IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 6, NOVEMBER 2015 3327
MPC-Based Frequency Control With Demand-SideParticipation: A Case Study in an Isolated
Wind-Aluminum Power SystemHao Jiang, Student Member, IEEE, Jin Lin, Member, IEEE, Yonghua Song, Fellow, IEEE, and
David J. Hill, Fellow, IEEE
Abstract—Aluminum production relies on the smelting processwhich consumes huge amounts of electrical energy. One possiblesolution to reduce the fossil fuel consumption by aluminumproduction is the integration of wind power. Based on this back-ground, this paper studies an isolated power system for aluminumsmelting production with a high penetration of wind power. Adynamic model of the aluminum smelter load (ASL) is introducedin this paper using the field experiment data. Based on this model,the dynamic model of the isolated system considering demand sideparticipation is proposed. The MPC-based frequency controller isproposed to keep the frequency deviation within a proper range( 0.1 Hz) under wind power fluctuation as well as to recover thesystem frequency after a large disturbance (such as one generatortrip). Finally, simulation results demonstrate the effectiveness ofthe proposed MPC based frequency controller.Index Terms—Aluminum smelter loads (ASLs), frequency con-
trol, isolated power system, model predictive control (MPC), windpower.
I. INTRODUCTION
A LUMINUM is widely used in many areas, and thereforethe requirement for aluminum is quite huge. The main
method for aluminum production is the smelting process whichtransforms oxides of aluminum into metal aluminum [1]. How-ever, this smelting process consumes a large amount of electrical
Manuscript received July 13, 2014; revised November 16, 2014; acceptedNovember 22, 2014. Date of publication December 18, 2014; date of currentversion August 03, 2015. This work was supported in part by National High-Technology Research and Development Program (“863” Program) of Chinaunder Grant 2014AA051901, the International S&T Cooperation Program ofChina under Grant 2014DFG62670, and the Chinese National Natural ScienceFunds under Grants 51207077 and 51261130472. Paper no. TPWRS-00953-2014.H. Jiang and J. Lin are with the State Key Laboratory of Control and
Simulation of Power Systems and Generation Equipment, Department ofElectrical Engineering, Tsinghua University, Beijing 100084, China (e-mail:[email protected]).Y. Song is with the State Key Laboratory of Control and Simulation of Power
Systems and Generation Equipment, Department of Electrical Engineering, Ts-inghua University, Beijing 100084, China, and also with the College of Elec-trical Engineering, Zhejiang University, Hangzhou 310058, China.D. J. Hill is with the Department of Electrical and Electronic Engineering,
The University of Hong Kong, Pokfulam, Hong Kong, and also with the Schoolof Electrical and Information Engineering, The University of Sydney, Sydney,Australia (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2014.2375918
energy, which typically results in enormous fossil fuel consump-tion. It is vital to reduce the fossil fuel consumption in aluminumsmelting process in order to accomplish the ambitious goal offossil fuel consumption reduction in China [2].One possible solution is the integration of wind power for
aluminum smelting production. However, since most aluminumsmelter loads (ASLs) are located far away from load centers,the cost of the transmission lines from the power system foraluminum production to the utility grid is quite high. Therefore,the owners of the ASL prefer to build an isolated power systemconsisting of coal-fired conventional power plants together withwind power for aluminum production locally.In the isolated wind-aluminum power system, frequency sta-
bility is the most critical technical issue. In [18], we proposeda local proportional controller to allow the ASL to participatein frequency control in this isolated system. The proposed con-troller uses frequency deviation as a feedback signal to simulatethe droop characteristic of the conventional generator. However,the controller designed for primary frequency regulation cannotrecover system frequency to its nominal value. We need to over-come this drawback of the proposed ASL controller in [18].In power systems, secondary frequency control (SFC) is
used to maintain frequency at its nominal value. The controltechnique for SFC which is still being put into practice is PI(Proportional-Integrator) based SFC. The huge advantage ofthe PI-based SFC is its simple structure and the clear physicalmeanings of its control scheme. Other advanced control tech-niques used in SFC are comprehensively reviewed in [3]–[5],such as optimal control [6], robust control [7], self-adaptivecontrol [8], AI-based control [9], and so on. However, thesecontrol methods cannot adequately deal with the multivariableconstraints of a complex power system, such as generation rateconstraints (GRCs). This drawback discounts their promisingcontrol performance when applied into real-world powersystems.A potential solution is model predictive control (MPC) which
