Operational optimization of an integrated solar

Energy 141 (2017) 1569e1584

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Operational optimization of an integrated solar combined cycle under practical time-dependent constraints Philip G. Brodrick*, Adam R. Brandt, Louis J. Durlofsky Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305-2220, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 July 2017 Received in revised form 23 October 2017 Accepted 9 November 2017 Available online 13 November 2017

Integrated solar combined cycles (ISCCs) need to be able to handle some of the most dynamic operating conditions of any power generation system in order to provide the flexibility of a natural gas combustion turbine while simultaneously utilizing variable incident solar irradiation. Yet to date, most work on ISCC design has focused on high-level treatments of system viability and potential impact, without thorough consideration of system operations. In this work, a computationally efficient ISCC model is constructed that includes detailed modeling of the heat recovery steam generator that links the natural gas and solar thermal systems. The model is validated against a model in the literature, and then used to perform computational optimization of the facility operations. Critically, a wide variety of practical system constraints are considered at each time step evaluated in order to ensure system feasibility under realistic conditions. It is shown that under different operating modes the ISCC design examined displays similar emission rates, yet significantly different profit ranges. A marked increase in the operating flexibility of the ISCC is observed when the outlet temperature of the solar heat transfer fluid is allowed to vary over the course of the day. © 2017 Elsevier Ltd. All rights reserved.

Keywords: ISCC HRSG Solar thermal Hybrid energy Systems analysis

1. Introduction Renewable energy will be an essential component of the effort to combat anthropogenic climate change, and effectively all long-range energy scenarios show a dominant contribution from renewable power [1]. However, the future energy system will be built one project at a time, and thus renewables will be used in concert with fossil-fuel based energy systems for at least the next few decades. This will require effective integration of fossil and renewable energy technologies. Renewable-fossil integration can be indirect, such as when the electric grid mediates power supply from a variety of fossil and renewable sources. Alternatively direct fossil-renewable integration is used in cases such as: daytime passive solar heating supplemented with fossil energy for cold spells and evenings; compressed air energy storage with gas-firing expansion; integrated solar combined cycle systems; or the solar reforming of methane to hydrogen. These options point to a set of key questions: under what economic and physical conditions does direct integration

* Corresponding author. E-mail address: [email protected] (P.G. Brodrick). https://doi.org/10.1016/j.energy.2017.11.059 0360-5442/© 2017 Elsevier Ltd. All rights reserved.

of renewable and fossil energy make sense? Why might direct fossil-renewable hybridization be appropriate in some sectors and not others? Are there applications that are uniquely suited to fossil-renewable hybridization? Do the benefits of direct hybridization outweigh the costs and complexities? How can such systems be operated to maximize the renewable fraction of energy in the mix? In this paper, the directly-hybridized integrated solar combined cycle (ISCC) is examined. The ISCC is a power cycle that generates electricity using both fossil fuel and solar thermal energy, directly combining the heat from both sources in a steam cycle. Here, focus is placed exclusively on ISCCs that use natural gas combustion turbines. These ISCCs are essentially modified natural gas combined cycles (NGCCs) where an extra heat transfer fluid (HTF) stream is integrated with the heat recovery steam generator (HRSG). Fig. 1 is an illustration of the major ISCC system components and mass transfer streams. Interest in ISCCs stems from the potential to ramp down the gas turbine during daylight hours, supplementing the power output using blended solar heat. Another benefit is the increased efficiency of the solar thermal system gained by operating at a lower and more narrow temperature range [2]. Such systems can inject the solar thermal heat into the steam generation system at a

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P.G. Brodrick et al. / Energy 141 (2017) 1569e1584

Fig. 1. High level overview of an ISCC. Electricity is produced from both the gas and steam turbines.

thermodynamically optimal location, reducing entropy generation and increasing the heat-to-electricity efficiency of the solar heat. ISCCs were conceptualized in 1993 [3], but were first explored in depth in the early 2000s [2,4]. In aggregate, findings suggest that higher solar field operating temperatures lead to higher efficiency, smaller solar fields (relative to the natural gas combustion turbine size) lead to higher exergy efficiency, and higher pressure solar steam extractions lead to higher system performance [5]. To date, only preliminary optimization work has been performed on ISCC systems, and detailed operating characteristics of these plants are not well explored. Careful operations optimization is a significant challenge because the properties of heat streams (temperature and flow rate) change significantly from hour to hour, potentially affecting the use of solar thermal energy in HRSGs with strict temperature constraints on different elements. Optimization work that has been presented has not been performed on a time-varying basis, but has focused instead on overall component efficiencies and steam pressures [6,7]. Several studies have, however, explored a variety of different system styles and configurations. In 2004, Dersch et al. investigated a single-pressure HRSG operated in several different locations and with different operating modes. Dersch et al. obtained a maximum annual solar contribution (ASC), the fraction of electricity from the ISCC attributed to the solar thermal system, of 5%, or up to 9% if thermal storage was included [4]. Under conditions in Barstow, California, Dersch et al. computed a levelized energy cost of just under 100 USD/MWh under 2002 economic conditions. Several later studies provided similar ~ o-Echeverri examined a fixed design results. Alqahtani and Patin and determined that only 3e15% ASCs are economically viable in ISCCs under a range of possible economic conditions [8]. Manente examined an existing NGCC in Italy and determined that the maximum ASC for an ISCC retrofit was about 5% [9]. In a separate study, Manente et al. examined a variety of new ISCC designs and identified a system with an ASC of 13% under static operating conditions [10]. While these studies have demonstrated the feasibility of ISCCs at a high level, practical ISCC design requires the time-dependent treatment of system operations. An ISCC must be able to function as an NGCC in hours without solar irradiation, and yet also maximize the utilization of solar energy during sunlit hours. The wide range of conditions that an ISCC must operate under is of critical importance. Indeed, without flexibility the ISCC concept loses substantial value. In this paper, a computationally efficient ISCC model that is

