j ourna l ho me pa g e: www.elsev ier .com/ locate /enbui ld
enewable energy unit commitment, with different acceptance ofalanced power, solved by simulated annealing
ohumír Garlíka,b,∗, Milos Krivanb
Department of Micro-Environmental and Building Services Engineering, Czech Technical University in Prague, Thákurova 7, 160 00 Prague, Czech RepublicDepartment of Management and Artificial Intelligence, Research Institute for Intelligence Buildings, Brno, Drobného 16, 602 00 Brno, Czech Republic
r t i c l e i n f o
rticle history:eceived 28 April 2013eceived in revised form 22 June 2013ccepted 26 July 2013
a b s t r a c t
This paper formulates a unit commitment optimisation problem for renewable energy sources distributedin a micro-grid formed by a complex of intelligent buildings of both office and residential characters,including a wide range of amenities. We present a description of the solution of this task using the simu-lated annealing heuristic optimisation technique. The simple experiment is performed in three differentvariants of acceptance of balanced power constraining condition. In one of the variants is used fuzzy
A building which is economically efficient, has low energy con-umption and low impact on the (external/internal) environment,llows multi-purpose use and reconfiguration of its internal areas,rovides the maximum amount of safety and comfort, and caneduce operating costs is called an intelligent building.
This article focuses on the optimisation problem of sortingenewable electrical energy sources distributed in an energy micro-etwork of a fictitious town comprising a complex of intelligentuildings, whereas the goal is to minimise the total costs for man-facturing a volume of electrical energy based on the prediction of
ts consumption during the considered period. Due to this reason,e need to also focus on the integrated and systemic solution of
he external intelligence of intelligent buildings – i.e. the choice ofenewable energy sources (RES) with respect to technical, operat-ng and investment costs in relation to our problem. Last but noteast, we will emphasise the significance of the present focus on
entralised and distributed efficient production of electrical energy.
Renewable energy sources are renewable non-fossil-based nat-ral sources of energy, specifically wind energy, solar energy,
∗ Corresponding author at: Department of Management and Artificial Intelligence,esearch Institute for Intelligent Buildings, Brno, Drobného 16, 602 00 Brno, Czechepublic.
geothermal energy, hydro energy, soil energy, air energy, biomassenergy, energy in landfill gas, energy in sewage gas and biogasenergy. For completeness, we may extend these energy sources toalso include the energy of oceans and seas, mining gas and lightning.
RES are renewable, ecologically harmless and can satisfy localenergy needs. RES also have a firm position in the global energysupply system. They are especially a basic part of the solutionof energy intensity of buildings and an essential prerequisite forlow-energy, passive, zero-energy and plus-energy buildings. In ourenergy micro-network, we use the following types of RES (basedon their merits): 1x cogeneration, 3x biomass, 3x wind, 3x hydro.Photovoltaic and geothermal energy is not accepted in the micro-network, as explained in the scenario specified in the “experiment”part. All applied RES implemented in the energy micro-networkare designed so that their economical aspects, costs, economic andtechnical efficiency were advantageous (both economically andenergetically) with respect to the users and realisation area.
A cogeneration unit (combined production of electrical andthermal energy – CPETE) simultaneously produces electrical andthermal energy. The basic financial characteristic of cogenerationunits is a quick return on investments. In some economic and tech-nical applications, a unit of high-capacity accumulators is used asan upgrade of cogeneration units.
The size of a cogeneration unit is chosen based on the user’s
consumption diagrams. Specifically, at least 55% of the year mustalways be covered. Our experiment uses the values of consumptiondiagrams for two days in a week (a workday and a non-workingday), whereas all installed RES are evaluated simultaneously. The
alues of the consumption diagrams were obtained from the actualperation of a selected area of users in our complex of intelli-ent apartment and office buildings, from the database of CEZ a.s.zech Republic. The results of the power consumption during thesewo days, which historically show little variance, are then used toompute the annual energy consumption. Based on the obtainedalues and distribution of their consumption during a day/year,he most advantageous choice turned out to be the installationf a cogeneration unit with an output of 200 kWe/314 kWt (elec-rical efficiency 32%, total CPETE efficiency 90%). The minimumnnual coverage of the cogeneration unit was determined to be0% of the year (4380 h), 365 days/12 h. However, the coverage isealistically expected to be higher. In our case, the cogenerationnit is first and foremost a source of electrical energy – which islso generated by hydro and wind power plants in the IB com-lex micro-network. In the case of such so-called island operations,ith only limited connection to the distribution network (and onlyith partial or exceptional energy withdrawal from the distributionetwork), there are higher regulation costs.
