OPTIMERING AV FJÄRRVÄRMEVATTENS FRAMLEDNINGSTEMPERATUR I MINDRE FJÄRRVÄRMESYSTEM

Forskning och Utveckling ORIENTERING FOU 2002:6 OPTIMERING AV FJÄRRVÄRMEVATTENS FRAMLEDNINGSTEMPERATUR I MINDRE FJÄRRVÄRMESYSTEM Ilkka Keppo och Pekka Ahtila, Helsingfors tekniska högskola

OPTIMERING AV FJÄRRVÄRMEVATTENS FRAMLEDNINGSTEMPERATUR I MINDRE FJÄRRVÄRMESYSTEM Ilkka Keppo och Pekka Ahtila, Helsingfors tekniska högskola ISSN 1403-4921

I Rapportserien publicerar projektledaren resultaten från sitt projekt. Publiceringen innebär inte att Svenska Fjärrvärmeföreningens Service AB tagit ställning till slutsatserna och resultaten. 2002 Svenska Fjärrvärmeföreningens Service AB

Sammanfattning I denna studie diskuteras problem med att välja den mest ekonomiska framledningstemperaturen för fjärrvärmesystem med flera alternativ för att producera värme. Produktionsproblemen är formulerade som en mixad integrerad linjär programmerings (MILP) problem. Fjärrvärmesystemet läggs därefter till manuellt. Resultatet visar den optimala framledningstemperaturen för olika utetemperaturer. I programmet bestäms, vilka anläggningar som bör användas under olika förhållanden och vilka förhållanden som är viktiga för mest ekonomisk drift. Kunderna approximeras med hjälp av Visual-Basic makron, som kalkylerar returtemperaturer och flödet av fjärrvärmevatten, beroende av utetemperatur och framledningstemperatur. Dessa värden fungerar också som indata och utdata för optimeringen. Värmen kan produceras med hetvattenpannor, kraftvärmeanläggningar, värmepump och/eller spillvärme från industrier. Flödet av fjärrvärmevatten kan inte delas mellan de olika anläggningarna, eftersom det skulle skapa ett icke-linjärt problem, men alla anläggningar kan vara kopplade i serie. Om det är mest ekonomiskt att använda endast en anläggning så går det också. Temperaturen mellan anläggningarna och producerad värme, i de olika anläggningarna bestäms även i optimeringen. När två fall med olika sätt att angripa olika ingående parametrar är kalkylerade, kan man utläsa att den högsta framledningstemperaturen vanligen är så låg som möjligt för de mest vanliga utetemperaturna. Priset för el är den främsta bidragande orsaken hur man väljer produktions-anläggning och hur stor produktionen blir från dessa anläggningar. 2

OPTIMISATION OF DISTRICT HEATING WATER S FORWARD TEMPERATURE IN A SMALL-SCALE SYSTEM Summary In this study we discuss the problem of selecting the most economical supply temperature for district heating (DH) system with several options for producing the heat. The production problem is formulated as a mixed integer linear programming (MILP) problem and the network is added manually. The results show the optimal supply temperatures for different outside temperatures. In the process it is also determined, which plants are used during different conditions and which conditions are essential for economic operation. The consumers are approximated with the help of a Visual-Basic macro, that calculates the return temperature and mass-flow of the DH water depending on the outside temperature and the supply temperature of the DH water. These values are then used for calculating the pumping costs and heat losses from the network. These values also function as the input and output values for the optimisation. The heat can be produced with a heating plant, CHP-plant, heat pump and/or using the secondary heat from industry. The flow of the DH water can t be divided between the plants since that would make the problem non-linear, but all the plants can be used in series. However, if it s economical to use only one plant, that s possible as well. The temperatures between the plants and the heat quantities produced by different plants are found out in the process of optimisation as well. When two cases with somewhat different approach to certain parameters are calculated, it can be seen that the optimal supply temperatures usually are as low as possible for the most common outside temperatures. The price of electricity is one of the main contributors to the choice of production plants and the quantity of production from these plants. 3

