Aalborg Universitet

Economic energy distribution and consumption in a microgrid Part 2

Tahersima, Fatemeh; Stoustrup, Jakob; Andersen, Palle; Madsen, Per Printz

Published in:Proceedings of the 19th IFAC World Congress, 2014

DOI (link to publication from Publisher):0.3182/20140824-6-ZA-1003.00078

Publication date:2014

Document VersionEarly version, also known as pre-print

Link to publication from Aalborg University

Citation for published version (APA):Tahersima, F., Stoustrup, J., Andersen, P., & Madsen, P. P. (2014). Economic energy distribution andconsumption in a microgrid Part 2: Macrocell level controller. In Proceedings of the 19th IFAC World Congress,2014 (1 ed., Vol. 19, pp. 4553-4559). IFAC Publisher. I F A C Workshop Series, DOI: 0.3182/20140824-6-ZA-1003.00078

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Economic energy distribution andconsumption in a microgrid

Part 2: Macrocell level controller

F. Tahersima, J. Stoustrup, P. Andersen, P. P. Madsen

Department of Electronic Systems, Aalborg University, Denmarkmaryamtsima@gmail.com, Jakob.Stoustrup@pnnl.gov, pa@es.aau.dk,

ppm@es.aau.dk

Abstract: Energy management of a small scale electrical microgrid is investigated. Themicrogrid comprises residential houses with local renewable generation, consumption and storageunits. The microgrid has the possibility of connection to the electricity grid as well to compensateenergy deficit of local power producers. The final objective is to fulfil the microgrid’s energydemands mainly from the local electricity producers. The other objective is to manage powerconsumption such that the consumption cost is minimum for individual households. In thisstudy, a hierarchical controller composed of three levels is proposed. Each layer from bottomto top focus on individual energy consuming units, individual buildings, and the microgridrespectively. At the middle layer, a model predictive controller is formulated to schedule thebuilding’s energy consumption using potential load flexibilities. The top level energy manageris designed to distribute available power resources among the houses or sell the remainder tothe electricity grid. Simulation results show the economically optimal energy consumption inthe buildings and economically efficient power trading between the houses.

Keywords: Microgrid control; Demand side energy management; Model predictive controller;Indirect control; Intraday electricity market price.

1. INTRODUCTION

The global movement is toward power production mostlyusing renewable energy resources rather than using fossilfuels which are environmentally polluting and are beingdepleted very fast. These renewable energy resources, forinstance solar, wind, biomass and geothermal are, bytheir nature, highly distributed compared to large con-centrated nuclear or fossil-fuel power stations. Regainingpower balance and allocation of resources in such a diverseand distributed energy market will be two big challenges.Smart grid as a newly emerging concept to be built uponthe existing infrastructure of power grid is to facilitatethe coordination among all the contributing production,consumption and storage units. In this scheme, a singlesmall-scale power consumer will be no longer an inac-tive component, but potentially will contribute to energymanagement of the smart grid by providing flexibility.Capability of power generation using local generation unitsand making use of storage devices increase flexibility of thegrid nodes.

Several world-wide studies have been conducted recentlyto propose new market, communication, and control lay-outs for the emerging large scale distributed energy sys-tems. Encourage, NeogridEU, iPower and FlexPower areexamples of many ongoing European and Danish projectsthat are going to develop methodologies with differentapproaches to overcome the smart grid imbalances.

1.1 Research Questions and Objectives

Embedded intelligent controls for buildings with renewablegeneration and storage (ENCOURAGE) aims to developembedded intelligence and integration technologies thatwill directly optimize energy use in buildings and enableactive participation in the future smart grid. The targetenergy saving for a network of buildings composed ofdistributed energy consumption, production and storageunits is 20% via design of supervisory control schemesthat coordinates among interplaying energy devices andbuildings Skou and et. al. (2010).

As part of Encourage, we are going to design a supervisorycontroller that integrate and manage all energy units in themicrogrid. The objectives are as follows:

• Energy needs of the microgrid are, as much as pos-sible, to be provided by local generation units whichare Photo Voltaic (PV) cells in our case study. Thepurpose is to minimize dependency to the grid power.

• The other objective is to minimize electricity con-sumption costs of individual households.

