1Production planning in a Virtual Power PlantM.G.C. Bosman, V. Bakker, A. Molderink, J.L. Hurink, G.J.M. Smit

Department of Electrical Engineering, Mathematics and Computer ScienceUniversity of Twente

P.O. Box 217, 7500 AE, Enschede, The Netherlandsm.g.c.bosman@utwente.nl

AbstractDistributed electricity generation is increasingly ap-plied in the electricity grid. This generation can be more energyefficient than conventional generation; however, a large scaleintroduction of distributed generators implies possible instabilityin the grid. A Virtual Power Plant (VPP) deals with this problemby controlling the distributed generators in such a way, that thecomplete group acts like a normal power plant. All generatorsneed to be steered individually, which makes the control morecomplex than the control of a normal power plant.

The VPP we describe in this paper consists of a large numberof microCHP (Combined Heat and Power) appliances. As theproduced heat of such a microCHP is completely consumedlocally, the production opportunities of the distributed generatorsare determined by the local heat demand. This heat demand canbe predicted one day ahead, see e.g. [2]. A feasible schedule ofa single generator ensures that the heat demand is supplied intime. The objective is to generate at the most profitable times.

In [3] a dynamic programming formulation is described whichschedules one generator optimally (for local objectives) withinreasonable time. We extend this method to the case of a VirtualPower Plant. The costs of the basic state changes in the dynamicprogramming formulation of the individual generators are al-tered, according to the objective of the VPP, which is to generatea predefined electricity pattern for a full day. Starting from thepoint of view of local objectives of individual generators the globalobjective of the VPP is gradually (iteratively) incorporated. Thisresults in a production planning that can be done in reasonabletime, compared to the planning horizon.

Keywords: distributed generation, scheduling

I. INTRODUCTION

Many types of small-scale electricity generators are intro-duced in the electricity network. Examples are photovoltaiccells, wind turbines and Combined Heat and Power (CHP) ap-pliances. The size of these electricity generators may vary fromsmall, household-scale appliances to larger, neighbourhood-scale installations. Compared to large fossil-fuel or nuclearpower plants these generators are at micro- to mini-level inthe field of electricity generators.

A single micro-generator has limited influence on the elec-tricity grid; it cannot destabilize the grid. However, very largeamounts of such generators can have impact on the grid; oncethey simultaneously decide to deliver electricity to the gridthis can lead to grid instability. Although individual micro-generators seem harmless, a large-scale introduction of themneeds to be controlled and regulated.

The paper is organized as follows. In Section II the conceptof a Virtual Power Plant (VPP) is introduced. Section IIIgives our approach to the production planning of a VPP. Adistributed scheduling method for this planning problem is

proposed in Section IV. The paper ends with results in SectionV and conclusions and recommendations in Section VI.

II. PRODUCTION PLANNING OF A VIRTUAL POWER PLANTA Virtual Power Plant (VPP) combines many small elec-

tricity generating appliances into one large, virtual and con-trollable power plant. This VPP is comparable to a normalpower plant in production size. However, the comparison endshere. Due to the geographically distribution of generators,the fysical electricity production from a VPP has a completeother dimension than the production from a large generatorthat is located at a single site. The wide-spread distributionof generators asks for a well-controlled generation method.Instead of steering one large generator all generators in aVPP can be individually steered. These generators must bescheduled to generate at different times of the day in such away, that the combined electricity production of all generatorsmatches the production of a normal power plant. Althoughthe steering of a VPP is more complex than the steering of anormal power plant, the use of large amounts of generatorswith small capacity (and limited runtime) results in moreflexibility in the production of electricity. This means that aVPP should be better capable of adapting its production, inthe scenario of fast changing differences between demand andsupply (which is likely in case more renewable resources aswind, sun or water are used for electricity production). Controlmethods for a VPP may focus on two different elements: offline methods

The planning of the production of individual generatorsfor a longer period (e.g. 24 hours), resulting in a aggre-gated production that matches the production of a normalpower plant;

online methodsThe need for online (re)scheduling methods for the pro-duction of individual generators, due to fast changing de-mands or deviating properties of the individual generator(e.g. changes in actual runtime or actual power output).

In this work, we focus on the first element; in particular,we focus on the production planning for one day ahead.