About the Authors Ilkka Keppo, M.Sc. (Tech.) is a researcher and a Ph.D. student at the laboratory of Energy Economics and Power Plant Engineering at the Helsinki University of technology. His work focuses mainly on the economic aspects of district heating and CHP-production. Pekka Ahtila, D.Sc. (Tech) is the professor of industrial energy engineering and power plants at the laboratory of Energy Economics and Power Plant Engineering at the Helsinki University of technology. His main research areas are energy efficiency in industry, renewable fuels, CHP-technology and process integration. 4

Förord Svenska Fjärrvärmeföreningen och den Finska Fjärrvärmeföreningen (Sky) har ett utbyte inom FoU. Utbytet sker i några olika projekt. Föreliggande rapport är ett resultat av detta utbyte. Projektet har ingått i Skys FoU-program TERMO. Genom detta samarbete kan svenska fjärrvärmebranschen ta del av resultat som annars ej skulle bli tillgängliga i Sverige. Naturligtvis har möjligheten till svensk styrning av projektet ej varit möjlig eller aktuell. Svenska Fjärrvärmeföreningen har genom Ture Nordenswan ingått i projektets referensgrupp. Svenska Fjärrvärmeföreningen ser positivt på samarbetet mellan länderna. Projektet har utförts av forkaren Ilkka Keppo och professor Pekka Ahtila vid Helsingfors tekniska högskola, institutionen för energi ekonomi och kraftverksteknik (Energy Economics and Power Plant Engineering). I Finland har det planerats för en projektredovisning vid en konferens och/eller publicering i en vetenskaplig tidskrift. Publicering i tidskriften sker i en kondenserad form. I föreliggande rapport publiceras rapporten i sin helhet. Anders Tvärne FoU-ansvarig, Svenska Färrvärmeföreningen 5

Contents 1 Introduction 7 2 Description of the system 8 2.1 District heating substations 8 2.2 District heating network 11 2.3 Heat production 12 2.3.1 Heating plant 13 2.3.2 CHP-plant 13 2.3.3 Heat pump 13 2.3.4 Secondary heat from industry 14 3 Optimisation of the system 15 3.1 Evaluation of the network and consumers 15 3.2 Optimisation of production and evaluation of the system 19 4 Results of optimisation 26 5 Conclusions 31 References 32 Appendix 1 33 Appendix 2 34 Appendix 3 35 Appendix 4 36 6

1 INTRODUCTION The forward temperature of district heating (DH) water has considerable effect on several economic and technical parameters within a district heating system. Combined heat and Power production benefits from low temperature levels, because more electricity can be produced. Other methods of production that are cheap, but can t raise the water temperature high enough, could be taken into wider use, if temperature levels were lower. Heat pumps and especially secondary energy from industry could be used a lot more efficiently, with lower temperature levels. On the other hand, the forward temperature has also an effect on the return temperatures of the water and low return temperatures would enable pre-heating of the water with cheap energy. Also now, when the electricity prices have been low, it s hard to tell whether the additional electricity production would really be profitable. In this study, two cases for a small district heating system will be calculated. The system has four different production facilities; CHP-plant, heating plant, heat pump and secondary energy from industry. The goal is to find out optimal forward temperatures for different outside temperatures. In the process it will also determined, which plants are used during different conditions and which conditions are essential for economic operation. 7

