improve current tracking control of thecascaded STATCOM and the system has strong robustnessIn [19] the discrete mathematic model of the modularmultilevel converter-based HVDC (MMC-HVDC) system isdeveloped and an improved MPC strategy is proposed forthe five-level MMCMoreover the improvedMPC strategy iscombined with the voltage-sequencing algorithm to reducecomputational burdens and realize the transmission power

control in the MMC-HVDC system and circulating currentelimination

In [20ndash23] the MPC strategies were applied to thecontrol of electric motors In [20] the authors proposeda MPC strategy combined with a disturbance observer(DOB) for regulating the torque of a permanent magnetsynchronous motor (PMSM) without the steady state errorIn the proposed strategy the online optimal solutions can beobtained without relying on a numeric algorithm based onthe property of the input matrix of the PMSM The resultsshow that the proposed MPC strategy ensures satisfactorytorque control performance A quasideadbeat MPC strategyfor induction motors was proposed in [21] By building arolling optimization problem the optimal switching statecorresponding to the optimal voltage vector was selected asthe output of the inverter The simulations and experimentalresults show that the proposed strategy can reduce com-putational time and ensure satisfactory static and dynamicperformance for torque

However the above researches mainly focus on thesteady state and have not studied operational performanceof inverters under renewable energy integration and systemdisturbances To deal with the above issues a FCS-MPCbased control strategy for the VSC-HVDC system is pro-posed The control strategy generates the reference valuethrough the outer loop and compares the reference valuewith the predicted value obtained under a given voltagevector Then the switching status corresponding to the valuefunction with the smallest difference is obtained and used inthe next sampling period which can achieve the fast trackingof the reference value Moreover abilities of the systemin resisting disturbances and fault recovery are enhancedby compensating delay and introducing weight coefficientsThe VSC-HVDC connected OWF system is modeled in theMATLABSimulink and simulation results validate that theproposed FCS-MPC strategy is superior to the tradition PIcontrol strategy under various situations such as wind powerfluctuation and fault occurrences

The contributions of this paper are summarized as fol-lows (1) a FCS-MPC based control strategy for the complexenergy system is proposed considering the renewable energyintegration and system disturbances (2) a MPC based delaycompensation technique is proposed Compared with theconventional PI control strategy the proposed FCS-MPChas the following advantages (1) it is easy to tune controlparameters (2) it can realize multiobjective optimization andincorporate constraints (3) there is no need to implement thedecoupling process (4) no PMWmodulators are required

2 Control Strategies for Wind Farm-SideVSC and Direct Driven Permanent MagnetSynchronous Generator

Figure 1 shows the typical configuration of the OWF con-nected to an external AC grid through the complex energysystem The complex energy system consists of the windfarm-side VSC (WF-VSC) the grid-side VSC (GS-VSC) andthe DC transmission system To ensure utilization of the

Complexity 3

Offshore wind farm

WF-VSC GS-VSC

Grid

2C

2C

2C

2C AC

+

-

+

-

P７+jQ７

T1

Udc1 Udc2

P＞＝ P３+jQ３

ZＭ

T2

Figure 1 Typical configuration of the wind farm connected to an external AC grid though the complex energy system

OWP and secure operation of the complex energy systemthe GS-VSC shouldmaintain the steadyDC voltage of the DCtransmission system

21 Control Strategy for the WF-VSC The mathematicalmodel of theWF-VSC in the synchronized rotating d-q frameis formulated as below

119871d119894sdd119905 = 119906sd minus 119894sd119877 + 120596푠119871119894sq minus Vsd

119871d119894sqd119905 = 119906sq minus 119894sq119877 minus 120596푠119871119894sd minus Vsq

119862d119906dcd119905 = 32 (119878sd119894gd + 119878sq119894sq) minus 119894dc

(1)

where 119906sd and 119906sq are the d-axis and q-axis components of thethree-phase voltage respectively 119894sd and 119894sq are the d-axis andq-axis components of the three-phase current respectivelyVsd and Vsq are the d-axis and q-axis components of thevoltage at the converter side respectively 119878sd and 119878sq arethe d-axis and q-axis components of the switching functionrespectively 120596푠 is synchronized angular velocity The directcontrol strategy is applied to maintain the voltage magnitudeand frequency at the WF side

The control structure of theWF-VSC is shown in Figure 2It can be seen that the voltage magnitude and phase at theWF side are controlled through commands in d-q axis andthe synchronized angular velocity of the WF-VSC To reducecontrol complexity the initial voltage angle at the WS side isset as zero and voltage magnitude components in d-q-axisare used for feedback control The differences between thereference values and real-time values of voltage magnitudeare used to obtain the modulation ratio and generate thetrigger pulse

22 Control Strategy for Direct Driven PermanentMagnet Syn-chronous Generator The typical configuration of the directdriven permanent magnet synchronous generator (PMSG) isshown in Figure 3 The direct driven PMSG system consists

AC

Wind FarmBWF

WF-VSC

dqabc

PWMulowastsd

usd

ulowastsq

usq

isdmax

PI PI

PI

isdmin

isd

ilowastsdisqmax

isqmin

ilowastsq

isq

Ls

PI

Ls

ulowastd

ulowastd

ej

usd

usq

Figure 2 Control structure of the WF-VSC

of the wind turbine PMSG generator-side converters andgrid-side converters

The double closed loop control strategy namely the outerloop of angular velocity and inner loop of current is appliedto the generator-side converter to achieve the MPPT Thegrid-side converter controls the DC voltage to ensure windpower integration In this paper the PMSG-based wind farmis represented by an equivalent single-machine model Sincethe dynamic response speed of the grid-side converter isfaster than the ones of the wind turbine and generator-sideconverters the wind turbine the PMSG and generator-sideconverters are simplified as an equivalent voltage resourceas shown in Figure 3 Different levels of wind power outputare simulated by controlling power output of the grid-sideconverter

The control strategy for the grid-side converter is shownin Figure 4 In this paper input wind power variation issimulated by controlling the grid-side converter of the PMSGbecause this study focuses on the verification of the abilitiesof the system with the proposed control strategy in resistingdisturbances and fault recovery under different situationssuch as wind speed variation and fault occurrence As shownin Figure 4 the actual wind speed is simulated by the windpower generator which generates the varying input windpower and obtains the d-axis component of the reference

4 Complexity

Pitch angle control

Control system

GS converterMS converter

GS converter

Ps+jQＭ

U＞＝

PＡＬＣ＞+jQＡＬＣ＞

U＞＝


PMSG

+

Figure 3 Typical configuration of the direct driven PMSG

PI

abcdqMeasurementunit

Wind power generator

PI dqabc PWM

u＞＝


iＱ

uＬ uＱiＱＫ

ilowastwfq

iＱ＞

ilowastwfd

+

-

Figure 4 The PI control structure of grid-side controller of the PMSG

value of the three-phase AC current The reference value ofthe three-phase AC voltage is compared with the measurevalue to obtain the q-axis component of the reference valueof the three-phase current through the PI unit Then the d-qaxis components of the three-phase current are adjusted byPI units and transformed using Park inverse transformationto control the converter