A. Problem description

We assume that the VPP has decided to produce a certainamount of electricity for the next 24 hours. This decisioncan be based on predictions of energy market prices, energyconsumption in the market and production opportunities ofthe distributed generators. Once a decision for a particular

2production scheme is made, this scheme must be followed,especially if the VPP acts on the energy market. To guaranteestability in the electricity grid, the VPP is supposed to deliverthe specified amounts; otherwise severe price penalties aregiven. So, the problem is to match the decided, and thus fixed,production pattern given by the scheme. The way to do this isby planning the production runs of the distributed generators.

The problem now can be reduced to the assignment ofproduction runs to different generators, subject to the globalrequirement of matching a given production pattern and tothe local requirements for the availability of ready-to-producegenerators at different times of the day.

The VPP production scheme is assumed to be known toa central entity within the VPP. The problem of using theproduction opportunities of the distributed generators to assignconcrete production runs to specific times on the day, canbe challenged in many ways. For example, the central entityitself may compute a schedule for all generators, based onproduction opportunity information from the generators. How-ever, this task of globally matching production and demand isknown to be NP-complete in the strong sense [4]. Therefore,we propose a method to distribute the scheduling of productionruns.

In this work the focus is on microCHP (Combined Heatand Power) appliances as distributed generators. This type ofgenerator generates heat and electricity simultaneously andon a household scale. Due to the use of a heat buffer, theelectricity generation in a house can be partly decoupledfrom the households heat demand. In combination with aheat demand prediction of the house this gives the schedulingfreedom to plan the runs of the generator.

III. PROPOSED APPROACH

A VPP can be organized in different ways. For example, in[6] a multiagent approach is presented; the results of field testsare shown in [5]. For an extended overview of literature ondistributed energy markets we refer to [8]. Below we introduceour own approach to organize a VPP.

The production opportunities of the individual microCHPappliances (which we use in our VPP) are limited by the heatdemand, since the basic use of the generator is to supply heatto the house. In our case this means that a prediction of the heatdemand of the next day determines the available run hours ofthe generator. Based on the predicted heat demand profile andthe heat level of the heat buffer at the start of the planninghorizon, the total amount of potential (maximal) productionand the total amount of necessary (minimal) production areknown. Note that potential production cannot be utilized ateach moment in time; the runs are subject to other constraintsand, therefore, production must be spread over the day accord-ing to these constraints (e.g. the spread heat demand over theday or the limited maximum heat production per time intervaland the limitations of the heat buffer that is used). In a VPPthe sum of the potential production of all generators gives theVPP production capacity. This potential also cannot be utilizedat free will, for similar reasons as in the case of a single house.Based on the potential production a planning can be made for

the production within a house, but also for a group of houses.However, the potential production is based on predictions andmay not be accurate anymore when the system is running. Forthis reason, the individual generators in the VPP need to berealtime controlled.

Our approach consists of three steps: Prediction

In the first step a prediction of the heat demand must bedone for each house. This local information is necessaryto decide the local production potential of the micro-generators. A neural network approach is used for thisprediction [2].

PlanningIn the second step the local production potential isassigned to actual runs, based on local (domestic) andglobal (VPP) objectives. The planning process is knownto be NP-complete in the strong sense [4]. Therefore,heuristics, as proposed in this work, need to be developed.

Realtime controlWhereas the first two steps can be done offline, themicrogenerator needs to be realtime (online) controlledtoo. In this realtime control the runs of individual micro-generators need to be rescheduled, if the reality differs toomuch from the prediction. A generic method for realtimecontrol can be found in [7].

A. Structure

In this subsection we introduce the structure that is used inour approach. This structure forms the basis for the planningmethod in Section IV. We use a hierarchical structure for plan-ning the runs. For scalability reasons the method divides thedistributed generators into groups of comparable and limitedsize. The group size should not increase with an increasingnumber of generators, since the method iteratively finds aschedule (see Section IV). When the number of generators pergroup would increase, the method could use more iterationsto find a good match. However, the number of iterations,that the scheduling method uses to match the production tothe demand, needs to be limited; otherwise the process ofscheduling takes too much time. For this reason we limitthe amount of generators per group. A hierarchical structurefacilitates the division into groups of limited size by the useof a number of levels, corresponding to the total number ofgenerators.

