Technical report

Delft University of Technology, Delft, The Netherlands

Multi-area predictive control for combined electricity and

natural gas systems

M. Arnold, R.R. Negenborn, G. Andersson, B. De Schutter

If you want to cite this report, please use the following reference instead:

M. Arnold, R.R. Negenborn, G. Andersson, B. De Schutter. Multi-area predictive control for

combined electricity and natural gas systems. In Proceedings of the European Control

Conference 2009 (ECC'09), Budapest, Hungary, pp. 1408-1413, August 2009.

Multi-Area Predictive Control for Combined Electricityand Natural Gas Systems

Michele Arnold, Rudy R. Negenborn, Goran Andersson, Bart De Schutter

Abstract— The optimal operation of an integrated electricityand natural gas system is investigated. The couplings betweenthese two systems are modeled by energy hubs, which serveas interface between the loads and the transmission infras-tructures. Previously, we have applied a distributed controlscheme to a static three-hub benchmark system. In this paper,we propose an extension of this distributed control schemefor application to energy hubs with dynamics. The dynamicsthat we consider here are due to storage devices presentin the multi-carrier system. We propose a distributed modelpredictive control approach for improving the operation ofthe system by taking into account predicted behavior andoperational constraints. Simulations in which the proposedscheme is applied to the three-hub benchmark system illustratethe potential of the approach.

Index Terms— Distributed control, model predictive control,electric power systems, natural gas systems, multi-carrier sys-tems

I. I NTRODUCTION

Nowadays, infrastructures, such as electricity, natural gas,and local district heating systems, are mostly planned andoperated independently of each other. In practice, however,these individual systems are coupled, as e.g., micro com-bined heat and power plants (µCHP) and other distributedgeneration plants (such as so-called co- and trigeneration[1]) are used more and more. It is therefore expectedthat integrated control of several such systems can yieldimproved performance. The various energy carriers availableand the conversion possible between them significantly affectboth the technical and the economical operation of energysystems. In particular, consumers get flexibility in supplyand could therefore decide in favor of, e.g., cost, reliability,system emissions, availability, or a combination of these.

Currently, research effort is addressing integrated controlof combined electricity and natural gas systems [2], [3]. In[3], the couplings between the electricity and gas systemsare modeled using the concept of energy hubs [4]. Theseenergy hubs serve as interface between the loads and thetransmission infrastructures of both types of systems. Theelectricity and natural gas system is then modeled as anumber of interconnected energy hubs.

Because of the increasing number of distributed generationfacilities with mostly fluctuating energy infeed (generation

M. Arnold (corresponding author) and G. Andersson are with thePower Systems Laboratory, ETH Zurich, Physikstrasse 3, 8092 Zurich,Switzerland, e-mail:{arnold,andersson}@eeh.ee.ethz.ch.R.R. Negenborn and B. De Schutter are with the Delft Center for Systemsand Control of Delft University of Technology, Mekelweg 2, 2628 CDDelft, The Netherlands, e-mail:r.r.negenborn@tudelft.nl,b.deschutter@dcsc.tudelft.nl. B. De Schutter is also withthe Marine and Transport Technology department of Delft University ofTechnology.

profiles), the issue of storing energy also becomes moreimportant. Electric energy storage devices are expensive andthe operation of them causes energy losses. In order to stillenable the electric energy supply in time, the operation of aµCHP device in combination with a heat storage device isconsidered. By optimally using the heat storage device, theµCHP device can be operated in order to follow the electricalload.

In [5], we have proposed a distributed control schemefor the steady-state optimization of energy hub systems. Athree-hub benchmark system is used there to illustrate theperformance of the approach. In that system, the individualenergy hubs determine in a cooperative way which actions totake. The models that the energy hubs thereby use are static,steady-state models. No dynamics are taken into account.