3 FCS-MPC Based ControlStrategy for GS-VSC

The FCS-MPC based control strategy for the GS-VSC isshown in Figure 5 As shown in Figure 5 the proposedcontrol strategy is applied to the DC voltage control of theGS-VSCThe DC voltage reference value 119906lowastdc is compared tothe actual value 119906dc and the difference between them is usedto generate the current reference value through the PI unitsThen the measurement unit collects three-phase grid voltage(e) and grid current (i) and these values are used to obtain

the predicted values in the 120572120573 coordinate system by using theproposed predicted models Finally a value function is usedto evaluate the difference between the predicted value andthe reference value The value function is optimized over arolling horizon to obtain the optimal switching combinationcorresponding to the value function with the smallest valueFinally the optimal switching combination is applied tocontrol the GS-VSC

As the most important blocks of the FCS-MPC basedcontrol strategy the predicted model of the GS-VSC andthe value function are described in detail in the followingsubsections In addition the method of delay compensationis also illustrated

31 Discrete Predicted Model of the GS-VSC The discretepredicted model of the GS-VSC is formulated and describedin this subsection The structure of the GS-VSC is shown inFigure 6TheGS-VSC consists of six IGBT and six antiparalleldiodes119906a119906b and119906c represent the three-phase output voltage

Complexity 5

AC

DC

GS-VSCBGS

Value function

Predicted model

Measurement unit

PI

ulowast＞＝ u＞＝

ilowast(k+2)S＜＝

i(k+2)

e(k) i(k)

abc

abc

Figure 5 FCS-MPC based control strategy for the GS-VSC considering delay compensation

idc iL

udc C

N

u

u＜

i

ib

ic

R L e

e＜

e＝

o

u＝

Figure 6 The structure of the GS-VSC

of the converter 119894a 119894b and 119894c represent the three-phase gridcurrent 119890a 119890b and 119890c represent the three-phase grid voltage119906a 119906b and 119906c represent the three-phase output voltage of theconverter L is the reactance R is the resistance and C is thecapacitance 119906dc 119894dc and 119894L are the DC voltage DC inputcurrent and DC output current respectively More details onthe structure of the GS-VSC can be found in [24ndash27]

To derive the predictedmodel of the grid current the GS-VSC should be modeled The dynamic equation of the gridcurrent in the three-phase stationary reference frame is asfollows

119871did119905 = u minus e minus 119877i (2)

where i is the vector of current u is the vector of outputvoltage of converter e is the vector of the grid voltage Vectorsi u and e can be expressed as

[[[iue

]]]= 23 [[[

119894a 119894b 119894c119906aN 119906bN 119906cN119890a 119890b 119890c]]][[[[

1a

a2

]]]]

(3)

where a= ej2휋3 119906aN 119906bN and 119906cN represent the three-phaseoutput voltage of the converter to the neutral point and canbe obtained using the following equation

119906xN = 119878x119906dc (x = a b c) (4)

where 119878x is the switching function representing the switchingstatus of each bridge arm of the converter 119906dc is the DCvoltage The 119878x can be expressed as follows [28]

119878x = 0 119906119901119901119890119903 119886119903119898 119894119904 119900119901119890119899 119897119900119908119890119903 119886119903119898 119894119904 1198881198971199001199041198901198891 119906119901119901119890119903 119886119903119898 119894119904 119888119897119900119904119890119889 119897119900119908119890119903 119886119903119898 119894119904 119900119901119890119899 (5)

Suppose that the sampling period is 119879푠 the derivative ofthe grid current can be discretized using the forward Eulerapproximation method as below

d119894d119905 asymp 119894 (119896 + 1) minus 119894 (119896)119879s (6)

6 Complexity

Table 1 Relation between the value function switching status and voltage vector

Value function Switching combinations (119878a 119878b 119878c) Voltage vectorsg0 000 1198800 = 0g1 100 1198801 = 23119906dcg2 110 1198802 = 13119906dc + 119895radic33119906dcg3 010 1198803 = minus13119906dc + 119895radic33119906dcg4 011 1198804 = minus23119906dcg5 001 1198805 = minus13119906dc minus 119895radic33119906dcg6 101 1198806 = 13119906dc minus 119895radic33119906dcg7 111 1198807 = 0

where i(k+1) and i(k) are sampling current values in k+1th andk-th sampling periods respectively Substitute (6) into (2) thepredicted current can be expressed as

119894 (119896 + 1) = 119879s119871 (119906 (119896) minus 119890 (119896)) + (1 minus 119877119879s119871 ) 119894 (119896) (7)

The expression of (7) in the 120572120573 coordinate system can beobtained using Clarke transformation as below

[119894훼 (119896 + 1)119894훽 (119896 + 1)] =119879푠119871 [

119906훼 (119896) minus 119890훼 (119896)119906훽 (119896) minus 119890훽 (119896)]

+ (1 minus 119877119879푠119871 )[119894훼 (119896)119894훽 (119896)](8)

where 119894훼(119896+1) and 119894훽(119896+1) are 120572-axis and 120573-axis componentsof the current in k+1th period respectively 119906훼(119896) and 119906훽(119896)are 120572-axis and 120573-axis components of the output voltage ofconverter in k-th period respectively 119890훼(119896) and 119890훽(119896) are120572-axis and 120573-axis components of the grid voltage in k-thperiod respectively As shown in (8) the current of the GS-VSC in k+1th period can be accurately predicted accordingto the current measurement of the GS-VSC ink-th periodwhich can achieve the fast tracking and control of theGS-VSCcurrent and enhance the ability of the GS-VSC in resistingsystem disturbances

32 Value Function Themain goal of theGS-VSC is to ensurepower balance of the VSC-HVDC transmission system andachieve wind power integration The control strategy of theGS-VSC is described as follows According to the desiredreference output and the current input of the GS-VSC theoutput voltage vector (U) of the GS-VSC can be obtained bydetermining the switching function value namely switchingstatus of each bridge arm of the converterThen based on theoutput voltage vector (U) grid voltage vector (E) and equiva-lent reactance119885s themagnitude and angle controllable there-phase current (119894a 119894b 119894c) can be obtained to control the inputand output power of the GS-VSC Therefore it is importantto determine the optimal output voltage vector (U) of the GS-VSC

It can be seen from (4) and (5) that the output voltagevector (U) is determined by the switching functions ofthree bridge arms namely 119878a 119878b and 119878c In the study

it is assumed that the GS-VSC is a three-phase two-levelconverter Considering there are three switching functionvalues (119878a 119878b and 119878c) there are eight possible switchingstates and eight corresponding voltage vectors MoreoversinceU0=U7 seven possible voltage output vectors are shownin Table 1