From the environmental viewpoint, cogeneration units are morehan acceptable. The chemical energy of biogas (which is used in ourase) is transformed in the cogeneration unit into electrical energyt an efficiency of 30% and into thermal energy at an efficiency ofp to 50%. This implies that the use of the cogeneration unit is onlyarranted when all of the produced thermal energy can be used at
he place of its operation. In our case, this is possible thanks to these of thermal energy in heating. An optimal consumption of elec-rical and thermal energy results in a total efficiency of up to 80%.xcess or lack of produced electrical energy requires the prepara-ion of conditions for its accumulation via a control system based on
closed or open control system linked to exceptional withdrawalf energy from the distribution network into the intelligent build-ng (IB) complex. A gradual increase of installed power in the areaf the intelligent building complex may lead to problems in theooperation of various RES, such as, e.g. cogeneration units, withhe existing distribution network. Problems arise from the territo-ial configuration of the network and the local network in relationo the localisation of decentralised RES, which may also be presentn areas where electrical energy was previously only supplied fromhe distribution network.
The type of cogeneration is selected based on media availabil-ty. The primary fuel for cogeneration units could be, e.g.: naturaliesel gas, propane-butane, biogas, or other fuels based on con-ultation with the manufacturer (for instance wood-gas obtainedn a wood-gas generation). In our case the fuel is gas-based andot steam-based. The energy conversion ratio from energy inhe primary fuel to electrical energy is significantly higher thann the case of steam-based cogeneration, and is approximately3–41%, while the thermal production efficiency is approximately5–57%. The total energy utilisation ratio in the fuel ranges between8% and 90%. We also need to consider other criteria related tohe conditions in the IB complex: daily and annual schedules ofhermal and electrical energy consumption; type of required warm-ater medium; availability of gas fuel and the output of presently
nstalled boilers and their thermal and pressure parameters.To produce one kWh of electricity, our cogeneration unit uses,
.g. CZK 2.50/kWh worth of natural gas, with service costs amount-ng to approximately CZK 0.40–0.60/kWh. If the price of electricalnergy from the distribution network exceeds CZK 3/kWh (whichs true in the Czech Republic), it is advantageous to operate theogeneration unit just to cover the complex’s own electrical energyonsumption and the additionally produced heat can be consid-
red “free”. In our experiment, electrical energy consumers pay forotal connected electrical power consumption and for on-peak con-umption, and a cogeneration unit can significantly reduce theseosts.
uildings 67 (2013) 392–402 393
Energy benefits of cogeneration. The goal of cogeneration, withrespect to reducing the consumption of primary energy sources(PES) may be expressed by simple mathematical formulas, specif-ically: Qu = E
�el+ Q
�vy′t− E+Q
�kj[GJ], where Qu is the amount of saved
thermal energy from fuel due to collective production of electricityand heat, E is the amount of electrical energy [GJ], Q is the amountof thermal energy [GJ], �el is the total efficiency of a condensationpower plant, �kj is the total thermal efficiency of a condensationsource and �vy′t is the total efficiency of a heating plant. If weassume the efficiency of the cogeneration unit to be equal to thatof a heating plant, the amount of heat saved in the fuel per unitof thermal energy delivered to the consumer may be computed asQuQ = E
Q
(1
�el− 1
�kj
). In our case, we can express e = E
Q , which is the
coefficient of the dependent electrical power (power/heat ratio).
From the formula above we then get QuQ = e
(1
�el− 1
�kj
). Based on
this formula, we can say that if the total efficiency of the cogen-eration unit is the same as the efficiency of a heating plant, thenthe amount of heat saved from PES is directly proportional to thepower/heat ratio. The value of e depends on the type and makeof the cogeneration source and its usual values can be obtainedfrom the table of certain cogeneration units offered on the globalmarket. When designing a cogeneration unit, it is always impor-tant to maximise its overall thermal efficiency. This is the only wayto reach maximum savings of primary energy sources. We tookthis fundamental intent into account when designing the “Cogener”cogeneration unit. As a result, we will obtain maximum energy effi-ciency of the cogeneration unit implemented in our micro-network.We note that an in-depth calculation would exceed the scope of thisarticle.
Biomass is created on Earth thanks to solar radiation and pho-tosynthesis and may be divided to “dry” and “wet” biomass. If thebiomass contains too much water, it is not suitable for combus-tion. Wet biomass, such as manure, slur and other agricultural andfood waste, sorted communal biological waste, or some crops suchas corn, may be successfully utilised in biogas stations. Biogas sta-tions produce electricity in cogeneration units. Most frequently,they comprise adjusted piston engines which power a generatorand are capable of transforming 30–40% of the energy in the biogasinto electric power, while about one half of the biogas energy istransformed into heat.
Dry biomass may be identified with solid biomass, whereasthe most frequently used materials for energy purposes are woodand specifically cultivated plants (quickly growing timber species,herbage). The fundamental advantage of dry biomass is that it accu-mulates energy well and may be easily stored for prolonged periodsof time. One hectare of a field will produce a mass containing 40 to90 MWh of energy, depending on the type of plant. It is only pos-sible to extract energy from solid biomass by combustion, whichproduces both thermal energy and gases. The thermal energy pro-duced in a biomass power plant may be used either for heating or fordrying stored biomass. Gases from the combustion, e.g. wood-gas,may be used for the production of electric power by re-combustion.
