System model

The standard PVT system for domestic hot water considered in this thesis, has a col-lector surface area of 6 m² in combination with a 200 l storage tank. The standard PVT system for combined domestic hot water and room heating considered in this thesis, has a collector surface area of 12 m²in combination with a a 200 l storage tank for domestic hot water and a 40 m³storage tank for room heating (see figure 5.5).

Note again that this large storage volume is less typical and represents an extreme case. For both systems also half and double collector areas will be considered, how-ever each time the tank volume and heat demand is kept constant.

The system model consists of the collector model (introduced in section 5.2.2), a heat storage tank model, an inverter model and a control strategy. Input for the collector model are the weather data and the collector inflow temperature from the storage tank T_w,in^col. Input of the heat storage tank model is the heat demand and the

inflow temperature from the collector T_in^tank.

Because the annual electrical and thermal efficiencies are required, the system performance during an entire year has to be modelled. To do so, the year is subdi-vided into time intervals of 15 minutes, during which weather conditions and heat demand are assumed to remain constant. Note that because the heat content of the tank(s) is not known at start of the simulation, multiple years are simulated to ob-tain a steady state, i.e. having the heat content of the tanks equal at the start and end of the year. The control strategy will be described first. Subsequently the weather conditions, the heat demand, the inverter model and the heat storage model, used in the PVT system model, will be introduced.

Control strategy

To maximise the thermal yield and to keep the temperature level within the required range, a control strategy is normally implemented. The control strategy used in this thesis will now be explained.

In the system for domestic hot water, there is only one 200 l storage tank. To prevent contamination with the bacterium of the species Legionella pneumophila in this domestic hot water tank, the water extracted should be heated to at least 60^◦C.

An auxiliary heater is normally present to guarantee this temperature level. In times of high solar irradiance, the water in the tank could become much hotter and the water extracted from the tank is mixed with cold water (indicated by the dashed line in figure 5.5) to keep the supplied tap water at a constant temperature of 60^◦C. To prevent boiling, the collector may heat the water up to a level of at most 95^◦C. If this level is exceeded, the collector pump is stopped and no more heat is extracted from the collector. Under this condition, known as stagnation, the temperature in the collector can exceed 150^◦C.

In the system for combined domestic hot water and room heating, the 200 l do-mestic hot water tank has priority, i.e. will be loaded first, as long as it has a tempera-ture of less than 60^◦C. If this is not the case then the coolest tank has priority, which in most cases will be the 40 m³tank for room heating. In this case the pump is only stopped if both tanks have reached their maximum allowed temperature of 95^◦C. In all systems, another criterium to stop the pump is in case the reduced temperature T_redexceeds 0.1. Pumping water through the collector under these conditions would most likely only cool the water down.

Weather data

The weather data of a test reference year (TRY) from de Bilt in the Netherlands [88]

are used with the collector model. This data contains the hourly values of the am-bient temperature, solar irradiance and wind speed of the complete year. The corre-sponding sky temperature was derived from this data. The data of the test reference

0 1 2 3 4 5 6 7 8 9 10 11

irradiation classes of 100 W/m² solar irradiance per class (kWh/m2y)

Figure 5.6:Illustration of the weather data for the test reference year. Left: Annual irradiation per irradiation class of 100 W/m². Right: Daily maximum and mini-mum temperatures during the year.

year does not correspond to one year in particular, but it is statistically representative for the Dutch climate.

The irradiance for a south facing plane with an inclination of 45^◦is 1100 kWh/m²y.

In the left panel of figure 5.6, the annual total solar irradiance per irradiance class is shown. Each class corresponds to an intensity interval having a width of 100 W/m². It can be seen that solar irradiance can reach an intensity of 1000-1100 W/m², how-ever most irradiance is received having a lower intensity. In the right panel of fig-ure 5.6, the daily maximum and minimum ambient temperatfig-ure are illustrated. The seasonal cycle is clearly visible with maximum temperatures roughly ranging from 0^◦C in winter to 25^◦C in summer.

Heat demand

For the domestic hot water heat demand, a standard withdrawal pattern is used, consisting of a withdrawal of 117 l of water per day at 60^◦C [89]. After correcting for the heat loss in the pipes between storage tank and water tap, the effective hot water withdrawal is 139 l of water per day at 60^◦C [90]. This daily pattern is repeated for every day of the year, amounting to an annual thermal energy demand of 2960 kWh (10.6 GJ). This demand is distributed as shown in the left panel of figure 5.7.

For the room heating demand, the demand of the Novem reference dwelling is used in the model [91]. This room heating demand is typical for a single-family town house built in 1999, in Dutch climatological conditions. The distribution of the room heating demand over the year is shown in the right panel of figure 5.7. It can be seen that there is a significant room heating demand from November till March. The annual heat demand for room heating is 2990 kWh (10.8 GJ) which is comparable to

0 3 6 9 12 15 18 21 24 0

2 4 6 8 10 12 14 16 18

time of day (h)

hot water withdrawal in (kg/15min.)

0 50 100 150 200 250

room heating demand (kWh/week)

J F M A M J J A S O N D

Figure 5.7: Left: Daily heat demand for domestic hot water heat on a 15 minute basis. The demand of 139 l/day corresponds to 2960 kWh/y. Right: Annual heat demand for room heating on a weekly basis. Total heat demand is 2990 kWh/y.

the annual heat demand for domestic hot water.