capable of evaluating ISCC operations under a wide variety of operating scenarios is presented and validated. Critically, this ISCC model takes into account many of the physical and practical operating constraints that a real plant would experience. These include, for example, ensuring the satisfaction of sufficient approach temperatures in the heat recovery steam generator, and maintaining minimum steam quality in turbines, at all time steps. This ISCC model is then used in combination with formal computational optimization to determine time-varying (constraint-satisfying) operational parameters, such as HTF mass flow rate (which impacts HTF inlet and outlet temperatures) and NGCC part loads, under four different operating strategies. Environmental and economic performance is assessed for each of the four strategies. Finally, the implications of this model are discussed, along with the potential for future integration into a design optimization framework. This paper is accompanied by online Supplementary Information (SI) that provides additional detail for the ISCC model. 2. Methods In this work an ISCC model is developed by extending an existing Hybrid Power Plant Optimization (HyPPO) platform. HyPPO is a modular codebase used to model both the design and operations of a variety of different types of power plants. The platform is written in Cþþ and is designed to execute quickly in order to facilitate the use of optimization techniques in continuous, integer, and categorical search spaces. HyPPO was initially developed by Kang et al. for the optimization of carbon capture power plants [11,12], and was expanded to explore solar auxiliary heat supply for carbon capture by Brodrick et al. [13]. This work draws heavily from these previous studies to adapt HyPPO to function for ISCC design and operations. This section proceeds as follows. First, an outline of each of the main physical components that comprise the ISCC is presented. The way in which the components are linked, and the resulting set of nonlinear algebraic equations, are then described. Finally, the series of feasibility constraints that limit converged solutions are discussed. For a more in-depth discussion of the methods outlined here, please see Brodrick [14]. 2.1. Physical components System components are illustrated in Fig. 1. Generally speaking, the system works as follows. A natural gas combustion turbine is operated at some load to directly generate electricity. The hot flue gas exiting the turbine is passed through an HRSG in order to heat water streams at multiple pressures. The flue gas is vented to the atmosphere at a much lower temperature, and water streams (now steam), are expanded through a series of steam turbines for electricity generation. Steam then flows through a condenser and is recycled. Independently, a second heat transfer fluid (HTF) is passed through a solar field where it absorbs energy from the sun and increases in temperature. The HTF is then passed through some subset of the heat exchangers in the HRSG, contributing to the generation of steam. One of the critical distinctions between the solar and gas sides of the system is that in the solar side the HTF is recycled back into the solar field, whereas in the gas side the HTF (flue gas) is vented to the atmosphere and any remaining exergy is lost. Consequently, energy not used in one pass of the solar HTF stream can be partially recovered. 2.1.1. Gas turbine The HyPPO ISCC natural gas combustion turbine model is based on higher heating value (HHV) efficiency, specific power,


flue gas exit temperature, and an empirically-based adjustment for partial load. The combustion turbine model used in this work is consistent with previous studies using HyPPO [11,13]. For this work, a turbine with an HHV efficiency of 36.7%, a specific power of 489 kJ/kg-exhaust, and a flue gas exit temperature of 648 C is used. The natural gas HHV is assumed to be 53,900 kJ/kg. Adjustment for part load behavior is based on results presented by Kim [15]. The flue gas heat capacity, which is used in the heat transfer equations inside of the heat exchanger module discussed in Section 2.1.4, is a linear function of absolute temperature T [K] [16]. The heat capacity (cp;fg ) is composition specific, and in this case the flue gas is assumed to be 3% CO2, 7% H2O, 75% N2, 15% O2. The heat capacity is given as

cp;fg ¼ c0p þ aT;

(1)

where c0p [J/(kg-K)] is a fitting constant, and a [J/(kg-K2)] is the slope of the fit. A c0p of 975 J/(kg-K), and an a of 0.225 J/(kg-K2), are used. In all operating conditions the flue gas composition remains constant because part load operation via simultaneous air and fuel flow modulation is assumed.

2.1.2. Steam turbine Steam turbine modeling is consistent with previous studies using HyPPO [11,13], with the additional inclusion of part-load effects. Each turbine is modeled as a series of multi-stage adiabatic expansions, as in Kim and Ro [17]. Each stage is treated as an isentropic expansion with a steam quality adjustment. In order to account for off-design loads, an adjustment is made using the methods described in Spencer et al. [18]. The method selected is based on empirical data for turbines greater than 16.5 MW operating at 3600 rpm, with a single governing stage and a condenser. In order to provide a more general form, Spencer et al. presented efficiency adjustments for a variety of turbine sections and conditions. Here, it is assumed that the system size and quality efficiencies have already been applied, and the Spencer et al. efficiency adjustments for the governing and main turbine sections are then used. The partial load efficiencies are applied after the full load net power output calculation. The unitless fractional throttle flow rate, FFR , which is the ratio of actual water mass flow rate (m_ w ) and design water mass flow rate m_ des w , is defined as

FFR ¼

m_ w m_ des w

:

(2)

The governing stage part load efficiency (Dhgov ) is then calculated as

Dhgov ¼ a00 þ a01 FFR þ a10 Dp þ a11 FFR Dp ;

(3)

where the a constants can be found in Table 1, and Dp is the pitch diameter of the governing stage (assumed to be 41.1 in. in this work). The general part load efficiency correction is described by

Table 1 Governing stage partial load efficiency coefficients [18]. Constant

Value

Units

a00 a01 a10 a11

21.8085 21.8085 0.573908 0.573908

[e] 1/ C 1/inches 1/ C -inches

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2 3 Dhgen ¼ b00 þ b01 FFR þ b02 FFR þ b03 FFR þ ln

2 3 ; þ b13 FFR b10 þ b11 FFR þ b12 FFR

PT PD

(4)

where the b constants can be found in Table 2, PT is the turbine throttle pressure, and PD is the design exhaust pressure. The partial load efficiency adjustments are designed to be applied sequentially to the overall system efficiency. Here, those sequential steps are combined into a single equation, coupled with N the full load net power output from all N stages E_ ST , for use in computing the total steam turbine work, E_ ST :

N 100 þ Dhgov þ Dhgen þ Dhgov Dhgen : E_ ST ¼ E_ ST 100

(5)

This efficiency penalty is in addition to other efficiency penalties due to condensation effects [11], as well as the power reduction due to the reduced flow rate of air and fuel.

