Optimization of a community solar heating system with a heat pump and seasonal storage

Optimization of a community solar heating system with a heat pump and seasonal storage

Solar Energy Vol. 33, No. 3/4, pp. 353-361, 1984 0038-092)(/84 $3.00 + .00 © 1984 Pergamon Press Ltd. Printed in the U.S.A. OPTIMIZATION OF A COMMU...

683KB Sizes 1 Downloads 36 Views

Solar Energy Vol. 33, No. 3/4, pp. 353-361, 1984

0038-092)(/84 $3.00 + .00 © 1984 Pergamon Press Ltd.

Printed in the U.S.A.

OPTIMIZATION OF A COMMUNITY SOLAR HEATING SYSTEM WITH A HEAT PUMP AND SEASONAL STORAGE P. D. LUND+ Helsinki University of Technology, Department of Technical Physics. SF-02150 Espoo 15, Finland (Received 17 October 1983: accepted 6 June 1984)

Abstract--The optimization of a district solar heating system with an electric-driven heat pump and seasonal heat storage is discussed. The optimization process comprises thermal, economic and system control analyses. Thermal and economic optima have been derived for collector area and storage volume simultaneously. The effects of different collector types and building loads are also investigated. Summertime charging of the storage by off-peak electricity has been applied to avoid severe peaking of auxiliary in the winter and to reduce the yearly energy cost. The thermal co-storage of electric energy is emphasized with systems which fail to supply heat for the heat pump during the winter heating season.$ It has been found that system costeffectiveness is only slightly affected as storage volume is increased beyond the optimum size. Large variations in the optima for different system configurations were found. The minimum cost of heat supplied in an optimal 500-unit community with 90% solar fraction was estimated at 8.9 ¢ kWh ~.

I. INTRODUCTION District solar heating with seasonal storage has been recognized as a most promising heat source for building applications at northern latitudes. These systems often employ an energy storage medium that is easily found in nature, for instance, soil, rock, rock caverns, aquifers, etc. [1]. Also separate water tanks may meet the annual storage capacity requirement [2]. Because of the large size of a storage-unit, it is most often utilized as a common central storage for a large group of houses. The storage is charged full during summer, and the stored heat is used for the winter load. At high latitudes, because of scarce radiation input in the winter, a heat pump is recommended for efficient storage as also for optimal control [3]. Several full-scale annual storage solar heating systems have been realized, mostly for research or demonstration purposes. Most of the experimental projects are located in Europe, especially in Sweden [4, 5]. So far, the largest installation is in Lyckebo, Sweden, where a 100,000 m 3 rock cavern is employed in a solar and electric resistance heating system for a 550-house community [6]. The optimization of the design of district solar heating systems is emphasized due to the large first costs, strict operational conditions, and numerous interactive thermal processes within the systems. The success and reliability of the optimization de~-1SES member. By thermal co-storage of electricity one means storage of heat produced by electricity, e.g. by electric resistance heating. In power plants, heat storages typically use condensate from the main loop or bleed steam.

pends mostly on the accuracy of the thermal performance simulations needed. In case of solar water heating systems with short-term storages, the optimization process is often based on correlations [7] or on full hour-by-hour simulations and the optimum may be derived for a large set of variables simultaneously. However, when large storage-units are applied the optimization process is becoming considerably more complicated to accomplish as a large numerical grid for the storage is required. Thus, one is faced with long computing times in order to improve the accuracy of the performance indices. Therefore, previous studies have commonly employed various utilization functions of day-by-day or even month-by-month simulations for the thermal performance analyses [8-10]. Minor attention has been paid to the system dynamics or to the storage as an integral part of the energy system. In high latitudes, those aspects play an important role because of quickly varying climatic conditions. In the optimizations use is made of a numerical computer program NORSOL which is especially designed for predicting the long-term behaviour of community solar heating systems. The program package, although not yet available for distribution, deals also with the system dynamics and includes separate subprograms for system optimizations and load profile analyses. NORSOL has been run successfully on UNIVAC lI00/E61 and the requirement of fast speed core memory is approximately 110 kwords [11]. The optimization of the parameters of district solar heating systems is approached by a combined thermal and economic analysis. The optima for var-