2 DESCRIPTION OF THE SYSTEM 2.1 District heating substations The connection used for the substations can be seen in appendix 1 (LLY K1/1992). This connection is one of the connections recommended by the Finnish District Heating Association. The heating load for each substation was 200 kw at the outside temperature of 30 C. The outside temperature and DH water s inlet temperature range from 30 C to +19 C and from 60 C to 115 C, respectively. The water temperatures in the radiator circuit depend on the outside temperature, and can be calculated from T 40 (1) co T outside T 2 28 (2) 5 ci T outside T co is the temperature of the radiator water leaving the heat exchanger and T ci is the temperature when the same water is again returning to the heat exchanger. The overall heat transfer coefficient (U) for the heat exchangers is calculated from 1 1 1 U = = p s (3) As can be seen from equation (3), the conduction term is left off. This is done because it has little effect on the overall heat transfer coefficient, but it would make the calculations considerably more complex. = p and = s are convection heat transfer coefficients for primary (DH water) and secondary (radiator, hot service water) circuits. 8

Substitute m m dh0 s S 0 (4) m m dh dh0 S (5) where m dh0 is the mass flow on the primary side at design conditions, m dh is the mass flow on the primary and m s is the mass flow on the secondary side (this can either be radiator flow or hot service water flow). For simplicity, the flow of hot service water is assumed to be a constant. Heat capacity and dynamic viscosity are assumed to be constants. This is again done to avoid unnecessary complexity. With these assumptions, Reynold s number depends only on the mass flow and Prandtl s number is a constant throughout the calculations. When the flow is turbulent, Nusselt s number depends on these numbers according to equation (6), where C, n and m are parameters. Nu C n Re Pr m (6) Since C and Prandtl s number are constants, Nusselt s number depends only on Reynold s number and therefore, only on the mass flow. In these calculations n is assumed to be 0.67 (Tyni, 1991) and the flow is assumed to be turbulent. Using the above assumptions, convection heat transfer coefficients depend only on Nusselt s number and thus from equations (4) and (5) we get = = p0 s S 0.67 0 (7) 9

The subscript 0 refers to the design conditions. S 0.67 1 1 S = 0.67 1 1 0 0 p0 0 = p0 = p0 U (8) Since the flow on the secondary side is a constant, we get S 0.67 0.67 1 S S = 0.67 1 1 0 0.67 0 p0 S = p0 = p0 U (9) U U S 0 1 0.67 S S 0.67 0 0.67 0 (10) The rate of heat transfer in a heat exchanger can be calculated from equation 11. Q AU, T lm (11) A refers to the heat exchanger area and,t lm is the log-mean temperature difference., T lm T T T T hi co T ln T hi ho T ho co T ci ci (12) The subscripts h, c, o and i refer to hot and cold streams and to their inlet and outlet temperatures in the heat exchanger. Since the heat exchanger area remains constant, equation (10) can also be used for the product of A and U. The product of A and U 0,as well as m dh0, are calculated from the design parameters. 10

2.2 District heating network Picture of the network can be found in appendix 2. Pressure losses are calculated from equations (13), (14) and (15). Equation (14) is known as Swamee and Jain equation., p N F 2 8 L H d 5 S m 2 dh (13) N 5.74 0.25 lg 0.9 Re A 3.71 2 (14) 4 m F d dh Re (15) s L is the length of the pipe, d s is the inner diameter of the pipe, H is water density, is dynamic viscosity and A is the relative roughness of the pipe. Multiplying the pipe lengths with a factor of 1.1 approximates single resistances. A pressure drop of 50 kpa is added for substations and production facilities. The required power for pumping is calculated from equation (16), where D is the pump efficiency (assumed to be 0.7). P, p m dh H D (16) Heat losses (W/m) are calculated from (17). B T G hi T 2 ho T ref (17) In these calculations, the reference temperature (T ref ) is the outside temperature. G is the heat conductance from the pipes per unit of pipe length. 11