emerged in the late 1970s and is now widely used in industryprocess control and related areas [10]. The huge advantage ofMPC over other control techniques is that it can consider systemconstraints explicitly in its model. In power system research,MPC has been proposed for SFC in several papers. For example,the work in [11] and [12] apply centralized MPC for SFC inpower systems considering GRC. The linear matrix inequality(LMI)-based MPC is proposed in [13] to achieve robustness
3328 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 6, NOVEMBER 2015
against parameter variations in power systems. DecentralizedMPC is proposed in [14] and [15] to decrease the computationalburden of online optimization for MPC. The distributed MPCwhich considers the interaction between subsystems is proposedin [16] and [17].The existing research [10]–[17] has investigated MPC appli-
cations in SFC in power systems. In their model for MPC study,all the generators in one area are represented by one aggregatedgenerator in one specific area. However, this aggregated modelcannot consider different features and constraints on each indi-vidual generator in the isolated system. In addition, the existingresearch [10]–[17] mainly focus on the control from the gener-ator side. However, as discussed in [18], the aluminum smelterloads from the demand side should also participate in frequencycontrol in order to avoid transient frequency issues in the iso-lated power system.The main contributions of this paper are given here.1) The dynamic characteristics of the ASLs are modeled in
this paper based on the data from a field experiment. To thebest of the authors’ knowledge, this is the first publishedmodel mentioning real-world dynamics of aluminumsmelter loads.
2) Based on the dynamic model of ASL and the frequencycontrol model considering individual generator and net-work topology proposed in [19], the state variables ofASLs are added to formulate a dynamic model of the iso-lated system with demand-side participation. This detailedmodel can consider the dynamics and constraints of eachindividual generator in the isolated system.
3) Based on the proposed dynamic model consideringdemand-side participation by ASLs, an MPC-based fre-quency controller (MPC-FC) is formulated, which is ableto consider the system constraints explicitly. In addition,the controller takes predicted dynamics of the system intoconsideration, which is vital for frequency control in thisisolated system under a large disturbance.
The remainder of this paper is organized as follows.Section II briefly introduces the components of the isolatedpower system. The steady state and the dynamic model ofaluminum smelter loads are introduced in Section III. InSection IV, the MPC-based frequency control problem ofthe isolated system without and with demand-side participa-tion is presented. Section V gives the simulation results anddemonstrates the effectiveness of the MPC-FC compared withthe PI-based controllers. In Section VI, we discuss the oper-ationality of the proposed MPC method using PowerFactoryand MATLAB cosimulation. Finally, Section VII concludes thepaper.
II. SYSTEM CONFIGURATION
This paper discusses an actual industrial power system foraluminum production which is located in Inner Mongolia [18].The single-line diagram of this system is as shown in Fig. 1, andthe main components in the system are:1) conventional synchronous generators. There are eight coal-
fired synchronous generators in the system. The total gen-eration capacity is 1800 MW (G1, G2: 100 MW, G3, G4:
Fig. 1. Main structure of the isolated industrial power grid.
Fig. 2. Simplified equivalent circuit of one ASL.
150 MW, G5, G6: 300 MW, G7, G8: 350 MW). Note thatthe self-use power of the generators is 10% of their ca-pacity, i.e., 180 MW in total.
2) loads. The main loads of this system are aluminum smelterloads (ASL1: 350 MW, ASL2: 440 MW, ASL3: 610 MW),1400 MW in total. The detailed model of the aluminumsmelter loads will be discussed later in Section III.
3) wind power plants. Two 400-MW wind farms, WF1 andWF2 with DFIG (Type 3), are integrated into the isolatedpower system to reduce fossil fuel consumption.
III. MODELLING OF ASLS
A. Simplified Equivalent Circuit of ASLs
The equivalent circuit of the aluminum smelter load is shownin Fig. 2 [18]. It consists of a full-bridge rectifier circuit with sixdiodes . There are six saturable reactorswhich are in front of the diodes in each branch. Eachsaturable reactor of can be represented as a control-lable inductor. The inductance value of , denoted by
, is controlled by the internal circuit in the saturable reactor.The dc-side components of the ASLs consist of an emf and theresistance load , which represent the internal resistant forceand the heat effect during the smelting process, respectively.
