Dynamic optimization of a hybrid solar thermal and fossil fuel system

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 108 (2014) 210–218 www.elsevier.com/locate/solener

Dynamic optimization of a hybrid solar thermal and fossil fuel system Kody M. Powell a,⇑, John D. Hedengren b, Thomas F. Edgar c a

The University of Texas at Austin, McKetta Department of Chemical Engineering, 200 E. Dean Keeton St., Stop C0400, Austin, TX 78712-1589, United States b Brigham Young University, Department of Chemical Engineering, United States c The University of Texas at Austin, McKetta Department of Chemical Engineering, United States Received 24 August 2013; received in revised form 10 May 2014; accepted 8 July 2014

Communicated by: Associate Editor Halime Paksoy

Abstract This work illustrates the synergy that exists between solar thermal and fossil fuel energy systems. By adding degrees of freedom and optimizing the system, more solar energy can be harvested by operating in a “hybrid” mode, where a portion of the demand is met by solar energy, with the remainder provided by a supplemental fuel, such as natural gas. This requires allowing temperatures in the solar field and storage tanks to vary, permitting the system to meet the demand by a combination of solar and fossil energy, rather than one or the other, and by allowing the heat transfer fluid to bypass storage. The addition of thermal energy storage provides the opportunity for dynamic optimization, where the degrees of freedom can be exploited over the entire time horizon to yield optimal results: maximizing the total amount of solar energy harvested. The problem is solved using a simultaneous solution method that concurrently minimizes the objective function and solves the system’s constraints. This methodology is demonstrated on a parabolic trough solar thermal plant with a two-tank-direct thermal energy storage system. Results show that 9% more solar energy can be harvested on a sunny day by using this methodology. On a day with intermittent sunlight, 49% more solar energy can be harvested with the same system. Dynamic optimization enables more cost effective solar integration in areas with lower or intermittent sources of solar incidence. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Dynamic optimization; Hybrid solar thermal systems; Thermal energy storage

1. Introduction Solar energy has tremendous potential to produce emission-free electricity (Zhang et al., 2013). With similarities to conventional power generation methods, solar thermal, or concentrated solar power (CSP), can be a low-cost alternative to fossil-fuel-based systems (Barlev et al., 2011). In order to provide reliable base load power, however, CSP systems must be equipped with large-scale thermal energy storage (TES) and/or a backup energy source, such as ⇑ Corresponding author. Tel.: +1 512 471 5150; fax: +1 512 471 7060.

E-mail address: [email protected] (K.M. Powell). http://dx.doi.org/10.1016/j.solener.2014.07.004 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.

natural gas or diesel fuel (Kuravi et al., 2013; Zhang et al., 2013). Because of the intermittency of solar energy, it generally must rely on other energy technologies to ensure that consumer demand for power is always met. Hybrid systems, which combine solar thermal and other energy technologies, have been proposed as an alternative to solar-only power generation (Peterseim et al., 2013). For instance, solar thermal power can be combined with conventional power generation technology so that solar energy is aided by proven power generation technology, such as gas and steam turbines (Jamel et al., 2013). When gas and steam turbines are used in tandem, solar energy can be used to

K.M. Powell et al. / Solar Energy 108 (2014) 210–218

211

Nomenclature Symbol Description AA absorber pipe cross-sectional area (m2) AA,i inner pipe cross-sectional area for absorber pipe (m2) AE glass envelope cross-sectional area (m2) AP,i inner pipe cross-sectional area for boiler pipe (m2) At tank area subject to heat transfer (m2) CA absorber pipe specific heat capacity (J/(kg K)) CE glass envelope specific heat capacity (J/(kg K)) CF heat transfer fluid specific heat capacity (J/(kg K)) hair ambient convective heat transfer coefficient (W/(m2 K)) hp convective heat transfer coefficient for inner pipe (W/(m2 K)) IC solar radiation incident on collector surface (W/m2) IN solar irradiance in direction of rays (W/m2) mass flow rate (kg/s) m_ PA,i inner absorber pipe perimeter (m) PA,o outer absorber pipe perimeter (m) PE,o outer glass envelope perimeter (m) PB,i outer boiler pipe perimeter (m) pumping power (MW) p_ pump power demanded (MW) q_ d solar thermal power (MW) q_ solar