Algorithm 1 gives the creation of the hierarchical structure.The scheduling process requires the structure to be capableof handling increasing amounts of generators. Therefore thegenerators are divided into groups of limited maximum sizey. Based on the number of generators different levels areintroduced at which groups of lower levels are aggregated inhigher order groups, again of maximum size y. The lowestlevel consists of the generators. The level above divides thesegenerators over the minimum possible number of groups(based on y). In the next levels these groups are includedin larger groups (consisting of maximally y sub groups), untilthere is only one group left in the highest level. The algorithmhas as input the lowest level (all generators) and returns a

3structure H consisting of all higher order levels H1 up to andincluding HL.

An example is shown in Figure 1. In this example a set of14 generators is used to create a structure with a maximumgroup size of 3.

The structure has the advantage that there is a differenceof at most one sub group in the group division at eachlevel. This extra sub group has size smaller or equal to thesmallest sub group in the group with the least number of subgroups. This means the imbalance in the structure (measuredas the difference in number of generators between largest andsmallest branch at level 2) can at most grow to:

yL2,

compared to the difference it could grow to in case allgroups are filled from the left:

yL1 1.

Algorithm 1 Create groups Gi and structure H =(H1, . . . ,HL) from generator set X = {x1, . . . , xn} withmaximum group size yRequire: X 6= , y 1Ensure:

i

Gi = X , Gi Gj = (i 6= j) and |Gi| yL dylog |X|eN d |X|y efor i = 1 to N doGi j iwhile j n doGi Gi xjj j +N

end whileHL,i Gi

end forHL {HL,1, . . . ,HL,N}k Lwhile k > 1 dok k 1for i = 1 to dNy e doHk,i j iwhile j N doHk,i Hk,i Hk+1,jj j + dNy e

end whileend forN dNy eHk {Hk,1, . . . ,Hk,N}

end whileH (H1, . . . ,HL)

IV. DISTRIBUTED SCHEDULING METHOD

In this section we propose a distributed method to create aschedule for the production runs of distributed generators. First

x1 x6 x11 x3 x8 x13 x5 x10 x2 x7 x12 x4 x9 x14

Fig. 1. An example of the hierarchical structure, produced by algorithm 1

we give an overview of the way we plan the generator runs of asingle generator in Section IV-A, using a Dynamic Program-ming approach. Then, this approach is extended in SectionIV-B to a form that can be used to solve the global (VPP)production planning problem. The notion of distributed DPsleads to the idea for an approximation heuristic. Section IV-Ccompletes this method, by introducing iterative reschedulingmethods to match the resulting global schedule to the fixedproduction pattern scheme. In this process the communicationstructure, given in Section III-A, is used.

A. Assignment of production runs based on heat demandpredictions: a Dynamic Programming approach

In [3] a Dynamic Programming formulation (DP) of theplanning problem in a single house is proposed. It dividesthe planning horizon T in N intervals of equal size andintroduces a state tuple (A,B,C) to describe the situation ineach interval. So, each interval has a set of states (A,B,C). Adenotes the number of intervals that the state of the microCHP(on or off) is unchanged until the start of the current interval(positive values indicating that the microCHP is running andnegative values indicating that the microCHP is off). B is thetotal number of intervals the microCHP has been running forthe whole planning period until the current interval and C isthe number of runs of the microCHP which have already beenfinished. For each interval j T and state (A,B,C) we definethe cost function Fj(A,B,C), which aims at minimizing thecosts from interval j until the end of the planning horizon,N , assuming that the current situation is characterized by thestate (A,B,C). The costs between two consecutive states insequential intervals can vary for different intervals and states.These costs represent the objective function (e.g. the inverseprice on the electricity market [1]); on the other hand, the hardconstraints on heat comfort, minimum runtime and minimumofftime can be deducted from the state description and arerepresented by costs of. The total amount of generated heatcan be deducted from the combination of A, B and C. Sincethe demand of each time period and the start level of the heatbuffer are known, we can deduce for each state in each timeperiod whether lower and upper levels of the heat buffer areexceeded or not. In case there is a violation, a penalty of is

4given to the corresponding state. The minimum runtime andofftime constraints now can be taken into account by lookingat the value of A and penalizing wrong state changes in theDP with a value of .