JIANG et al.: MPC-BASED FREQUENCY CONTROL WITH DEMAND-SIDE PARTICIPATION 3329
Fig. 3. Block of the transfer function .
Fig. 4. Comparison of the data from the field experiment and the data fromstate space model of ASL1.
B. Dynamic Model of ASLsThe steady-state model of an ASL was derived in our pre-
vious paper [18]. Please see [18, (1) and (2)] for details. Here,, the dynamic model of ASLs is introduced, which is used forfrequency control in this isolated power system. We use the dataobtained from the field experiment on ASL1 in Inner Mongoliato build this dynamic model.The ASL can be modelled as a transfer function , as
shown in Fig. 3. The input and output of the transfer functionare the incremental power reference signal andthe incremental active power consumption .In our experiment, a 0.107-p.u. step-down signal is given
to the input signal , and the solid line in Fig. 4 showsthe output signal . Note that this curve is similar to a stepresponse of an over-damped second-order system. Therefore,we use a second order transfer function to approximate it asfollows:
(1)
The transfer function in (1) can be transferred to thestate space model with state variablesand the control variable as follows [21]:
(2)
where and .The output of the state space model with the same step input
signal is shown as the dashed line in Fig. 4. The dashed linematches the solid line quite well, especially in the first few sec-onds. Therefore, the approximation state space model of theASLs appears to be proper for simulating the dynamics of theASL. Note that, although the power of the ASL needsapproximately 7 s to reach the steady value , thepower decreases significantly in the first few seconds. In thiscase, with a 0.107-p.u. step-down signal, the decreased poweris about 6% p.u. in 2 s. The decreased power of the aluminumload in such a short time is vital for supporting the system fre-quency under large disturbance.
IV. MPC-BASED FREQUENCY CONTROL WITHDEMAND-SIDE PARTICIPATION
Here, we introduce an MPC-based frequency control schemewith demand-side participation. As mentioned in Section I, anaggregated model for all the generators in one area cannot con-sider different features and constraints on each individual gen-erator. Therefore, we need to model each generator and eachASL, respectively. This model ensures that we can consider dif-ferent features and constraints on the generators and the ASLsaccurately.
A. State Space Model of the Conventional GeneratorsThe state equation of the th conventional generator is as
follows:
(3)
where , and, , are the incremental valve gate position,
incremental mechanical power, and incremental speed of theth generator, respectively, is the incremental powerreference signal of the th generator, is the incrementalelectrical power of the th generator, , and are thetime constants of the governor, the turbine and the generator ofthe th generator, respectively, is the generator gain of theth generator, and is the governor droop of the th generator[22].Equation (3) can be written in condensed form as follows:
(4)
The state equation of conventional generators in total in theisolated system is
(5)
where
B. State Space Model of the ASLsThe state space model of the aluminum smelter loads is dis-
cussed in Section IV-C. Equation (2) gives the state equation ofan aluminum smelter load. This equation can be written in con-densed form as follows:
(6)
where
3330 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 6, NOVEMBER 2015
The state equation of aluminum smelter loads in total inthe isolated system is
(7)
where
C. State Space Model of the Isolated SystemWith Demand-SideControlHere, , we will combine the state equations of the conven-
tional generators and the ASLs together to obtain the state equa-tion of the whole isolated system.The state equation (5) can be used to calculate the dynamics
of the generators. However, the electrical power of the gen-erators cannot be obtained directly. It is related to thetopology of the system. In fact, we have the following sensi-tivity matrix after load flow calculation at steady state:
(8)
The active power are strongly coupled with phase angle intransmission grid. Therefore, we use the dc approximation tosimplify (8). The incremental angle of the first generatoris treated as the reference angle. Therefore, we can get the fol-lowing equation by deleting the variable and the column in
corresponding to generator 1 [19]:
(9)
Nowwe separate power of the conventional generator powersand load powers . Note that we consider wind power(this variable can be treated as negative load), power
of aluminum smelter loads and power of conventionalloads altogether in here. Then, (8) becomes
(10)
can be eliminated, and then we obtained
(11)
where
and , , and are incremental wind power,incremental power of aluminum smelter loads and incrementalpower of conventional loads, respectively, and , , and
are the columns of corresponding to , ,and .Note that, in this paper, we consider that the wind production
can be represented by a negative load due to the following rea-sons. First, the wind turbines in this isolated power system are
DFIGs and they are all operated under maximum power pointtracking (MPPT) mode. This means the wind power output isdetermined by the wind speed under steady state. Second, ac-cording to [23] and [24], the DFIG's complete decoupling fromsystem frequency with fast field-oriented controller (FOC). Thismeans that the wind power output is not affected by the fre-quency dynamics during system transients.We can substitute (11) into (5) to obtain the following state
equation, which includes the new state variable :
(12)
where
.... . .