The traditional GS-VSC uses the double closed loopstructure (outer loop of power and inner loop of current) todetermine the switching functions (119878a 119878b and 119878c) to controlthe AC voltage output and current (power output) of the GS-VSC However parameters of the PI controller are sensitive tothe systemparameters and it is difficult to tune PI parametersIn addition the feedforward compensator term affected bythe circuit parameters is required to be decoupled in thetraditional control strategy To overcome these issues a FCS-MPC based control strategy is proposed

FCS-MPC is a model-based closed loop control methodBased on the eight possible switching combinations andeight corresponding voltage vectors (U) the predicted GS-VSC current value of the next period can be obtained usingthe discrete predicted model of the GS-VSC given by (8)Then comparing the predicted value with the reference valueusing the value function defined in (9) the optimal switchingcombination corresponding to the smallest value of valuefunction is obtained and used to generate trigger pulse whichcan achieve the optimal control of the GS-VSC

g = 10038161003816100381610038161003816119894lowastg훼 (119896 + 1) minus 119894g훼 (119896 + 1)10038161003816100381610038161003816+ 10038161003816100381610038161003816119894lowastg훽 (119896 + 1) minus 119894g훽 (119896 + 1)10038161003816100381610038161003816

(9)

where 119894g훼(119896 + 1) and 119894g훽(119896 + 1) are the real and imaginaryparts of the predicted current vector in the k+1 period undera given voltage vector respectively 119894lowastg훼(119896+1) and 119894lowastg훽(119896+1) arethe real and imaginary parts of the predicted current vectorin the k+1 period under a given voltage vector respectively

Repeat the above procedures in the following samplingperiods and thus the output current of the GS-VSC isoptimized and controlled over the rolling horizon Basedon the above analyses compared with the traditional PIcontrol-based double closed loop control strategy the FCS-MPC strategy controls converters directly according to thelimited switching combinations As such there is no needto implement the decoupling process and the complex PItuning process Moreover no modulators are required and

Complexity 7

multilevel constraints can be considered In particular thereis the lowest calculation complexity when two-level converteris used

33 Consideration of Delay Compensation in the ProposedStrategy The difference between the current reference andcurrent measurement is used to construct the objective func-tion namely the value function in (9) which transforms theproblem of finding the optimal modulation satisfying controltargets into a problem of finding the optimal switchingcombination corresponding to the value function with thesmallest value However the current reference in (9) is thevalue in the future period which causes delay in the controlof the GS-VSC and affects the control accuracy and responsespeed of the GS-VSC with the FCS-MPC strategy To dealwith this problem this study proposes to modify the valuefunction using the predicted current value in k+2th periodThe predicted function of current in k+2th period is

119894 (119896 + 2 | 119896) = 119879s119871 (119906 (119896 + 1) minus 119890 (119896 + 1))+ (1 minus 119877119879s119871 ) 119894 (119896 + 1)

(10)

where i(k+1) and 119894(119896 + 2 | 119896) are the predicted currents inthe (k+1)-th and (k+2)-th periods using information collectedin k-th period respectively u(k+1) is the output voltage inthe (k+1)-th period e(k+1) is the grid voltage in the k+1thperiod

The value function considering the delay compensation isas follows

g = 10038161003816100381610038161003816119894lowastg훼 (119896 + 2 | 119896) minus 119894g훼 (119896 + 2 | 119896)10038161003816100381610038161003816+ 10038161003816100381610038161003816119894lowastg훽 (119896 + 2 | 119896) minus 119894g훽 (119896 + 2 | 119896)10038161003816100381610038161003816

(11)

To ensure the stability of the DC voltage under the faultoccurrence andwind power fluctuation theDC current erroris introduced into the value function as below

g = 10038161003816100381610038161003816119894lowastg훼 (119896 + 2 | 119896) minus 119894g훼 (119896 + 2 | 119896)10038161003816100381610038161003816+ 10038161003816100381610038161003816119894lowastg훽 (119896 + 2 | 119896) minus 119894g훽 (119896 + 2 | 119896)10038161003816100381610038161003816 + 120582 1003816100381610038161003816119906lowastdc minus 119906dc1003816100381610038161003816

(12)

where 120582 is the weight coefficient The predicted value of theDC voltage is introduced to the value function to improvethe stability of the DC voltage under steady state and faultoccurrences

34 The Algorithm of the FCS-MPC Based Control StrategyThe algorithm of the FCS-MPC based control strategy isillustrated in Figure 7 and has the following steps

Step 1 Formulate the mathematical model of the GS-VSCbased on the eight switching combinations and the rela-tion between the switching combination and correspondinginputoutput voltage and current

Step 2 Construct the discrete-timemodel in order to predictthe values of control variables in future periods

Start

Real-time measurement

YesNo

No

Yes

i (k)e (k)U＞＝

Set initial of gＩＪ as infinite

Predict current i(k+1) (7)

for p=07

Predict current i(k+2|Ｅ) (10)

Calculate value function (12)

gltgＩＪ

gＩＪ=g op=i

i=7

Figure 7 The flow chart of the FCS-MPC algorithm for GS-VSC

Step 3 Based on the switching states currently appliedconstruct the discrete current model (8) in order to predictthe current in k+1th period

Step 4 Predict the current in k+2th period for each possibleswitching combination

Step 5 Use the value function representing the expectedperformance of the system to evaluate all possible switchingcombinations

Step 6 Choose the voltage vector corresponding to the valuefunction with the smallest value and obtain the correspond-ing optimal switching combination

Step 7 Update the status of switches based on the optimalswitching combination and go back to step 2 for the nextsampling period

4 Case Studies

The VSC-HVDC connected offshore WF as shown inFigure 1 is modeled in the MATLABSimulink to validatethe efficiency of proposed FCS-MPC strategyThe simulationparameters are listed in Table 2

41 Case 1 Wind Power Fluctuation The comparisonsbetween the proposed FCS-MPC strategy and traditional PIdouble closed loop control strategy under the wind power

8 Complexity

Table 2 Simulation parameters

Parameters ValuesRated capacity of wind farms PMW 4 times 300DC voltage119906dckV plusmn320Length of DC transmission line km 300DC capacitor C120583F 75Reactance of line LmH 200Sampling period119879s120583s 50Number of time steps 60000

P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast

MPC control １lowast

PI control

1 11 12

t (s)05 1 15 2

(a) Active and reactive power absorbed by grid

MPC controlPI control

1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent

(b) Grid voltage and current

t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage

Figure 8 Response characteristics with two strategies under wind power fluctuation

fluctuation are carried out in this caseThewindpower outputis 600MW between 0s to 1s and increases to 1100MW at 11sand then remains unchanged It is assumed that the windfarm operates with the unity power factor The simulationresults of theGS-VSCwith two strategies are shown in Figures8(a)ndash8(c)