2.1.3. Solar thermal field In this work, focus is placed on parabolic trough systems, presently the most common form of solar thermal power generation. A parabolic trough solar field is composed of a series of long rows of parabolic mirrors, which focus solar radiation onto a receiver tube through which a HTF flows. Each trough rotates to track the sun and maximize the incident direct normal irradiation (DNI). Trough rows are grouped into blocks, and blocks are repeated in parallel to scale up. Within each block, the flow rate of the HTF is adjustable in order to vary the outlet temperature of the HTF, as a function of the environmental conditions and inlet HTF temperature. The selection of the HTF is critical to system performance because of the limits the HTF may impose on operating temperature ranges. In this work, Therminol-VP1 is used as the HTF. Therminol-VP1 can operate over a relatively wide range of temperature in both the liquid and the vapor phase, while maintaining a low dynamic viscosity and high heat capacity throughout the operating temperature range [19]. Therminol-VP1 properties are summarized in Table 4. The specific heat is given by:

cp;HTF ¼ a0 T 4 þ a1 T 3 þ a2 T 2 þ a3 T þ a4 ;

(6)

where T [ C] is the temperature of the fluid, and the values a0 to a4 can be found in Table 3 [19]. Detailed simulation of a solar field is computationally expensive. When coupled with the rest of the ISCC components in the context of optimization, such computations become prohibitive. Consequently, a “proxy” model to recreate predicted solar output from the well-established System Advisor Model (SAM) [20] is generated. The parabolic trough model within SAM provides a solar field simulation using a wide variety of environmental, operating, Table 2 General partial load efficiency coefficients [18] (all values are unitless). Constant

Value

b00 b01 b02 b03 b10 b11 b12 b13

60.75 66.85 29.75 35.85 17.5 20.02 0.525 3.045

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P.G. Brodrick et al. / Energy 141 (2017) 1569e1584 Table 3 Therminol VP-1 specific heat capacity coefficients [19]. Constant

Value

Units 1011

a0

4:4172

a1

2:9879 108

a2

5:9591 106

a3

2:414 1.498

a4

103

J/(kg- C5) J/(kg- C4) J/(kg- C3) J/(kg- C2) J/(kg- C)

and design characteristics to determine the hourly performance of the solar field [21,22]. SAM models radiative heat loss, shading between troughs, thermal inertia of the equipment, location, temperature, and cloud cover, among many other effects. With the proxy model, the aim is to capture the effects modeled within SAM indirectly, treating SAM results as empirical data to be predicted with a much simpler and faster model. The proxy model relates system inlet and outlet HTF temperatures to the total mass flow rate of HTF. The proxy estimates this relationship at each hour of the year for a given location. The proxy model is created using data generated by executing 1315 SAM simulations at our template location (Dagget CA). Each SAM simulation is performed with different field inlet and outlet temperatures set, and SAM results for HTF flow rate are collected for all hours of the year. Thus 107 SAM data points are collected. Using these SAM results, a functional form is constructed with specific fitting coefficients for each hour. The following expression is then used to predict HTF flow rate using HTF hot and cold temperatures:

m_ HTF ¼

h c0 ðtÞ c1 ðtÞTHTF h c THTF THTF

;

(7)

h c where m_ HTF [kg/s] is the mass flow rate of the HTF, THTF and THTF [ C] are the HTF power block inlet (hot) and outlet (cold) temperature respectively, and c0 ðtÞ [kg/s- C] and c1 ðtÞ [kg/s- C2] are the two fitting coefficients. Both coefficients are fit for each hour of the year, t. In order to validate the proxy model, 10% of the SAM results were randomly withheld from the proxy model fit and were subsequently used to verify the proxy model performance. The proxy model was found to predict actual SAM simulations with a high degree of accuracy: the validation r2 value is 0.998, and a relative root mean squared error is 4.2%. Fig. 2 displays the model performance by plotting the HTF mass flow rates predicted by the proxy model against the SAM simulated HTF mass flow rates for the holdout set. The proxy model slightly underpredicts the SAM HTF mass flow rates in the 100e300 kg/s range and slightly overpredicts SAM HTF mass flow rates above 400 kg/s. However, overall error is small and within the margin of error of other model components. Because the holdout data span many simulations across each hour of the year, a density plot is used for visual clarity. The colour at each location in the plot indicates the number of points in that location. Details regarding individual SAM simulations as well as

Table 4 Therminol-VP1 properties [19]. Property

Minimuma

Maximuma

Units

Temperature Viscosity Heat Capacity Vapor Pressure

12 5.48 1.52 0.5

400 0.134 2.76 1470

[ C] [mPa s] [kJ/(kg-K)] [kPa (abs.)]

a Refers to location in operating range, with respect to temperature.

Fig. 2. Graphical representation comparing SAM simulation and proxy-model predicted HTF mass flow rate for 10% holdout data set. The plot is in density form, with colour saturation indicating the number of data points grouped in each pixel, for all temperatures and all hours of the year. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the process for generating the proxy model coefficients are provided in the Supplementary Information. The proxy model is approximately 106 times faster than SAM. SAM simulations take of order 10 s each, while the proxy model can be evaluated > 105 times per second. This appreciable speedup is due mainly to the fact that the proxy model condenses all SAM physics e including radiation, convection, shading etc. e into a simple function of hot and cold HTF temperatures. In addition to this high degree of speedup, the proxy model also predicts flow rate 1 h at a time, whereas SAM models a solar thermal plant at set design flow rates at a given location for the entire year. This alteration is vital for hour-by-hour operations optimization wherein hourly flow rates may need to be adjusted to respect heat exchanger constraints (see below). While the proxy model of course cannot predict SAM outputs exactly, the error seen in Fig. 2 is quite small and is acceptable for optimization problems where speed is paramount. The use of the proxy model is limited to conditions within the original training ranges explored in SAM.

2.1.4. Heat exchange elements The HRSG is made up of a series of heat exchanger elements which provide an interface between different HTF and water streams within both the NGCC and ISCC models. Heat exchanger elements in this work are modeled similarly to Kang et al. [11]. There are four different types of heat exchanger elements e economizers, evaporators, superheaters, and reheaters. Economizers raise the water temperature up to near the boiling point. Evaporators, which are modeled as if they also contain a steam drum, raise the water the last few degrees to enter the vapor dome, and then boil the water to the saturated vapor state. Superheaters raise the temperature of steam above the saturated condition, and reheaters act as superheaters that come after steam has already passed through a steam turbine. Heat exchange elements can be either solar or gas elements (i.e., use either solar or gas HTF), and the heat transfer equations differ accordingly. Each heat exchanger is modeled using the effectiveness-NTU method (‘number of transfer units’). Using the effectiveness-NTU


method, the heat transfer across the element as a function of the heat exchanger area (A) and the heat transfer coefficient (U) is calculated. Each heat exchange element is governed by five equations. Three equations are inter-element equations balancing water mass flow, water enthalpy, and flue gas temperature at element interfaces. The other two equations are internal to each heat exchanger element, and define the heat exchange between the HTF and water streams. With the assumption that shell losses are negligible, the energy balance can be written as

Q_ HTF ¼ Q_ w ;

(8)

where Q_ [W] is heat transfer rate and the subscripts HTF and w refer to heat transfer fluid and water respectively. The system heat transfer is limited by the heat exchanger properties via the effectiveness equation

εCmin DTmax ¼ Q_ HTF ¼ Q_ w ;