Equation (12) is the state equation of the isolated powersystem without demand side participation. To study frequencycontrol with demand-side participation, we need to integrate thestate equations of ASLs (7) into (12) to get the state equationof the isolated power system
(13)
where
Equation (13) is the state equation of the isolated powersystem with demand-side participation which can be written incondensed form as
(14)
Note that (13) is able to deal with the trip of a conventionalgenerator in addition to wind power fluctuation or conventionalload disturbance with the following modifications.1) After a generator trips, the node corresponding to the
tripped generator turns from PV node to PQ node. There-fore, all of the variables and sensitivity matrices in (10)have different dimensions. These matrices need to berecalculated.
2) The trip of the generator can be treated as a load distur-bance in . The disturbance value is the power outputof the generator before it trips.
JIANG et al.: MPC-BASED FREQUENCY CONTROL WITH DEMAND-SIDE PARTICIPATION 3331
Similarly, the model is able to deal with the trip of one ASLby treating it as a load disturbance in and removing thecorresponding state variables in the state equation.
D. MPC-Based Frequency Control AlgorithmThe MPC-based frequency control (MPC-FC) is to solve the
following problem at every sampling instant:
(15)
where , , and are the weighting matrices corre-sponding to the state variables of conventional generators, thecontrol variables of conventional generators, and the controlvariables of aluminum smelter loads, respectively, ,
, and are the amplitude constraints ofthe control variables of conventional generators and aluminumsmelter loads, respectively, is the ramping constraintof the generators, is the prediction step (note that theprediction step and the control step are the same in thispaper), and , , and are system matrices derived from, , and in (14) after discretization with the sampling time. The explicit expressions of , , and are given as
(16)
Problem (15) is a quadratic programming (QP) problem,which can be solved by MATLAB/CPLEX and other tools.Note that the amplitude constraints of the generators are deter-mined by the steady-state operation status. These variables needto be calculated before applying the MPC-FC to the isolatedpower system. From the mathematical point of view, ifand are set to zero, then (15) corresponds to the casewithout demand side participation. Therefore, (15) is able todeal with both the cases with and without demand-side partici-pation. In addition, the weighting matrices in the MPC-FC willneed adaptation to the circumstances, as will be shown later.
E. Flowchart of the MPC-FCFig. 5 shows the flowchart of the MPC-FC.
V. CASE STUDYHere, , simulation results are presented to demonstrate the ef-
fectiveness of the proposedMPC-based frequency controller for
Fig. 5. Flowchart of the MPC-FC.
TABLE IPARAMETERS FOR LFC SIMULATION IN THE ISOLATED SYSTEM
the isolated power system. The main parameters for simulationare listed in Table I. The sampling time is set to 0.5 s. Theprediction and control steps ( and ) for MPC-FC are bothset to ten steps (5 s). The GRC constraint for each generator isset to 0.2 p.u./min. The constraint on the control variable ofeach ASL is 0.1 p.u. and 0.1 p.u..The quadratic programming problem (QP) in the MPC-FC issolved by CPLEX 12.4 in MATLAB [25].
A. Wind Power Fluctuation
The wind power penetration level is more than 40% in thisisolated power system. Therefore, the impacts of wind powerfluctuation on frequency control in the system should be studied.The main simulation parameters of PI based frequency con-troller (PI-FC) and theMPC-FC are shown in Table II. Note that,for the MPC controller, the weighting of the control variableson each ASL is much larger than that of the control variableson each generator to ensure the MPC-FC prefers to use conven-tional generators for frequency regulation. In addition, the con-straint on the angle speed deviationis added to each generator to ensure the frequency deviation is
3332 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 6, NOVEMBER 2015
TABLE IIMAIN SIMULATION PARAMETERS FOR WIND POWER FLUCTUATION
Fig. 6. Membership functions for ACE and .