• The energy manger i.e. a supervisory controller is sup-posed to work with the existing single loop controllersin the building for instance heating thermostats.

However, the first two objectives might be conflicting,in which case priority would be with individuals’ bene-fit. For example, there might be time intervals, duringwhich power demand of a house exceeds its production.Assuming that power is provided by the grid at a lower

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price rate than the neighbouring production units in themicrogrid, power would be purchased from the grid. On theother hand, policies could be enacted to promote balancebetween power production and consumption within themicrogrid, for instance price of the locally produced powercould be kept always lower than the grid electricity price.

The last objective is to be fulfilled by design of a hierarchi-cal control structure that is shown in Fig. 1. The hierarchyis explained in Section III in more details.

Fig. 1. Controller hierarchy for the microgrid energy man-agement

1.2 Literature on Demand-Side Load Management

There are two mainstream approaches for energy consump-tion/production management toward a smarter electricgrid i.e. direct and indirect control. The former relatesto a set-up where an energy node in the grid informs theaggregator of its potential flexibility on consumption orproduction. The load flexibility is to be provided by meansof some storage facilities. In return, the aggregator controlsthe unit based on the predicted flexibility within the limitsand costs agreed upon in advance Biegel (2012). In thelatter approach, price incentives are sent to distributedenergy resources in order to encourage individual unitsfor example detached houses, residential or office buildingsto consume electricity when energy surpluses in the gridby shifting their power demands, and use local energyresources or the stored energy when there is power con-gestion or deficit in the grid Pinson (2012); Moslehi andRanjit (2010).

The concept of indirect control within the smart grid isconceptually studied and classified in two main categoriesin Heussen et al. (2012b). One type of indirectness involvesnot direct control command but only an incentive. Op-eration of electrical power systems based on nodal pricecontrol was firstly addressed in the studies conducted byFred Schweppe which is summarized in Schweppe et al.(1988). Many researches were conducted ever since study-ing different aspects of market-oriented approach for theelectrical power system sector Jokic et al. (2009); Alvarado(1999); Alvarado et al. (2001); Alvarado (2003).

A novel generalized framework for modelling a storagenode in the grid is proposed in Heussen et al. (2012a).It models any type of interactions among the energygenerators/consumers and storage devices, energy leakagesin transmission lines and due to energy conversions viadefinition of a generic power node. A control-oriented

approach to modelling and optimization of microgridsis proposed in Parisio and Glielmo (2011). It exploitsModel Predictive Control (MPC) in combination withMixed Integer Linear Programming (MILP) Bemporadand Morari (1999). Load shifting based on price incentivesfor households in a microgrid is addressed in recent studiesusing optimal controller in Pedersen et al. (2011). MPCwas previously addressed in Tahersima et al. (2012) forheating load management of a single residential building.Also, Tahersima et al. (2011) suggests an assistant chartthat quantifies energy flexibility of households.

Main focus of the current work is on indirect control ofhouseholds’ energy consumption in a microgrid. A modelpredictive controller is formulated that systematicallyfinds the energy consumption pattern of flexible loads pro-vided that knowledge about other loads and productionsand the building dynamics are available. In the proposedscheme electricity can also be sold to the grid and con-sumption can be curtailed if convenient. In contrary to theavailable literature, a hierarchical controller rather than acentralized one is proposed . The first advantage is that theexisting stand-alone single-loop controllers at the devicelevel are exploited. The new integrating and optimizinglayer connects to the lowest layer by commanding a generalreference signal to the single loop controllers. The system-wide controller is designed in a receding horizon fashion inorder to incorporate building energy flexibilities based ona dynamical model, future preferences and disturbances.

The paper is structured as follows: the microgrid casestudy is described in the next section. Section III describesthe hierarchical control strategy for energy distributionin the microgrid in more details. Focus of the paper isexplained in this section. The optimal pattern for energyconsumption of one building is achieved by solving anon-line optimization problem which is formulated basedon the receding horizon control approach in Section IV.Section V presents the simulation results that comparescost benefits of the economic controller against the energyoptimizing controller. Finally, Section VI concludes thepaper.

1.3 Nomenclature

All the parameters and control variables that we used inthe formulations are described in Table I.