As shown in Figures 8(a)ndash8(c) the GS-VSC with twostrategies can quickly respond to theWF power output varia-tion and achieve steady wind power integration Comparedwith the traditional double closed PI control strategy theFCS-MPC adopts the single loop (outer loop of voltage)control strategy which enables the GS-VSC to have a fasterresponse speed and higher response accuracy as shownin Figures 9(a)ndash9(b) Moreover as shown in Figure 9(c)the DC voltage of the VSC-HVDC system is restoredto the reference value more rapidly when the FCS-MPCcontrol strategy is used because the term involved in theDC predicted voltage is considered in the value functionTherefore the GS-VSC with the proposed FCS-MPC strategycan ensure the steady operation of the VSC-HVDC system

and has better performance under the steady state opera-tion

42 Case 2 AC Fault Occurrence at Grid Side It is assumedthat a three-phase short-circuit fault occurs at grid side at 2sand lasts for 10msThe response characteristic of the GS-VSCsystem is shown in Figures 9(a)ndash9(c)

As shown in Figure 9 when the traditional PI controlstrategy is applied to the GS-VSC the fault occurrence hasbig impacts on the active reactive power outputs voltageand current outputs of GS-VSC and they are restored tothe reference values slowly In addition due to the limitedability of the traditional PI control strategy in controlling theDC voltage the DC voltage cannot be restored to referencevalue within 3s as shown in Figure 9(c) However whenapplying the proposed FCS-MPC strategy the impacts of thefault occurrence on the outputs of GS-VSC are limited andthe activereactive power outputs and voltage and currentoutputs ofGS-VSCare restored to the reference values rapidlyMoreover the DC voltage is restored to the reference value

Complexity 9

MPC control PI control

P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P

(a) Active and reactive power absorbed by the grid


05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215

(b) Grid voltage magnitude and current magnitude

18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)

(c) DC voltage of VSC-HVDC

Figure 9 Response characteristic VSC-HVDC with two strategies under AC fault occurrence at grid side

within 25s because the predictive control for the DC voltageis considered in the proposed strategy thus improving theability of the GS-VSC in controlling the DC voltage underfault occurrences

43 Case 3 DC Fault Occurrence It is assumed that a DCline fault occurs at the left side of the DC transmission line at20s and lasts for 100ms The response characteristics of theVSC-HVDC system with two control strategies are shown inFigures 10(a)ndash10(e)

As shown in Figure 10(a) the active and reactive powerdecrease to -2200MW and -2000MW respectively in the PIcontrol strategy while both the active and reactive powerdecrease to -1000MW in the proposed FCS-MPC strategy Asshown in Figures 10(b) and 10(c) the AC voltage decreases to075 pu and the maximum transient current reaches 5 puthat far exceeds the maximum tolerant level of the GS-VSCWhen the FCS-MPC strategy is applied to the GS-VSC asshown in Figures 10(d) and 10(e) the AC voltage decreases to09 pu and the maximum transient current is 24 pu It canbeen seen that the fluctuations of AC voltage AC current andactivereactive power are smaller in the proposed FCS-MPCstrategy which demonstrates the better performance of theFCS-MPC strategy

44 Case 4 Grid Voltage Drops To further validate the effec-tiveness of the proposed FCS-MPC strategy the simulationsare conducted when grid voltage drops It is assumed that thegrid voltage decreases from 1pu to 05 pu at 20s and thevoltage remains 05 pu for 100msThe simulation results areshown in Figures 11(a)ndash11(e)

As shown in Figures 11(a)ndash11(e) when the proposedFCS-MPC strategy is applied the active power decreases

to 540MW and is restored to the normal level at 214sThe reactive power has a very small fluctuation The ACvoltage can be restored to 10 pu rapidly after the fault iscleared and there is a very small fluctuation in AC currentHowever when the PI control strategy is used the activepower decreases to 550MW and is restored to the normallevel at 225s The reactive power increases to 500Mvar and isrestored to the normal level slowly Likewise the AC voltageand AC current are restored to the normal level slowlyTherefore the FCS-MPC strategy makes the system moreresistant to system disturbances

45 Case 5 Comparative Analysis of Harmonic Distor-tion Rates of Cases1-4 Perform the Fourier analyses underselected conditions namely the period (12s-14s) in Case 1with the maximum wind power output and periods (23s-25s) in Case 2-Case 4 The distortion rates of the AC voltageand AC current under different operation conditions areshown in Table 1

As shown in Table 3 Cases 1-4 represent the Fourieranalysis results under the steady state conditions under thewindpower fluctuation underAC fault occurrence at the gridside underDC fault occurrence and under grid voltage droprespectively It can be seen from Table 1 that in the proposedFCS-MPC strategy the distortion rates of grid-connectedvoltage and current of GS-VSC are lower than 1 which isfar lower than the one in the traditional PI control strategy

5 Conclusions

To overcome the issues in the operation of the complexenergy system this study proposes a FCS-MPC based novel

10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119

(b) Grid voltage with PI control strategy

Curr

ent (

pu

)

t (s)

3

0

minus3

232119

(c) Grid current with PI control strategy

Volta

ge (p

u)

t (s)

1

0

minus1

232119

(d) Grid voltage with FCS-MPC strategy

Curr

ent (

pu

)

t (s)

3

0

minus3

232119

(e) Grid current with FCS-MPC strategy

Figure 10 Response characteristic with two control strategies under DC fault

Table 3 Harmonic distortion rates of Cases 1-4 with the FCS-MPC and PI strategy

Current VoltageFCS-MPC PI FCS-MPC PI

case 1 098 155 053 225case 2 062 205 048 294case 3 037 422 042 520case 4 048 359 075 694

control strategy The proposed control strategy has a simplecontrol structure removes the inner loop of current andcomplex PI parameter tuning process and achieves multiob-jective optimization of the complex energy systemMoreoverthe proposed control strategy considers the impact of delayand introduces the term of the DC voltage prediction in thevalue function to improve the stability of DC voltage controland enhances the abilities of the complex energy system in

resisting disturbances and recovering after faults The simu-lation results under the wind power fluctuation three-phaseshort circuit fault and grid voltage drop validate that thesystem with the FCS-MPC strategy has better dynamic char-acteristics and parameter robustnessMoreover the proposedstrategy improves the abilities of the VSC-HVDC in resistingdisturbances and fault recovery and reduces distortion ratesof the grid-connected voltage and current of the GS-VSC

Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119

(b) Voltage at grid side with PI control strategy

Curr

ent (

pu

)

1

0

minus1

t (s)232119

(c) Current at grid side with PI control strategy

Volta

ge (p

u)

1

0

minus1

t (s)232119

(d) Voltage at grid side with FCS-MPC strategy

Curr

ent (

pu

)

1

0

minus1

t (s)232119

(e) Current at grid side with FCS-MPC strategy

Figure 11 Response characteristic with two control strategies when grid voltage drops

