2. Theoretical performance calculation CSPP
2.2 Solar filed
2.3.1 Stratification Storage the Multi-‐Node-‐model
Liquid storage tanks are operated at a significant degree of stratification. The degree of stratification in real operation is strongly dependent on the design of the tank and its location.
In the multi-node model heat storage is modeled and divided into N nodes in order to display the stratification layers. In order to formulate the necessary equations, it will be appropriate to set some assumptions about how the liquid will be entering the tank and how the distribution to the several nodes takes place. The density of the liquid is dependent on the temperature. Therefore we can assume that the storage material will find its way to the node with the same temperature as the liquid. As it is displayed in figure 6 the mass flow coming from the collector field mc finds its way to a node according to its temperature between Ts,1 and Ts,3. The same physical effect can be discovered when the liquid enters the tank upstream.
Figure 6: Three-node stratification liquid storage tank [SETP].
In the three node-model displayed in graph 6 the nodes are counted from the top to the bottom. The liquid flow inside of the tank however, can run from the bottom to the top or the other way around depending on the thermodynamic conditions of the different layers. A collector control function Fic can be defined in order to determine, which layer receives the thermal energy coming from the solar field. [SETP; S.384]:
FiC =
During the operation of the solar field the control functions can be non-zero only for one node. The liquid returning from the power block can be controlled in the same way like the mass flow coming from the collector field. Therefore the control function FLi is established [SETP; S.384]:
Equation (2.29) follows the same assumption as for equation (2.28). Therefore only one control function can be set 1 during an operation.
The net flow between the nodes can now be either up or down. This depends on the magnitudes of the load flow rates and the values represented in the two control functions (2.28) and (2.29) at any particular instance. It is appropriate to define a mixed flow rate in order to describe the net flow rate into node I from node i-1 in the
multi-node model. The equations for calculating these flow rates can be presented as
By using the control functions (2.28 and (2.29) it is now possible to describe the energy balance for each node i. This function can be expressed as [SETP; S.385]:
midTs,i
Here the first term representing the heat losses to the to the environment with the temperature Ta. By increasing the number of nodes the model can be used for describing processes in highly stratified tanks. Therefore equation (2.33) can be seen as the basic description of the energy balance. Furthermore the model allows adding a heating system in one or more nodes or going into more details for the description of the thermal losses. For solving equation (2.33) numerical integration can be performed by techniques like the explicit Euler or the Runge-Kutta methods.
However, for this type of storage model very little experimental evidence for supporting the results are available. Nevertheless, the assumptions are all based on physical facts.
2.3.2 The Plug-Flow Model
The plug flow model is another possibility for describing a stratification tank. Here different layers, flowing around in the tank are the focus of interest. When the heat transport fluid is entering the tank a new layer is simply added to the model. On the other hand when liquid is leaving the tank a layer will be removed from the model.
The size of each segment varies depending on the flow rate and the time increments set for the calculation.
Figure 7 presents a heat storage tank according to the plug and flow model with four layers. On the x-axis the temperature will be marked, while the y-axis represents the
height of the storage. Vi presents the volume of each storage layer.
Figure 7: Plug and Flow model whit 4 layers [SLP].
Here, losses on the surface of the tank occurring. The temperature change of each layer i can be detected with the following equation [SLP; S.30]:
mi dTs,i
The definition mi represents the mass at each layer, Ts,I the Temperature of the layer, U represents the heat transfer coefficient, A is the outer area of the storage and Ta
stands for the ambient temperature.
Both models have their advantages and disadvantages. The decision which model is used in the simulation has to be determined by considering the required accuracy, the available data sets, and the available computational capacity.
2.4 Power Block
The “heart” of the CSP plant is the power block: here the thermal energy delivered either from storage or from the solar field is transferred into electrical energy. In previous chapters, the process has been described for how to harvest and transfer solar energy, as well as the transport and storage of thermal energy. Here a closer look of how the thermal energy is transformed into electrical energy is undertaken.
For CSP plants, well-established techniques are used. These techniques are depending theoretically on the Clausius-Rankine cycle.
2.4.1 Carnot Cycle
Cycle processes play a very important roll in the mean of transferring thermal energy into mechanical energy. The ideal thermodynamic cycle is the Carnot process. It has
the maximum thermodynamic efficiency, the Carnot efficiency *c. This is because all changers of states are reversible. In practical applications this efficiency can never be reached but is used for indicating the thermodynamic quality of a real process.
Figure 8 shows the Carnot cycle in a p,V and a T,S diagram it can be seen that all parts of the cycle are reversible.