Fig. 7. The membership functions for and .
TABLE IIIFUZZY TUNING RULES FOR AND
kept within 0.1 Hz in the isolated system under wind powerfluctuation.We also design a Fuzzy PI frequency controller (Fuzzy
PI-FC) based on [26]. The parameters and in the FuzzyPI controller is tuned by defuzzification of the grade of bothACE and ACE. The membership functions for ACE and
are shown in Fig. 6. The membership functions forand are shown in Fig. 7. The fuzzy rules are listed in
Table III. The method for defuzzification is the center of gravitydefuzzification. Tables IV and V list the detailed values of theFuzzy PI controller.We compare the system dynamics of the following four cases
assuming the initial wind power output at 200 MW: 1) PI-FC;2) Fuzzy PI-FC; 3) MPC-FC without wind power predictionerror; and 4) MPC-FC with wind power prediction error, which
TABLE IVPARAMETERS OF THE FUZZY PI CONTROLLER
UNDER WIND POWER FLUCTUATION
TABLE VPARAMETERS OF THE FUZZY PI CONTROLLER UNDER THE N-1 SCENARIO
is modeled as the Gaussian distribution with the standard de-viation 10 MW (5% of the initial wind power output).The wind power prediction data and actual data are shown inFig. 8(a). The dynamics of the grid frequency and the totalactive power of ASLs of the four cases are shown inFig. 8(b) and (c), respectively.The first case is the PI-FC with , , and the
second case is the Fuzzy PI-FC. As can be seen from the blacksolid line and the black dashed line in Fig. 8(b), the frequencydeviations of the two cases exceed the desired boundary ( 0.1Hz) and the maximum deviation is almost 0.3 Hz. This is be-cause both the PI and the Fuzzy PI controller only use past andreal-time information without considering future dynamics ofthe system. In addition, the total active powers of ASLsunder these two controllers in Fig. 8(c) are fluctuating all of thetime. This might bring some negative effects on the smeltingapparatus such as life reduction.The third case is the MPC-FC without wind power prediction
error. This is the ideal case that the actual wind power is exactlythe same as the prediction. As can be seen from the blue solidline in Fig. 8(b), the frequency deviation is kept within 0.1 Hz.This is because MPC-FC is able to handle the constraints on thefrequency deviation. Note that the fluctuation of the total activepower of ASLs in Fig. 8(c) also decreases compared withthe former PI-FC case by setting higher weighting on ASL'scontrol variable compared with the weighting on a conventionalgenerator's control variable.The last case is MPC-FC considering wind power prediction
error. This case is more practical compared to the third case. Theresult is plotted by the blue dashed line in Fig. 8(b), which showsthat the frequency deviation sometimes exceeds 0.1 Hz regionslightly. There are two reasons for this. First, the MPC-FC useswind power prediction data for calculating the control variables.When the wind power prediction error is large at some time, the
JIANG et al.: MPC-BASED FREQUENCY CONTROL WITH DEMAND-SIDE PARTICIPATION 3333
Fig. 8. (a) Wind power prediction and actual data. (b) Dynamics of the gridfrequency and (c) total active power of ASLs with PI-FC, FuzzyPI-FC, and MPC-FC without and with prediction error during 1-min windpower fluctuation.
frequency deviation is also increased due to the difference be-tween prediction and actual data; secondly, the MPC-FC some-times cannot obtain a feasible solution. Therefore, the frequencyconstraints need to be relaxed to guarantee the feasibility of theMPC-FC. This also leads to the result that the frequency devia-tion exceeds 0.1 Hz. Note that, although the frequency devia-tion is not strictly kept within 0.1 Hz, the maximum deviationis not increased by more than is acceptable in practice.In summary, the advantages of theMPC-FC over the PI-based
(both the traditional PI and the Fuzzy PI) controllers for fre-quency control under wind power fluctuation is as follows.1) The MPC-FC is able to limit the frequency deviation
in the desired range (50 0.1 Hz) since it can con-sider this constraint on system frequency explicitly. Asa comparison, the system frequency under the PI-FC orFuzzy PI-FC exceeds the desired boundary. Therefore,the control performance of the MPC-FC is better than theother two controllers.