353

354

P.D. LUND

ious solar fraction requirements are derived for collector area and storage volume simultaneously, and are found by minimizing two objective functions. These two variables were chosen because of their significant effect on the solar fraction and the high investments. F o r large solar installations with electricity as backup, an accurate operating strategy has also to be planned to avoid severe peaking of auxiliary power in the winter and hence also high energy costs. Particularly, if special time-varying electricity rates are available, thermal storage of off-peak electricity may offer cost savings. In this paper, an approach is presented for the optimization of a community solar heating system with annual storage and a heat pump. The method is applied to estimate the effects of different system configurations especially on the system economics. Two types of collectors are employed and the impact of passive solar utilization on a community scale is discussed. Helsinki (60°N) is used as the reference site in the calculations.

2. THE SYSTEM CONFIGURATION The solar energy system for which the optima are derived is sketched in Figs. l(a) and (b). The central heat storage-unit consists of a cylindrical uninsulated rock cavern which is supposed to be stratified. The cold bottom water is fed to the solar collectors to maintain good thermal efficiency. Two types of collectors are considered. These include single-glazed flat-plate collectors with non-selective absorbers which are integrated into the southfacing roofs of the houses with 60 ° tilt angle. The second collector type is a parabolic trough with a concentration ratio of 10. The concentrators are centrally placed in a separate collector field and track the sun in the E - W plane with a 60 ° inclined N - S axis. The heating system is sized for a 50- or a 500house district. The overall design is partly based on a realized community solar heating system, the Kerava solar village near Helsinki [12]. The livingarea is 100 m 2 per house and the space heating load is 33.3 GJ yr - ] . F o r the passive solar house anal-

ysis, we use houses with 120 m z living-area and the standard space load is then increased to 45.2 GJ y r - ]. F o r the hot water need one assumes 14.4 GJ y r - t in both cases. The well-insulated heat distribution network and low-temperature heat utilization in the houses enable a minimum delivery temperature of 50°C. Each house has a separate heat exchanger to extract heat for space heat and hot water load from the central heat distribution network. Should the temperature of the water storage drop below 50°C, a heat pump is used to raise the temperature of supplied heat. Minimum allowed temperature of the heat source (storage) for the heat pump is 5°C below which point an electric boiler is switched on. The maximum temperature of the storage is limited to 90°C. To allow a flexible control scheme, the upper section of the storage may also be used as a diurnal storage. Then, the heat pump may be used to charge the diurnal storage during winter nights for daytime heat load in order to smoothen load peaking. The storage dimensions are chosen so that the overall heat loss surface area of the cylindrical rock cavern is minimized. This criterion is fulfilled by choosing

r

= ( V ~ ':3

\~/

h = 2r

3. METHOD OF STUDY

3.1. Simulation m o d e l The performance, economic, and operating strategy analyses are accomplished by a computational simulation model N O R S O L [11]. A simplified block diagram of the program is shown in

BOILER

!

HEAT STORAGE

(2)

where r is the radius, h is the height, and V is the volume of the cylindrical storage. Because of the use of a heat pump, system efficiency is, however, only slightly affected by changes from the optimal shape.

I_ I SEASONAL

(1)

I SPACEHEAT AND HOTWATER LOAD

Fig. l(a). Schematic of a seasonal storage solar heating system.

Optimization of a community solar heating system

355

Fig. l(b). System flow diagram. Storage discharge shown: 1, solar collectors; 2, heat distribution network: 3, rock cavern storage; 4, rock; 5, heat exchangers; 6, condenser of heat pump; 7, evaporator of heat pump; 8, boiler. Fig. 2. The computer code contains all necessary subroutines for the simulation of a complete community solar heating system. The N O R S O L package comprises about 10,000 FORTRAN IV lines and the memory requirement is 110 kwords. A comprehensive description of the mathematical formulation is given in Ref. [11]. The two-variate parameter optimizations are performed by day-by-day simulations as shorter time steps would have resulted in prohibitly long computing times. Now an entire years' simulation takes 60 s of CPU-time on U N I V A C 1100/E61 and 70-100 iterations were sufficient to reach to optimim. However, for the operating strategy and passive solar analyses, 1 h simulation time steps were used, and one years' performance simulation required 3600-5600 s of computer time. Thus, the

load profiles and auxiliary costs were accurately assessed. The building heat load model also accounted for transient heat flows within building components. 3.2.