supplement the steam cycle in an integrated solar and combined cycle (ISCC) power plant (Cau et al., 2012). With concentrating solar collectors, solar heat can be delivered at higher temperatures to improve the Carnot efficiency of a solar gas turbine, where the air is heated by solar radiation before entering the gas turbine (Barigozzi et al., 2012; Schwarzbo¨zl et al., 2006). Hybrid solar systems have also been proposed to include chemical processes, such as methane steam reforming as an intermediate step before combustion and delivery to a gas turbine (Sheu and Mitsos, 2013) or chemical looping combustion (Jafarian et al., 2013). Studies have also been done to determine how CSP can be coupled with other renewable technologies, such as wind, to better match consumer electricity demand (Vick and Moss, 2013). Hybridization of CSP with other power production technologies represents a paradigm shift: rather than competing with other technologies as a sole power source, CSP can be used to complement these technologies. For instance, combining solar thermal systems with a fossil fuel, such as natural gas, gives the system operator more flexibility to determine how to run the system. While

q_ supp rE,i rA,o t TA TAIR TSKY TB TE TF U V w x z b v eA eE goptical qA qE qF r

supplemental thermal power (MW) inner glass envelope radius (m) outer absorber pipe radius (m) time (s) temperature of absorber pipe (K) ambient air temperature (K) effective sky temperature for radiative heat transfer (K) boiler water temperature (K) temperature of glass envelope (K) temperature of heat transfer fluid (K) storage tank overall heat transfer coefficient (W/(m2 K)) volume of fluid in storage tank (m3) width of mirror aperture (m) distance along solar collector length (m) distance along boiler pipe length (m) conversion factor for pumping power to thermal power (MWth/MWe) control move penalty coefficient (None) absorber pipe emissivity (None) glass envelope emissivity (None) total optical efficiency (None) absorber pipe density (kg/m3) glass envelope density (kg/m3) heat transfer fluid density (kg/m3) Stefan–Boltzmann constant (W/(m2 K4))

these fossil fuels are generally thought of as backup fuel sources to use during periods of cloud cover, dynamic optimization reveals that there are times when it is beneficial to use natural gas as a supplement while so that solar collectors can be run at lower temperatures. Optimizing the system so that the maximum amount of solar energy is harvested allows the solar and fossil components of the system to perform synergistically, resulting in more efficient performance. TES, when combined with CSP, provides additional flexibility, so that power can be produced on demand (Manenti and Ravaghi-Ardebili, 2013; Powell and Edgar, 2012; Slocum et al., 2011). These degrees of freedom can also be exploited using optimization, so that an objective can be maximized or minimized over a time horizon (Lizarraga-Garcia et al., 2013; Wittmann et al., 2011). The goal of this work is to illustrate that the addition of fossil fuel to a CSP system can actually increase the total amount of solar energy that can be harnessed. This requires dynamic optimization, so that the degrees of freedom from both the backup fuel and the TES can be fully exploited to achieve an objective: maximizing the total solar energy collected over a 24 h period.

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assembly, as shown in Fig. 2. These energy balances are used to compute temperature as a function of distance down the collector assembly as a Partial Differential Equation (PDE). The heat transfer fluid exchanges heat by convection with the absorber pipe. Its energy balance is shown in (1). qF C F AA;i

Fig. 1. A parabolic trough CSP plant with two tank direct TES system. The heat sink block is used to represent the load.