In this paper, we propose an extension of the distributedcontrol scheme presented in [5] for application to energyhubs with dynamics. Here, we in particular consider thedynamics due to storage devices present in the combinedelectricity and natural gas system. We propose to use adistributed model predictive control (MPC) scheme, in whichthe operation of the hub system over a certain predictionhorizon is considered and in which actions that give the bestpredicted behavior are determined by the individual energyhubs. By using such a predictive approach, the energy usagecan be adapted to expected fluctuations in the energy pricesand to expected changes in the load profiles. A variety ofdistributed MPC approaches have been applied to differentapplication areas, summarized in [6].

This paper is organized as follows. In Section II themathematical model of the considered multi-carrier systemisgiven. In Section III we first discuss a centralized MPC ap-proach for the overall system and then propose a distributedMPC approach. Simulation results applying the method toa three-hub benchmark system are presented in Section IV.Section V concludes this paper and outlines directions forfuture research.

II. M ODELING

In this section, the model of the combined electricity andnatural gas network is presented. The equations for powerconversion and power storage within the energy hubs andfor power transmission between the hubs are given.

A. System setup

We study general systems consisting of interconnectedenergy hubs. As example benchmark system we considera system consisting of three hubs that are interconnected

Fig. 1. System setup of three interconnected energy hubs. Active poweris provided by generatorsG1, G2, G3. HubsH1 and H2 have access toadjacent natural gas networksN1, N2.

by an electricity and natural gas transmission system, asillustrated in Fig. 1. The electricity system and the gas systemare connected via energy hubs. An energy hub is a networknode that includes conversion, conditioning, and storage ofmultiple energy carriers. It represents the interface betweenthe energy sources and transmission lines on the one handand the power consumers on the other hand. The energy hubis a modeling concept with no restrictions to the size of themodeled system. Single power plants or industrial buildingsas well as bounded geographical areas such as whole townsand cities can be modeled as energy hubs.

In the system under study, each energy hub represents ageneral consumer, e.g., a household, that uses both electricityand gas. Each of the hubs has its own local electrical energyproduction (Gi, with electric power productionPG

e,i, fori ∈ {1, 2, 3}). Hub H1 has access to a large gas networkN1, with gas infeedPG

g,1. In addition, hubH2 can obtaingas from a smaller local gas tankN2, modeled as gasinfeed PG

g,2. Each hub consumes electric powerPHe,i and

gas PHg,i, respectively, and supplies energy to its electrical

load Le,i and its heat loadLh,i. The hubs contain converterand storage devices in order to fulfill their energy loadrequirements. For energy conversion, the hubs contain aµCHP device and a furnace. TheµCHP device couples thetwo energy systems as it simultaneously produces electricityand heat from natural gas. HubsH1 and H2 additionallycomprise a hot water storage device. Compressors (Cij , for(i, j) ∈ {(1, 2), (1, 3)}) are present in the gas network withinthe pipelines originating from hubH1, at which the largegas network is located. The compressors provide a pressuredecay and enable the gas flow to the surrounding gas sinks.

There are several ways in which electrical and thermalload demands can be fulfilled. This redundancy increasesthe reliability of supply and at the same time providesthe possibility for optimizing the input energies, e.g., usingcriteria such as cost, availability, emissions, etc.

B. Energy hub model

Since we consider an optimization over multiple periods,the equations are defined per time stepk. For each of thethree energy hubs, the electrical loadLe,i(k) and the heatload Lh,i(k) at time stepk are related to the electricityPH

e,i(k) and gas hub inputPHg,i(k) as follows:

[

Le,i(k)Lh,i(k)

]

=

[

1 νg,i(k)ηCHPg,e,i

0 νg,i(k)ηCHPg,h,i + (1 − νg,i(k))ηF

g,h,i

] [

PHe,i(k)

PHg,i(k)

]

, (1)

whereηCHPg,e,i andηCHP

g,h,i denote the gas-electric and gas-heat ef-ficiencies of theµCHP device (which are assumed to be con-stant in this paper1), and whereηF

g,h,i denotes the efficiency ofthe furnace. The variableνg,i(k) (0 ≤ νg,i(k) ≤ 1) repre-sents a dispatch factor that determines how the gas is dividedover the µCHP and the furnace. The termνg,i(k)PH

g,i(k)defines the gas input power going into theµCHP and thepart (1 − νg,i(k))PH

g,i(k) defines the gas input power goinginto the furnace. As the dispatch factorνg,i(k) is variable,different input vectors can be found to fulfill the output loads.This offers additional degrees of freedom in supply.