2) The MPC-FC avoids unnecessary adjustment on the ASLs'power so the aluminum production is less affected. This
TABLE VIMAIN SIMULATION PARAMETERS FOR GENERATOR TRIP EVENT
Fig. 9. (a) Dynamics of the grid frequency and (b) total active power of ASLswith PI-FC, Fuzzy PI-FC, and MPC-FC when G3 (150 MW) accidently
trips with 200-MW wind power.
is because we set much larger than in this sce-nario, which means the generators are used for frequencyregulation in priority. Therefore, the fluctuations of theASLs’ power under MPC control decrease compared withthe PI-based controllers.
B. N-1 ScenarioHere, we consider a large disturbance scenario: one gener-
ator trip event (N-1) of the isolated system under PI-FC, FuzzyPI-FC andMPC-FC. Themain simulation parameters are shownin Table VI. The parameters for PI-FC are the same as for thewind power fluctuation simulation. However, when one gener-ator trips, the system frequency deviation is of most importanceto the isolated power system. Therefore, the weighting ofin MPC-FC is increased and is much larger compared with theweighting of the control variables of the conventional genera-tors and the ASLs. This ensures effective responses from theconventional generators and the ASLs after the generator tripevent. Here, we set to . Note that, in prac-tice, it needs some adaptive process or intelligence to set theweightings.We consider the trip of G3 (150 MW) when the wind power
output is 200 MW as the first N-1 scenario. The dynamics of thegrid frequency and the total active power of ASLs areas shown in Fig. 9.
3334 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 6, NOVEMBER 2015
In the first PI-FC case corresponding to the solid line inFig. 9(a), the frequency nadir is below 49.3 Hz, and it takesmore than 60 s for the recovery of the system frequency. In ad-dition, the active power of the ASLs is decreased to 1350 MWin Fig. 9(b) compared to the original 1400 MW. This results inthe reduction of aluminum production.The second case corresponds to the Fuzzy PI-FC, which is
shown as the dashed–dotted line in Fig. 9(a) and (b). With thisFuzzy PI-FC, the frequency nadir increases to about 49.4 Hzdue to larger power decrease from the ASLs compared with thefirst case with PI-FC. At the same time, the overshoot is alsodecreased with this Fuzzy PI-FC. However, the settling time isstill is more than 60 s, which is more or less the same as the firstcase.Compared with the former two cases with PI-based FC, the
frequency nadir is lifted to over 49.6 Hz with the MPC-FC cor-responding to the dashed line in Fig. 9(a). The recovery time ofthe system frequency is also decreased to less than 20 s. More-over, as can be seen in Fig. 9(b), the active power of the ASLsreturns to its nominal value (1400MW) after the participation infrequency regulation. This is because the weighting of the ASLsis much larger than the weighting of the conventional genera-tors. Therefore, the MPC-FC is able to coordinate the controlbetween conventional generators and ASLs.In the second scenario, we consider the trip of G5 (300 MW)
when the wind power output is 200 MW. In this scenario, ASL1(350 MW) must be shed to maintain active power balance, oth-erwise the system frequency will fall below 48.5 Hz, and theentire system will collapse.The first case is the PI-FC. It can be seen from the solid line
in Fig. 10(a) that the frequency rushes over 50.5 Hz due to thesurplus active power after ASL1 is shed. This may result in theactivation of high frequency protection of the other generatorsand ASLs in the isolated system.The second case corresponds to the Fuzzy PI-FC, which is
shown as the dashed–dotted line in Fig. 10(a) and (b). The fre-quency zenith decreases to about 50.6 Hz due to faster and largerpower increase from the ASLs with this Fuzzy PI-FC. However,the frequency zenith still exceeds the safe threshold, which is50.5 Hz in this isolated system.Finally, we examine the control performance of the MPC-FC
corresponding to the dashed line in Fig. 10(a) and (b). TheMPC-FC is able to restrict the frequency zenith under 50.4 Hzso that the activation of high frequency protection is avoided.Meanwhile, the recovery time is also reduced to under 20 scompared with that in the former two cases. In addition, theMPC-FC can also bring the active power of ASL2 and ASL3back to the nominal value in 20 s.In summary, the advantages of MPC-FC over the PI-based
controllers for frequency control in the N-1 scenarios are asfollows.1) The MPC-FC is able to lift the frequency nadir when one
small generator trips and restrict the frequency zenith whenone large generator trips. This is due to its ability of con-sidering future dynamics. This ability allows the MPC-FCto take control actions as early as possible. In addition,the MPC-FC is able to recover the system frequency to itsnominal value much faster than the PI-based controllers.