(9)

where ε is the effectiveness of the heat exchange, and Cmin [W/K] is the minimum of the two stream heat capacities. The components of Equations (8) and (9) are now considered in more detail. First, the heat transfer rate of the HTF can be calculated as

in out THTF Q_ HTF ¼ CHTF THTF

(10)

in out Q_ HTF ¼ cp;HTF ðT HTF Þðm_ HTF Þ THTF ; THTF

(11)

where cp;HTF ðT HTF Þ [J/(kg-K)] is the specific heat capacity of the in þ T out Þ. If HTF as a function of the mean temperature T HTF ¼ 12 ðTHTF HTF the element is a gas heat exchange element, then the specific heat capacity is calculated using Equation (1). If the element is a solar thermal heat exchange element, then the specific heat capacity is dependent on which HTF is used in the solar field. The heat transfer rate of the water stream is computed directly as

Q_ w ¼ m_ w how hiw ;

(12)

where how [J/kg] is the enthalpy of the outlet water stream and hiw [J/ kg] is the enthalpy of the inlet water stream. In order to solve Equation (9), the remaining left-hand side components ε and DTmax also need to be defined. The maximum temperature difference DTmax is the difference between the maximum hot stream temperature and the minimum cold stream temperature. If the heat exchanger is a gas heat exchanger, the effectiveness εgas is calculated with the assumption that while each heat exchanger element is overall counterflow, internal to the element there is single pass crossflow heat exchange, with the tube-side fluid (water) unmixed and the shell-side fluid (HTF) mixed. Under this assumption, heat exchanger effectiveness can be calculated as described in Kays and London [23] as

εgas ¼

1εp Cr npass 1εp 1ε C npass p

1εp

r

1 Cr

;

(13)

where Cr is the ratio of the minimum to the maximum heat capacity of the two streams. The number of pipe passes in the HRSG element, npass , is calculated based on the HTF-side heat exchanger area and a reference system heat exchanger geometry, as in Kang et al. [11]. The effectiveness of a single pass of counterflow exchange εp is given by

8 > < 1 expðð1 expðNTU Cr ÞÞCr Þ εp ¼ 1 > : ð1 Cr expð 1 þ expðNTU ÞÞÞ Cr

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if Cmax ¼ Cunmixed ; otherwise: (14)

In the event that the heat exchanger is an evaporator, Cr ¼ 0 because the heat capacity of the water stream is infinite during boiling, and consequently εp ¼ 1. In this case, instead of the normal water inter-element mass balance the outlet condition of the evaporator is required to be equal to dry saturated steam enthalpy, hsat;v , for the given pressure P:

hevap w;o ¼ hsat;v ðPÞ:

(15)

Solar heat exchangers are assumed to operate under direct counterflow heat exchange, as in Wagner and Gilman [22], which gives the solar heat exchanger effectiveness εsol as

εsol ¼

1 expð NTU ð1 Cr Þ Þ ; 1 Cr expð NTU ð1 Cr Þ Þ

(16)

based again on Kays and London [23]. Finally, the number of heat transfer units, NTU [unitless] is calculated as

NTU ¼

ðUAÞelem ; Cmin

(17)

where Aelem [m2] is the heat transfer fluid-side area of the heat exchanger, and Uelem [W/(K-m2)] is the element-specific heat transfer coefficient. 2.2. System design, solutions, and feasibility In this work an ISCC with a 250 MW gas turbine, a 48 ha solar thermal field, and a three-pressure HRSG is used. The system selected is illustrated in Fig. 3, with the low-pressure water streams drawn in blue, the intermediate-pressure streams drawn in green, and the high-pressure streams drawn in purple (referred to as LP, IP, and HP from here onwards). The UA values and pressures of the gas-side heat exchangers are shown in Table 5, and the solar thermal UA is 1901 kW-K. Without solar irradiation, and with the gas turbine at full load, this system produces 369 MW. As illustrated, the LP stream (3 bar) comes from the condenser and passes through a series of heat exchangers to raise the temperature using exhaust gas from the gas turbine. After an IP stream (15.7 bar) splits off from the LP stream, a portion of the IP stream is evaporated in a solar thermal heat exchanger, after which it is merged with the IP stream from the gas side. The HP stream (57.2 bar) is heated entirely with the exhaust gas from the gas turbine. Using the solar thermal energy to augment IP stream evaporation has been explored in prior literature (e.g., [10]) and is seen as a promising potential ISCC configuration. Future work will explore a variety of ISCC configurations. With the HRSG configuration established, the nonlinear system of algebraic equations to be solved for arbitrary operating conditions can be generated. These equations are defined by the mass and energy balances, along with the enthalpy and temperature continuity conditions described above. In total, five equations per heat exchanger are required, or 75 in total with this design. The equations are shown in their residual form, along with further description, in the SI. Additional information is also provided in Brodrick [14]. To solve the system of equations, a heuristic initial guess is first generated [14], and then a damped Newton method is used to solve the system. The damped Newton

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Fig. 3. ISCC heat exchanger configuration and water stream flow path. Water is extracted prior to the intermediate-pressure evaporator, evaporated in the solar heat exchangers, and then injected back into the HRSG prior to the intermediate-pressure superheater. On injection, the two intermediate-pressure streams (which have different mass flow rates) merge together before proceeding through additional gas heat exchangers.

method works by defining a search direction based on the Jacobian matrix, and then applying a damping coefficient if necessary in order to guarantee that the scaled residual vector continues to decrease. The Eigen linear algebra package [24] was used to implement the damped Newton method using an LU decomposition of the Jacobian matrix. A variety of constraints guide the model to physically sensible and realistic solutions. There are two general types of constraints: physical constraints and practical constraints. HyPPO is designed to relax many physical limitations in order to achieve converged solutions as often as possible. However, this causes many numerical solutions to arise with unphysical characteristics, such as a negative mass flow rate. This unphysical behavior is eliminated by imposing physical constraints. Physical constraints include maintaining a minimum solar thermal HTF temperature differential, bounding the solar thermal HTF minimum and maximum temperatures, avoiding pinch points in the heat recovery steam generator, and ensuring positive mass flow rates of water streams. On the other hand, practical constraints ensure realistic operating states and long-term equipment durability. Practical constraints include the enforcement of a minimum evaporator approach temperature, a minimum steam quality in steam turbine outlets, and a minimum flue gas exit temperature from the HRSG. Further details on all of the constraints are available in the SI. 2.3. Multi-temporal simulations In order to evaluate an ISCC design, it must be simulated across multiple operating and economic conditions that a real plant Table 5 Sizes and pressure levels of each gas-side heat exchanger of the ISCC. Index