Technical equipment for the utilisation of biogas still requiresrelatively steep investments, however it significantly contributesto the economics of agricultural businesses and also to environ-mental protection. High efficiency may only be reached when usingall produced thermal energy.
Biogas produced in biogas stations (BGS) is used to powerelectric generators in cogeneration units. The combustion of purebiomass has the advantage of not harming the environment, since
the amount of CO2 produced in this way equals the amount of CO2the biomass captured/used during its growth. The only resulting airpollutant is NOx. Biogas stations need not always produce only elec-tricity. Today it is possible to transform biogas into bio-methane,
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94 B. Garlík, M. Krivan / Energy
hich may be sent to the natural gas distribution network. Theroduction of gas allows the utilisation of the green bonus, which
s a very strong argument for the construction of many more biogastations during a gas crisis.
The product of biomass is biofuel, which may be solid, liquid or gas. Especially gas fuels such as biogas are a significant meansf producing electric and thermal energy, as a fuel for gas motorsnd cogeneration units. Biogas is created from agricultural biomasshrough the fermentation process. The by-products of the fermen-ation process are excellent fertilisers for growing crops.
With respect to optimising cooperation between KJ with IBnd ES, it is necessary to use a sufficiently large biogas tank toecure continuous operation. The amount of energy contained inhe fuel depends on the biofuel used. For selected plants, this rangesetween 14.4 and 16.5 GJ t−1.
Verification of the actual availability of the necessary volumef biomass (incl. its price at the source) is one of the importantrerequisites for the success of the project, i.e. for supplying the
B complex with electricity. As will be discussed further on in thecenario in the “experiment” section of this article, the applicationf biomass proves to be very efficient.
Aside from monitoring energy efficiency, it is also necessaryo take into account the economic aspects of utilising renewablenergy sources. It turns out that using biomass is energy-efficientspecially when biomass is used where it is produced (i.e. ideally ifhe producer and the user of biomass is the same), which is exactlyur case. The energy utilisation of biomass should focus especiallyn the use of waste and residual biomass, since the energy potentialf this biomass is significant. Biomass from the maintenance of theandscape and from public greenery is also becoming a significantource today.
We agree with the importance of biomass as one of the mostrequently used renewable sources in the future. It has an enor-
ous energy potential, which needs to be used by applying efficientechnologies and supported by legislative and political precautions.ased on analyses, the biomass potential ranges between 9 and2.5 million tonnes of dry matter per year, of which 5.1 to 6.5 mil-
ion tonnes of so-called residual biomass are available immediately.urrent estimates of the Ministry of the Environment of the Czechepublic state that the present utilisation of biomass amounts topproximately 1.9 million tonnes, which represents one third of theotential of residual biomass and one fifth of the realisable biomassotential.
Wind power plants – similarly as most utilisable forms of energyn Earth, wind is also powered by solar energy. Wind power plantsransform the kinetic energy of air currents (wind) into electricnergy. For kinetic energy Ek of a moving mass of air, we have:k = 1/2mu2 = 1/2�Vu2 [m – air weight; u – wind speed; � – airensity; V – air volume].
The output which could be obtained by the full (100%) utilisationf the kinetic energy of wind flowing through a unit surface per-endicular to the wind direction is called the wind power density. It
s usually specified in W/m2 and may be computed as: P = 1/2�u3.he output of a wind turbine, which is entered in W (watts), fol-ows: P = 1/2cpS�u3 [S – surface area covered by the rotor; cp –ower coefficient]. The theoretical maximum value of the coeffi-ient cp max is 0.593 based on the so-called Betz limit, however ineality the values of cp are not usually higher than 0.5.
The amount of electrical energy produced is specified in kWh,Wh or GWh and is related usually to the period of one year (in this
ase it is also necessary to specify the time period, e.g. MWh/year).he production depends on the amount of wind in the area, the
utput curve associated with the wind energy and technical as wells other circumstances (breakdowns, maintenance, frost, etc.).
Currently, the output installed in the Czech Republic at the priceevel of 2012 exceeds 220 MW. The national action plan of the Czech
uildings 67 (2013) 392–402
Republic estimates that in 2020 only 1.5 million MWh will be pro-duced from wind, i.e. about 1% of the electrical energy producedin the Czech Republic. It is clear that wind power will never be asignificant part of the energy plan of the Czech Republic. Yet, windpower represents a pure source of energy and it would be a pity notto use it. It is also a means of reducing CO2 emissions and increasingenergy self-sufficiency. Our experiment is based on these facts andincludes 300 kW of power generated by wind, i.e. the installation ofthree wind power plants. Currently, this represents the installationof 0.2% of the power of wind power plants from the total volumeof 173 MW (produced in 2020) permitted by Czech regional andgovernment bodies. Due to the trend of lowering the cost of energyproduced from wind power plants and the increasing competitive-ness of wind energy, our solution – experimental realisation – isthe determining factor for implementing this application.