The main challenge in the creation of a DP is to limit thenumber of states in the description. In this DP formulation aselection of states is formed for (the start of) each interval,based on the available states in the previous interval and thebinary decision to switch the microCHP on (x = 1) or off(x = 0) in the previous interval. In this way the state spacegrows exponentially with the intervals (2 new states for eachprevious state). However, many states are visited multipletimes from different previous states and the requirement tooffer guaranteed heat comfort excludes many states. So, inpractice the number of states could be limited sufficiently.Figure 2 shows an example for two state changes that arepossible from a certain state (3, 13, 2). In the given case,switching the microCHP off (xj = 0) is not possible, eitherdue to minimum runtime constraints (MR > 3) or due to heatdemand (in this case the lower level is reached at the start oftime period j). The decision to leave the microCHP running(xj = 1) has attached costs of 2, based on the relative desireto let the microCHP run in period j.

. . .

. . .

0BBBBB@. . .. . .

(3, 13, 2). . .. . .. . .

1CCCCCA

0BBBBB@. . .

(4, 14, 2). . .. . .

(1, 13, 3). . .

1CCCCCA. . .. . .

(xj = 1)

2

(xj = 0)

j 1 j j + 1

Fig. 2. State changes from (3,13,2) with corresponding costs

Via a backtracking algorithm the value of F0(0, 0, 0) canbe calculated. The path(s) corresponding to this value give thestate tuple changes which correspond to the xj values.

1) Properties of the DP: Since there are O(N3) statetuples and there are N time periods to evaluate, the dynamicprogramming approach of the single house model has runtimeO(N4). In practice, the DP approach is a suitable method tosolve the problem of scheduling single houses to optimalitywithin reasonable time, when the interval length of the deci-sions is > 5 minutes. This is indicated by the dashed verticalline in Figure 3. In this figure, the computation time of theDP is plotted against the number of intervals (each of a fixedsize) of the scheduling problem for 24 hours. Two cases areused; the first one represents a day in winter, where in case2 the heat demand is halved (heat demand is an importantfactor, since this represents the production potential, which isreflected in the total number of states and, thus, in computationtimes). In the case, when the interval length of the decisionsis > 5 minutes, the state space of the DP has an acceptablesize and the optimum is found within 5 minutes, given bythe dashed horizontal line in Figure 3. An interval length of5 minutes is a good trade-off between precision and data [9],so our choice for the interval lengths is acceptable.

0 100 200 300 4000

500

1,000

1,500

2,000

# intervals

com

puta

tion

time

(s)

case 1: winter heat demandcase 2: halved heat demand

Fig. 3. Computation times for the DP approach for different numbers ofintervals

B. Distributed DP

A DP can be a fast method to find an optimal solution forsingle houses. On the other hand, the problem of scheduling afleet of houses introduces an extra dimension to the problem.Now, the houses need to cooperate in the sense of electricitygeneration. Together, they must produce a total electricitypattern that matches a predefined production plan. When thiscooperation is applied to the DP formulation the state spaceexplodes, since the DP needs to combine the information of allhouses in a single state definition. This DP is not suitable to beused to solve the problem of scheduling a fleet to optimalitywithin reasonable time, if we want to be able to solve instanceswith similar interval lengths as in the problem of schedulingsingle houses.

However, the single house DP can still be used in anapproximation heuristic. The concept of the single house DPis that it produces an optimal planning for the runs of thegenerator, where the objective is market price-oriented. Ouridea of distributed DP is to match the desired productionand the planning of the VPP, by using the local computationcapacity of the houses. The local production is still plannedfrom the viewpoint of local comfort and price optimization.However, the globally decided production plan must eventuallybe matched. This is done by steering the market prices that areused in the local DPs. So, relatively fast local DPs are usedin a VPP perspective and steering elements are introduced torearrange these local schedules.

A central entity within the VPP is located at the top of thehierarchy as in Section III-A. Since the total production planis known here, the central entity can steer temporary schedulesinto the right direction. This entity can ask lower level nodes toproduce a certain part of the total production plan. The steeringgoes via artificial costs, which can be interpreted differently bythe various end groups or can be surpassed differently by thelevels in between. For example, if a node at a certain level hasfullfilled its part of the total production plan, it suppresses newartificial cost changes and leaves the substructure unchanged.

5Of course it takes several iterations to eventually match thetotal production plan at the top of the hierarchy with thedistributed planning. A detailed description of this iterativesteering is given in Section IV-C.