Pressure [bar]

Element Type

UA [kW-K]

0 1 2 3 4 5 6 7 8 9 10 11 12 13

15.67 15.67 57.18 15.67 57.18 57.18 57.18 198.05 57.18 198.05 57.18 198.05 57.18 57.18

Economizer Economizer Evaporator Economizer Evaporator Evaporator Evaporator Superheater Evaporator Superheater Evaporator Superheater Evaporator Evaporator

1235.88 1132.94 152.82 595.72 36.20 403.19 1547.12 26.85 1887.57 317.95 1343.79 527.24 1963.96 317.96

would certainly face. Simulation convergence is not guaranteed for a particular set of conditions [14], so a sweep through operating decision variables is conducted in order to find as many converged solutions as possible. Three operating variables are evaluated on an hourly basis: part load of the gas turbine (upl ), solar focus rate (usf ), and mass flow rate of the solar HTF (um ). Gas turbine part load (upl ) controls the rate of energy entering the HRSG from the gas system. As discussed above, the part load utilization of the gas turbine entails an efficiency penalty, from which the fuel use is calculated. In this work, the gas turbine part load fraction is bounded between 0.6 and 1.0, which is the range achievable with simultaneous modulation of air and fuel flow rates. Some literature suggests that part load fractions could drop as low as 0.4 or 0.5 with different modes of gas turbine operations, however 0.6 was selected as a conservative lower bound for presently realistic operations [15,25]. Solar focus rate (usf ) provides a similar control on the rate of energy entering the HRSG from the solar side via the solar HTF. The solar focus rate is varied by slightly altering the concentration angle of a fraction of the parabolic troughs in the solar field, which prevents incident solar energy from entering the system in those trough sections. However, in contrast to the part load of the gas turbine, there is no efficiency penalty associated with defocussing the solar field. Because many rows of troughs run in parallel in a large system, it is assumed that these rows could be systematically defocused, and there is a sufficient number of them such that focus rate can be treated as effectively continuous. From an economic perspective, if the solar system is viewed in isolation, it is almost never desirable to defocus the solar field, as this wastes solar energy. However, if the full amount of energy available from the solar field cannot be used within the ISCC within a given time step, most likely due to thermal constraints, it is important to be able to defocus. By varying solar HTF mass flow rate (um ), dynamic systems operations are enabled under the full range of external conditions experienced by an ISCC. Specifying the mass flow rate of the solar HTF through the system has the effect of changing the solar field inlet and outlet temperatures, as these variables are coupled together in the complete system of equations for the ISCC (Equation (7)). By allowing HTF mass flow rate and temperature to vary throughout the day, the system flexibility is increased compared to maintaining a fixed HTF temperature. Allowing um to vary allows consistent and fast solution convergence. The bounds of um are determined using Equation (7) coupled with the minimum and maximum solar HTF temperatures, which gives


um;min ðtÞ ¼

c0 ðtÞ c1 ðtÞðTmax Þsol ðTmax Þsol ðTmin Þsol

;

(18)

and

um;max ðtÞ ¼

c0 ðtÞ c1 ðtÞððTmin Þsol þ ðDTmin Þsol Þ ðDTmin Þsol

;

(19)

where ðDTmin Þsol is the minimum feasible temperature difference between the inlet and outlet solar field temperatures (30 C in this work).

2.4. Operations evaluation procedure In order to optimize the ISCC operations, ISSC evaluations (solutions to the governing system of nonlinear equations) must be possible at various combinations of the three operating variables (upl , usf , and um ) at each time step. Given an arbitrary set of (upl , usf , um ), it is often difficult, however, to determine an initial guess for the governing nonlinear equations that leads to a converged solution within a reasonable number of Newton iterations. Therefore, rather than attempt to compute the ISCC state variables during the course of an optimization run, the solutions for a discretized set of operating variables are precomputed prior to any optimization of the operations. This is accomplished by systematically ‘pre-seeding’ the algorithm with converged inputs from a neighboring point, which leads to rapid and consistent convergence. The discretization used in this work is as follows: Let the set of gas turbine part load values be Spl , the set of solar focus rates be Ssf , and the set of solar HTF mass flow rates be Sm . For each upl 2Spl , the 2D plane determined by upl, Ssf , and Sm is evaluated, which will be referred to as the solar operations plane (illustrated in Fig. 4). Because the system of equations can be solved most rapidly and consistently when the solar focus rate is 0 (i.e., when the system operates as an NGCC with no influence from the solar field), it is first evaluated at the point in the solar operations plane where usf ¼ 0, and then evaluated at the rest of the points within Ssf in a given time step. By repeating this procedure at each solar

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focus rate, all (discretized) operating variable combinations within the given time step are evaluated. The search within a particular solar operations plane begins at the anchor point (usf ), where an evaluation is attempted using the heuristic initial guess (see SI). If successful, the algorithm proceeds through the points in the solar operations plane, using the closest point as a pre-seed (initial guess) at each step. If a particular solution fails, the step size between the pre-seed point and the failed point is reduced, and the evaluation is repeated (recursively until success). Complications arise because of the existence of combinations of operating variables that have no solution. Consequently, the number of step size reductions is limited to two, and if no solution is found the algorithm proceeds to the next point in the search space. In some cases a ‘backsweep’ procedure is employed: if during the search a solution is found to a particular point and a neighboring, previously attempted, point does not have a solution, that point is then re-evaluated using the new solution as the initial guess. Backsweeping helps to limit failed simulations to locations where there truly is no physical solution. See SI for more details. 2.5. Selection of representative days Ideally, all hours of the year would be simulated for each design. However, each additional time step evaluation induces an additional computational cost. Therefore, the year is modeled with a small number of representative days. A series of representative days, rather than a set of representative hours, is created in order to capture inter-hour effects within both the solar field and the electricity markets. Similar to previous work [13], k-means clustering [26] is applied in order to reduce the 365 days of the year into a more computationally tractable number. Each representative day is composed of a 72-element vector comprised of 24 hourly electricity prices (from 2010 in Southern California) and 48 solar thermal proxy-model coefficients (coefficients c0 and c1 for each of 24 h from Daggett, California). Before clustering, the dataset is normalized by centering each of the 72 elements on zero and scaling each element such that the magnitude of the standard deviation is one. Because the two proxy-model coefficients are coupled, the combined proxy-model coefficients are given the same weight as the electricity price in each hour. Clustering using the k-means algorithm is then applied using 200 starting points (generated both randomly and with the kþþ algorithm) to reduce sensitivity to the initial guess [27]. Using 10-fold cross validation, the decline in mean hourly percent deviation between representative days and the full year is determined as a function of the number of representative days (cluster number k). Results are shown in Fig. 5. At six representative days, the decrease in mean hourly normalized error has slowed. While adding additional days would reduce the error further, diminishing returns are evident and optimization computational effort increases greatly. Therefore, six representative days are used in this work. The selected six representative days are plotted along with the daily data in Fig. 6. Both low and high electricity prices are captured, as are low and high solar thermal proxy-model coefficients. The weights, displayed in the legend, indicate the relative contribution of each cluster. Weights are calculated by finding the fraction of days closest to each cluster centroid. 3. Operations optimization

Fig. 4. Illustration of the operations search space for a single hour. The anchor point (first point evaluated) is in red, and in black are all hours in a single solar operations plane. Each plane is evaluated independently. The range of um (solar HTF mass flow rate) values changes from hour to hour. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

In this section the optimization formulation is described, and a range of theoretical operating modes that represent different ISCC management goals are considered.