G 2 R e R m (18) R e is the heat resistance of one pipe. R e 1 2 F i d ln d o i (19) The thermal conductivity of the insulation is i. Outer and inner diameters of the insulation are marked with d o and d i. R m 1 2 F s ln a 1 4 b red 2 (20) Equation (20) takes into account: a) the interaction of the pipes and b) the convection from ground to air. s is the thermal conductivity of the soil. Variable b is the distance between the return and supply pipes centres. a red a = s g (21) = g is the convection heat transfer coefficient for convection from the ground to ambient air. The distance from the pipes centre to the ground is marked with variable a. 2.3 Heat production In this study heat can be produced with a heating plant, CHP-plant, heat pump and/or using the secondary heat from industry. In order to find the best possible production combination a linear optimisation model is created. Because of this, all the functions that define the production have to be linear. This will certainly have an effect on the accuracy of the model, but it should still give an accurate enough approximation for optimal temperatures and production combinations. 12

2.3.1 Heating plant The heating plant efficiency from fuel to DH water is 90 %. Temperatures after the plant are thus calculated from a simple energy balance. 2.3.2 CHP-plant The electricity production of the CHP-plant is approximated according to equation (22) (Tyni, 1991). Coefficients are scaled according to maximum output, except for the coefficient that is used with heat load. P 168.3 0.59 Q 2.87 T in 0. 68T out (22) T in and T out are the inlet and outlet temperatures for DH water. Efficiency for both heat and power production is 85 %. 2.3.3 Heat pump In reality, the functions that define how heat pump works are anything but linear. Because of this the heat pump is approximated quite roughly. The approximation of temperature after the pump is calculated from equation (23). T out 1.30 T 27.96 in (23) In addition to this, the heat pump can t raise DH water s temperature above 85 C. These restrictions are made since COP-value (COP = heat gained/electricity used) has to be a constant. When above-mentioned restrictions are used, COP-value remains above three and this number is thus chosen to be the constant COP-value. Electricity production can then be calculated using an energy balance and a COP-value of three. 13

2.3.4 Secondary heat from industry In reality, the mass flows of available secondary energy from industry are far greater than the ones used in this study. The mass flows are scaled down to make the system consist of four different production possibilities with somewhat similar maximum capacities. The temperature levels are different in the two cases that are discussed in chapter 3. In the first case the temperature of the flow coming from industry remains 60 C throughout the year. The mass flow also remains constant. In the second case the flow from industry has different parameters for winter and summer. Heat transfer is modelled using energy balances. A temperature difference of 5 C is required for the heat exchange. 14

3 OPTIMISATION OF THE SYSTEM Economic evaluation of the system consists of two parts; network and production. According to previous studies (Zhao et al. 1998) network dynamics do not play a vital role and the optimal forward temperature depends mainly on production combination and parameters. In this study, only production is included in the optimisation model and costs coming from pressure and heat losses in the network are added manually. 3.1 Evaluation of the network and consumers The required mass flow of DH water and the temperature of returning DH water for different forward and outside temperatures are calculated using a Visual Basic macro that was created based on the equations presented in chapter 2.1. Macro uses equation (11) and calculates the necessary heat load that is based on the flow on the secondary circuit. If Q from equation (11) isn t large enough, macro increases mass flow by 0.001 kg/s. This has an effect on U and the outlet temperature. This same iteration is done for all three heat exchangers while taking also into account how the heat exchangers are connected to each other. Minimum temperature difference allowed is 5 C and as can be seen from equation (12), counterflow heat exchangers are used. The basic principle of the macro is based on Kukkonen, 1999. The hot service water flow consists of a cold-water flow, which comes to the first heat exchanger at the temperature of 10 C, and of a circulation flow that comes back to the second heat exchanger at the temperature of 50 C. The final temperature of the service water is 55 C. These flows are calculated assuming that during an average year the heating of hot service water requires about 30 % of the energy that is used for space heating. The result matrix has all the required mass flows and return temperatures of DH water. However, since the network and substations are assumed to be old and designed for certain 15