The storage device is modeled as an ideal storage incombination with a storage interface. In the considered setup,hot water storage devices are implemented. The relationbetween the heat power exchangeMh,i(k) and the effectivelystored energyEh,i(k) at a time stepk is defined by thefollowing equation:

Mh,i(k) =1

eh,i

(

Eh,i(k) − Eh,i(k − 1) + Estbh,i

)

, (2)

where eh,i is the storage efficiency,Eh,i(k) denotes thestorage energy at the end of periodk, andEstb

h,i represents thestandby energy losses of the heat storage device per period(Estb

h,i ≥ 0). For hubsH1 and H2 two hot water storagedevices are implemented. Equation (1) is therefore completedwith additional storage power flows:

[

Le,i(k)Lh,i(k) + Mh,i(k)

]

=

[

1 νg,i(k)ηCHPg,e,i

0 νg,i(k)ηCHPg,h,i + (1 − νg,i(k))ηF

g,h,i

] [

PHe,i(k)

PHg,i(k)

]

. (3)

C. Transmission network

For the transmission networks of both the electricitynetwork and the gas network, power flow models based onnodal power balances are implemented. The power flowsfor the electricity network are formulated as nodal powerbalances of the complex power, according to [3], [7]. Thepower flow equations for the pipeline network are based onnodal volume flow balances. The model of a gas pipelineis composed of a compressor, with pressure amplificationpinc, and a pipeline element. More information about thegas network model used can be found in [3].

1However, the efficiencies can also be dependent on, e.g., theconvertedpower level.

D. Combined energy hub transmission network model

The combined electricity and gas network is obtained bycombining the above stated power flow models. For eachtime stepk an algebraic state vectorz(k) and a dynamicstate vectorx(k) are defined. The algebraic state vectorincludes the variables for which no dynamics are explicitlydefined. The dynamic state vector includes variables forwhich dynamics are included. Hence,

x(k) =[

ETh (k)

]T(4)

z(k) = [VT(k) θT(k) pT(k) pT

inc(k)

(PHe )T(k) (PH

g )T(k)]T (5)

where- V(k) = [V1(k), V2(k), V3(k)]T and θ(k) =

[θ1(k), θ2(k), θ3(k)]T denote the voltage magnitudesand angles of the electric buses, respectively,

- p(k) = [p1(k), p2(k), p3(k)]T denotes the nodal pres-sures of all gas buses,

- pinc(k) = [pinc,1(k), pinc,2(k)]T denotes the pressureamplification of the compressors,

- PHe (k) = [PH

e,1(k), PHe,2(k), PH

e,3(k)]T denotes the elec-tric inputs of the hubs, and

- PHg (k) = [PH

g,1(k), PHg,2(k), PH

g,3(k)]T denotes the gasinputs of the hubs.

- The two storage devices in hubH1 and H2 are incor-porated in vectorEh(k) = [Eh,1(k), Eh,2(k)]T.

At each time step, the control variablesu(k) are definedto include the active power generation of all generators, thenatural gas imports of all gas networks and the dispatchfactors of each hub, i.e.,

u(k) =[

(PGe )T(k) (PG

g )T(k) νTg (k)

]T, (6)

where

- PGe (k) = [PG

e,1(k), PGe,2(k), PG

e,3(k)]T denotes the activepower generation of all generators,

- PGg (k) = [PG

g,1(k), PGg,2(k)]T defines the natural gas

imports and- νg(k) = [νg,1(k), νg,2(k), νg,3(k)]T describes the dis-

patch factors of the gas input junctions.