2. A MICROGRID OF SEVERAL DETACHEDHOUSES

In this section the main characteristics of the concernedmicrogrid are summarized . Although a specific microgridis describe, the formulations can be generalized to anysimilar microgrid system.

One of the demonstration sites of the Encourage projectthat is the focus on in this study, is a network of eightresidential buildings i.e. detached houses located in North-ern Denmark. Each house is equipped with Photo Voltaic(PV) cells with capacity of producing 4kW of electricity.Thus, electricity needs of an individual house is providedpartly by solar cells and the remainder could be boughtfrom both other producers in the microgrid and the mainelectricity grid. That depends on the energy price provided

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Table 1. Symbols and Subscripts

Nomenclature

A surface area (m2)C thermal capacitance (kJ/kg ◦C)h sampling timeKp proportion gainN prediction horizonQ power flow (kW )t timeT building temperature (◦C)Tint integration timeU thermal transmittance (kW/m2 ◦C)w electricity power (kW )ρdiscomf discomfort weight in the cost function (DKK/◦C)ρbuy electricity buying price from grid (DKK/kWh)ρsell electricity selling price to grid (DKK/kWh)ρcurt curtailment weight in the cost function (DKK/kWh)ξ integral stateβ curtailment coefficient

Subscripts

buy buying (power or price)cmf comfort (temperature)heat electrical floor heating (heat flow)k current time instantout outdoor (temperature)pv photo voltaic (power)ref reference (of building temperature)sell selling (power or price)tol tolerance (temperature defined by users)

by each energy source. Indoor air is heated by electricalfloor heating in the houses. Measurements show that elec-trical space heater, electric water heater, appliances, andlighting respectively account for highest to lowest powerconsumption in a building. A satellite view of the housestaken from Google map is depicted in Fig. 2.

Fig. 2. The demonstration site including 8 residentialhouses with photovoltaic cells on top of the roofs

All the houses are similar and very well insulated. Thehouses are occupied by diverse types of families i.e. youngcouples, families with children and pensioners who arecouple or single. The chosen occupancy diversity allowstesting different consumption profiles for load control andenergy exchange between the houses which is the normalcase in a medium to large scale power island. Some housesare occupied mostly in evenings and weekends, while theothers consume power often times during a week.

The microgrid is always connected to the grid. Thereforethe islanded-mode is never imposed to the microgrid

physically. However, the strategies should be enacted inorder to make it as independent as possible from the grid.Therefore, it can purchase and sell electricity from/to thegrid at any time. However, the objective is to make thetrading in only one direction at a time, meaning that aslong as there is power demands in the microgrid, no powerwill be sold to the grid.

The microgrid local power generators are renewable, non-dispatchable sources. There is no specific energy storagedevice to store energy for a later use. However, the buildingthermal mass is a dynamic energy buffer which can becharged in a controlled way, but the discharge is notcontrollable, although is predictable. The stored energy,naturally is in thermal form. Thus, this storage capacitymakes the heating and cooling loads flexible to a certaindegree determined by the building dynamics.

3. ENERGY MANAGEMENT STRATEGY

The optimal use of storage capacity and the loads can helpto keep the balance in the microgrid. For this purpose weneed to define flexibility of energy loads of the buildingswhich are building blocks of our microgrid.

We have categorized various energy loads in the building tothree types i.e. shift-able loads, curtail-able loads and non-flexible loads. The last type of loads are not controllablefor example appliances and multimedia devices that aredirectly interfered with by the user. The first two typesare controllable, although differently which depends onthe type of the variable being controlled and residentsexpectation of comfort. To give an insight, lets compareheating with lighting; A heater is controlled normally tomaintain a specific thermal comfort criterion which is oftenspecified either by a profile of reference temperature orupper and lower boundaries. In either case, time intervalof heating possibly can be shifted depending on inherentheat capacity of the building and thermal tolerance degreeof the building’s residents. For example, the larger heatcapacity of the building and the higher tolerance of theoccupants, flexibility in time of heating is higher. Onthe other hand, light is not store-able and it is neededinstantly. Therefore, it would only be possible to cut downor dim the light when it is not needed for instance whendaylight is available or motion is not detected in theroom. For a taxonomy on different type of loads pleasesee Petersen et al. (2013).