mass flows, a maximum increase for mass flow is assigned. A mass flow increase of 25 % compared to the design values is allowed since networks and substations are usually oversized. Pressure and heat losses are calculated from the temperatures and mass flows that are gained from the iterations. Pipes are dimensioned according to the original design flows. The return temperatures can be seen in figure one. 60 55 50 45 55-60 50-55 45-50 40-45 35-40 30-35 25-30 20-25 15-20 Return temperature of DH water, C 40 35 30 25 20 15 61 64 67 70 73 76 79 82 85 88 91 94 97 10 10 10 10 11 11 0 3 6 9 2 5 Forward temperature of DH water, C 70 61 52 43 Inlet temperature of the 34 radiator circuit, C 25 Figure 1. Return temperature of DH water as a function of DH water s and radiator circuit s forward temperatures Figure 1 still has values that are infeasible because of excessive mass flows. These are trimmed from the group of possible optimal solutions when production is optimised. Radiator circuit s inlet temperature depends on the outside temperature according to equation (1). 16

Resulting mass flows are presented in figure 2. 3.5 3 2.5 2 3-3.5 2.5-3 2-2.5 1.5-2 1-1.5 0.5-1 0-0.5 Mass flow of DH water, kg/s 1.5 1 0.5 0 70 64 Inlet temperature of the radiator circuit, C 58 52 46 40 34 28 22 60 65 70 75 80 85 90 95 100 115 110 105 Forward temeprature of DH water, C Figure 2. Mass flow of DH water as a function of DH water s and radiator circuit s forward temperatures From this picture it can be seen that the required mass flow rises rapidly when the temperature difference becomes small. All the mass flows that are above 1 kg/s are too large to be taken into account during the optimisation. Pressure losses are shown in figure 3. 17

Pressure losses 4000000 3500000 3000000 2500000 3500000-4000000 3000000-3500000 2500000-3000000 2000000-2500000 1500000-2000000 1000000-1500000 500000-1000000 0-500000 2000000 Pressure losses (Pa) 1500000 1000000 500000 66 73 80 Forward temperature of DH water, C 87 94 101 108 115 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 Radiator circuit s inlet temperature, C 0 Figure 3. Pressure losses as a function of DH water s and radiator circuit s forward temperatures In this picture can also be seen how a small temperature difference and large mass flows cause rapidly increasing pressure losses. The highest pressure losses that are seen in the picture are coming from the options that aren t available during optimisation because of the mass flow restrictions. Required pumping energy is calculated from the pressure losses. The price for electricity is different in the two cases that will be calculated. In the first case the price is always 150 FIM/MWh. In the second case the price for electricity changes with the outside temperature. Heat losses are presented in figure 4. 18

Heat losses 120000 100000 100000-120000 80000-100000 60000-80000 40000-60000 20000-40000 0-20000 80000 60000 Heat losses (W) 40000 20000 66 Forward temperature of DH water, C 73 80 87 94 101 108 115 22 26 30 34 38 42 46 50 54 58 62 66 70 Radiator circuit s inlet temperature, C 0 Figure 4. Heat losses as a function of DH water s and radiator circuit s forward temperatures The pumping energy that is transferred to DH water is assumed to be enough to keep the DH water s temperature on the same level throughout the network. The price for heat losses was 100 FIM/MWh. 3.2 Optimisation of production and evaluation of the system Production is optimised using mixed integer linear programming (MILP). Different production plants are placed in series (Figure 5), since if they could be placed in parallel, energy balances would make the problem nonlinear. Because of the nonlinear nature of an energy balance, the mass flow has to be a parameter. Because of this, the forward and return temperatures are also given as parameters and the optimal temperature is sought by comparing the optimisation results done with different forward temperatures. 19