The most important parameter for the production of electricpower from wind is the wind speed. The energy of wind is propor-tional to the cube of the wind speed, so, e.g. a wind speed of 5 m/shas twice the energy than a wind speed of 4 m/s. Thus, it holds thatthe wind speed is greater at higher altitudes. The wind speed thusgrows logarithmically with height above the terrain. Thus, we seea trend of building increasingly large machines (rotor diameters of40 to 100 m, pole height of 80 to 110 m). This is due to the resultinglower unit costs for energy production and maximal utilisation ofsuitable suits, which are a limiting factor. Inland, we see machineswhich have an output of 100 to 2000 kW. On the sea (near the coast)one can find turbines with outputs of up to 5 MW.
If the investment expenses are lower than CZK 38,500/kW ofinstalled power and the annual output exceeds 1900 h per year,the payback period is fifteen years. Of course, if the power plantis cheaper than the payback period will be shorter. If wind blowsmore frequently at the given site and the annual utilisation exceeds1900 h (good sites in the Czech Republic reach utilisations of up to2500 h per year), the payback period will again be shorter.
In our case, where the goal of the experiment is to systemat-ically reduce electrical power costs and all associated costs, weneed to assess the economic aspects of individual RES. The basisfor assessing the economic efficiency (of a wind power plant) iscomparison of average annual costs with annual earnings. Theuse of wind energy is economically efficient if its annual earnings(converted from actually produced output to CZK) exceed aver-age annual costs. To determine these values, it is important todetermine the investment costs (costs for buying the equipmentused in the wind power plant), operating costs (non-investmentcosts, such as the total costs for usual business activities: wages,materials, etc.) and the production costs of the wind power plant.Regarding these production costs, we may use the actual utilisableoutput of wind (Ps), i.e.: Ps = Pv · � = �
8 · D2 · � · w3 · � [W]; where� is the efficiency of the rotor (0.2–0.35), D is the blade diame-ter [m], w is the wind speed [m/s], � is the air weight (density)[kg/m3] and Pv is the theoretically utilisable output. By simpli-fying this formula, we get: Ps = C · D2 · w3. This implies that theamount of power generated will grow quickly with higher windspeeds, and on the other hand will be small at lower wind speeds.The power coefficient (efficiency) of the wind motor is specifiedby: � = Ps/Pv. By assuming that in our experiment we have sta-ble winds with an average wind speed of 7.5 ms−1, we deducefrom generally available norms and tables that the specific windspeed is 6 ms−1 even at an altitude of 100 m above the terrain(which is suitable). In specific cases, it is necessary to look at thewind frequency curve, which specified how often wind of a certainspeed is available, and the characteristics curve of the distribution
function of wind speed, whose shape and position depend on theaverage wind speed at the given location. From the distributionfunction we may easily compute the probable annual productionof electric power, and we may do the same from the formula
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=∫ d
0S · � · w2/2 · � · d� ≈
(1000/1200
)· Pn[kWh/r]; where S is
he area covered by the rotor [m2], � is the number of days in theear when the wind motor is working [days] and Pn is the power of aind motor at wind speed wn [kW]. We may use the value analysisethod to assess the suitability of investments with the assessing
riterion K, where K = N/P[CZK/kWh]; here N represents the totalosts (specific investment and operating costs and specific interest)nd P is production (kWh).
If we make an economic efficiency check on our solution, where:osts are CZK 35,000–40,000/kW (statistical average value of sim-lar selected realisations in the Czech Republic); service life is 20ears; annual depreciation is circa CZK 2000/kW; produced energys (1000–1200) kWh. Then the price of produced electrical energys 2000/1000 = CZK 2/kWh from depreciation write-off alone. Theesults of the economic checks specified above indicate that thenstalled wind power plant is economically advantageous in ourase. The price of electric energy produced from wind is similar tor even the same as for other RES in the micro-network.
The realisation of the wind power plant itself is associatedith solving problems such as selecting a good site (noise,
troboscopic effect). It is necessary to also take into account pos-ible collision with other technologies, such as radiolocation andelecommunication connections, airline corridors, transport andnergy infrastructure. The noise produced by a wind power plant,specially of aerodynamic origin, plays a key role in their realisa-ion. At the foot of a wind power plant, the sound intensity is about0–55 dB, which is significantly below the level of usual noise in aity.
Hydro power plants comprise two different systems: aydrological-hydraulic system of watercourses and an electri-cation system (a system for the production, distribution andonsumption of electrical energy). The property we are interestedn is that the electric energy consumption at a given moment is notirectly related to the flow in the watercourses at that moment.
The solution of our micro-network, which includes a hydroower plant, needs to be based on the knowledge of how to applyrimary or secondary hydro-energy potential. The application ofrimary hydro-energy potential, i.e. a natural water current, is theost efficient source of energy. Secondary hydro-energy potential
s created in pumped storage hydro plants. Energy may be obtainedrom water by using its flow (kinetic energy), its pressure (poten-ial/pressure energy), or both simultaneously.