Now, the model that we use to represent the combinedelectricity and gas network can be conveniently written as

x(k + 1) = f(x(k), z(k),u(k)) (7)

0 = g(x(k), z(k),u(k)), (8)

summarizing the power flow equations of the electricity andgas system, and the hub equations.

III. C ONTROL PROBLEM FORMULATION

In this section we discuss the control of the systemintroduced above. We first discuss how MPC can be usedin the form of a centralized, supervisory controller that canmeasure all variables in the network and that determinesactions for all actuators. Due to practical and computationalissues implementing such a centralized controller may notbe feasible. Individual hubs may not want to give access

model

optimization

prediction

actionscontrol

objective,constraints

systeminputs

control

MPC controller

measurements

Fig. 2. Illustration of model predictive control.

to their sensors and actuators to a centralized authority andeven if they would allow a centralized authority to takeover control of their hubs, this centralized authority couldhave computational problems with respect to required timewhen solving the resulting centralized control problem. Wetherefore also discuss a distributed MPC scheme, in whichthe control is spread over the individual hubs.

The goal of either control scheme is to determine valuesfor the control variablesu(k) in such a way that the costs forelectricity generation and natural gas usage are minimized.Hence, the control problem can be stated as determining theinputs u(k) in such a way that the control objectives areachieved, while satisfying the system constraints.

As control strategy we propose to use MPC. MPC [8],[9] is a control strategy that uses an internal model formaking predictions of the system behavior over a predefinedprediction horizon with lengthN , thereby also taking intoaccount operational constraints. MPC is suited for controlof multi-carrier systems, since it can adequately take intoaccount the dynamics of energy storage devices and thecharacteristics of the electricity and gas networks. MPCoperates in a receding horizon fashion, meaning that ateach time step new measurements of the system and newpredictions into the future are made. By using MPC, actionscan be determined that anticipate future events, such asincreasing or decreasing energy prices.

In Fig. 2 MPC is illustrated schematically. At each controlstep k, an MPC controller first measures the current stateof the system,x(k). Then, it determines using (numerical)optimization which control inputu(k) to provide by findingthe actions that over a prediction horizon ofN time stepsgive the best predicted performance according to a givenobjective function. The control variables determined for thefirst prediction step are applied to the system. The systemthen transitions to a new state,x(k + 1), after which thecycle starts all over.

A. Centralized model predictive control

In the centralized MPC formulation there is a singlecontroller that determines the inputsu(k) for the wholenetwork. The control objective2 is to minimize the energy

2In addition to the stated objectives, it would be straightforward to alsoinclude voltage regulation and power flow limitations as control objectives.

costs, represented by the following system-wide objectivefunction:

J =

N−1∑

l=0

∑

i∈G

qGi (k + l)(PG

e,i(k + l))2

+ qNi (k + l)(PG

g,i(k + l))2, (9)

whereG includes all generation units, i.e., the tree generatorsand the two natural gas imports. The prices for electricitygenerationqG

i (k) and for natural gas consumptionqNi (k) can

vary throughout the day. The centralized control problemformulation is now stated as

minu(k)

J(x(k + 1), z(k), u(k)) (10)

subject to

x(k + 1) = f(x(k), z(k), u(k)) (11)

g(x(k), z(k), u(k)) = 0 (12)

h(x(k), z(k), u(k)) ≤ 0, (13)

where the tilde over a variable represents that variableover a prediction horizon ofN steps, e.g.,u(k) =[ u(k)T, . . . ,u(k + N − 1)T ]T. The inequality constraints(13) comprise limits on the voltage magnitudes, active andreactive power flows, pressures, changes in compressor set-tings, and dispatch factors. Furthermore, power limitations onthe hub inputs and on gas and electricity generation are alsoincorporated in (13). Regarding the storage devices, limitson the storage contents and the storage flows are imposed.