1 2 3 4 Figure 5. Connection of the plants All the plants have four binary variables attached to them. These binary variables tell if the plant is the first, second, third or fourth in series. These variables can all be zero for a plant and only one of them can be 1. Only one plant can occupy one place in the series. Two different cases are optimised. Second case has few variations when compared to the first case so only the first case is presented here as a whole. For second case, only the alterations are presented. y f e prod con min H Q H P P (24) This is the objective function. Subindex y refers to production plant (CHP, heating plant, heat pump, secondary energy) and subindex x refers to the position in the series of plants. H y refers to the price of fuel for plant y. Heating plant uses heavy fuel oil that costs 130 FIM/MWh. CHP-plant uses biofuel with a cost of 50 FIM/MWh. The price for secondary energy from industry is 40 FIM/MWh. H e is the price of electricity. In the first case price was 150 FIM/MWh. General restrictions: Q T n Tn m c p 1 (25) This function tells how the heat flow from plant y placed in position x affects the DH water s temperature. T 1+n is the water temperature after the plant and T n before the plant. 20

T T( x 1) y (26) This restriction makes sure, that the temperature after the plant, is at least as high as it was before the plant. T x T 3T x1 (27) This function calculates the temperature after point x. All the plants that aren t placed in position x, transfer no energy to the DH water, so the temperature after these plants is same as before them. Q Qmax y y 0 (28) This formulation makes sure, that if plant y isn t in position x (y =0), the heat it produces must also be zero. It also makes sure, that the plant can produce no more than what is defined as it s maximum capacity (Q max y ). In the first case, maximum heat load for CHP was 1323 kw, for heat pump 1000 kw and for heating plant 3000 kw. Secondary energy from industry has restrictions of different nature. 4 y x1 1 (29) This function says, that only one plant can be placed in one position. 4 y y1 1 (30) This makes sure, that one plant can only be placed in one position. 21

CHP restrictions Qmin y Q 0 (31) If a CHP-plant is operated in partial load, it s efficiency is reduced. Since this can t be taken into consideration because of the linearity requirement, a minimum load is determined. This function says, that if a CHP-plant is placed in position x, it must produce at least a certain amount of energy. Minimum load is 504 kw. P a y b Q c W1 d W 2 (32) This is the same as function (22) except for the binary variables and variables W 1 and W 2. The latter variables are taken into use to avoid bilinear functions. Bilinear function means, that a binary variable is multiplied with a continuous variable. Here we have to multiply temperatures with binary variables. This can be avoided by replacing the product with a new variable and then adding the following restrictions. W n T f y (33) W n T y r (34) These two functions make sure, that if the binary variable is zero, also the new variable must be zero. They also tell, that the new variable has the same upper and lower bounds for temperature as T would have. These limits are the forward and return temperature of DH water. W W W 1 T T f 1 y (35) 1 T Tr 1 y (36) 2 Tx 1 T f 1 y (37) 22

W 2 Tx 1 Tr 1 y (38) These functions connect the new variable with the temperature in question. They make sure, that if the binary variable is one, the new variable is equal to the temperature variable. Q f P D CHP Q D CHP (39) This function calculates the fuel consumption for the CHP-plant. P prod P (40) Equation (40) sums together the electricity production. The only restriction valid only for the heating plant is equation (41), which defines the fuel consumption. Q f Q D L (41) Restrictions for secondary heat from industry. Q T t T j m t c p (42) This equation tells how much energy is transferred from the flow coming from the industry. In the first case the temperature of the flow (T t ) is 60 C and the mass flow is 3 kg/s. T j T 1 x 1 5 M y (43) T t T 5 M 1 y (44) Equations (43) and (44) make sure, that the temperature difference is at least 5 C at both ends of a counterflow heat exchanger, that is used for the heat exchange. M is a big 23

number that makes sure that if the binary variable is zero, this function won t affect the solution. Restrictions for the heat pump. y = T > Tx 1 M 1 (45) This equation is the same as function (23). The only difference is the big-m formulation, which is done for the same reasons as mentioned above. T M 1 y Tmax lp (46) Equation (46) defines the maximum temperature, that the heat pump can achieve. This temperature is 85 C and the big-m formulation is also again used. P con Q COP (47) Equation (47) tells how much electricity the heat pump uses. The value for COP is three. P con P con x (48) This equation sums together the electricity consumptions. In the first case, the price for electricity is constant and this price is also used when calculating the pumping costs for network. In the second case, four changes are made: 1. Temperature and mass flow from the industry are different during winter and summer. Winter starts when the outside temperature drops below 5 C. Mass flows are 9.8 kg/s for summer and 11.7 kg/s for winter. Temperatures are 71 C for summer and 65 C for winter. The temperatures are from Kilponen et al. 2000. These temperatures, and 24