Fig. 10. (a) Dynamics of the grid frequency and (b) total active power ofASLs with PI-FC, Fuzzy PI-FC, and MPC-FC when G5 (300 MW) ac-cidently trips with 200-MW wind power.
The oscillations of the system frequency is also avoidedwith the MPC-FC.
2) The MPC-FC allows the ASLs to participate in frequencyregulation in a more proper manner. In the first secondsafter the large disturbance, the ASLs' power changes largerthan the power under the PI-based controllers. After thewhole system settles down (about 20 seconds after thelarge disturbance), the ASLs’ power also returns to itsnominal value. As a comparison, the ASLs’ power differsfrom its nominal value with the PI-based controllers.
VI. POWERFACTORY AND MATLAB CO-SIMULATION
Here, we present the co-simulation results with PowerFactoryand MATLAB to discuss the practicality and operationality ofthe proposed MPC method. PowerFactory is widely used andcommonly accepted in power system research, specifically fordynamic simulation [27]. We build the refined isolated powersystem model in PowerFactory to simulate its dynamics and weuse MATLAB for MPC optimization. The generators are rep-resented by the seventh-order model [22]. The exciter model isshown in Fig. 11 while the governor model is the same as in (3).We compare the following three cases to verify the effectivenessof the proposed MPC method.1) MATLAB simulation case. This case is the same as all the
cases in Section V. The system dynamics are simulatedusing (13) with MATLAB.
2) Open-loop control case. Compared to case 1, the systemdynamics are simulated using PowerFactory instead ofMATLAB. However, the control variables are the same asthose in case 1. This case is called open-loop control case
JIANG et al.: MPC-BASED FREQUENCY CONTROL WITH DEMAND-SIDE PARTICIPATION 3335
Fig. 11. ST1A exciter model.
Fig. 12. Diagram of the three PowerFactory and MATLAB co-simulationcases.
since there is no feedback, i.e., no state variables are sentfrom PowerFactory to Matlab for MPC optimization.
3) Closed-loop control case. This case is the most practicalcase. The system dynamics are simulated using PowerFac-tory. All of the state variables in the system are sent fromPowerFactory to MATLAB at each time step for MPC op-timization. The control variables are updated byMPC opti-mization inMATLAB. After theMPC calculation, the con-trol variables are sent back to PowerFactory. This proce-dure is repeated every step until the end of the simulation.
The comparisons among all the three cases are shown inFig. 12.We consider the trip of G3 (150 MW) when the wind power
output is 200 MW, which is first case in Section V-B. The MPCparameters are the same as in Section V-B. The dynamics ofthe grid frequency and the total active power of ASLscorresponding to the three cases are as shown in Fig. 13.The first case is the MATLAB simulation case corresponding
to the solid line in Fig. 13(a) and (b). The result of this case wasalready discussed in Section V-B. With the help of MPC, therecovery time of the system frequency is less than 20 s whilethe active power of the ASLs returns to its nominal value (1400MW) after the participation in frequency regulation.The second case is the open-loop control case. Note that in
this case the system dynamics are simulated using PowerFac-tory instead of MATLAB while the control variables are thesame as in case 1. Therefore, the ASL power shown asthe dotted line in Fig. 13(b) is the same as the solid line corre-sponding to case 1. However, the system frequency shown asthe dotted line in Fig. 13(a) has more oscillations and longer re-covery time compared to that in case 1. This means the controlperformance is worse in case 2 compared to that in case 1.
Fig. 13. (a) Dynamics of the grid frequency and (b) total active power ofASLs with three cases whenG3 (150MW) accidently trips with 200-MWwind power.