2. System 2.1. Model development Parabolic troughs are the most prevalent and technologically mature CSP receiver technology (Giostri et al., 2012), and therefore, provide an ideal demonstration of how optimization can improve CSP systems. This work uses the model developed by Powell and Edgar of a 1 MWth parabolic trough CSP plant (Powell and Edgar, 2012). A simplified plant schematic is shown in Fig. 1. This system uses a two-tank direct method for TES, where the heat transfer fluid, a synthetic oil in this case, flows from the cold tank, is heated in the solar field, and is delivered to the hot tank. The fluid flows from the hot tank, as heat is delivered to the steam generator (labeled heat sink) and the (now cooled) fluid returns to the cold storage tank. In a CSP system, this would represent the steam generator, which produces steam for a turbine, but it can also represent an industrial heating load. The load is held constant using a combination of solar and gas energy, so modeling the power block was out of the scope of this study. As demonstrated in Powell and Edgar (2012), the solar field is modeled by computing spatially-dependent energy balances on the heat transfer fluid, receiver tube, and glass envelope. Direct normal irradiance (DNI) is reflected off the parabolic mirrors and focused onto the receiver

Fig. 2. A cross-sectional view of the parabolic mirror reflecting rays into the receiver assembly. Available from Powell and Edgar (2012).

@T F @T F _ F ¼ mC þ hP P A;i ðT A  T F Þ @t @x

ð1Þ

The absorber pipe exchanges heat with the heat transfer fluid as well as with the glass envelope by radiation. Convection between these surfaces is assumed negligible because of the vacuum between them. The absorber pipe also has a source term (IC) as it absorbs the solar flux after it is reflected off of the mirrors. The absorber pipe energy balance is shown in (2). qA C A AA

@T A ¼ hp P A;i ðT F  T A Þ @t   r   P A;o T 4A  T 4E þ I C goptical w  1eE rA;o 1 þ eE rE;i eA ð2Þ

In addition to exchanging heat with the absorber pipe loses heat by radiation to the environment by convection and radiation. The absorber pipe energy balance is shown in (3). qE C E AE

@T E ¼ @t

r 1 eA

E þ 1e eE



rA;o rE;i

   P A;i T 4A  T 4E

   reE P E;o T 4E  T 4SKY  hAIR P E;o ðT E  T AIR Þ ð3Þ

This set of PDEs can be approximated as a set of Ordinary Differential Equations (ODEs) by spatial discretization of the receiver assembly. See (Powell and Edgar, 2012) for more detailed information about the model development and the assumptions made in this model. Because radiative heat losses are proportional to T 4, they can be significant at high temperatures, making it critical to consider these losses when determining optimal operating conditions. Increased flow rates through the solar field reduce the operating temperature of the field and therefore, the heat losses. Increased flow rates, however, also mean more power consumed by pumping and reduced Carnot efficiency in the power block. The efficiency also changes with the solar flux level, making it important to consider optimizing in real-time (Jianfeng et al., 2012). If a dispatchable energy source, such as natural gas, is available, high power cycle efficiencies can still be achieved while minimizing radiative heat losses. Temperature in the solar field can be adjusted so that efficiency is maximized, while the system relies on the backup heat source to reach the appropriate temperature for the power cycle. Mass and energy balances are used to describe the thermal storage tanks, with the mass balance given in (4) and the energy balance in (5).

K.M. Powell et al. / Solar Energy 108 (2014) 210–218

dV ¼ m_ in  m_ out dt dðVT Þ qF C F ¼ C F ðT in m_ in  T m_ out Þ  UAt ðT  T AIR Þ dt

qF

ð4Þ ð5Þ

The model used in this work deviates from Powell and Edgar’s work in that a storage bypass (shown in Fig. 1) is added. The ability to bypass the storage tank can be used to prevent mixing fluids at different temperatures, which leads to destruction of exergy. This was not an issue in the previous work because the solar field outlet temperature was maintained at a constant level, so tank temperature fluctuated very little (Powell and Edgar, 2012). Adding a bypass gives the system an additional mode of operation to use in optimization. The model for the steam generator is based on an energy balance between the heat transfer fluid in the boiler tubes and the steam/water mixture (assumed saturated) on the shell side of the boiler. This simple model, also from Powell and Edgar (2012) is given in (6). qF C F Ap;i