Inverter

The inverter has a maximum input power P_max^inv for converting direct current to al-ternating current. When the inverter is operating between 0.25· P_max^inv and P_max^inv, the efficiency of the inverter is about 94%. For lower input power, the inverter is much less efficient. The inverter efficiency curve used in the model, shown in the left panel of figure 5.8, is based on the curve of a commercially available inverter [92]. The inverter size P_max^inv has to be chosen such that a maximum overall system efficiency is obtained, in principle. Because in this thesis different collector areas and PV tech-nologies are used, a somewhat simple approach is used: in each simulation P_max^inv is chosen to be equal to the peak power of the installed laminates.

Additionally, the power loss due to the electrical resistance in the cabling between the collector and inverter is taken into account. The resistance of the cabling is such that during peak power 2% of the electric power is lost due to ohmic loss.

Heat storage tank model

As indicated in the right panel of figure 5.8, the energy content of the storage tank is affected by two flows. At one side there is the collector loop, with a flow rate φ_c, taking water from the bottom of the tank and returning it at an elevated temperature.

At the other side there is the demand loop, with a flow rate φd, taking water from the top of the tank and returning the same amount at a reduced temperature. Note that in practice it is compulsory to separate the water of both loops by means of a heat

T1

T2

T3

TN

collector loop

demand loop

0 0.2 0.4 0.6 0.8 1

0.8 0.85 0.9 0.95 1

P^inv/P^inv max

inverter efficiency (%)

Figure 5.8: Left: Efficiency of the inverter as a function of relative input power P^inv/P_max^inv. Right: Schematic overview of the stratified heat storage tank divided into segments of uniform temperature. Inter-segment flows are indicated.

exchanger. Here it is assumed that this heat exchanger is located outside the tank on the collector side and is perfect in terms of effectiveness.

Heat storage tanks are designed to avoid mixing of water of different temper-atures to maintain good thermal stratification. Having a stratified tank instead of a tank of uniform temperature has two advantages. Firstly, the water extracted at the demand side (top) has a relatively high temperature, so less auxiliary heating is required. Secondly, the water extracted at the collector side (bottom) has a rel-atively low temperature, which is beneficial for the efficiency of the collector (see section 5.2). Therefore the degree of the stratification is an important system param-eter.

Van Berkel [93] has studied stratification inside a heat storage tank both numeri-cally and experimentally. He uses a figure of merit (FOM) for indicating the degree of stratification. The definition of FOM is given in appendix A and theoretically FOM ranges from 1 for a perfectly stratified tank to 0.63 for a fully mixed tank. In practice various storage tank designs exist with varying degree of stratification. Both storage tanks used in the model are assumed to have a degree of stratification which is in between fully mixed and perfectly stratified.

Because a complete computational fluid dynamics (CFD) model of the storage tank is computationally very expensive, simplified storage tank models have been developed, of which the multinode model is frequently used [94]. In this model the storage tank is divided into N segments, each segment being characterised by a temperature Tn, with n = 1 . . . N . As a result of buoyancy effects, water entering a stratified tank will rise or descend to match its density and thereby its temperature.

In the numerical model it is assumed that water enters the tank in the segment of best matching temperature, which helps to maintain good stratification in the tank. If the collector loop and/or the demand loop are active, water flows from one segment to

the next as indicated by the vertical arrows in the right panel of figure 5.8. Given an initial temperature distribution and inflow temperatures, the temperature distribu-tion a small time step later can be determined by solving the energy balances. More details of the multinode model are given in appendix A.

The temperature of the water coming from the collector depends on the weather conditions and is therefore variable. In the tank for domestic hot water, the water extracted at the demand side is replenished by water from the mains, which is as-sumed to have a constant temperature of 10^◦C. In the storage tank for room heating the demand loop is closed and water returning from the load is assumed to have a fixed temperature of 25^◦C. Note that because the return temperature is fixed, the amount of heat extracted for room heating is controlled in the numerical model by the flow rate.

The choice of the number of segments N in the model determines the degree of stratification. The simplest case with only one tank segment N = 1 corresponds to a fully mixed tank of uniform temperature (FOM=0.63). The limiting case of N → ∞ corresponds to a perfectly stratified tank (FOM=1). The exact relationship between N and FOM is given in appendix A. According to Duffie [84], the case with N = 3 (FOM=0.78) represents a reasonable compromise between the two extreme cases.

Therefore in this thesis N = 3 is used for both the domestic hot water tank and the room heating tank.

Heat loss from the tank to the ambient is taken into account as well and the fol-lowing assumptions are made. Both tanks are cylindrical with a height-to-radius ratio of 3. The domestic hot water tank is located in a room of 20^◦C while the big room heating tank is underground and surrounded by a temperature of 10^◦C. The heat loss is proportional to the surface area of the tank and inversely proportional to the thickness of the thermal insulation layer. For the 200 l domestic hot water tank an insulation thicknesses of 5 cm is used, resulting in a heat loss of 1.0 W/K. For the 40 m³room heating tank an insulation thicknesses of 30 cm is used, resulting in a heat loss of 5.7 W/K.