Figure 8: Carnot cycle p,V and T,s Diagram [TDK].
As it is displayed in the graph above, the process consists of two isothermal and two reversible adiabatic changes of state. The isothermal expansion form state (1) takes place by adding thermal energy Q12 and performing work W12. A reversible adiabatic expansion takes place from state (2) to state (3). The isothermal compression between states (3) and (4) releases the thermal energy Q34 and must be supplied by work W34. Lastly, by reversible adiabatic compression the working gas is brought back to state (1).
By using the first law of thermodynamics the process can be described as [TDK;
S.66]:
# dU = "W + "Q # #
(2.35) Taking into consideration, that the change of energy in a closed cycle is zero, the formula (2.35) can be simplified to [TDK; S.66]:
$ " W = # "Q $
(2.36) Equation (2.36) shows that the sum of all added and removed work is equal to zero.Therefore, it can be defined as [TDK; S.66]:
W
1,2+ W
2,3+ W
3,4+ W
4,1+ Q
1,2+ Q
3,4= 0
(2.37) From equation (2.37) the Carnot efficiency can be explained only by the added and removed thermal energy in the cycle [TDK; S.66]:"th =1# (#Q3,4)
Q1,2 =1# TT31 (2.38) By using the entropy difference the thermodynamic efficiency can be also descript as the relation of temperature T3 and T1. This efficiency finally can be used for evaluating the quality of any other circular process.
2.4.2 Clausius-Rankine Cycle
In the CSP plants the water steam cycle is operated on the basic concept of the ideal Clausius-Rankine cycle. The primary working medium here is water/steam.
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Figure 9 represents all essential parts of a power block, and the T,s diagram for the related Clausius-Rankine cycle.
Figure 9: Schematic drawing of a steam power plant and the T,s Diagram of a Clausius-Rankine cycle [TDK].
The cycle starts with a reversible adiabatic compression (1.2) by the feed water pump (P), the compression takes place in the liquid phase. Followed by an isobaric heat addition (2.3) in the evaporator. The heat source in case of a CSPP is the thermal energy provided by the solar field or the thermal storage. The heat switch over takes place in several heat exchangers (KE). When reaching the evaporation line (3) an isobaric–isothermal heating up of the steam is taking place (3.4).
Followed by another isobaric heat adding (4.5) in the superheated (Ü). After superheating the steam a reversible adiabatic expansion (5.6) takes place in the steam turbine (T), where the thermal energy is transformed into mechanical energy and again transformed by the generator (G) into electrical energy. Finally the water steam mix is isobaric condensates (6.1) in the condenser (Ko) until it reaches the
evaporation line (1). Bringing the thermal energy into the cycle between point (2) and (5) can be described as [TFI; S.188]:
Q•add =m•(h5 "h2) (2.39)
Where m represents the mass flow of the water/steam, and h5 and h2 are the specific enthalpy values at point (5) and (2) out of graph 8. The enthalpy values can be either taken from the water steam table or form the h,s diagram.
The transferred energy in the turbine (5.6) can be calculated by [TFI; S.187]:
P = m•(h6 "h5) (2.40) In the formula above m stand for the mass flow of the steam, h6 and h5 are the enthalpy values in state (5) and (6). In the condenser the thermal energy of the exhaust steam will be removed according to the function [TFI; S.188]:
Q•0 =m•(h1"h6) (2.41)
The energy consumption of the feed water pump can be calculated by the water/steam mass flow m together with the specific volume of the condensate and the pressure increase between (1.2) [TFI; S.189]:
PP =m• v1(p2"p1) (2.42)
In formula (2.42) Pp stands for the power consumption of the feed water pump, and v1 is the specific volume of the condensate. From equations (2.30) through (2.42) it is possible to calculate the thermodynamic efficiency of the ideal Clausius-Rankine cycle. In most of the cases the power used by the feed water pump compared to the energy generated in the steam turbine is very small. Therefore this power is not taken into consideration when calculating the thermal efficiency [TDK; S.120]:
"th = P
Q• =1# Q•0
Q• (2.43) It becomes obvious that even in a reversible process cycle the thermal efficiency in the Clausius-Rankine cycle is lower the efficiency in the Carnot cycle (equation 2.38).
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So far all processes in the cycle were considered as being reversible, but in reality these processes are irreversible. The change of state in the working medium (water/steam) in the feed water pump, the steam generator, the turbine and the condenser are irreversible. This leads to differences in the operation points. Figure
10 displays this difference between a reversible and an irreversible cycle.