The control hierarchy as shown in Fig. 1 composes threedifferent layers. The task of each layer and the connectionbetween the layers are described in the following.

• Device layer at the bottom of hierarchy comprisessingle loop controllers for controllable (shift-able andcurtail-able) loads, controllable generation units (notavailable) and storage devices (not available). It isresponsible for maintaining set-points and light ad-justment.

• Cell (building) level at middle of hierarchy includesa system-wide controller that keeps the economy andcomfort in balance. It minimizes the cost of electricityconsumption while maintaining the comfort levels de-termined by the user. A priori knowledge about build-ing dynamics, comfort preferences, weather changes,

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Fig. 3. Block diagram of the hierarchical supervisory con-troller. Inputs to the MPC are: Electricity intra-daymarket price, Pre-set user-defined comfort tempera-ture (Tcmf ), forecast of outdoor temperature (Tout),Prediction of electricity generation by PVs (Wpv),Predicted consumption profile of curtail-able (Qcurt)and non-flexible loads (Qload). Output control signalsare: a reference temperature (Tref ) to HVAC systemcontroller and a coefficient of curtailment (β) to thelighting system controller.

power generation and price of electricity are needed.The forecast inputs are supplied by a prediction mod-ule which is part of Encourage. This layer receives sta-tus signal from device controllers i.e. heating/coolingthermostats and provide them with reference signals.

• Microgrid level at the top is responsible for distri-bution of locally generated energy among householdswith energy demands. It receives predictions of powersurplus profile (for sale) and power needs profile (tobe purchased) from the system-wide controllers in themiddle. Based on these inputs, it predictively assignssurplus power in the microgrid among the demandinghouses. The system-wide controller is designed suchthat power produced by PVs are consumed by theproducing house at the first place. The excess isdistributed by the power trading scheduler among theother houses with power deficit. It predictively deter-mines the constraints on the amount of buying energyand selling energy for each house in the microgrid.

4. CELL-LEVEL CONTROLLER

Block diagram of the hierarchical supervisory controllerat the cell level is depicted in Fig. 3. We have chosenModel Predictive Controller (MPC) as the system-widecontroller Maciejowski (2002). The reason for this choiceis that, all the system disturbances and future referencescan systematically be incorporated into the MPC. On theother hand, the middle layer has to provide a foreseenestimate of surplus and demand power to the powerscheduler at the top layer. This feature would alreadybe embedded in the system-wide controller if we choosea receding horizon controller. At the bottom layer we havedesigned Proportional Integral (PI) controller for heatingloads. Light curtailment is done based on inputs fromsensors measuring light or detecting motion.

4.1 Optimization Problem

The optimization problem is formulated in a recedinghorizon framework. An economic solution is achieved bypenalizing power purchase from the utility grid and themicrogrid in the cost function. Economic benefit of powersale to the grid and microgrid is also incorporated. Also,discomfort i.e. deviation from a comfort temperature pro-

file is penalized. The other term in the cost function isrelated to curtailment penalty.

minTref ,β,wsell,wmgsell,wmgbuy

N∑k=1

(ρdiscmf (k)|T (k)− Tcmf (k)|

+ρbuy(k)wbuy(k) + ρmgbuy(k)wmgbuy(k) +

ρcurtβcurt(k)Qcurt(k))−ρsell(k)wsell(k)− ρmgsell(k)wmgsell(k)

s.t. (1)

T (k + 1) = a11T (k) + a12ξ(k) + b1Tref (k) + e1Tout(k)

ξ(k + 1) = a21T (k) + a22ξ(k) + b2Tref (k)

Qheat(k) = c1T (k) + c2ξk + dTref (k)

0 ≤ Qheat(k) ≤ Qmax−Ttol(k) ≤ T (k)− Tcmf (k) ≤ Ttol(k)

0 ≤ βcurt ≤ 1

0 ≤ wsell(k)

0 ≤ wmgbuy(k) ≤ wmaxmgbuy(k)

wminmgsell(k) ≤ wmgsell(k)

wbuy(k) + wmgbuy(k) = Qheat(k) + (1− β(k))Qcurt(k)