C. Iteratively reassignment of production runs via steeringsignals

As mentioned before, each group has an entity, whichcollects the planned runs from the generators and reports backto the central entity. Within the structure, communication takesplace between some elements of subsequent levels. We makea distinction between two types of communication: the planned production runs, which are the results of local

scheduling methods; steering signals, which are used as input for the local

scheduling problems.Aggregated production plans are forwarded to higher levelentities, whereas steering signals are sent to lower levelentities. The idea behind the structure is that at each leveldifferent steering signals can be given, such that locally moreor less independent adjustments to the generator schedulesare made. The balancing properties of the structure play animportant role in this, since substructures can be coped within a similar way, at the same level as well as at differentlevels. Therefore a generic way of using steering signals can beapplied to the method at all levels, which allows substructuresto be coped with based on the actual deviations of the localplan and the realisation.

Once this generic way of using steering signals can beshown to need a limited amount of iterations to reach thematching of the underlying substructure, we can apply themethod on large scale. In combination with the use of the localmatching, we define two ways of choosing steering signals: steering 1

In the first steering method, the artificial additional coststhat is used in the steering process, decreases linearlywith each iteration. This cost is added to the current costsfor the state changes, only at state changes where thecurrent planned production of the substructure exceedsthe desired production. The idea is that exceeding plannedproduction is rescheduled at other times, by increasing thecosts attached to the current states, where the planningexceeds the desired production. The starting value of theartificial costs is in the order of the maximum cost in theoriginal DP and decreases linearly to 0.

steering 2The second method uses the same idea of decreasingadditional costs as in the first steering method. In additionto this method, each individual DP now only changes itsplanning, if at least a minimum number of decisions ischanged with respect to the previous DP calculation. Thisis done to introduce a certain threshold for individualhouses, before the current production plan is altered.

V. RESULTSIn this section we show the results of our distributed

scheduling method. We give the iterative and distributed

production planning of one subgroup. However, due to thebalancing properties of the structure, subgroups are compara-ble and it should be possible to extend the method to a largescale VPP.

The instances of our tests consist of a subgroup of 50houses. Each house contains a microCHP and a heat bufferof 10 kWh, and has a heat demand of 84 kWh of a winterday. The costs for the state changes are the inverted pricesof the APX day ahead market [1]. In Figure 4 the squaredmismatch between the fleet production plan and the predefinedproduction pattern is plotted against the number of iterations.The total production potential is divided equally over theintervals and defines the production plan of the VPP. It can

0 5 10 15 20 250

1

2

3104

# iterations

squa

red

mis

mat

ch

steering 1steering 2

Fig. 4. Squared mismatch between fleet production plan and predefinedproduction pattern

be seen in Figure 4 that the squared mismatch is drasticallyreduced within 10 iterations. The method overcompensatesin some iterations, resulting in alternating improvements anddeteriorations. This phenomenon also takes place, when thesecond steering method is applied. However, the overshootingstabilizes, since decreasing additional costs are used. Onlyminor differences between the two steering methods can benoticed. The first method seems to perform slightly better thanthe second method, if a large number of iterations is allowed,since small changes in local production plans are taken intoaccount.

In Figure 5 the objective value (normalized profit on theAPX day ahead market) is given. The dashed horizontal linewith value 1 represents the optimal (normalized) profit of the50 houses, when each of these houses uses a DP with onlylocal objectives. The dashed horizontal line with value 0.91represents the optimal (normalized) profit, when the houses co-operate in a VPP and the total production exactly matches thedefined plan. After 10 iterations the objective value stabilizesclose to the optimal value of 0.91. This shows that the squaredmismatch in Figure 4 after 10 iterations has an acceptable size;this size can be used as a stop reference to decide after howmany iterations a substructure has approximated its desiredproduction plan good enough.

60 5 10 15 20 250.7

0.8

0.9

1

1.1

0.91

1

# iterations

norm

aliz

edob

ject

ive

valu

esteering 1steering 2

Fig. 5. Objective values

VI. CONCLUSION AND RECOMMENDATION

In this paper we describe a distributed scheduling methodto plan the production of a Virtual Power Plant. A balancedcommunication structure is proposed, in which groups of afixed maximum size are divided over a minimal number oflevels.

From the results in Section V we conclude that the dis-tributed scheduling method for a VPP is possible with a limitednumber of iterations. Within 10 iterations the method reachesan acceptable approximation of the global optimum.

In future work we want to extend the generic steeringmethod to a large scale implementation. Also, other steeringmethods can be developed.

VII. ACKNOWLEDGEMENTS

This research is conducted within the SFEER project(07937) supported by STW, Essent and GasTerra.

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