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max

upl ; um ; usf

E upl ; um ; usf ;

(20)

where produced electricity, E [MWh], is defined as

X E uhpl ; uhm ; uhsf wh E upl ; um ; usf ¼

(21)

h2H

The variable w is weight, h indicates the hour, and H is the set of all hours in the (six) representative days. Each operating decision variable vector in the electricity maximization function above is composed of jHj ¼ 144 components, which are confined to the discretized space of that variable, as

uhpl 2Spl ; uhm 2Sm ; uhsf 2Ssf ch2H:

Fig. 5. Deviation of actual data from representative days for increasing numbers of days.

Similarly, in the case of profit maximization, the objective function takes the form of

max

P upl ; um ; usf ;

3.1. Problem setup

upl ; um ; usf

Using the design shown in Fig. 3, and sizing information given in Section 2.2, the operations of the ISCC are optimized for a series of different objectives. In each optimization, HyPPO ISCC simulations for each hour of the six representative days are performed. In each hour, solar operations planes are constructed using 12 gas turbine partial loads ranging from 0.6 to 1.0, 30 solar HTF mass flow rates, and 10 solar defocus rates, for a total of 3600 solutions per hour. Computation time varies significantly in different hours, but on average the evaluation of all discretized states within 1 h with solar irradiation requires approximately 1.5 core hours to solve. In hours without solar irradiation, no solutions are generated for usf > 0, and solutions are obtained in seconds. Solving all hours, with and without irradiation, within the six representative days requires approximately 90 core hours (note that this computation load lends itself easily to parallelization). Four different objective functions are assessed to view different potential ISCC operating modes. These objective functions are:

where P [USD/year] is profit, defined as

1. 2. 3. 4.

Electricity maximization, Profit maximization, Constant electricity output, and Constant HTF outlet temperature.

In the first objective, electricity maximization, the objective function takes the form of

(22)

X P uhpl ; uhm ; uhsf wh ; P upl ; um ; usf ¼

(23)

(24)

h2H

and the operating decision variable vectors are discretized as in Equation (22). In both of these cases, the objective function is subject to

hop ðuÞ 0;

(25)

where hop is the full set of physical and practical operating constraints for all hours considered. With the selected design, this entails 33 constraints per hour, or 4752 over the six representative days. In the case of the constant-output objective, the goal is to maintain a baseload power supply, while displacing as much gas as possible. This is accomplished by constraining the electricity output in each hour to be within 2% of the maximum electricity output when no solar energy is available (upl ¼ 1; um ¼ 0; usf ¼ 0), referred to as constant-output constraints. After applying constant-output constraints, the solar electricity output is maximized, which is calculated indirectly as the difference between the total electricity and the electricity produced by the system without incident solar. This gives an objective function of

Fig. 6. Six representative days used in this work. Coloured lines show the representative days, and dashed gray lines show all days of the year. The legend in (b) indicates the fraction of the year represented by each day. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


max

upl ; um ; usf

4. Validation of HyPPO ISCC model

E upl ; um ; usf E upl ; 0; 0 ;

(26)

subject to the constant-output constraints

1 0 Eð1; 0; 0Þ E uhpl ; uhm ; uhsf A 0:02 @ Eð1; 0; 0Þ

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ch2H;

(27)

in addition to the operating constraints defined in Equation (25), and with the operating decision variable vectors bounded as in Equation (22). Finally, the constant HTF outlet temperature optimization is performed by selecting the HTF outlet temperature that maximizes the number of hours with feasible operating states. In this case the HTF outlet temperature at all time steps is constrained to fall within ±5 C of the target HTF outlet temperature. Each hour is simulated independently by assuming that interhour effects on the system are negligible. This allows us to simulate each hour on a separate processor core, and therefore leverage thousands of cores simultaneously across multiple operating conditions and hours. In concert with the fact that the decision variables within each hour are confined to a specified discretization, this enables the use of an exhaustive search over the discretized operations objective function space. The largest neglected inter-hour effect is the thermal gain or loss from the HTF in the solar field resulting from changing the HTF inlet and outlet temperature throughout the course of the day (Qneg ). By calculating Qneg for the optimal results from all three objectives, Qneg was found to be less than 1% of the solar energy output for the current hour, on average, with a maximum of 4.9%. This neglected effect has both positive and negative impacts on solar thermal output, depending on the time of day.

The NGCC portion of the HyPPO model has been previously verified against two different NGCC configurations in the literature [28,29] by Kang et al. [11]. However, the HyPPO ISCC model has yet to be verified against a model including solar integration. In this work the model is validated against cases in the literature from Manente et al. [10], for both a three-pressure NGCC as well as for a three-pressure ISCC configuration. 4.1. Three-pressure NGCC validation Manente et al. [10] developed a three pressure NGCC model using the software package ThermoFlex®. Several minor modeling differences exist between the HyPPO ISCC framework and what is described in Manente et al. [10]. First, the configurations between the two models differ slightly. In Manente et al., the intermediate and high-pressure water extractions were both from the same location in the low-pressure water stream. The HyPPO flow path was adjusted accordingly. Manente et al. included a deaerator element, which was modeled by adding a small amount of area to the first economizer. Additionally, they treated the HP reheaters as two successive heat exchange units, whereas here the successive units are grouped into a single reheater. Finally, the reheat strategy was adjusted to match that used by Manente et al. [10] (see Brodrick [14] for further detail). Several small adjustments to the physical components were also necessary. The gas turbine was altered to meet the specifications of the Siemens SGT5-4000F data used by Manente et al. [10] and water-side pressure drops were added to match their specified values. ThermoFlex® uses the log-mean temperature difference (LMTD) method for solving the heat transfer equations throughout the HRSG, while the HyPPO model uses the effectiveness-NTU

Fig. 7. Validation of model against NGCC (a) and ISCC (b) cases from Manente et al.