@T F @T F _ F ¼ mC þ hp P B;i ðT B  T F Þ @t @z

ð6Þ

_ F ðT B;in  T B;out Þ q_ solar ¼ mC

depending on the optimal solution, which is a function of ambient conditions over the course of the time horizon. Because these conditions fluctuate, dynamic optimization requires the incorporation of weather forecast data where the problem can be resolved at a later time step to account for any changes that occur in the forecast or the plant itself (Zavala et al., 2009). CSP plants are particularly dependent on DNI, so dynamic optimization requires a DNI forecast. While this is beyond the scope of this work, it is assumed that a reliable DNI forecast is available using methods similar to those found in Marquez and Coimbra (2013, 2011). With TES, a backup fuel source, and a reliable DNI forecast, the CSP system can be optimized so that the solar energy collected and delivered to the heat sink over the time horizon is maximized. Alternatively, the backup fuel used can be minimized, while maintaining a specific thermal power output to the heat sink. The objective function (9) is designed to minimize the total supplemental and pumping energy needed, while maintaining a constant total heat output. Z tf min ðq_ supp þ bp_ pump Þdt ð9Þ u

The CSP plant produces thermal power at a constant rate, by a combination of solar heat and supplemental heat. This power output is held fixed at 1 MWth, therefore, when the solar power is below this level, the supplemental fuel is burned to bring the system up to the set point of 1 MWth. The solar heat output is represented by a steady state relationship, given in (7), where thermal power is calculated from the rate of heat transfer in the boiler. ð7Þ

The supplemental heat is used whenever solar heat is below the 1 MWth set point, as given in (8).  1  q_ solar ; if q_ solar < 1 MWth q_ supp ¼ ð8Þ 0; otherwise 2.2. Optimization problem formulation Because of the intermittency of solar irradiance and the nonlinearities of the system, controlling the temperature in the solar field is not a trivial task (Camacho et al., 2007a, 2007b). Often, model-based control techniques are recommended. In general, these techniques use a predictive model of the system to solve for optimal performance in terms of tracking a set-point or rejecting disturbances (Gallego and Camacho, 2012; Ga´lvez-Carrillo et al., 2009). A model predictive control (MPC) strategy can be very effective in regulating the system’s faster dynamics, i.e. those of the solar collectors. The addition of TES introduces slower dynamics to the system and additional opportunities for optimizing over a longer time horizon while leveraging the degrees of freedom that TES provides. Using storage, solar heat can be collected and stored/delivered at different temperatures,

213

t0

The decision variables in this system are the heat transfer fluid flow rates through the solar field, through the bypass loop, and from the hot tank. While there are a total of five flow rates, only three are independent because of the mass flow relationships that exist at flow junctions: namely the junction that combines the bypass flow with the flow out of the hot tank (10) and the splitter at which the flow into the hot tank is separated from that going through the bypass line (11). m_ bypass þ m_ hot;out ¼ m_ sink m_ bypass þ m_ hot;in ¼ m_ field

ð10Þ ð11Þ

Additionally, a steady state energy balance around the junction that combines bypass flow and flow from the hot tank is used to determine the temperature of the fluid before it enters the heat sink. This relationship is shown in (12).   C HTF m_ bypass T field;out þ m_ hot;out T hot ¼ m_ sink C HTF T B;in ð12Þ Inequality constraints are also added to the system to ensure that only physically implementable solutions are obtained. These constraints include non-negativity and upper limits for flow rates (13), upper and lower limits for storage volumes of both tanks (14), and upper limits on field outlet temperature (15). The flow limits in (13) apply for all flow rates in the system. 0 6 m_ 6 m_ max V min 6 V tank 6 V max