+Qload(k) + wsell(k) + wmgsell − wpv(k)

in which k is the time instant and N is the predictionhorizon. ρdiscmf and ρcurt are coefficients of penalty forthermal discomfort and curtailment of the appertainingcurtail-able loads, respectively. Control variables are cur-tailment coefficient β, sold power to the grid wsell, soldpower to the microgrid wmgsell and the reference temper-ature of the building Tref . Predicted signals and systemdisturbances include comfort temperature profile Tcmf ,buying and selling price with the grid: ρbuy and ρsell,buying and selling price within microgrid: ρmgbuy andρmgsell, discomfort penalty ρdiscmf , curtailment penaltyρcurt, curtail-able and inflexible loads Qcurt and Qload, andelectricity generation of PV cells wpv, all for the next 24hours. Amounts of energy for buying and selling appearin the same equations, but optimization will not result inbuying and selling amounts to be non-zero in the sametime step if as assumed ρsell ≤ ρmgsell ≤ ρmgbuy ≤ ρbuy.Boundaries on building temperature Ttol and maximumheat flow Qmax are the known parameters.

The two boundaries on trading power with the microgridare supplied by the macrocell-level controller. It deter-mines the minimum power which can be purchased fromthe microgrid wmaxmgsell, or the maximum power which canbe purchased by the microgrid wmaxmgbuy.

Prediction model in the MPC governs a closed loop systemof the building and floor heating with PI control. Buildingdynamics are described using a first order model. PI con-troller parameters Kp and Tint are determined using a stepresponse test. Considering the sampling time h = tk+1−tk,thermal capacitance of the building envelope and furni-ture C, and total thermal transmittance of the buildingenvelope UA parameters of the closed-loop discrete timesystem are: a11 = 1 + h

CUA, a12 = hC , b1 = h

CKp,

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e1 = hCUA, in the second line a21 = h

Kp

Tint, a22 = 1 and

b2 = hKp

Tint, and in the last line c1 = − h

CKp, c2 = hC and

d = hCKp. For a detailed description on deriving the closed

loop model please see Tahersima et al. (2013).

The design of building-level controller in Tahersima et al.(2013) was studied via simulations and included a discus-sion how to determine the controller coefficients. In thenext section the structure of the microgrid-level energyscheduler is described and an algorithm for running thewhole hierarchical controller is proposed.

5. MACROCELL LEVEL CONTROLLER

Electricity demand of the houses in the microgrid areto be supplied by the locally installed PV cells. Thepositive remainder electricity will be sold to the grid andthe negative remainder will be purchased from it. Eachhouse fulfills its own power demand at the first place.The second priority is the microgrid’s energy demand. Thepower scheduler is designed according to this consumptionstrategy as described in the following.

5.1 Power Trading Method

The total power surplus and demand in the microgrid willbe predicted at every time step h for the time horizon ofN time steps, see Fig. 4. For this purpose, we rely on thepredicted power surplus and demand by the MPC.

Fig. 4. Prediction of power surplus and deficit in themicrogrid as a function of time

The prediction of power for sale or purchase in the next 24hours for all the houses gives us total power demand andsurplus in the microgrid:

wdemand(k) =

M∑i=1

wibuy(k)

wsurplus(k) =

M∑i=1

wisell(k) (2)

for k = 1, ..., N , the time step, N represents the predictionhorizon and for i = 1, ...,M , with M a the total number ofhouses.

A share of total power surplus will be assigned to eachdemanding house. For a fair distribution, this share willbe proportional to the house’s demand as described in thefollowing.

wmaxmgbuy(i, k) =wibuy(k)

wdemand(k)wsurplus

wminmgsell(i, k) =wisell(k)

wsurplus(k)min(wsurplus, wdemand) (3)

5.2 Power Management Algorithm

The algorithm through which the hierachical controllermanages power distribution and consumption in the micro-grid is given in this section. At each time step the followingsteps are performed.

• Step 1- At t = k solve the MPC optimization problemfor each house neglecting all terms related to wmgboth in the cost function and constraints. Therebywbuy, wsell, Qheat and β will be derived.

• Step 2- Calculate constraints on the maximum buyingpower from the microgrid and minimum selling powerto the microgrid using formula (2) and (3).

• Step 3- Solve the complete optimization problem foreach house considering the constraints on tradingpower with the microgrid.