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method. Consequently, the ThermoFlex® UA values and water pressures determined by Manente et al. were used and then the resulting temperature and mass flow rate outputs from HyPPO were compared to [10]. Fig. 7(a) shows the percentage deviation for mass flows and temperatures, measured relative to corresponding values from Manente et al. [10]. The differences are very minor, with deviations of less than about 2% for each heat exchanger water inlet and outlet temperature, flue gas inlet and outlet temperature, flue gas flow rate, and water mass flow rate. While the heat exchange modeled by HyPPO matches the data from Manente et al. with a high degree of accuracy, there is a much larger deviation in the electricity production from the steam turbines. Using the specified isentropic efficiencies of 86.5%, 90.9%, and 93.3% for the high, intermediate, and low-pressure turbines respectively, electricity output is calculated. The deviation in electricity output between the two models is 6.9%, 13.7%, and 1.8% for the HP, IP, and LP steam turbines respectively. Overall, HyPPO finds a power output that is 3.9% greater than that in Manente et al. Therefore, the steam turbine model in Manente et al. likely contains some other modeling assumptions not reflected in HyPPO. 4.2. Three-pressure ISCC validation To verify the HyPPO ISSC model, the ISCC 1 configuration described in Manente et al. [10] was simulated. This ISCC

configuration has the same gas-side configuration as the NGCC model verified above, and the same adjustments were made to the HyPPO ISCC model as were applied for that comparison. On the solar side, this ISCC configuration extracts high-pressure steam after the last high-pressure economizer, and reinjects this steam prior to the first high-pressure superheater. Only the solar evaporator is used. Manente et al. provided the solar field nominal direct normal irradiation (857 W/m2), ambient air temperature (15 C), total field aperture (197,200 m2), and assorted parabolic trough properties [10]. With no location to account for latitudinal effects, or time of day to account for angle and shading offsets, the base case location (Daggett, California) was selected, and a specific set of SAM proxy-model coefficients were constructed according to the provided specifications. The set of proxy model coefficients was clustered into a single day (as described in Section 2.5), and noon was selected for nominal conditions. On the solar-side, the UA values were not available, nor were either the solar HTF inlet and outlet temperatures or the solar HTF mass flow rate data. However, because the solar thermal heat exchanger is exclusively an evaporator and there is virtually no water temperature change (and consequently an infinite effectiveness), by specifying a large UA value a close match was obtained. The level of agreement between gas-side elements is shown in Fig. 7(b), showing that flue gas inlet and outlet temperature, and

Fig. 8. Operations of an ISCC in electricity maximization mode for the six representative days. Shaded areas represent the range of feasible values, while lines indicate optimum values. In the electricity output (b), the gray shading represents electricity produced from the gas turbine.


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Fig. 9. Operations of an ISCC in profit maximization mode for the six representative days. Shaded areas represent the range of feasible values, while lines indicate optimum values. In the electricity output (b), the gray shading represents electricity produced from the gas turbine.

water mass flow rates in the gas heat exchangers match with less than a 5% deviation, except for the water mass flow rate through the evaporator and superheater. Here, the deviation reaches 18%, but this is an artifact of the extremely low water mass flow rate through these heat exchangers (3.0 kg/s in the evaporator as opposed to 123.9 kg/s in the economizer). The absolute deviation is on the same order as in the other heat exchangers (around 0.7 kg/s). The mass flow rate of water through the solar heat exchanger, 77.5 kg/s, also matches the corresponding value provided in Manente et al. to within 3.2%. Finally, while the individual turbine electrical outputs were not provided by Manente et al., the system total electrical output matches within 6.1%, at 197.1 MW. While some differences do exist, as noted, there is a sufficient level of agreement between the two independent models to consider the thermodynamic modeling in HyPPO to be validated. 5. Results and discussion Using the design and methods discussed in the previous sections, the ISCC is now optimized under four distinct operating modes: electricity maximization, profit maximization, constant electricity output and constant HTF outlet temperature. The HRSG configuration used in all cases is shown in Fig. 3, and the overall system is described in Section 2.2. To evaluate the system profit, a natural gas price of 5 USD/GJ (5.28 USD/mmBTU) and electricity prices from Southern California in 2010 (with a multiplier of 1.5) are

used. Results are based on weather data from Daggett, California (see Section 2.1.3 for details). A series of plots in Figs. 8e11 show the results from each optimization. Results are shown for each of the six representative days. In rows d, e, and f of these figures, the shaded areas show the feasible regions and the solid curves depict the optimized solution. Starting with results for electricity maximization mode in Fig. 8, row f depicts the solar field inlet (blue) and outlet (red) HTF temperatures, as determined in the ISCC solution. A lower mass flow rate corresponds to a higher temperature difference, and vice versa. Fig. 8(e) shows NGCC part load, while Fig. 8(d) displays the solar utilization. The NGCC part load is a direct decision variable, upl , while the solar utilization is a product of the solar focus rate decision variable usf and the environmentally-determined maximum solar thermal available heat. These bottom three plots show (directly or indirectly) all three of the decision variables used in the operations optimization. Fig. 8(c) displays the electricity price, which is an input parameter. Fig. 8(b) shows the total electricity produced by the ISCC (blue), as well as the amount of electricity produced directly from the gas turbine (gray). Finally, Fig. 8(a) shows the hourly profit, which is a function of the electricity price, electricity production, fuel use, and fuel price. The range of possible profits is shaded, while the optimum is drawn as a solid line. Fig. 8 demonstrates that the system always runs at full load even when this entails a loss in profit (recall that the objective function here is electricity

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Fig. 10. Operations of an ISCC in constant-output mode for the six representative days. Shaded areas represent the range of feasible values, while lines indicate optimum values. In the electricity output (b), the gray shading represents electricity produced from the gas turbine.