ð13Þ ð14Þ

T field;out 6 T max

ð15Þ

Because it is desirable to represent the system as a continuous set of equations so that efficient solution methods can be implemented, the logical relationship in (8) requires

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re-formulation. A mathematical program of equilibrium constraints (MPEC) is introduced. This set of equations, shown in (16)–(19), uses complementarity constraints to enforce some logical conditions. q_ solar  q_ d ¼ tp  tn q_ supp ¼ q_ d  q_ solar þ tp

ð16Þ ð17Þ

tp tn 6 0 tp ; tn P 0

ð18Þ ð19Þ

The inequality in (19) ensures that each of these slack variables (tn and tp) are nonnegative, while the inequality in (18) ensures that at least one of them must always be zero. Although, at the solution, the product of the left hand side of (18) will be zero, the use of an inequality constraint is observed to give better convergence properties by allowing the solver more freedom to search the solution space before arriving at the final solution. When the left hand side of (16) is negative (meaning that the solar heat falls short of the demand), tp must equal zero. Eq. (17) then determines the supplemental power needed to reach the set point. When the left hand side of (16) is greater than or equal to zero (meaning that the solar heat meets or exceeds demand), the supplemental heat required is zero by (16) and (17). See Baumrucker and Biegler (2009), Baumrucker et al. (2008) and Raghunathan and Biegler (2003) for more information on MPEC formulations. With all of the constraints developed, the dynamic optimization problem becomes the total supplemental and pumping energy subject to the system model (see Eq. (20)). Each of the constraints shown in (10)–(19) must be satisfied at every point in the time horizon. Z tf min ðq_ supp þ bp_ pump Þdt þ / ð20Þ m_ field ;m_ bypass ;m_ hot;out

t0

s.t. (10)–(19) In order to prevent excessive control moves and ensure an optimal solution that could be reasonably implemented, the problem is carefully tuned using the extra term (/) in the objective function. This term adds a small penalty to the objective function to prevent the decision variables from changing too drastically from one time step to another, resulting in operational wear and tear due to cycling of valves, pumps, and thermal cycling. When properly tuned, this ensures that the system yields a smoother optimal solution that would be more easily executed in an actual system. A quadratic penalty term is used in this work and is shown in (21). This function penalizes the square of changes in the control moves (u) from one time step (i  1) to the next (i), including the most recent past control move (u0). The variable e determines the magnitude of this penalty term in the objective function and is determined through trial and error that balances energy use with excessive movement of the process. While adding the penalty term yields more smooth solutions, it also negatively impacts the objective function, so this term must be care-

fully tuned so that significant energy savings are still achieved. /¼

N X

2

vðui  ui1 Þ

ð21Þ

i¼1

2.3. Solution method The system represented in (10)–(19) contains both differential and algebraic equations, making it a system of Partial Differential Algebraic Equations (PDAEs). Optimizing while ensuring that all PDAEs are satisfied, can be numerically challenging due to the large number of variables and equations from the discretized system. While three degrees of freedom are identified at each time instance, these variables must be chosen continuously over a time horizon, making a large set of feasible potential solutions. To reduce the dimensionality of the problem, the time horizon is discretized into smaller increments so that the solution has a finite number of decision variables. Using a sequential method, the decision variables for each time interval are specified pre-simulation. Given these inputs, the simulation is then carried out to compute the value of the objective function. This is repeated multiple times until the gradient of the objective function can be approximated using finite differences. Because the sequential method requires simulating the system repeatedly, it is generally inefficient for problems with many decision variables. The more efficient simultaneous method is employed in this work. This method approximates differential equations as algebraic equations using orthogonal collocation on finite elements transforming the set of equations into a purely algebraic representation. The optimization problem can then be solved using standard Nonlinear Programming (NLP) solvers. For more information about simultaneous solution strategies for dynamic optimization, see (Biegler, 2007). The dynamic optimization problem is formulated and solved using APMonitor, an advanced modeling language, which specializes in solving and optimizing DAE systems using the simultaneous method (Hedengren, 2012). This software package allows the user to input the differential model equations, equality constraints, inequality constraints, and decision variables directly. The software then simultaneously solves both the simulation and optimization. This solution method has many advantages including the efficiency with which the algorithm obtains an optimal solution. Because it solves the optimization, constraints, and simulation simultaneously, only one “simulation” is needed. The sequential method, by contrast, requires simulation of the system many times so that the objective function can be computed for each combination of decision variables. 3. Results The dynamic optimization scheme formulated above is evaluated under three different scenarios: (1) a sunny day with no cloud cover, (2) a day with partial cloud cover in