The optimization problem (10)–(13) is a nonlinear pro-gramming problem [10], which can be solved using opti-mization problem solvers for nonlinear programming, suchas sequential quadratic programming [10]. In general, thesolution space is non-convex and therefore finding the globaloptimum cannot be guaranteed with numerical methods.

B. Distributed model predictive control

In the distributed MPC formulation, there is no singlecontroller, but there are multiple controllers which act ina cooperative way. Each controller is responsible for itsown part of the overall system. In our case there are threeindividual controllers each of which controls a particulararea. In addition, the compressors in the gas networks arecontrolled by the controller of energy hubH1.

In the distributed MPC formulation each individual con-troller has its own control objective. In particular, the objec-tive functions of the three controllers are:

J1 =

N−1∑

l=0

qG1 (k + l)(PG

e,1(k + l))2 + qN1 (k + l)(PG

g,1(k + l))2

(14a)

J2 =

N−1∑

l=0

qG2 (k + l)(PG

e,2(k + l))2 + qN2 (k + l)(PG

g,2(k + l))2

(14b)

J3 =N−1∑

l=0

qG3 (k + l)(PG

e,3(k + l))2. (14c)

Each control agent is responsible for the hub variables andall system variables of the nodes connected to it. For the firstcontroller, the state and control vectors for each time stepk

are defined asx1(k) = [E1(k)]T (15)

z1(k) = [V1(k), θ1(k), p1(k), pinc,1(k), pinc,2(k),

PHe,1(k), PH

g,1(k)]T (16)

u1(k) = [PGe,1(k), PG

g,1(k), νg,1(k)]T (17)

The state and control vectors for the second and thirdcontroller are defined similarly according to Fig. 1 (greyareas).

Each controller solves its own local MPC problem usingthe local model of its hub. However, this local MPC problemdepends on the MPC problems of the other controllers,since the electricity and gas networks interconnect the hubs.Therefore, the MPC optimization problems of the controllershave to be solved in a cooperative way. This is not onlyto ensure that the controllers choose feasible actions, butalso to allow the controllers to choose actions that areoptimal from a system-wide point of view. The distributedMPC approach that we propose in this paper is based onusing the Lagrangian relaxation procedure derived in [11] forsetting up the MPC optimization problems of the individualcontrollers and for determining which information has to beexchanged among the controllers.

We next illustrate the mathematical procedure to de-compose a general centralized MPC optimization problemof a centralized controller into optimization problems forindividual distributed controllers. The procedure is illustratedon a system consisting of two interconnected areas, extensionto three or more areas is straightforward.

Consider two areasA and B which comprise the systemvariablesyA(k) and yB(k), respectively. For demonstrationpurposes, we collect all variables introduced above in avector y(k), e.g., yA(k) = [xA(k), zA(k), uA(k)]T . Thecentralized MPC optimization problem is then specified as

minuA(k), uB(k)

J(yA(k), yB(k)) (18)

subject to g(yA(k), yB(k)) = 0. (19)

Here, only equality constraints are explained for demonstra-tion purposes. Inequality constraints are handled analogously.

For decomposing the centralized MPC optimization prob-lem, both the objective and the equality constraints areseparated and assigned to a responsible control agent (Fig.3).Both areas comprise constraints involving only the ownsystem variables,gA(yA(k)), gB(yB(k)). Besides them, so-called coupling constraints are introduced, containing vari-ables from both areas (marked by a hat). Regarding theobjectives, both objective functions consist of two parts.Thefirst term expresses the main objective originating from theoverall objective function (18). The second term is respon-sible for the coordination between the agents and consistsof the coupling constraints introduced above. As indicatedin Fig. 3, the coupling constraints are kept explicitly ashard constraints in the constraint set of one control agent

Fig. 3. Decomposition procedure applied to a two-area system(areaA:yA(k), areaB: yB(k)) and variables to be exchanged after each iterationcounters.