The main reason for this change is as follows: the system dy-namics simulated in Matlab is derived using the sensitivity ma-trix [(10)], which is a linearized equation near the equilibriumpoint at steady state. However, when one generator trips, thesystem deviates from its equilibrium point. Therefore, the statevariables in PowerFactory simulation differ from the predictedvalues calculated by MATLAB using (13). The control perfor-mance is thus worse under the same control variables.The third case is the closed-loop control case corresponding
to the dash-dotted line in Fig. 13, which is the most practicalone. As can be seen in Fig. 13(a), the system frequency dy-namics are almost the same as those in case 1. The difference isless than 0.05 Hz around the nadir. Also, the ASL powerin Fig. 13(b) differs slightly from that in case 1 and in case 2.Compared with case 2 with open-loop control, the control per-formance in this case is obviously improved. This improvementis due to the feedback at each step, i.e., the state variables aresent from PowerFactory to MATLAB. As discussed above, thestate variables are not exactly the same as predicted values cal-culated inMATLAB. Therefore, the update of the state variablesfrom PowerFactory to MATLAB is able to correct the predic-tion errors. Under the help of this correction, the control perfor-mance is improved compared to that in case 2.We compare the closed-loop control case (case 3) with real
power system control in Fig. 14. In fact, when MPC is appliedto the real power system, the state variables are sent from powersystem components (generators, aluminum smelter loads, etc.)to the dispatch center for MPC optimization at each step. Afterreceiving the newest state variables, the dispatch center solvethe MPC optimization problem and send the calculated con-trol variables back to the power system components. The whole
3336 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 6, NOVEMBER 2015
Fig. 14. Comparison between the closed-loop control case (case 3) and realpower system control.
process in real power system control is very similar to that incase 3. Since the effectiveness of the proposed MPC method incase 3 is demonstrated, the proposed MPC method is also con-firmed to be practical in real power system control.
VII. CONCLUSIONThis paper continues the discussion on the frequency sta-
bility issues in the isolated power system in Inner Mongoliain [18]. In order to overcome the drawbacks of the ASL localcontrollers proposed in [18], the dynamic model of ASL loadsis first introduced in this paper based on the field experimentdata. We also improve the dynamic model proposed in [19] toconsider demand-side participation by aluminum smelter loads.The improved dynamic model is suitable for frequency controlstudy in the isolated system. An MPC-based frequency con-troller is proposed to keep the frequency deviation within aproper range under wind power fluctuation as well as to recoverthe system frequency under some large disturbance. Simulationresults demonstrate the effectiveness of the proposed MPC-FCin the isolated power system.In this paper, wind power is considered as negative load
without any control. Future work will focus on the coordinatedcontrol scheme of all the system components including conven-tional generators, aluminum smelter loads and wind turbines inthis isolated system.
APPENDIX
The exciter model used in PowerFactory is the ST1A modelshown in Fig. 10 [22]. The typical parameters in this model are
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Hao Jiang (S’12) was born in Tangshan, China, 1987. He received the B.S. de-gree in electrical engineering from Tsinghua University, Beijing, China, in 2010,where he is currently working toward the Ph.D. degree in electrical engineering.His research interests include wind power control integration.
Jin Lin (S’11–M’12) was born in 1985. He received the B.S. and Ph.D. degreesin electrical engineering from Tsinghua University, Beijing, China, in 2007 and2012, respectively.He is currently a Lecturer with the Department of Electrical Engineering, Ts-
inghua University, Beijing, China. His research interests are in grid integrationtechnology of renewable energy and dynamic power systems.
Yonghua Song (F’08) was born in January 1964. He received the B.Eng. degreefrom Chengdu, China, in 1984, and the Ph.D. degree from China Electric PowerResearch Institute in 1989.He was a Postdoctoral Fellow with Tsinghua University, Beijing, China, from
June 1989 to March 1991. He then held various positions at Bristol University,Bath University, and John Moores University from 1991 to 1996. In January1997, he was appointed a Professor of Power Systems at Brunel University,where he was Pro-Vice Chancellor for Graduate Studies from August 2004. In2004, he was elected Fellow of the Royal Academy of Engineering (UK). Hereturned to TsinghuaUniversity in February 2009 as a Professor with the Depart-ment of Electrical Engineering. He is now the Executive President of ZhejiangUniversity, Hangzhou, China. His research areas include smart grid, electricityeconomics, and operation and control of power systems.
David J. Hill (M’76–SM’91–F’93) currently holds the Chair of Electrical Engi-neering at the University of Hong Kong. He is also a part-time Professor at TheUniversity of Sydney, Australia. His research interests are in control, networks,power systems, and stability analysis.Prof. Hill is a Fellow of the Society for Industrial and Applied Mathematics,
the Australian Academy of Science, and the Australian Academy of Techno-logical Sciences and Engineering; he is also a Foreign Member of the RoyalSwedish Academy of Engineering Sciences.