K.M. Powell et al. / Solar Energy 108 (2014) 210–218

Available

Power (MWth)

2 1.5 1 0.5

6:30 AM

4:30 AM

2:30 AM

12:30 AM

10:30 PM

8:30 PM

6:30 PM

4:30 PM

2:30 PM

12:30 PM

10:30 AM

8:30 AM

0

6:30 AM

Fig. 4. Solar power available and delivered when using a standard control scheme on a day with partial cloud cover in the morning.

650 550 450 350

Field Storage 6:30 AM

4:30 AM

2:30 AM

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10:30 PM

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250

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The simulation is first run using the control scheme from Powell and Edgar (2012), where the solar field outlet temperature is controlled to a constant level using the solar field flow rate as a manipulated variable. Once sufficient storage is available, the thermal power output is controlled using the flow through the heat sink as a manipulated variable. The results for the scenario with a partly cloudy morning are shown in Figs. 4–7. As Fig. 4 indicates, the power can be controlled very effectively using the stored energy in the hot tank. The solar field outlet temperature, shown in Fig. 5, is also maintained easily. The two tank storage system serves as a buffer between the supply side (the solar field) and the demand side (the heat sink) of the system. As Fig. 6 indicates, the flow rates in each of these sections can be altered individually, leading to the conclusion that, given sufficient storage, the temperature and power of the CSP plant can be controlled independent of each other. The storage system also allows the CSP plant to continue producing thermal power for several hours beyond sunset, as there is stored energy in the tanks until roughly 11:00 PM, as Fig. 7 shows. These simulation results highlight the value of TES in rejecting disturbances and extending the operating hours of a CSP system. The TES decouples supply and demand of energy so that power can be regulated to meet demand, despite fluctuating solar irradiance, provided that stored energy is available in the TES system. When the power delivered by solar falls short of the 1 MWth set point, the backup source of energy can be activated so that the system delivers a constant supply of heat.

Delivered

Temperature (K)

3.1. Standard control scheme

2.5

Fig. 5. Solar field outlet temperature and hot storage tank temperature when using a standard control scheme. 8 Field

7

Sink

6

Flow (kg/s)

the morning, then clear skies in the afternoon, and (3) a day with intermittent sunshine throughout the day. The DNI values (accounting for tracking and optical losses) shown for each scenario are shown in Fig. 3.

215

5 4 3 2 1

DNI (W/m2)

6:30 AM

4:30 AM

2:30 AM

12:30 AM

10:30 PM

8:30 PM

6:30 PM

4:30 PM

2:30 PM

12:30 PM

Fig. 6. Heat transfer fluid flow rates when using a standard control scheme.

Sunny

700

Partly Cloudy

600

Intermittent

500 400 300 200 100

6:30 AM

4:30 AM

2:30 AM

12:30 AM

10:30 PM

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0

10:30 AM

800

8:30 AM

As demonstrated in the above results, TES gives a CSP system enhanced operational ability so that both power

6:30 AM

0

3.2. Dynamic optimization

Fig. 3. DNI in W/m2 for each of the three scenarios explored in this study. These DNI values already account for optical losses and east/west tracking of the parabolic mirror arrays.

and temperature can be regulated effectively with a relatively simple control scheme. TES also gives the CSP system additional degrees of freedom which can be exploited through optimization. This allows the solar component of the system to perform synergistically with the supplemental fuel so that optimal performance is achieved, in this case, minimizing the total amount of supplemental fuel that must be consumed while meeting a constant 1 MWth demand for 24 h. In order to achieve this, the 24 h time horizon is discretized into 15 min increments, during which, each decision variable (flow rate) is held constant. The optimal results are shown in Figs. 8–11.