Optimizationprocedure

Several different optimization techniques have been presented for solar heating systems mainly with short-term storage-units [13]. The analyses of district solar heating systems with annual storage are often approached by plotting the solar fraction or costs as a function of one variable at a time and the optimum is derived from the graph [14]. The present method combines a similar procedure with a gradient method. The parameter optimization approach is based on a combined thermal and economic analysis using

Component models:

I~tat

Tracking I Fig. 2. Computer program NORSOL.

356

P. D. LUND

collector area (A~) and storage volume (V) as the variables to be optimized simultaneously. The optimum is derived from the following objective functions

f(Ac, V, k)

=

fo

(3) (4)

O(Ac, V) = g(V)V + aAc = min!

where f is the parameter and variable dependent solar fraction, fo is the required solar fraction, g is the storage unit cost, a is the collector unit cost, and ~ represents a large set of constant system parameters. • is the first costs associated with the collector and storage installations. The flow chart of the calculation process is shown in Fig. 3. First V is set equal to Vmi, (--20 m 3 house -~) and the corresponding Ac satisfying

the required solar fraction as expressed by eqn (3) is determined iteratively by numerical simulations. A gradient method is used, the quasi-Newton method, to find the proper value of Ac. To speed up the search for Ac and to reduce the number of iterations, eqn (3) is preferably expressed for the gradient method as a function which decreases monotonically towards a minimum, for instance (f - fo) 2 = rain!

where the optimum value of Ac gives f = f0. Next V is set to V,~, + 8V and the same procedure is carried out. The procedure is continued until the upper limit of storage volume is reached ( - 2 0 0 - 3 0 0 m 3 h o u s e - ' ) . Typically, the interval [Vmi,, Vmax] is divided into 15-20 steps. The first stage of the optimization process re-

ISET V1 = Vmin I ~/)0 =oo ,i=I

1 QUASI-NEWTON METHOD

SOLVE A~ FROM

F(A~,Vi) = FQ

1. I--

CALCULATE

i/Aic,V i)

STORE ! i Vi ~i*' Ac"

SEARCHFOR ~9(Ac,V)= MIN!

Ivi

(5)

= vi-l+~V

YES

(A c , V ) o p t i m a l

Fig. 3. Flow chart of the parameter optimization process.

Optimization of a community solar heating system suits in a large set of (Ac, V) pairs which all satisfy a predetermined solar fraction f0. The final optimal (A,., V) pair is determined by eqn (4) which represents an economic minimum. In the computer code, the two optimization stages are for simplicity performed simultaneously as also indicated by Fig. 3. It should be noticed that eqn (3) may be solved simultaneously for Ac and V by the gradient method. However, because of the nature of gradient methods, the optimum thus obtained does not necessarily represent a global optimum but may be a local one. For the capital costs (a and g) in eqn (4), the following estimates are used. The cost of the flatplate collectors including installation is $180 m -2 and for the parabolic troughs $280 m -2 respectively. For collector pipings, an additional $50 m -2 is estimated. The storage cost function is well represented by a decreasing function

g(V) = 22 +

{(,¢00)

,/2 + 1.5-v/2°°°} . 100

357

where Co is a yearly fixed customer cost ($2000), Cb is the price of base load plant generated electricity, Cp is the price of peak load electricity, C,n is the power demand charge ($22.2 kW-~), Pmax is the maximum demand of electricity in winter, and Pb and Pp are the levels of base and peak electricity consumed, respectively. The pricing of electric energy depends much on the electric utility. In some Scandinavian countries, there has been a tendency to use seasonal rates. Accordingly it is assumed that winter electricity (October-May) is rated twice that of summertime off-peak electricity, OrCb = $27.8MWh ~andCp = $55.6MWh-~for Finnish conditions. A lower pricing may also be applied for winter night-times but this possibility is excluded here. The only way to reduce the auxiliary cost besides increasing the solar fraction is to reduce wintertime use of electricity. This may be realized only if we allow thermal co-storage of electricity in summer for the winter load. The charging of the storageunit by electricity is favoured if the following relation holds

(6) o~(Cp - Cb)Es q- CmAPmax - d f LTCp > 0

where V is expressed in m s and g in $ m -3. The storage investment includes excavation, tightening and other necessary construction works. Recent studies [15] indicate some reductions in storage costs which may slightly shift the optima to larger storage capacities. A district solar heating system contains also area and volume independent costs which are discussed in more detail in the appendix. These cost items are not, however, relevant for the two-variate parameter optimizations considered here.