The construction of large hydro plants represents a significantnterference into the environment (creation of a dam, flooded areas,hange of hydrological regime). There is basically no potential leftor their construction in the territory of the Czech Republic. Onhe other hand, small hydro plants (SHP) may still be built. Anotherption is the installation of modern and more efficient turbines andnits in current SHPs. In the Czech Republic, an SHP constitutes aevice with an output of under 10 MW, while in the EU the limit
s 5 MW. In the care of our experiment, we consider three hydrolants each with an output of 200 kW.
The hydro-generator is the basic part of a hydro plant, and com-rises a water turbine connected to an electrical generator. Themount of electrical energy produced may be computed as follows:he total efficiency can be expressed as �c = �t · �g · �p · �tr, and thushe resulting formula for the power plant output is P = � · g · Q · H · �c
kW], i.e. P = 9810 · Q · H · �c [kW], where: �t = 0.75–0.93 – type andize of hydraulic output, �g = 0.85–0.97 – generator efficiency,p = 0.94–0.98 – transformation losses (if the generator is not on
ensity [kg/m3] – usually 1000 kg/m – used in the formula for
, g – gravitational constant (9.81 m/s2), H – altitude differenceetween water levels – drop [m] and Q – turbine flow rate [m3/s].he used drop is obtained from the basic energy balance of a hydro
uildings 67 (2013) 392–402 395
plant by using Bernoulli’s equation. For approximate calculationsin the case of large hydro plants, we consider their efficiency tobe �c = 0.80–0.85 and in the case of small hydro plants �c ≤ 0.75. Ina simplified form, we obtain P = k × Q × H [kW], where k is a con-stant ranging between 5 and 7 for small and between 8 and 8.5 formedium/large hydro plants. The total output of the hydro plant isgiven by the sum of outputs of individual hydro-generators. Theamount of electrical energy produced by a hydro plant (per year),assuming a total output of P (watts) for a time period of t operatinghours, equals: E = P • t [kWh]. The number of operating hours duringthe year is calculated based on the number of days M during whichthe turbine can operate within the selected control range (at least4000 h).
In our case, we consider a drop of 1.5 m and a flow rate of 18 m3/s(k = 7.5) to produce 200 kW. To this end, we consider the use of atotal of three Kaplan turbines – standard flow-reaction turbines.Another possible variant would be the Francis turbine, which is themost frequently used type of turbine for most small hydro plants.The Francis turbine may be used for drops of at least 0.8 m and ischeaper than the Kaplan turbine.
In their base variants, both proposed turbines allow excellentregulation, however Kaplan’s turbine is difficult to manufacture (itis advantageous for our experiment though, as it may be used fordrops between 1 and 20 m and for flow rates between 0.15 andseveral m3/s, individually even up to tens of m3/s). It is suitableespecially for small hydro plants on weirs and rivers – which is ourcase.
The economics of an SHP are interesting mainly due to the factthat the production of electrical energy will become more and moreprofitable, since it may be expected that the manufacturing costswill remain the same during all of its service life. We make our com-parison based on the economic indicator of the production price of1 kWh. In our case, with a drop of 1.5 m, it is necessary to ensurethat the installed device is used in the long-term. Otherwise thedevice would be inefficient. The profitability of the construction ofhydro plants is assessed based on whether their operation ensures,within a required period, not only the return of the invested finan-cial resources, but also proportional annual earnings amountingto at least the designated interest rate. The base relation betweeninput factors is expressed as K = A · rn−1
rn·(r−1) [CZK] , where K rep-resents the used financial resources [CZK], A is the average annualearnings from the operation ensuring the economic return of theinvestment within the required period of n years [CZK], r expressesthe interest rate (r = 1 + p/100, where p is the interest rate in % [–]),n is the payback period of a loan or the payback period for investedfinancial resources [years]. We set the sum of discounted annualinstalments A (after deduction of interest) to equal the initial debtA. The value of the fraction in the relation for K expresses the time(in years) required to pay off the initial debt via regular annualinstalments. The average annual earnings A in the formula for Krequired to pay off the investments are based on the differencebetween earnings and costs related to the operation of an SHP. Ifthe actual value of A exceeds its value in the formula for K, theninvestments in an SHP are more advantageous (assuming a solventinvestor) than saving money in a bank. In our case, the constructionof such an SHP would be very economically sound.
Calculation. The costs for the construction of a single SHPdistributed in our micro-network which produces 1.7 millionkWh/year are as follows: The time (in years) required to pay offthe initial debt via annual instalments is 7 years based on the for-mula for K. At an interest rate of 14%, the payback period for theloan is n = 10 years.
The total investments into a single SHP in our experimentdepends on local conditions (which we defined in the “experiment”section).
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What will be the price of a small hydro turbo-system with anutput of 200 kW on the defined flow rate?
The Wather1 turbo-system has an output of P = 200 kW (cal-ulated from formula P = Q·H·k) with the specified drop and flowate:
Wather1: H = 1.5 m, Q = 18 m3/s, k = 7.5diameter of the turbine wheel OK = 1600 mmprice of technology for Wather1 will be K = CZK 7 millionA = earnings – costs (related to SHP operation)The value of A is: A = CZK 8.2 million (price per 1 kWh = CZK 4.83,
he SHP will produce 1.7 million kWh in our experiment).If A > K (which holds in our case) → the investment is advanta-
eous. Other installed SHPs (Wather2 and Wather3) have the samearameters as Wather1. We will thus skip further calculations.