Figure 10: Real Celsius Rankine Process T,s Diagram [KWT].
The dotted line presents the real process, where the continuous line shows the ideal process. The main differences, which can be acknowledged in figure 10, are:
a: irreversible compression in the feed water pump b: pressure losses in the steam generator
c: irreversible expansion in the steam turbine d: pressure losses in the condenser
The increase of pressure in the feed water pump is irreversible. Because of this an increase of the entropy can be noticed. The change of state taking place in reality is not from (1.2) it is from (1.2r). Here the pressure increase from p2 to p2r is the same as the pressure reduction of the working medium in the steam generator, caused by friction in the pipe. In modern steam plants the parasitic load of the feed water pump can be assumed with around 2%-3% of the generated power. The irreversible behavior in the steam generator is mainly dependent on the temperature difference between the working medium and the heat transport fluid from the solar field. Furthermore, the movement of the working medium through the steam generator leads to a pressure drop. The lost energy of the working medium h2r-h2 has to be added also by the feed water pump.
Depending on the irreversible expansion in the steam turbine only state (4r) is reached at the outlet of the steam turbine. The additional heat, which has to be removed in the condenser, logically is increasing according to:
"Q• =h4r #h4 (2.44) Consequently, the efficiency of the real Clausius-Rankine cycle in reduced by [TFI;
S.192]:
"#th = "Q• Qadd
(2.45)
Finally the irreversible behavior in the condenser is dependent on the technical necessary temperature difference and the pressure loss because of friction in the piping system.
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The first possibility to increase the efficiency of the water steam cycle is increasing the temperature and pressure of the working medium before entering the turbine.
Figure 11 shows the thermodynamic consequence of this procedure in a T,s-diagram.
Figure 11. Increasing of the main steam parameters [KWT].
For the processes 1234 and 12’3’4’ the amount of energy removed by the condenser is equal, but the yield energy in the process 12’3’4’ is higher than in the process 1234. This is displayed in figure 11 by the greater area covered by the process 12’3’4’. For the process 12’’3’’4’’ the removed heat in the condenser is less compared to the other process cycles in the graph above. The temperature at point (3’’) is mainly limited due to material reasons. However for solar thermal power plants this procedure is less interesting because of the temperature which can be reached by the collectors is around 400°C nowadays, where in conventional plants the steam temperature is already at around 600°C. Furthermore, a limit in the scenario shown above is the amount of wet steam allowed in the last stages of the steam turbine.
Due to erosion on the steam turbine blades, the amount of wet steam must be reduced as much as possible.
Another optimization of the Clausius-Rankine cycle is possible, the so-called reheating. This means that the working medium is reheated after a partial expansion
in the high-pressure stage of a steam turbine. The following T,s-diagram shows the thermodynamic consequences of this procedure.
Figure 12: Water steam cycle with reheating [KWT].
The process (3.4) presents the expansion in the high-pressure stage of the steam turbine (4.5) is the reheating process in the steam generator and (5.6) is again the expansion in the intermediate and low-pressure stage of the turbine. The thermodynamic efficiency, not including the feed water pump, can now be defined as [KWT; S.70]:
"th =1# T6(s6 #s1)
h3 #h1+h5 #h4 (2.46) Equation (2.46) shows that for increasing the thermal efficiency by using a reheat system the average temperature of the added heat in the reheater has to be higher than the average temperature of the cycle without a reheating system. The average temperature of the basic process can be calculated as [KWT; S.70]:
Tzu,1 = h3 "h1
s3 "s1 (2.47)
Where the average temperature for the reheating process is calculated [KWT; S.71]:
Tzu,2= h5"h4
s5"s4 #0.5(T4+T5) (2.48) In normal operation conditions the temperature for the reheating system is equal to the temperature of the main steam temperature (T5=T3). Therefore, the efficiency will be increased if Tzu2>=Tzu1. This lead to [KWT; S.72]:
T
4> 2T
zu,1" T
5 (2.49) Another advantage of the reheating stage can be seen in the reduced amount of wet steam in the low-pressure part of the steam turbine.Increasing the cycle efficiency is also possible by adding a preheating system. It heats up the feed water above the condensation temperature, and therefore the efficiency of the Clausius-Rankine cycle gets closer to the efficiency of a Carnot cycle. In practical use the steam for heating up the feed water comes from several stages of the steam turbine.
Figure 13: Regenerative feed water preheating [KWT].