and added as soft constraints to the main objective of theother control agent (modified Lagrangian relaxation proce-dure [11]). The weighting factors of the soft constraints arethe Lagrangian multipliers obtained from the optimizationproblem of the other area. Both the objectives and thecoupling constraints depend on variables of the other area,indicated by the superscripts. To handle this dependency,the optimization problems of the control agents are solvedin an iterative procedure. At each iteration steps, the MPCoptimization problems of both control agents are solvedindependently of each other, while keeping the variablesof the neighboring area constant. After each iteration, thecontrol agents exchange the updated values of their variablesas indicated in Fig. 3, i.e., the variablesys+1

i (k) and the

Lagrangian multipliersλs+1

i (k). Convergence is achievedwhen the exchanged variables do not change more thana small toleranceγtol in two consecutive iterations. Incontrary to conventional Lagrangian relaxation procedures,a faster convergence is achieved as the weighting factors arerepresented by the Lagrangian multipliers of the neighboringoptimization problems [11].

Applying this procedure to combined electricity and gassystems, the electric power flow and gas flow equationsat the peripheral buses serve as coupling constraints. Forthe studied three-hub system, the active power balances ofall nodes of the electricity system enforce a coordinationas they depend on the neighboring voltage magnitudes andangles. Regarding the gas system, the nodal flow balances ofall buses depend on the pressures of the neighboring busesand therefore enforce a coordination as well. Summarizing,for each area, there exists one coupling constraint for theelectricity and one for the natural gas system, specified in [3].

IV. CASE STUDY

In this section a case study is presented in which the pro-posed distributed MPC scheme is applied to the illustrativethree-hub system. However, the scheme is general and notonly valid or applicable for the system depicted in Fig. 1.The performance of the distributed approach is comparedwith the performance of the centralized MPC approach. Thesolverfmincon provided by the Optimization Toolbox ofMatlab is used [12].

A. Simulation setup

Each hub has a daily profile of its load demand andalso of the energy prices. In this preliminary case study, a

1 2 3 4 5 6 7 8 9 10 11 120

1

2

3

Time step k

Load

s [p

.u.]

Le,i

Lh,1

Lh,2

1 2 3 4 5 6 7 8 9 10 11 120

2

4

6

8

Time step k

Pric

es [m

.u./p

.u.2 ]

q1G q

2G, q

3G g

1N g

2N

Fig. 4. Profile for electricityLe,i(k) and heat loadsLh,i(k) (upper plot)and prices for electricityqG

i(k) and natural gas consumptionqN

i(k) (lower

plot).

perfect forecast is assumed, in which no disturbances withinthe known profiles are occurring. The generation costs areminimized for a simulation horizonNsim = 10. The lengthof the prediction horizonN is chosen asN = 3. Hence, anoptimization overN time steps is runNsim times, at eachtime stepk implementing only the control variable for thecurrent time stepk and then starting a new optimization attime stepk + 1 with updated system measurements.

Given are the price and load profiles of all hubs (Fig. 4).The electricity loadLe,i and the gas import pricesqN

i remainconstant over time. Variations are assumed only in the pricesof the electric energy generation unitsqG

i (k) and in the heatload of hubH2, Lh,2, in order to exactly retrace the storagebehavior. Further details about the coefficients and simulationparameters used can be found in [3].

B. Single simulation step

In order to evaluate whether the solution determined bythe distributed algorithm is feasible for the real system, thefollowing simulation is run. In Fig. 5 the quality of theintermediate solutions in case that these would be appliedto the system is shown. The distributed MPC optimizationproblem is is solved at time stepk = 1, for N = 3.At each iteration counters, the overall system costs areshown, when applying the control variables determined bythe distributed algorithm to the system. The dotted valuesrefer to the infeasible solutions. As the number of iterationsincreases, the distributed MPC converges, and, in fact, thesolution obtained at the end of the iterations approaches thesolution obtained by the centralized MPC approach (200.98p.u.). After iteration 16, the values of all control variablesare feasible. After 39 iterations, the algorithm converges.