K.M. Powell et al. / Solar Energy 108 (2014) 210–218 160

Cold Tank

160

Cold Tank

140

Hot Tank

140

Hot Tank

Tank Volume (m3)

Tank Volume (m3)

216

120 100 80 60 40 20

60 40

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12:30 AM

10:30 PM

8:30 PM

6:30 PM

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12:30 PM

10:30 AM

6:30 AM

8:30 AM

0

Fig. 10. Storage tank volumes when using dynamic optimization. 8

2.5 Delivered

Field

7

Available

Sink

6

Flow (kg/s)

2.0

Power (MWth)

80

6:30 AM

4:30 AM

2:30 AM

12:30 AM

10:30 PM

8:30 PM

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Fig. 7. Volume of heat transfer fluid in the hot and cold tanks when the system uses a standard control scheme.

1.5 1.0

Bypass

5 4 3 2

0.5

1 6:30 AM

4:30 AM

2:30 AM

12:30 AM

10:30 PM

As Fig. 8 shows, the system is operated in hybrid mode when using dynamic optimization. During the morning, when there is less solar energy available, the only a portion of the 1 MWth is delivered by solar with the rest being made up by the supplemental fuel. During this same period, the heat is collected at a lower temperature, just over 600 K, as Fig. 9 shows. Because there is less energy being absorbed the solar field, reaching temperatures in excess of 650 K requires low solar field flow rates (as in Fig. 6), which mean longer residence times and more heat loss due to radiation. The optimal solution avoids much of this heat loss as it keeps the field flow rate high (Fig. 11) and the

8:30 PM

Fig. 9. Solar field outlet temperature and hot storage tank temperature vs. time with dynamic optimization.

6:30 PM

6:30 AM

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2:30 AM

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10:30 PM

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4:30 PM

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350

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Fig. 8. Thermal power available and delivered using the dynamic optimization scheme on a day with partial cloud cover in the morning.

6:30 AM

0 8:30 AM

6:30 AM

0.0

Temperature (K)

100

20 8:30 AM

6:30 AM

0

120

Fig. 11. Heat transfer fluid flow rates when using dynamic optimization.

temperature lower. The system does not store energy during this period (Fig. 10). When the cloud cover dissipates and more solar energy is available, the solar field temperature increases and the corresponding flow rate decreases. The system begins storing the higher temperature fluid and meeting the entire load with solar heat. As the solar energy begins decreasing in the late afternoon, the system goes back into hybrid operation with the solar heat gradually tailing off. Correspondingly, the supplemental fuel usage gradually increases to keep the system at a constant power output of 1 MWth. 4. Discussion of results In order to demonstrate the value of dynamic optimization of the solar thermal system, three days with differing solar irradiances simulated using both the standard control method and the optimized version. These three scenarios are shown in Fig. 3. While only the optimal results for the scenario with the partly cloudy morning are shown (for brevity), similar results are observed in the other two scenarios. The results are summarized in Figs. 12 and 13. Fig. 12 shows the total solar energy collected in each scenario for each control scheme. Fig. 13 shows the total solar efficiencies defined as the total amount of solar energy delivered to the heat sink over the total amount of solar energy available (not accounting for optical losses). As the figures indicate, the optimal results show a significant

K.M. Powell et al. / Solar Energy 108 (2014) 210–218

16.79

15.4

Standard

Optimal

13.46 11.75 7.25 4.85

Sunny

Partly Cloudy

Intermittent

Fig. 12. Total solar energy collected in MWth for each scenario.