(8)

where ~ is the storage recovery factor (-0.6-0.9), Es is the amount of electricity stored in summer and LT is the yearly heat load. The first term in eqn (8) gives the savings in energy costs and the second is due to the reduction of power peaking (AP .... ). The last term represents the loss of solar energy harnessing due to an increased storage temperature. Equation (8) naturally assumes that there is enough storage capacity. The storage capacity itself is also worth increasing if

Rg(V) dV < CmAPmax 3.3. Operating strategy In this study, an operating strategy describes how the electric-driven auxiliary systems are controlled. At northern latitudes, seasonal system control may greatly influence the yearly auxiliary energy costs as the use of a heat pump or boiler is unavoidable in winter, and time-varying electric utility rates may exist. The peaking of heat load in solar villages in winter may be several megawatts. Here the system control analysis is made separately from the parameter optimizations. The former kind of analysis is particularly emphasized if there is not enough solar heat in the storage for the heat pump during the main heating season. The primary objective of an optimal operating strategy is to minimize the yearly cost of auxiliary energy. Electricity is used as a backup, this cost may be expressed as C = Co + Cb fl

yr

Pb(t) dt

+ Cp f

yr

Pp(t) dt + CmPmax (7)

+ LT(Cb+Cp~ df+et(Cp-Cb)Es \ / 2

(9)

where R is a discount factor. A larger rock cavern may also increase the solar fraction (dr). The final control strategy depends much on the total system configuration and should be planned separately for each system. The load management and the decisions concerning the operation of an energy system may be approached by dynamic programming [16]. Here only an on/off-type control scheme is used and the optimum conditions are searched for by comparing the effects of different charging power levels in summer.

4. RESULTS 4.1. Optimal collector area and storage volume Figure 4 summarizes the behaviour of the objective function qb for different storage volumes and solar fractions. The community comprises 50 units

358

P. D. LUND J~ 100 l

lo

E

"° c-

10

% o~

1.0

~o

(.~

o t-

o

[

1

I

20000

0.1 0

I 2000

I I I 4000 6000 8000 Storage votume (rn])

I 10000

Fig. 4. The collector and storage investments (~b)for a 50 unit district with fiat-plate collectors. Solar fractions and optimal storage volume to collector area ratios (V/At) are also indicated.

and flat-plate collectors. The ratio of storage volume to sollector area (m3/m 2) is also indicated for the optima. The storage size is varied between 1000 and 10,000 m 3. It should be noticed that even though the first costs (cb) associated with higher solar fractions exceed always those of lower ones, the lifetime costs may, however, be lower depending on future energy costs, interest rates, etc. The optima shown for given solar fractions remain naturally unchanged. For a small solar fraction ( - 3 0 % ) , the solar heating system meets mainly the summertime load, and the hot water need. F o r higher solar fractions, the requirement of seasonal storage increases rapidly, as also the storage to collector ratio. Thus it is more economic to increase the storage size than to use large collector installations. Also the collector efficiency is improved as the storage is at a lower temperature. In case a heat pump were not utilized, the situation would be quite opposite as the lower temperature limit of useful heat is set to 50°C and the storage recovery factor would be low [3]. The striking growth of d~ at small storage volumes is due to reduced collecting efficiency. The reduction is then compensated by increasing the collector area in order to maintain the required yearly solar fraction. F o r small volumes, solar heat has also to be collected during low insolation conditions. From a purely economic standpoint, a better

I 60000 Storage

I

I

I

100000 v o l u m e (m 3)

I _ lt.O000

Fig. 5. The cost function d~for a 500 unit district with flatplate collectors. cost-effectiveness is obtained when the size of the community is increases. Figure 5 shows the cost function ~bfor a 500 unit district employing a similar system configuration as before. For the optima, a 40-50% reduction in collector and storage costs per house is observed. The reason for this lies in the rapid drop of storage unit costs at large volumes. With the 500 unit district, the performance indices are slightly improved as larger storage units are employed and storage heat losses increase only proportional to - V ~/3 if storage temperature is held

:_---

E 9-, tO O t-

\

1 0

I 20000

30%

n

I I ] 60000 100000 S t o r a g e v o l u m e (m 3)

Fig. 6. The cost function ~bfor a 500 unit community with parabolic troughs.