• Step 4- References generated by MPC i.e. Tref and βwill be sent to the single loop controllers. Actual soldand purchased power will be calculated at the nexttime step. The total power consumption is:

wi =

{wisell if wi ≥ 0−wibuy if wi ≤ 0

At t = k + 1, we can calculate the actual powersold/purchased to/from the grid or microgrid at t = k.If wi ≥ 0, then sold power to the grid and microgrid forindividual houses are:

wimgsell =wisell∑i w

isell

×min

(∑i

wisell,∑i

wibuy

)wigsell =wisell − wimgsell (4)

If wi ≤ 0, then purchased power from the grid andmicrogrid for individual houses are:

wimgbuy =wibuy∑i w

ibuy

×min

(∑i

wisell,∑i

wibuy

)wigbuy =wibuy − wimgbuy (5)

6. SIMULATION RESULTS

Simulation results for energy management of the microgridcase study are presented and discussed in this section.Parameters of the building dynamics are chosen based ondata from a low energy building i.e. very similar to thedemonstration houses described in Section 2. The samplingtime is one hour equal to the time interval of variations inpredicted price profile. Predicted signals are assumed tobe available one day ahead. This is specifically importantfor the price profile which is settled in an hourly basis aday ahead in the Elspot trading system.

The power price is determined by balance between supplyand demand and fixed from 12:45 CET each day to beapplied from 00:00 CET the next day Nordpool (2013).Therefore the prediction horizon for MPC is chosen 1 day.Price signals are taken from the Nordpool database fora period of one week in February 2013. Weather data isalso taken from Danish Meteorological Institute (DMI).PV cells production data is achieved from Jadevej casestudy. Power price traded within the microgrid will be set

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between grid’s power prices, such that it encourages thelocal produces to sell their power to the local customersand the local customers to buy from local producers.

The formulated MPC is implemented in Matlab usingCVX optimization toolkit. In the microgrid, two differentpower consumption profiles are assigned to the houses.Fig. 5 and Fig. 6 depict energy management of two houseswith different consumption profiles. Power shifting andshedding are performed based on electricity price, weatherdata, and prediction of non-flexible loads. Perfect forecastwere assumed in all the simulation scenarios in this paper.

Fig. 5. a) Building type 1- Energy management of thebuilding with more power consumption and less flex-ibility. comfort temperature is 23 ◦C and it is limitedbetween 20 and 26 ◦C in the comfort zone. Qcurtailedis the power consumption after curtailment i.e. (1 −β)Qcurt. At the peak of price, the flexible loads arezero and only inflexible load is consuming the expen-sive power.

Fig. 6. b) Building type 2- Energy management of thebuilding with less power consumption and more flex-ibility. comfort temperature is 20 ◦C and it is limitedbetween 17 and 26 ◦C in the comfort zone.

Comparison of the 8 houses are depicted in the next fourfigures: Fig. 7, Fig. 8, Fig. 9, Fig. 10.

Fig. 7. . Outdoor temperature, total power generation byPV cells, power consumption and traded power

Fig. 8. Indoor temperature variations of each house isshown

Fig. 9. Power consumption of houses loads

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Fig. 10. Power traded with the grid and within the micro-grid. Average sold and purchased power is shown.

Cost of consumption for house type 1 has been 6.6 DKKper day while it was 4.5 DKK per day for the house type2. Moreover, the monetary benefit of selling power is 2.26and 3.36 for houses type 1 and 2 respectively. In total, thecost benefit of more flexibility in type 2 compared to type1 was 73% which is considerable. It is worth mentioningthat the energy price does not include tax which is infact a large share of power price in Denmark. Considering70% tax the monetary benefit due to consumption shiftwill be negligible. However, in future a high rate of taxmight be diminished or redistributed in order to encourageconsumers to be flexible.

7. CONCLUSION

The paper suggests a hierarchical control structure asan energy management system of a microgrid. MPC inthe building-level works in combination with device layercontrollers by supplying them with control references. Theresults show that with reliable price predictions substantialsavings in energy costs are obtainable for a consumerwhich implement a predictive controller. The microgridlevel energy manager schedules energy distribution in themicrogrid based on the buildings demand and surplus inevery iteration. The prediction of disturbances and gridprices assumed perfect which is not realistic. In the futurestudies we consider prediction error and uncertainties inthe study.

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