Nomenclature

119906sd 119906sq d-axis and q-axis components of thethree-phase voltage119894sd 119894sq d-axis and q-axis components of thethree-phase current

Vsd Vsq d-axis and q-axis components of thevoltage at the converter side119878sd 119878sq d-axis and q-axis components of theswitching function120596s Synchronized angular velocity119906a 119906b 119906c Three-phase output voltage of theconverter119894a 119894b 119894c The three-phase grid current119890a 119890b 119890c The three-phase grid voltage119906a 119906b 119906c The three-phase output voltage of theconverter119871 Reactance119877 Resistance

119862 Capacitance119906dc 119894dc 119894L The DC voltage DC input current andDC output current

i u e The vector of current the vector of outputvoltage of converter and the vector of thegrid voltage119906xN x=a b c the three-phase output voltage ofthe converter to the neutral point119878x x=a b c the switching functionrepresenting the switching status of eachbridge arm of the converter119906dc The DC voltage of the VSC-HVDC system119894(119896) The sampling current value in k-thsampling period119894훼(119896 + 1) 120572-axis component of the current in(119896+1)-th period119894훽(119896 + 1) 120573-axis component of the current in(119896+1)-th period

12 Complexity

119906훼(119896 + 1) 120572-axis component of the output voltage ofthe converter in (119896+1)-th period119906훽(119896 + 1) 120573-axis component of the output voltage ofthe converter in (119896+1)-th period119890훼(119896 + 1) 120572-axis component of the grid voltage in(119896+1)-th period119890훽(119896 + 1) 120573-axis component of the grid voltage in(119896+1)-th period119894g훼(119896 + 1) The real part of the predicted current inthe (119896+1)-th period under a given voltagevector119894g훽(119896 + 1) The imaginary part of the predictedcurrent in the 119896+1th period under a givenvoltage vector119894lowastg훼(119896 + 1) The real part of the reference current inthe (119896+1)-th period under a given voltagevector119894lowastg훽(119896 + 1) The imaginary parts of the referencecurrent in the 119896+1th period under a givenvoltage vector120582 The weight coefficient119894(119896 + 2 | 119896) The predicted current value in the(119896+2)-th period using informationcollected from 119896-th period119892op The initial value of the value function

Data Availability

The no secret-involvement data used to support the findingsof this study are available from the corresponding authorupon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been funded by the State Grid CorporationScience andTechnology Project titled ldquoResearch andDemon-stration of the key technologies for application of groupElectrochemical Energy Storage Power Stations in the UHVHybrid ACDC receiving-end power gridrdquo

References

[1] O Noureldeen and I Hamdan ldquoDesign of robust intelligentprotection technique for large-scale grid-connectedwind farmrdquoProtection andControl ofModern Power Systems vol 3 no 3 pp169ndash182 2018

[2] Y W Shen D P Ke Y Z Sun D S Kirschen W Qiao andX Deng ldquoAdvanced auxiliary control of an energy storagedevice for transient voltage support of a doubly fed inductiongeneratorrdquo IEEE Transactions on Sustainable Energy vol 7 no1 pp 63ndash76 2016

[3] D Zheng A T Eseye J Zhang and H Li ldquoShort-term windpower forecasting using a double-stage hierarchical ANFISapproach for energy management in microgridsrdquo Protection

and Control of Modern Power Systems vol 2 no 2 pp 136ndash1452017

[4] Z Ma H Chen and Y Chai ldquoAnalysis of voltage stabilityuncertainty using stochastic response surfacemethod related towind farm correlationrdquo Protection and Control of Modern PowerSystems vol 2 no 2 pp 211ndash219 2017

[5] M Soliman O P Malik and D T Westwick ldquoMultiple modelpredictive control for wind turbines with doubly fed inductiongeneratorsrdquo IEEE Transactions on Sustainable Energy vol 2 no3 pp 215ndash225 2011

[6] M D Spencer K A Stol C P Unsworth J E Cater and S ENorris ldquoModel predictive control of a wind turbine using short-termwind field predictionsrdquoWindEnergy vol 16 no 3 pp 417ndash434 2013

[7] S Kouro P Cortes R Vargas U Ammann and J RodrıguezldquoModel predictive controlmdasha simple and powerful methodto control power convertersrdquo IEEE Transactions on IndustrialElectronics vol 56 no 6 pp 1826ndash1838 2009

[8] A Gosk Model Predictive Control of a Wind Turbine [MSthesis] Technical University Lyngby Denmark 2011

[9] J Rodriguez and P Cortes ldquoPredictive control of power con-verters and electrical drivesrdquo IEEE Transactions on IndustrialElectronics vol 63 no 7 pp 4472ndash4474 2016

[10] S Rivera S Kouro B Wu et al ldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevel con-verter applicationsrdquo IEEETransactions on Power Electronics vol29 no 10 pp 5592ndash5604 2014

[11] G Li andM R Belmont ldquoModel predictive control of sea waveenergy converters ndash part i a convex approach for the case of asingle devicerdquo Journal of Renewable Energy vol 69 pp 453ndash4632014

[12] J D Barros J F Silva and E G Jesus ldquoFast-predictive optimalcontrol of npc multilevel convertersrdquo IEEE Transactions onIndustrial Electronics vol 60 no 2 pp 619ndash627 2013

[13] G Li ldquoNonlinear model predictive control of a wave energyconverter based on differential flatness parameterisationrdquo Inter-national Journal of Control vol 90 no 1 pp 68ndash77 2017

[14] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[15] P Cortes A Wilson S Kouro J Rodriguez and H Abu-Rub ldquoModel predictive control of multilevel cascaded H-bridgeinvertersrdquo IEEE Transactions on Industrial Electronics vol 57no 8 pp 2691ndash2699 2010

[16] M Narimani B Wu V Yaramasu C Zhongyuan and NR Zargari ldquoFinite control-set model predictive control (FCS-MPC) of nested neutral point-clamped (NNPC) converterrdquoIEEETransactions on Power Electronics vol 30 no 12 pp 7262ndash7269 2015

[17] K S Alam D Xiao D Zhang and M F Rahman ldquoSimplifiedfinite control set model predictive control (FCS-MPC) withextended voltage vectors for grid connected convertersrdquo in Pro-ceedings of the 2017 Australasian Universities Power EngineeringConference AUPEC 2017 pp 1ndash6 Australia November 2017

[18] H Jiefeng Z Jianguo L Gang G Platt and D G DorrellldquoMulti-objective model-predictive control for high-power con-vertersrdquo IEEE Transactions on Energy Conversion vol 28 no 3pp 652ndash663 2013

[19] L Zhu X Fu X Hu et al ldquoModel predictive control ofmodular multilevel converter for HVDC systemrdquo Power SystemProtection and Control vol 42 no 16 pp 1ndash8 2014