Optimization of a community solar heating system

359

Table I. Optimal collector areas and storage volumes for three different solar communities System It f0 (%) A~,oot (m 2 house l) Vopt (m3 house ]) (V/Ac)opt (m3 m- 2)

30 13 20 1.5

System 25

50 24 82 3.4

70 29 160 5.5

30 10 29 2.9

System 3§

50 20 I10 5.5

70 28 164 5.8

30 7 20 2.9

50 13 56 4.4

70 25 72 2.9

+ A 50 unit district with flat-plate collectors. $ A 500 unit district with flat-plate collectors. § A 500 unit district with parabolic troughs. which indicates that the flatness of the optimum may be obtained by a proper storage cost function and thermal performance. Solving eqn (10) for Of/OV, one finds that an increase of storage volume improves the yearly collector output by 50-100 k w h m-3 at the optima.

constant. One can also observe that for high solar fractions (->50%) 4) increases slowly beyond the optimum volume, because of lower operational temperature, and the collector area may be reduced without affecting the solar fraction. By changing the collector type to parabolic troughs as shown in Fig. 6, the values of 6 are dropped by approximately 30% for the optima. This actually reflects only the better thermal efficiency of concentrators as the annual solar radiation received by both collector types is about the same. The storage capacity requirement is consequently only about 50% of that with flat-plate collectors and a smaller collector area is also necessary. Table 1 summarizes the findings for the three system configurations. It should be mentioned that there is a certain range of storage volumes and collector areas around the optimum values which fulfil the criteria defined by eqns (3) and (4). Consequently, there is some uncertainty in the values of (V/Ac)ovt shown in Table 1. Especially for System 1 with a 70% solar fraction (see Fig. 4), 06/OV ~ 0 for V ~ 155-200 m 3 house i and (V/Ac)opt ~- 5.48.2. At the optimum one also has the following condition

a

-~

=

_

~c o

4.2. A n e x a m p l e on the effects o f s y s t e m control In solar assisted heat pump systems, severe peaking of the auxiliary is caused if the heat content of the heat source, which in this case is the solar heat stored in the rock cavern, runs out before or during the main heating season. With adequate storage capacity, co-storage of electric energy in the form of heat during the off-peak season may prevent such situations or smoothen the severest peaking. Consider a typical system configuration with a 70% solar fraction in Fig. 5 with V = 100,000 m 3 and Ac = 11,800 m 2. The storage capacity is large enough to also store heat from electricity. The behaviour of this system is characterized by severe peaking of auxiliary power in the winter as the collectors are not capable of providing enough heat for the heat pump for about a week. The peak demand of electricity is then 1628 kW. However, by charging the storage from 1 June to 1 September by a 50

(10)

OV

10o ~J~ j_

,~ \ \

k

i fl ~

. average house • passive solar house --,,a -p a,eco lec,ors

\

x ~ -- parab°ltri°ughs c

~ 10~- \--o~ l r ~ L_

n

,

0

,

,

,

I

,

,

,

,

I

100,000 200,000 Storage volume (m3)

,

,

,

,

I_

300,000

Fig. 7. Present values of life-cycle costs for different solar configurations vs storage volume and solar fraction as parameter.

360

P.D. LUND

Table 2. Itemized present values of life-cycle costs (%) for optimal concentrator systems with passive utilization. Discount rate (real) is 4%, fuel escalation rate is 2%, and lifetime is 20 years Item

Solar fraction:

Collectors and storage Heating plant (heat pump, boiler, pipings, etc.) Passive solar Maintenance and repair Auxiliary energy costs Total Present value of total life-cycle cost (million $)

kW net effect round-the-clock (total 109 MWh), the peaking is reduced to 603 kW. The yearly energy cost savings would be approximately 10%, caused mainly by a reduced power demand cost. 4.3.