The concept and disposition of the hydro plant in our micro-etwork is based on the method of creation of the drop, which in
ts final form corresponds to the technical solution of the utilisa-ion of hydro energy at a certain section of the river course. Specialechnology for the utilisation of hydro energy from water towers isurrently a development trend. Inclusion of such technology woulde an interesting alternative for our experiment. In practice, wateranks may be found in every country, usually near housing agglom-rations. All that is required is the installation of a hydro-motor, e.g.nto the armature chamber in the tower.
Photovoltaics. Note: In our experiment, photovoltaics are notncluded in the distribution micro-network. The reason is that athe area where the RES are installed, the predominant weathers cloudy. Solar cells do not provide sufficient output on cloudyays, as discussed in the experiment scenario. With respect to anverview of RES, we will only briefly summarise the basic functions,pplications and advantages of photovoltaics.
Photovoltaic systems allow the direct transfer of solar energy tolectrical energy, without any moving mechanical parts. The basiclement allowing the transfer of solar energy to electrical energys a solar cell, i.e. a large-surface semiconductor element, wherehotovoltaic tension is created via solar radiation. Solar energyhich reaches the surface of a photovoltaic panel, i.e. the amount
f absorbed radiation H, depends on the slope and bearing of theurface, i.e. its general orientation. Thus we choose an optimal slopef the surface of the panel of about 35◦ to maximise the amount ofbsorbed radiation.
All parameters of photovoltaic cells are provided under so-calledtandard testing conditions (STC), i.e. at a radiation intensity (w.r.t.M spectrum 1.5) of 1000 W/m2 and a temperature of 25 ◦C.
In case of a chain of serial cells, the total output of the moduleay drop considerably due to the partial or complete shading of
ome cells. Thus cells or parts of the chain are bridged by bridgeiodes. During real-time operation, it is also necessary to protectells from unfavourable environmental conditions. Weather mayegenerate the parameters of modules. The service life of modules
s defined as the amount of operating time before the efficiency ofodules drops by 20% (i.e. to 80% of their initial value).Geothermal energy (GTE) is available everywhere, stable and
asy to regulate. Direct utilisation in the form of heat or its transfero electrical energy may significantly contribute to regional energyndependence. Current GTE technologies require relatively largenvestments, but provide significant savings when compared to
ost other energy sources. Additionally, GTE does not have a neg-tive impact on the environment, and in fact the use of geothermalnergy does not fundamentally depend on natural or human-madelimatic conditions. Our experiment does not include GTE, and thuse will not discuss this form of energy in detail.
In conclusion, we may say that in relation to sorting energyources in a micro-network of a complex of intelligent buildings,t is important to minimise the costs specified above, especially
ith respect to selecting the type, build and settings of RES. Due to
uildings 67 (2013) 392–402
the complexity of the problem as a whole, this process is usuallycarried out relatively independently on three levels (production,transfer and consumption), i.e. instead of a single optimum weonly find three sub-optima. Dynamically variable fluctuations ofthe supplied and withdrawn electrical energy from RES due tothe non-continuousness of their availability is a technically knownproblem. Since the subject of the article is a deterministic solution,as opposed to a stochastic one, we do not discuss the harmonisa-tion of the fluctuations of deliveries and withdrawals of electricalenergy.
2. Unit commitment
The task of unit commitment is an optimisation problem witha goal of minimising the total costs of producing the volume ofenergy given by the prediction of its consumption for the con-sidered period, sampled e.g. by hours [4–40]. In other words, thisconstitutes a plan for the sorting of sources and their generatedoutputs covering the predicted consumption in each hour of thegiven period.
The optimisation problem may in general formally be expressedas follows:
f : Rn → R f
(�x0)
= min�x ∈ ˝
f(�x
) ⊂ R
n (1)
where �x0 is the optimum, whereas � specifies the area of admissiblesolutions containing the optimum as given by operating-technicalparameters of sources, and whereas f represents the cost functiongiven by a sum of operating and start-up costs for sources inte-grated in the given period:
, t ∈ {1, −, T} and Pi (t) resp. Ai, Bi, Ci resp. xi (t)are the nominal output resp. cost coefficients resp. state of the i-thsource in time t, and furthermore N resp. T is the number of sourcesin the network resp. the number of time snaps of the consideredperiod.
Admissible solutions are in general specified by the followingequality:
∑i
Pixi (t) = C (t) (3)
where C(t) represents a prediction of the consumption in the appro-priate hour of the considered period. Constraint condition (3) canbe accepted its direct inclusion into the objective function fg, forexample in the following ways (4) resp. (5):
g(�x (t)
)=
∑i
Pixi (t) − C (t)
fg(�x
)= f
(�x)
+ wg2(�x
)(4)
fg(�x
)= f
(�x)
− w�(
g(�x
))(5)
�(
g(�x
))= (�P −
∣∣g (�x)∣∣)/�P g
(�x)
∈ 〈−�P, �P〉
�(
g(�x
))= 0 g
(�x)
/∈ 〈−�P, �P〉
where w is the weight of the condition (3), � is the fuzzy numberzero (Fig. 1) and P is the maximum permissible power balancedeviation.