Complexity 13

[20] J Holtz and S Stadtfeld ldquoA predictive controller for the statorcurrentvector of AC machines fed from a switched voltagesourcerdquo in Proceedings of the International Power ElectronicsConference pp 1665ndash1675 1983

[21] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley Hoboken NJ USA 2012

[22] T H Mohaned J Morel H Bevrani and T Hiyama ldquoModelpredictive based load frequency control design concerningwind turbinesrdquo International Journal of Electrical Power ampEnergy Systems vol 43 no 1 pp 859ndash867 2012

[23] A Calle-Prado S Alepuz J Bordonau J Nicolas-ApruzzeseP Cortes and J Rodriguez ldquoModel predictive current controlof grid-connected neutral-point-clamped converters to meetlow-voltage ride-through requirementsrdquo IEEE Transactions onIndustrial Electronics vol 62 no 3 pp 1503ndash1514 2015

[24] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearch onthe protection coordination of permanent magnet synchronousgenerator based wind farms with low voltage ride throughcapabilityrdquoProtection andControl ofModern Power Systems vol2 no 2 pp 311ndash319 2017

[25] Y-W Shen D-P Ke W Qiao Y-Z Sun D S Kirschen andC Wei ldquoTransient reconfiguration and coordinated control forpower converters to enhance the LVRT of a DFIG wind turbinewith an energy storage devicerdquo IEEE Transactions on EnergyConversion vol 30 no 4 pp 1679ndash1690 2015

[26] Y W Shen L Q Liang M J Cui F Shen B Zhang and T CuildquoAdvanced control of DFIG to enhance the transient voltagesupport capabilityrdquo Journal of Energy Engineering vol 144 no2 Article ID 04018009 2018

[27] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive sliding modecontrolrdquo Protection and Control of Modern Power Systems vol4 no 4 pp 34ndash41 2019

[28] M Alsumiri L Li L Jiang and W Tang ldquoResidue theorembased soft sliding mode control for wind power generationsystemsrdquo Protection and Control of Modern Power Systems vol3 no 3 pp 247ndash258 2018

Hindawiwwwhindawicom Volume 2018

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Complex AnalysisJournal of


OptimizationJournal of



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International Journal of


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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

2 Complexity

support the system voltage and improve the transient stabilityof the systemThe simulation results show that the PV powerplant is able to support the voltage with the proposed strategyin the low voltage situation

In [14ndash17] the FCS MPC strategy was used to optimizethe control of inverters A mixed logical dynamical (MLD)model for inverters was proposed in [15] By treating theMLD model as a predictive model a FCS-MPC strategy forinverters was developed The proposed strategy considersthe discreteness of inverters and selects the switch statecorresponding to the optimal objective value as the controlsignal for inverters to control the output voltage The simu-lation and test results validate that the proposed FCS-MPCstrategy can improve the output voltage quality of invertersTo improve the conventional FCS-MPC strategy a multistepprediction FCS-MPC strategy for converters is proposed in[15] in which the optimal and suboptimal control actions areconsidered in one control cycleThe optimal control action isdetermined in a fashion that the control action is optimal intwo control cycles Simulation results show that the proposedmultistep FCS-MPC scheme can improve the quality of theoutput voltage of the three-phase inverter and reduces thetracking error of the reference voltage as compared withthe conventional FCS-MPC In [16] the authors proposeda FCS-MPC strategy for a four-level converter to controloutput currents and voltages of flying capacitors A discretemodel of the converter is developed to obtain switchingstates During each sampling period the predicted variablesare evaluated by an evaluation function and the optimalswitching state with the minimum cost value is selected andapplied to the converter In [17] the authors proposed asimplified FCS-MPC with extended voltage vectors for two-level three-phase grid-connected converters The proposedalgorithm uses multiple voltage vectors for the predictionprocess to reduce the ripple in the grid currentMoreover theproposed approach utilizes a preselection scheme along witha simplified MPC approach to reduce the number of voltagevectors used in the proposed strategy Simulations show thatthe proposed strategy retains the effectiveness obtained inthe case where all the voltage vectors are used and at thesame time the current ripple is not adversely affected and thecontrol delay is effectively reduced

Improved MPC strategies were proposed for the STAT-COM and multilevel converters in [18 19] A novel controldelay elimination for the MPC strategy was proposed in[18] for the control of the cascaded STATCOM The MPCbased optimization problem was proposed and simplified forthe possible switching states Based on the further recursionof the simplified MPC based model the effect of controldelay on the control performance is reduced The simulationresults show that the proposed delay elimination for theMPC strategy can improve current tracking control of thecascaded STATCOM and the system has strong robustnessIn [19] the discrete mathematic model of the modularmultilevel converter-based HVDC (MMC-HVDC) system isdeveloped and an improved MPC strategy is proposed forthe five-level MMCMoreover the improvedMPC strategy iscombined with the voltage-sequencing algorithm to reducecomputational burdens and realize the transmission power

control in the MMC-HVDC system and circulating currentelimination

In [20ndash23] the MPC strategies were applied to thecontrol of electric motors In [20] the authors proposeda MPC strategy combined with a disturbance observer(DOB) for regulating the torque of a permanent magnetsynchronous motor (PMSM) without the steady state errorIn the proposed strategy the online optimal solutions can beobtained without relying on a numeric algorithm based onthe property of the input matrix of the PMSM The resultsshow that the proposed MPC strategy ensures satisfactorytorque control performance A quasideadbeat MPC strategyfor induction motors was proposed in [21] By building arolling optimization problem the optimal switching statecorresponding to the optimal voltage vector was selected asthe output of the inverter The simulations and experimentalresults show that the proposed strategy can reduce com-putational time and ensure satisfactory static and dynamicperformance for torque

However the above researches mainly focus on thesteady state and have not studied operational performanceof inverters under renewable energy integration and systemdisturbances To deal with the above issues a FCS-MPCbased control strategy for the VSC-HVDC system is pro-posed The control strategy generates the reference valuethrough the outer loop and compares the reference valuewith the predicted value obtained under a given voltagevector Then the switching status corresponding to the valuefunction with the smallest difference is obtained and used inthe next sampling period which can achieve the fast trackingof the reference value Moreover abilities of the systemin resisting disturbances and fault recovery are enhancedby compensating delay and introducing weight coefficientsThe VSC-HVDC connected OWF system is modeled in theMATLABSimulink and simulation results validate that theproposed FCS-MPC strategy is superior to the tradition PIcontrol strategy under various situations such as wind powerfluctuation and fault occurrences

The contributions of this paper are summarized as fol-lows (1) a FCS-MPC based control strategy for the complexenergy system is proposed considering the renewable energyintegration and system disturbances (2) a MPC based delaycompensation technique is proposed Compared with theconventional PI control strategy the proposed FCS-MPChas the following advantages (1) it is easy to tune controlparameters (2) it can realize multiobjective optimization andincorporate constraints (3) there is no need to implement thedecoupling process (4) no PMWmodulators are required