Standard

65.6%

71.5%

This operating scheme requires accurate forecasts of the operating conditions, most notably DNI, for the upcoming day. While these forecasts will not always be accurate, the optimization scheme can be implemented on a dynamic basis, similar to model predictive control, where a control move is implemented for a single time step. At the next time step, the state variables are measured and the problem is re-solved using the most recent forecast information. Stability of the system can also be enhanced by introducing a hierarchical control scheme, where temperature set points are determined from the dynamic optimization. These set points can then be fed to lower-level controllers, which adjust flow rates to ensure that these temperature set points are maintained.

Optimal

5. Conclusions and future work

70.2%

65.7%

61.3% 44.0%

Sunny

217

Partly Cloudy

Intermittent

Fig. 13. Solar heat collection efficiency for each scenario. The efficiency does not account for optical losses.

improvement in every case. This is largely due to the heat loss avoided by operating at lower temperatures. On the sunny day, only marginal improvements are shown because the optimal temperature is very near the controlled temperature in the standard control case. However, on the days when less solar energy is available, operating at lower temperatures provides more dramatic improvement. On the day with intermittent cloud cover throughout the day, the efficiency improvement is significant. This is largely due to the fact that heat is collected at lower temperatures. This can only be done when the plant is operated in “hybrid” mode, with the supplemental fuel being used to provide a significant portion of the load. Operating in this manner allows the system to get the most benefit from solar energy, which means minimizing heat losses in the solar field and the total supplemental fuel when considering the entire 24-h period. Dynamic optimization of hybrid CSP systems with TES requires adjustment of several operational conditions to yield optimal results. TES gives the system flexibility to collect and deliver heat at different temperatures and with different flow rates. When temperatures are allowed to vary, heat losses can be minimized. This requires relaxing the constant solar power condition and allowing the system to be supplemented with a fossil fuel. Dynamic optimization exploits these degrees of freedom so that solar energy and the fossil fuel can be synergistic in a manner that results in maximum benefit of solar energy.

This work illustrates that solar energy can actually be enhanced using fossil fuels. This requires additional degrees of freedom and solving an optimization problem to exploit the operational flexibility. TES is beneficial because it provides additional flexibility so that the system can shift loads to different times. The addition of TES makes the problem a dynamic optimization problem, which can be solved with an efficient simultaneous method. Operating the plant in “hybrid” mode with optimization shows that some synergy exists between a solar thermal system and a fossil fuel system. This suggests that perhaps the best paradigm to adopt is that solar and fossil energy should complement each other, rather than compete with each other. Using this methodology, the system takes much greater advantage of “lower grade” solar energy. While CSP plants are most prevalent in desert climates with high annual amounts of DNI, adopting a “hybrid” paradigm can expand the geographical areas where CSP systems may be technologically and economically viable. The system modeled is a small scale (1 MWth) system, which relies on parabolic trough technology. As larger, more efficient, and higher temperature CSP systems become more prominent, some of the ideas from this study can be incorporated into the design. This will likely require novel TES systems and materials. As research on solar thermal energy continues, it will be beneficial to consider hybrid operation in the design of these plants. References Barigozzi, G., Bonetti, G., Franchini, G., Perdichizzi, A., Ravelli, S., 2012. Thermal performance prediction of a solar hybrid gas turbine. Sol. Energy 86, 2116–2127. Barlev, D., Vidu, R., Stroeve, P., 2011. Innovation in concentrated solar power. Sol. Energy Mater. Sol. Cells 95, 2703–2725. Baumrucker, B.T., Biegler, L.T., 2009. MPEC strategies for optimization of a class of hybrid dynamic systems. J. Process Control 19, 1248– 1256. Baumrucker, B.T., Renfro, J.G., Biegler, L.T., 2008. MPEC problem formulations and solution strategies with chemical engineering applications. Comput. Chem. Eng. 32, 2903–2913.

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