Effect of passive solar heating

Passive solar heating has proven to be one of the most promising and cost-effective forms of solar space heating applications in cold climates [17]. Combined with other appropriate energy saving means, the yearly space heating demand of a singlefamily house may be reduced by 40-70% [18]. The utilization of passive solar heating in a district solar heating system offers interesting possibilities to decrease the overall investment in solar devices. The major drawback of passive solar houses is that the main load occurs only during 3-4 months, which would reduce the overall system efficiency if hot water production were not also considered. A well-insulated passive solar house is considered with a direct gain window (30 m z) and with 120 m z of heated floor area. To increase the heat storage capacity of the building, 300 kg of concrete per m z of floor area is added to major building components. The heat transfer coefficients for the walls, roofs, and floor are 0.21, 0.16 and 0.29 W m - 2 K -1, respectively. The indoor temperature is allowed to vary between 20 and 26°C. The comparisons of different system configurations are made by evaluating the present values of the lifetime costs. The necessary data for the economic analysis is shown in the appendix. In Fig. 7 the present values of total life-cycle costs are shown for the most interesting systems as a function of storage volume and solar fraction as a parameter. Here the solar fraction is expressed as the ratio of the active solar contribution to the overall heat load. Thus, the energy savings for systems with passive utilization are greater than for those with standard load. For instance, the passive load (including hot water load) is 40% of the standard load which means that for a 50% solar fraction the load is reduced to ½ x 0.6 = 0.3, i.e. by 70% in comparison with the reference system. F o r communities with fiat-plate collectors, the life-cycle costs increase with higher solar fractions.

50

Fractional costs (%) 70

90

18.9 29.6

24.4 31.3

36.2 26.7

17.5 12.9 21.1 100 11.6

17.7 12.9 13.8 100 11.6

19. I 13.9 4.1 100 10.7

The use of passive solar indicates a clear cost reduction as the active solar system may be smaller due to a lower heat demand. The most cost-effective alternative was found to be the combined passive and concentrator option. Though not shown in Fig. 7, the differences between a 50, 70 and 90% solar fraction would be very marginal even though the highest one after all is the most cost-effective. It should be noticed that the use of a boiler may be omitted for solar fractions in access of 70% which reduces the capital costs. The itemized fractional costs for the optimal concentrator systems with passive solar utilization are shown in Table 2. The first costs associated with the collectors and storage are typically at most one third of the overall lifetime costs. A major cost item arises from the collector and storage independent investments such as heat pump, pipings, control system, valves, etc. (classifted under the heating plant), the costs of which are difficult to reduce. The relatively high maintenance cost arises from the fact that so far existing district solar heating systems have not avoided faults and modifications after start-up [4]. With a 2% fuel escalation rate, a 4% discount rate (real) and a 20 year lifetime, the life-cycle cost of heat supplied would be ¢8.9 k W h - ~ for the 90% system with concentrators and passive solar houses. Compared to ordinary electric resistance heating, which is regarded as perhaps the cheapest form for small-scale heating in Scandinavia, the most advantageous solar option gives a 5-20% higher lifetime cost.

5. CONCLUSIONS The optimization procedure, described in the text, is very effective in finding optimum values for collector areas and storage volumes for different community solar heating configurations and solar fraction requirements. The method of approach is based on computer simulations and it may be applied to derive optima also for other parameters than collector area and storage volume. The numerical computer program N O R S O L employed for the study is intended to be run on relatively fast

Optimization of a community solar heating system computers and was applied both to hour-by-hour and day-by-day simulations. The general conclusion is that systems with concentrating collectors reduce both collector area and storage volume in comparison with flat-plate collectors due to better thermal collector operational efficiency. A shift to larger storage sizes per house when moving from 50 to 500 unit communities was also observed, because of rapidly decreasing storage unit costs at large volumes. The overdimensioning of the storage unit increased only slightly the first costs associated with the storage and collector installations as a higher storage capacity reduces the collector area requirement. When considering the overall lifetime cost of a community solar heating system, passive and energy-efficient buildings improve the cost-effectiveness. The most advantageous system configuration employed both passive solar and concentrating collectors indicating a 8.9¢ kWh - J price for the lifecycle cost of heat produced. This system is marginally more expensive than the ordinary electric resistance heating system. The cost-effectiveness is naturally affected by the discount rates. The cost estimates presented include also some extra costs typical for prototype installations which may be neglected for future system configurations as the system reliability is expected to improve. By optimal control strategy, the yearly fuelcost of a specific solar community was reduced by 10%. The improvement was achieved by co-storage of off-peak electricity in the form of heat and with a time-varying price of electricity.