2 Control Strategies for Wind Farm-SideVSC and Direct Driven Permanent MagnetSynchronous Generator

Figure 1 shows the typical configuration of the OWF con-nected to an external AC grid through the complex energysystem The complex energy system consists of the windfarm-side VSC (WF-VSC) the grid-side VSC (GS-VSC) andthe DC transmission system To ensure utilization of the

Complexity 3

Offshore wind farm

WF-VSC GS-VSC

Grid

2C

2C

2C

2C AC

+

-

+

-

P７+jQ７

T1

Udc1 Udc2

P＞＝ P３+jQ３

ZＭ

T2







(1)




AC

Wind FarmBWF

WF-VSC

dqabc

PWMulowastsd

usd

ulowastsq

usq

isdmax

PI PI

PI

isdmin

isd

ilowastsdisqmax

isqmin

ilowastsq

isq

Ls

PI

Ls

ulowastd

ulowastd

ej

usd

usq





4 Complexity

Pitch angle control

Control system


GS converter

Ps+jQＭ

U＞＝


U＞＝


PMSG

+


PI



PI dqabc PWM

u＞＝


iＱ

uＬ uＱiＱＫ

ilowastwfq

iＱ＞

ilowastwfd

+

-








Complexity 5

AC

DC

GS-VSCBGS

Value function

Predicted model

Measurement unit

PI


ilowast(k+2)S＜＝

i(k+2)

e(k) i(k)

abc

abc


idc iL

udc C

N

u

u＜

i

ib

ic

R L e

e＜

e＝

o

u＝






[[[iue

]]]= 23 [[[

119894a 119894b 119894c119906aN 119906bN 119906cN119890a 119890b 119890c]]][[[[

1a

a2

]]]]

(3)


119906xN = 119878x119906dc (x = a b c) (4)


119878x = 0 119906119901119901119890119903 119886119903119898 119894119904 119900119901119890119899 119897119900119908119890119903 119886119903119898 119894119904 1198881198971199001199041198901198891 119906119901119901119890119903 119886119903119898 119894119904 119888119897119900119904119890119889 119897119900119908119890119903 119886119903119898 119894119904 119900119901119890119899 (5)


d119894d119905 asymp 119894 (119896 + 1) minus 119894 (119896)119879s (6)

6 Complexity




119894 (119896 + 1) = 119879s119871 (119906 (119896) minus 119890 (119896)) + (1 minus 119877119879s119871 ) 119894 (119896) (7)


[119894훼 (119896 + 1)119894훽 (119896 + 1)] =119879푠119871 [

119906훼 (119896) minus 119890훼 (119896)119906훽 (119896) minus 119890훽 (119896)]

+ (1 minus 119877119879푠119871 )[119894훼 (119896)119894훽 (119896)](8)








(9)



Complexity 7



119894 (119896 + 2 | 119896) = 119879s119871 (119906 (119896 + 1) minus 119890 (119896 + 1))+ (1 minus 119877119879s119871 ) 119894 (119896 + 1)

(10)




(11)



(12)





Start


YesNo

No

Yes

i (k)e (k)U＞＝



for p=07



gltgＩＪ

gＩＪ=g op=i

i=7







4 Case Studies



8 Complexity



P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast


PI control

1 11 12

t (s)05 1 15 2



1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent


t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage







Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 3

Offshore wind farm

WF-VSC GS-VSC

Grid

2C

2C

2C

2C AC

+

-

+

-

P７+jQ７

T1

Udc1 Udc2

P＞＝ P３+jQ３

ZＭ

T2







(1)




AC

Wind FarmBWF

WF-VSC

dqabc

PWMulowastsd

usd

ulowastsq

usq

isdmax

PI PI

PI

isdmin

isd

ilowastsdisqmax

isqmin

ilowastsq

isq

Ls

PI

Ls

ulowastd

ulowastd

ej

usd

usq





4 Complexity

Pitch angle control

Control system


GS converter

Ps+jQＭ

U＞＝


U＞＝


PMSG

+


PI



PI dqabc PWM

u＞＝


iＱ

uＬ uＱiＱＫ

ilowastwfq

iＱ＞

ilowastwfd

+

-








Complexity 5

AC

DC

GS-VSCBGS

Value function

Predicted model

Measurement unit

PI


ilowast(k+2)S＜＝

i(k+2)

e(k) i(k)

abc

abc


idc iL

udc C

N

u

u＜

i

ib

ic

R L e

e＜

e＝

o

u＝






[[[iue

]]]= 23 [[[

119894a 119894b 119894c119906aN 119906bN 119906cN119890a 119890b 119890c]]][[[[

1a

a2

]]]]

(3)


119906xN = 119878x119906dc (x = a b c) (4)


119878x = 0 119906119901119901119890119903 119886119903119898 119894119904 119900119901119890119899 119897119900119908119890119903 119886119903119898 119894119904 1198881198971199001199041198901198891 119906119901119901119890119903 119886119903119898 119894119904 119888119897119900119904119890119889 119897119900119908119890119903 119886119903119898 119894119904 119900119901119890119899 (5)


d119894d119905 asymp 119894 (119896 + 1) minus 119894 (119896)119879s (6)

6 Complexity




119894 (119896 + 1) = 119879s119871 (119906 (119896) minus 119890 (119896)) + (1 minus 119877119879s119871 ) 119894 (119896) (7)


[119894훼 (119896 + 1)119894훽 (119896 + 1)] =119879푠119871 [

119906훼 (119896) minus 119890훼 (119896)119906훽 (119896) minus 119890훽 (119896)]

+ (1 minus 119877119879푠119871 )[119894훼 (119896)119894훽 (119896)](8)








(9)



Complexity 7



119894 (119896 + 2 | 119896) = 119879s119871 (119906 (119896 + 1) minus 119890 (119896 + 1))+ (1 minus 119877119879s119871 ) 119894 (119896 + 1)

(10)




(11)



(12)





Start


YesNo

No

Yes

i (k)e (k)U＞＝



for p=07



gltgＩＪ

gＩＪ=g op=i

i=7







4 Case Studies



8 Complexity



P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast


PI control

1 11 12

t (s)05 1 15 2



1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent


t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage







Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








4 Complexity

Pitch angle control

Control system


GS converter

Ps+jQＭ

U＞＝


U＞＝


PMSG

+


PI



PI dqabc PWM

u＞＝


iＱ

uＬ uＱiＱＫ

ilowastwfq

iＱ＞

ilowastwfd

+

-








Complexity 5

AC

DC

GS-VSCBGS

Value function

Predicted model

Measurement unit

PI


ilowast(k+2)S＜＝

i(k+2)

e(k) i(k)

abc

abc


idc iL

udc C

N

u

u＜

i

ib

ic

R L e

e＜

e＝

o

u＝






[[[iue

]]]= 23 [[[

119894a 119894b 119894c119906aN 119906bN 119906cN119890a 119890b 119890c]]][[[[

1a

a2

]]]]