B. Garlík, M. Krivan / Energy and Buildings 67 (2013) 392–402 397
Fig. 1. Fuzzy number �.
Fig. 2. Dependence of probability on increase of energy.
3
ssiPofaorlartei
Fig. 3. Dependence of probability on temperature.
. Simulated annealing
Evolutionary algorithms are used to find a solution withufficient quality for large-scale general optimisation tasks in aufficiently short time. Evolutionary algorithms inspired by naturenclude a whole spectrum of optimisation heuristic techniques, e.g.article swarm resp. Ant Colony optimisation, genetic algorithmsr simulated annealing. Heuristics may be described as a procedureor searching the solution space via shortcuts, which are not guar-nteed to find the correct solution but do not suffer from a rangef problems of conventional optimisation methods such as e.g. theequirement of connectivity or differentiability of the criterion orink function, the problem of respecting constraints, being stuck in
shallow local minimum or divergence. However, their applicationequires the configuration of certain free parameters, which need
o be setup based on the specific optimisation task – these may.g. include the starting or final temperature and the number ofterations of the simulated annealing algorithm described below
Fig. 4. Freezing of solution.
Fig. 5. Simulated annealing algorithm.
and based on the evolution of thermodynamic systems. In physics,annealing is a process where an object, heated up to a certain hightemperature, is being gradually cooled down to remove internaldefects in the object. The high temperature causes the particles inthe object to rearrange randomly, which destroys defects in thecrystal lattice, and the gradual cooling then allows the particlesto stabilise in equilibrium points with a lower probability of thecreation of new defects.
Consider the case that the cost function argument (2) unambigu-ously specifies the macroscopic state of a certain thermodynamicsystem with energy equal to the function value. Then we canexpress its thermodynamic probability:
P (Ei) =∣∣{�x ∈ R
n| f(�x
)= Ei
}∣∣ (6)
as the number of micro-states corresponding to it.If we immerse this system with various macro-states with ener-
gies Ei in a thermal reservoir, then the Boltzmann equation forthe unit size of the Boltzmann constant together with the Taylorexpansion of a differentiable function, allows us to express theentropy of the reservoir after the temperatures equilibration forE = E0 + Ei = const. and E > >Ei as follows:
S (Ei) = S (E) − dS (E)dEi
Ei = ln P(E − Ei) (7)
and then, by using the definition of temperature dS(E)/dE = 1/T(T > 0), we can express the thermodynamic probability of a macro-state of the thermal reservoir as a function of the energy of the
macro-state of the inserted system, i.e. by the following Boltzmannfactor:
P (E − Ei) = ce− EiT (8)
3 and Buildings 67 (2013) 392–402
omt
p
p
wottc
tocta
iptthaam“dcsTd
98 B. Garlík, M. Krivan / Energy
The simulated annealing algorithm is based on the perturbationf an optimum candidate and a following decision on its replace-ent by a perturbation in each iteration of the algorithm based on
he Metropolis criterion [1]:
(�xi → �xj
)= P(Ej)
P(Ei)= e− �E
T �E > 0
(�xi → �xj
)= 1 �E ≤ 0
hich expresses the probability of the system transferring fromne macro-state to another, where �E = Ej – Ei and �E/T expresseshe increase of entropy, i.e. in accordance with the second law ofhermodynamics an impossible event is artificially redefined as aertain event in the specified criterion.
The sequence of accepted perturbations, i.e. acceptable solu-ions to the optimisation task, forms a Markov chain with memoryf order one, i.e. the occurrence of the given solution is onlyonditioned by the occurrence of the previous solution. The per-urbations which lie outside of the area of admissible solutions areutomatically rejected.
From p(�f) (Fig. 2), it is clear that a significantly “worse” solutions accepted with respect to the previous solution at a much lowerrobability than a slightly “worse” solution. p(T) (Fig. 3) may be usedo control the probability of the acceptance of the solution duringhe iteration cycle. We initiate the iteration cycle with a sufficientlyigh temperature to ensure that almost every proposed solution isccepted for a certain period of time, which will allow an initialpproximation of the solution to “escape” areas with shallow local
inima. Later on, we reduce the temperature so that almost no
worse” solution is accepted, i.e. during the iteration cycle we coolown the system representing the optimisation task from a suffi-iently high temperature to a sufficiently low temperature until aolution is “frozen” in a sufficiently deep local minimum (Fig. 4).he temperature drop may be modelled e.g. as an exponentiallyecreasing function:
Fig. 7. System view on the concept of intel
Fig. 6. Micro grid in a complex of intelligent buildings.