361

central heating system with heat pump. Studsvik Report, Studsvik/EP-81/2 (1980). 9. F. Baylin and S. Sillman, System analysis techniques for annual cycle thermal energy storage solar systems. Solar Energy Research Institute, Golden, Colorado, SERI/RR-721-676 (1980). 10. S. Sillman, Performance and economics of annual storage solar heating systems. Solar Energy 27, 513528 (1981). 11. P. D. Lund, Computational simulation of solar heating systems with seasonal heat storage. Helsinki University of Technology, Report TKK-F-A507 (1983). 12. P. D. Lund, R. M~kinen, J. T. Routti and H. Vuorelma, Simulation studies of the expected performance of Kerava solar vollage. Int. J. Energy Res. 7, 347-357 (1983). 13. E. Michelson, Multivariate optimization of a solar water heating system using the Simplex method. Solar Energy 29, 89-100 (1982). 14. D. Breger. A solar district-heating system using seasonal storage for the Charlestown, Boston Navy Yard Redevelopment Project. Argonne National Laboratory, Argonne, Illinois, ANL-82-90 (1982). 15. P. Margen, L. Engvall, A. Wesslrn, C. Strrm and P. Axenborg, Large solar heating systems. Swedish Council for Building Research, Report R20:1982 (1982) in Swedish. 16. J. M. Cardi, P. Morand, Y. Lenoir, M. Pottier and P. Chouard, An optimal control strategy for space heating systems using long term heat storage. Proc. Int. Conf. on Subsurface Heat Storage. Stockholm, Sweden, 6-8 June (1983). 17. M. Suvanen et J. T. Routti, Simulation par ordinateurs des maisons a energie solarie passive dans les latitudes nordiques. Confdrence lnternationale l'Architecture Solair. Cannes, France, December (1983). 18. M. Suvanen. P. D. Lund and J. T. Routti, Combined passive and active solar heating with high solar fraction. Proc. Solar World Congress, Perth. Western Australia, 14-19 August (1983).

REFERENCES

1. P. Margen, Seasonal thermal storage. Swedish Council for Building Research, Document D4:1981 (1981). 2. F. Baylin, R. Monte and S. Sillman, Annual-cycle thermal energy storage for a community solar system: details of a sensitivity analysis. Solar Energy Research Institute, Golden, Colorado, SERI/TR-355-575 (1980). 3. P. D. Lund, A comparative study of community solar heating systems for northern latitudes. Helsinki University of Technology, Report TKK-F-A512 (1983). 4. J.-O. Dalenb~ick, E. Gabrielsson and B. Ludvigsson, Three Swedish group solar heating plants with seasonal storage. Swedish Council for Building Research, Document D5:1981 (1981). 5. E. Kjellson, B. Perers, H. Zinko and L. Astrand, Solar district heating with evacuated collectors. Swedish Council for Building Research, Document D10:1982 (1982). 6. L. A,strand and E. Kjellson, Solar district heating in Uppsala, Sweden. Proc. Solar World Congress, Perth, Western Australia, 14-19 August (1983). 7. W. A. Beckman, S. A. Klein and J. A. Duffle, Solar Heating Design by the f-Chart Method. Wiley, New York (1977). 8. R. H~kansson and S. Rolandsson, MINSUN. A data program for minimizing the cost function of a solar

APPENDIX

ITEMIZED COSTS OF A DISTRICT SOLAR HEATING SYSTEM Flat-plate collectors Parabolic troughs Collector pipings Heat distribution network Circulation pumps, valves, heat exchangers Electric resistance heating (boiler) Heat pump Controllers, instrumentation, data acquisition Transformer Rock cavern storage Cost of water (sewage cost) Building site Design and administration costs Direct gain windows Yearly maintenance and repair costs

$180 m 2 $280 m 2 $50 m- ~ $1910 house ~ $110-170 house $980 house $1760-2350 house $104,000 + $280 house$5000 + $170 house $26-204 m ~ $0.8 m -3 $325 house 3-8% of the first costs $38 m -2 of living area $4 m-2 of living area