(3)


119906xN = 119878x119906dc (x = a b c) (4)


119878x = 0 119906119901119901119890119903 119886119903119898 119894119904 119900119901119890119899 119897119900119908119890119903 119886119903119898 119894119904 1198881198971199001199041198901198891 119906119901119901119890119903 119886119903119898 119894119904 119888119897119900119904119890119889 119897119900119908119890119903 119886119903119898 119894119904 119900119901119890119899 (5)


d119894d119905 asymp 119894 (119896 + 1) minus 119894 (119896)119879s (6)

6 Complexity




119894 (119896 + 1) = 119879s119871 (119906 (119896) minus 119890 (119896)) + (1 minus 119877119879s119871 ) 119894 (119896) (7)


[119894훼 (119896 + 1)119894훽 (119896 + 1)] =119879푠119871 [

119906훼 (119896) minus 119890훼 (119896)119906훽 (119896) minus 119890훽 (119896)]

+ (1 minus 119877119879푠119871 )[119894훼 (119896)119894훽 (119896)](8)








(9)



Complexity 7



119894 (119896 + 2 | 119896) = 119879s119871 (119906 (119896 + 1) minus 119890 (119896 + 1))+ (1 minus 119877119879s119871 ) 119894 (119896 + 1)

(10)




(11)



(12)





Start


YesNo

No

Yes

i (k)e (k)U＞＝



for p=07



gltgＩＪ

gＩＪ=g op=i

i=7







4 Case Studies



8 Complexity



P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast


PI control

1 11 12

t (s)05 1 15 2



1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent


t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage







Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 5

AC

DC

GS-VSCBGS

Value function

Predicted model

Measurement unit

PI


ilowast(k+2)S＜＝

i(k+2)

e(k) i(k)

abc

abc


idc iL

udc C

N

u

u＜

i

ib

ic

R L e

e＜

e＝

o

u＝






[[[iue

]]]= 23 [[[

119894a 119894b 119894c119906aN 119906bN 119906cN119890a 119890b 119890c]]][[[[

1a

a2

]]]]

(3)


119906xN = 119878x119906dc (x = a b c) (4)


119878x = 0 119906119901119901119890119903 119886119903119898 119894119904 119900119901119890119899 119897119900119908119890119903 119886119903119898 119894119904 1198881198971199001199041198901198891 119906119901119901119890119903 119886119903119898 119894119904 119888119897119900119904119890119889 119897119900119908119890119903 119886119903119898 119894119904 119900119901119890119899 (5)


d119894d119905 asymp 119894 (119896 + 1) minus 119894 (119896)119879s (6)

6 Complexity




119894 (119896 + 1) = 119879s119871 (119906 (119896) minus 119890 (119896)) + (1 minus 119877119879s119871 ) 119894 (119896) (7)


[119894훼 (119896 + 1)119894훽 (119896 + 1)] =119879푠119871 [

119906훼 (119896) minus 119890훼 (119896)119906훽 (119896) minus 119890훽 (119896)]

+ (1 minus 119877119879푠119871 )[119894훼 (119896)119894훽 (119896)](8)








(9)



Complexity 7



119894 (119896 + 2 | 119896) = 119879s119871 (119906 (119896 + 1) minus 119890 (119896 + 1))+ (1 minus 119877119879s119871 ) 119894 (119896 + 1)

(10)




(11)



(12)





Start


YesNo

No

Yes

i (k)e (k)U＞＝



for p=07



gltgＩＪ

gＩＪ=g op=i

i=7







4 Case Studies



8 Complexity



P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast


PI control

1 11 12

t (s)05 1 15 2



1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent


t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage







Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








6 Complexity




119894 (119896 + 1) = 119879s119871 (119906 (119896) minus 119890 (119896)) + (1 minus 119877119879s119871 ) 119894 (119896) (7)


[119894훼 (119896 + 1)119894훽 (119896 + 1)] =119879푠119871 [

119906훼 (119896) minus 119890훼 (119896)119906훽 (119896) minus 119890훽 (119896)]

+ (1 minus 119877119879푠119871 )[119894훼 (119896)119894훽 (119896)](8)








(9)



Complexity 7



119894 (119896 + 2 | 119896) = 119879s119871 (119906 (119896 + 1) minus 119890 (119896 + 1))+ (1 minus 119877119879s119871 ) 119894 (119896 + 1)

(10)




(11)



(12)





Start


YesNo

No

Yes

i (k)e (k)U＞＝



for p=07



gltgＩＪ

gＩＪ=g op=i

i=7







4 Case Studies



8 Complexity



P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast


PI control

1 11 12

t (s)05 1 15 2



1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent


t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage







Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 7



119894 (119896 + 2 | 119896) = 119879s119871 (119906 (119896 + 1) minus 119890 (119896 + 1))+ (1 minus 119877119879s119871 ) 119894 (119896 + 1)

(10)




(11)



(12)





Start


YesNo

No

Yes

i (k)e (k)U＞＝



for p=07



gltgＩＪ

gＩＪ=g op=i

i=7







4 Case Studies



8 Complexity



P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast


PI control

1 11 12

t (s)05 1 15 2



1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent


t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage







Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








8 Complexity



P(M

W) Q

(MVa

r)

0

500

1000

0

500

1000 ０lowast


PI control

1 11 12

t (s)05 1 15 2



1 11 12

05

1

t (s)05 1 15 2Cu

rr a

nd v

olt

mag

nitu

des (

pu

)

0

02

04

06

08

1VoltageCurrent


t (s)05 1 15 2


DC

volta

ge (k

V)

635

650

665

５lowast＞＝

(c) DC voltage







Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 9


P(M

W) Q

(MVa

r)

minus200

minus200

500500

1200

1200

t (s)18 24 3

195 205 215Q

P



05

1

0

voltagecurrent

Cur

and

volt

mag

nitu

des (

pu)

0

02

04

06

08

1

t (s)18 24 3

195 205 215


18 24 3

DC

volta

geof

the V

SC-H

VD

C sy

stem

(kV

)

600

700

800

600

700

800

PI control

MPC control

t (s)











5 Conclusions


10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








10 Complexity

P(M

W) Q

(MVa

r)

PI control

MPC control

t (s)

1500

500

minus500

minus1500

minus2500232119

P

Q


Volta

ge (p

u)

1

t (s)

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

t (s)

3

0

minus3

232119








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 11

t (s)

P(M

W) Q

(MVa

r) MPC control

PI control

P

Q

1000

500

0

232119


Volta

ge (p

u)

t (s)

1

0

minus1

232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119


Volta

ge (p

u)

1

0

minus1

t (s)232119


Curr

ent (

pu

)

1

0

minus1

t (s)232119



Nomenclature





12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








12 Complexity


Data Availability




Acknowledgments


References





















Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 13

















Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








finite control set model predictive control for complex...

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