T = T0e− iter� � = − N
ln(
T∞/T0) T∞ ≈ lim
iter→∞T0e− iter
� = 0 (9)
where T0 resp. T∞ are the initial resp. final temperatures and N isthe number of iterations of the algorithm (Fig. 5).
4. Experiment
The scenario of the following computational experiment is asfollows: Let us assume a complex of intelligent residential and officebuildings and with a wide spectrum of associated amenities (Fig. 6)[2] with a further concretization (Fig. 7) [3] with the applicationof building management system. The complex, located near the
foothills of a mountain range, is near a small river flowing from alake, with a sufficient slant to build hydro-electric plants. The vicin-ity of the mountains provides stable winds which are of sufficientpower to build a park with wind power plants. Next to the complex,
ligent buildings, such as eco-houses.
B. Garlík, M. Krivan / Energy and Buildings 67 (2013) 392–402 399
here is a cogeneration plant which supplies the complex with heatnd power. Due to the highly developed agricultural production inhe inland areas nearby, a biomass power plant has been built nearhe complex. Due to the dominant cloudy weather in the consid-red period, the photovoltaic power cells located in the complexo not provide sufficient output, and so these will not be included
n the experiment. To retain the reliability of the delivery of power,he complex is connected to high-voltage power lines from powerupplier.
In the specified experiment, the complex is supplied by electricalower from ten synchronous generators, the cost characteristicsnd technical limitations of which are specified in Table 1.
The objective of the experiment is a proposal for an ordering ofources for a typical workday, for which predictions of the hourlyonsumptions are available, see (Fig. 8).
The parameters of the optimisation algorithm T0 resp. T∞ resp. Nere set to the values 100 resp. 10−6 resp. 105 for the experiment.
he mechanism for setting the initial temperature was based onts default estimate and subsequent increase up to a value whereuring the first circa ten percent of iterations almost all perturba-ions are accepted, which is an analogue to the heating up of thebject during annealing. Similarly, the mechanism for setting thenal temperature was based on its default estimate and subsequentecrease up to a value where during the circa last ten percent of
terations almost no perturbations which increase the value of theost function are accepted. The mechanism for setting the number
f iterations was based on their default estimate and subsequentradual increase up to a value such that its further increase did not
Fig. 8. Predicted daily diagram of consumption. Tab
le
2U
nit
com
mit
men
t
of
vari
ant
0.
Para
met
res
Dat
e:
25-0
1-20
13
Init
Tem
p
1.00
0000
Fin
al
Tem
p
0.00
0001
Iter
Res
ult
s
Sup
ply
1
2
3
4
5
6
7
8B
iom
ass1
0
0
0
0
0
0
0
0B
iom
ass2
0
0
0
0
0
0
0
0B
iom
ass3
0
0
0
0
0
0
0
0W
ath
er1
200
200
200
200
200
200
200
200
Wat
her
2
200
200
200
200
200
200
200
200
Wat
her
3
200
200
200
200
200
200
200
200
Win
d1
0
0
0
0
0
0
0
0Ei
nd
2
0
0
0
0
0
100
100
100
Win
d3
100
100
100
100
100
100
100
100
Cog
ener
200
200
200
200
200
200
200
200
Tota
l [kW
]
900
900
900
900
900
1000
1000
1000
Load
[kW
]
854
839
823
815
825
912
926
927
Dif
f [kW
]
46
61
77
85
75
88
74
73
400
B. G
arlík, M
. K
rivan /
Energy and
Buildings 67
(2013) 392–402
Table 3Unit commitment of variant 1.
Parametres
Date: 25-01-2013 Time: 15:29:25
Init Temp 1.000000 Final Temp 0.000001 Iter Limit 1000 Cost0[CZK] 4729.452 Cost [CZK] 4145.234 dCost [CZK] 584.218
here NT resp. NG is the number of hours resp. generators.The resulting unit commitment proposals are listed in
ables 2–4, where in the zero variant the condition (3) is reflectedy the fact that every random proposal of the outputs, whose sumoes not exceed the predicted load, is automatically rejected, and
n the first resp. the second variant is used for an objective functionhape (4) resp. (5).
. Conclusion
A comparison of the Tables 2–4 shows that the smallest devia-ions from zero power balance were achieved in the second variant,he use of fuzzy model deviation (5), while the largest deviationsrom zero power balance were achieved in the first variant by itsirect inclusion in the objective function (4). Weight of the condi-ion (3) in the objective function (4) and (5) have been set to thealue 10−2 and 103, respectively. As reference costs covering thelectricity consumption costs in the considered time period theosts for continuously running power sources were chosen (seeable 1), i.e. 4730 CZK. Table 5 shows maximal deviations fromero power balance of the power output in kW units and the sizesf balance against the regional electric power supplier in kW unitsncluding the total cost of power sources integrated in the microrid in CZK for the whole planned day.
In terms of energy self-sufficiency of a complex of intelligent
uildings implies that as the best way of the acceptance condition3) is its fuzzy model. It is not desirable to equalise power balancet the expenses of regional electricity distributor, even in one ofwo directions.
[
uildings 67 (2013) 392–402 401
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