the ratio between mass flows, are from the hottest stream that is not used within the mill. 2. Electricity price depends on the outside temperature. Hourly values for the price of electricity and the outside temperature from year 2000 were compared and an approximation was made. This approximation is presented in equation (49). H e a e T outside b (49) where a and b are parameters. The values found for a and b are a = 7.6*10-5 and b = 88.087. However, the hourly outside temperatures in 2000 never went below 14 C. Because of this equation (49) rises far to quickly during very cold outside temperatures. To eliminate this, equation (49) is only used for temperatures above 16 C. For colder temperatures, price is approximated thus, that the price keeps rising until it reaches the price of 1000 mk/mwh when it is -25 C. From there on, the price is constant and from 16 C to 25 C the price rises linearly. This price is also used for the pumping costs. 3. The CHP-plant can function partly as a condensing plant. This is achieved with an additional heat load variable that is added to functions (28), (31), (32) and (39). This variable only affects electricity production, fuel consumption and the minimum and maximum loads. It doesn t have an effect on the DH water s temperature. 4. The heating plant maximum capacity was reduced to 1000 kw and heat pump was scaled down to a maximum capacity of 500 kw. 25

4 RESULTS OF OPTIMISATION The optimal forward temperatures for case one can be seen in figure 6. Optimal forward temperature of district heating water 120 100 Forward temperature of DH water, C 80 60 40 20 0-40 -30-20 -10 0 10 20 30 Outside temperature, C Figure 6. Optimal forward temperatures for different outside temperatures, case 1. The exact temperatures and costs can be seen from appendix 3, where Combination of production tells which plants are used and in which order (I = Industry, C = CHP, P = Heat Pump, H = Heating plant). The sudden rise in optimal temperature happens, when the CHP-plant has to be shut down because of the minimum load restriction. The temperature rises all the way to 80 C, when the outside temperature is +14 C. This happens because when using this forward temperature, the CHP-plant can still be used. Figures 7 and 8 show how the total costs are distributed between production and network. 26

Cost distribution 60 Production costs, FIM/h Network costs, FIM/h 50 40 FIM/h 30 20 10 0-29 -27-25 -23-21 -19-17 -15-13 -11-9 -7-5 -3-1 1 3 5 7 9 11 13 15 17 19 Outside temperature, C Figure 7. Cost distribution, case 1. Share of total costs for network and production 100.0% 90.0% 80.0% Network Production 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% -29-27 -25-23 -21-19 -17-15 -13-11 -9-7 -5-3 -1 1 3 5 7 9 11 13 15 17 19 Outside temperature, C Figure 8. Share of total costs, case 1. 27

The curve in figure 6 can be approximated with the trendline presented in equation (50). The trendline is valid from 29 C to +13 C. T F 0.0421T 2 outside 0.6249 T outside 62.084 (50) R-squared value for the approximation is 0.9975. The optimal forward temperatures of district heating water for case 2 to are presented in figure 9. Optimal forward temperature of district heating water 120 100 Forward temperature of DH water, C 80 60 40 20 0-40 -30-20 -10 0 10 20 30 Outside temperature, C Figure 9. Optimal forward temperatures for different outside temperatures, case 2. Exact figures for costs and temperatures are in appendix 4. In figure 9 two peculiar changes can be seen in the optimal forward temperature. First jump happens, when the outside temperature is 21 C. This jump is caused by the rising price of electricity. At this point electricity is so expensive, that it is the only thing that matters. Lower forward 28