C. Simulation of multiple time steps

When minimizing the energy costs over the full simulationof Nsim time steps, a total cost of 850.62 p.u. is obtained forthe above given load and price profiles. Applying centralizedMPC, the overall costs are lower, 849.78 p.u., since, due tothe imposed convergence toleranceγtol of the distributedalgorithm, the centralized approach finds a slightly differentsolution at some iteration steps. In Fig. 6, the active power

0 5 10 15 20 25 30 35 40140

160

180

200

220

240

260

Iteration counter s

Ove

rall

cost

s [p

.u.]

Fig. 5. Intermediate solutions of the distributed algorithmapplied to thesystem. Dotted lines represent infeasible solutions, solidlines are feasiblesolutions.

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

Time step k

Hub

H2: C

ontr

ol v

aria

bles

[p.u

.]

Pe,2G P

g,2G

Fig. 6. Active power generationPGe,2 and natural gas importPG

g,2 of hubH2 over time.

generation and the natural gas import of hubH2 are shown.As can be seen, active power generation is reduced at timesteps with higher generation costs, i.e., time steps 4–7 andtime step 10. During these time steps more gas is consumed.The electrical loads are now predominantly supplied by theµCHP devices in order to save costs. Most of the gas isdiverted into theµCHP device and less into the furnace.For still supplying the heat load, the heat storage devicescome into operation. Figure 7 shows the content of bothstorage devices evolving over the time steps. Both storagedevices start at an initial level of 1.5 p.u. Since the heatload at hubH2 is increased by 20% at time steps 3-5 (Fig.4), storageE2 attempts to remain full before this increaseand then operates at its lower limit during the heat loadpeaks. At the proceeding electricity price peaks (time steps6, 7) both storages are recharged. The electrical loads aremainly supplied by theµCHP devices and all excessive heatproduced during these time steps is then stored in the storagedevices. Storage deviceE1 is refilled more thanE2, as hubH2 has a limited gas access.

If the controllers have a shorter prediction horizon thanN = 3, the storage devices are filled up less and also later.With a prediction horizon length ofN = Nsim, the storagedevices are filled up earlier and the lowest costs are obtained,although calculation time becomes considerably longer andthe system is insensitive to unknown changes in the load andprice profiles.

V. CONCLUSIONS AND FUTURE RESEARCH

In this paper we have proposed a distributed model pre-dictive control (MPC) approach for control of energy hubsystems. A distributed MPC scheme is proposed, such thatdynamics due to, e.g., storage devices, forecasts on energyprices and demand profiles, and operational constraints can

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

Time step k

Sto

rage

con

tent

s [p

.u.]

E1

E2

Fig. 7. Evolution of storage contents (E1, E2) over time.

be taken into account adequately. We have applied this ap-proach for minimizing generation costs of a particular three-hub integrated electricity and natural gas system. In a casestudy, we have analyzed the quality of intermediate solutionsobtained throughout the iterations of the proposed approachto ensure that applying the control to the real system yieldsfeasible solutions. In future research the performance underdifferent control horizons will be compared. Furthermore,conditions and measures for guaranteeing convergence haveto be investigated more precisely. In addition, we will addressthe incorporation of disturbances in the scheme instead ofassuming perfect forecasts.

ACKNOWLEDGMENTS

This research is supported by the project “Vision of Future Energy Net-works” (VoFEN) of ABB, Areva T& D, Siemens, and the Swiss FederalOffice of Energy, the European 6th Framework Network of Excellence”HYbrid CONtrol: Taming Heterogeneity and Complexity of NetworkedEmbedded Systems (HYCON)”, the BSIK project “Next GenerationInfras-tructures (NGI)”, the Delft Research Center Next Generation Infrastructures,the European STREP project “Hierarchical and distributed model predictivecontrol (HD-MPC)”, and the project “Multi-Agent Control ofLarge-ScaleHybrid Systems” (DWV.6188) of the Dutch Technology Foundation STW.

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