Figure 13 gives a schematic overview of the preheating process. It is clearly shown that the heat is shifted from b to a by using the preheating system. In order to avoid evaporation effects in the feed water the water is pressurized. The thermal efficiency of the water steam cycle can now be calculated as [SLP; S.33]:
"th =1# h3#h1'
T1(s4 #s1) (2.50) Increase in efficiency mainly depends on the reduction of the mass flow through the condenser. This results in a reduction of the condenser losses.
Another conclusion of the preheating system is that the steam mass flow to the high-pressure part of the steam turbine is increasing where the steam flow in the low pressure and intermediate pressure part is decreasing. This leads, depending on sealing losses in the turbine, to an increase of the internal turbine efficiency.
2.4.3 Steam Turbine
A steam turbine is an axial turbo engine, in which the thermal energy stored in the steam is converted into mechanical, mainly rotational energy. For the transition of the enthalpy into kinetic energy the working medium is seeded up in the nozzles. These nozzles are composed by the outlines of the guidance wheels. After this a switch of flow direction of the working medium takes place by using the rotating wheels. As a reaction of the impulse forces occurring now on the wheels, a torque is created and transferred to the turbine shaft. The set of a guidance wheel and a rotational wheel is
called turbine stage. Figure 14 gives an overview of the construction concept of a modern steam turbine.
Figure 14. Schematic drawing of a high-pressure turbine [KWT].
The construction schema above shows the inner cover a, the outer cover b, the labyrinth sealing c and the turbine shaft d.
Furthermore, figure 14 is giving an overview of how the thermal energy stored in the steam is transferred into the kinetic energy of the shaft. Simplified the power produced by a steam turbine can be calculated out of the enthalpy drop over the turbine, the steam mass flow, and the turbine efficiency [KWT; S.261]:
PT =
"
T m• #h (2.51)The turbine efficiency *T is depending on several losses occurring during the energy conversion in the turbine. For an easier understanding of the turbine efficiency we can calculate the efficiency like [KWT; S261]:
"T ="i"mech (2.52)
In formula (2.52) *i is considered as the inner efficiency. It is depending on losses occurring on the wheels, which are manly friction losses. Gap losses depending on the design of the turbine and ventilation losses are also recognized in this factor.
Furthermore, losses depending on wet steam and losses occurring during the steam are leaving the turbine because of rearrangement in the flow direction. As a benchmark the inner efficiency for modern turbine can be assumed to be between 93% and 95%.
The mechanical efficiency *mech includes steam losses in the labyrinth sealing as well as friction losses between shaft and bearings. Because of using modern hydraulic bearings for carrying the turbine shaft the efficiency here can be assumed whit 98%
or 99%. All the assumptions above are related to the design point of the steam
turbine, which is normally at the maximum rated power of the turbine.
The turbine power however is controlled by the steam mass flow. This is affecting the efficiency as well as the net power output of the generator. The relationship between the steam mass flows for the different operation modes (full load or part load) are described by the cone law of Stodola [KWT; S.261]:
m•T
m•0 = p"2T #p$2T
p"20#p$20
T"0
T"T
(2.53)
Here # stand for the entrance of the turbine and % stands for the turbine outlet, 0 characterizes the full load operation, where T represents part load behavior. Over the years, several possibilities like fixed pressure operation, sliding control or equivalent sliding pressure have been established for the control of the steam turbine. Based on equations (2.53), the operation mode of the steam turbine, and also the part load behavior of a CSPP can be assumed.
This chapter has outlined theoretical relations used for the developed model explained in chapter 4. However not only were technical factors taken into consideration for the simulation but also a recourse assessment for CSP plants in North Africa is undertaken in the next. !
.
3. Recourse Assessment for CSPP
3.1 Land Recourse Assessment
Using numerous criteria such as ground structure, water bodies, slope, shifting sand, protected and/or restricted areas, forest, and agricultural covered areas allows for the detection of land resources, which would permit the placement of concentrating solar collector fields. For collecting these data sets from the DLR are used, witch finally all combined in order to yield a map of usable areas. Some of the used criteria can be seen as optional. For instance, tourist areas or agricultural areas can be transformed into potential sites for CSP plants. Other information like slope of the terrain or water
Using numerous criteria such as ground structure, water bodies, slope, shifting sand, protected and/or restricted areas, forest, and agricultural covered areas allows for the detection of land resources, which would permit the placement of concentrating solar collector fields. For collecting these data sets from the DLR are used, witch finally all combined in order to yield a map of usable areas. Some of the used criteria can be seen as optional. For instance, tourist areas or agricultural areas can be transformed into potential sites for CSP plants. Other information like slope of the terrain or water