maximization). However, solar utilization (row d) is not always maximized. This is because at full load of the gas turbine, maximum solar utilization is infeasible, and the amount of electricity gained by running the gas turbine at full load exceeds the amount that would be produced by taking full advantage of the solar resource at a reduced gas turbine part load. In profit maximization mode, shown in Fig. 9, the operations are considerably more variable. Generally speaking, the gas turbine part load responds to the electricity price, while maintaining a high level of solar thermal utilization. Morning hours in days 2, 3, 5, and 6 result in full turndown of the gas turbine (Fig. 9(b)). The gas turbine part load is bound between 0.6 and 1. If the gas turbine was allowed to turn off completely it is likely it would do so during these hours, though that is less practical for an operating plant due to the thermal stresses and costs incurred from frequent shutdown and startup. As a consequence, the profit is maximized with a low gas turbine partial load (Fig. 9(e)), and consequent reduced electricity output (Fig. 9(c)). In constant-output mode, shown in Fig. 10, the gas turbine is turned down during hours of maximum solar availability in order to keep the electricity production of the system constant. Fig. 10(a) shows that during these periods of reduced gas turbine part load, the profit is still maximized (or very close to maximized), indicating that the efficiency of the solar integration is quite high. Notably, the system is able to maintain an electricity output that is quite level throughout the entire day while still utilizing the available solar

resource. Constant HTF outlet temperature mode is a more traditional way of operating a solar thermal field. Results for this mode of operation are presented in Fig. 11. As shown, the system is able to take advantage of the solar resource while maintaining a near constant HTF outlet temperature (f). However, the range of feasible conditions for the HTF inlet is reduced compared with the other optimization modes (Figs. 8e10). Additionally, the gas turbine is forced to ramp down during several hours in order to maintain this HTF outlet temperature, resulting in a less smooth electricity output. In order to compare the different operating modes presented in Figs. 8e11, several high-level characteristics are summarized in Table 6. Many of the values are fairly consistent, which is due in large part to the relatively small contribution of the solar thermal system to the overall electricity output. Profit is generally the most variable, being highest when optimized for, and lowest in the constant-temperature mode. Notably, the CO2 intensity is fairly consistent in all operating modes except for the profit maximization mode, likely due to the high degree of gas turbine ramping that occurs in profit maximization, and the corresponding part-load efficiency penalties that are incurred. All CO2 intensities are lower than a HyPPO NGCC, which has a CO2 intensity of approximately 350 kg/MWh. The solar conversion efficiency, defined as the conversion efficiency of the solar thermal HTF to electricity, is also fairly consistent across all designs. These values compare favorably


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Fig. 11. Operations of an ISCC in constant-temperature mode for the six representative days. Shaded areas represent the range of feasible values, while lines indicate optimum values. In the electricity output (b), the gray shading represents electricity produced from the gas turbine.

Table 6 Summary characteristics from the operating modes presented in Figs. 8e11. Operating Mode

Annual Solar Contribution

CO2 Intensity [kg/MWh]

Mean Annual Electricity [MWh/h]

Profit [106 USD/year]

Solar Conversion Efficiency

Maximum Electricity Maximum Profit Constant Output Constant Temperature

3.11% 3.69% 3.94% 3.12%

332.27 336.11 332.21 332.27

381.06 350.31 368.20 378.13

14.39 15.75 12.61 9.49

34.81% 35.27% 36.62% 35.17%

to a stand-alone solar thermal facility described in Kelly et al. [2], which has a solar conversion efficiency of 32%. The ASC values in Table 6 are quite modest e in the range of 3e4%. These values are markedly lower than some ASCs reported in the literature (e.g., the 13% ASC for static operating conditions reported in Manente et al. [10]). The low ASC values obtained here are largely due to the use of a robust design that is capable of feasibly operating under a realistic range of operating conditions. Results from this analysis indicate that many systems that are feasible when only a nominal input solar irradiation is considered violate various thermodynamic constraints within the HRSG at off-design conditions. These findings provide motivation to identify alternate ISCC configurations that are feasible under a range of realistic operating conditions, and yet have higher ASC values. Subsequent work will use the modeling capability described here to optimize design variables along with operational variables and will show that, through application of this procedure, ASC values approaching

20% can be achieved. A key aspect that is not captured in Table 6 is the relative lack of flexibility of the constant-temperature operating mode compared with the other operating modes. Fixing the HTF outlet temperature reduces a degree of freedom of the system, and precludes the full range of possible gas turbine part load and solar focus rate combinations that would otherwise be possible. This is demonstrated here for 2 h (hour 12 of days 2 and 4, or the hours with highest and lowest solar availability at noon) in Fig. 12. In Fig. 12, the increase in feasible operating conditions (shown in green) when the HTF outlet temperature is allowed to fluctuate (top) compared to when it is held constant at the HTF temperature that provides the maximum number of feasible conditions across all hours is evident. The reduced feasibility of the constant-temperature operating mode is further explored by examining the number of feasible states for all hours where the solar resource is available. Fig. 13 demonstrates that when the output temperature remains flexible,

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Fig. 12. Feasibility of ISCC operations during maximum and minimum noon solar availability. The top two panels show the feasibility of a flexible system, while the bottom two panels show the feasibility of a system operating with a constant output heat transfer fluid temperature.

6. Concluding remarks

Fig. 13. The number of feasible operating states at each of the hours in the six representative days with solar availability. The hours are ranked by the number of feasible operating conditions in the style of a price duration curve.

the number of feasible operating conditions is significantly higher than when the output temperature is held constant. This flexibility has the potential to be quite valuable in electricity markets where the power plant is called on to respond to demand. More flexible systems can not only meet a wider range of requirements, they are more likely to be able to do so in an economically superior manner.

In this work a computationally efficient model for analyzing and optimizing the time-dependent operations of an integrated solar combined cycle (ISCC) was presented. The model entails mass and energy balances of all HRSG components, along with representations of gas and steam turbines and the solar thermal parabolic trough system. An extensive set of hour-by-hour physical and practical constraints is included in the model. The operations of the solar thermal field are represented via a proxy model constructed from detailed (and time consuming) simulations of the System Advisor Model (SAM). The overall ISCC model was incorporated into the existing Hybrid Power Plant Optimization (HyPPO) framework. The ISCC model presented here was verified against an independent model presented in the literature, showing strong agreement between the two. This model was then used to optimize the operations of the ISCC with multiple different objectives: maximum overall electricity output, maximum profit, constant electricity output, and constant HTF outlet temperature. These optimizations were based on evaluations over (six) representative days, determined though a clustering procedure. While the CO2 intensity of each of the systems was relatively consistent (between 332 and 336 kg/MWh), the profit from the system varied considerably more (9.49e15.75 million USD/year). The ISCC flexibility was demonstrated to increase considerably through use of a variable HTF outlet temperature. This required treating the mass flow rate of the HTF through the solar thermal system as an operating variable


to be optimized. A large number of gas turbine and solar focus rate operating states that were not feasible when the system was operated with a constant HTF outlet temperature (even an optimized constant HTF outlet temperature) became available with the flexible HTF mass flow rate. A critical aspect of the treatment presented here is that at each time step a full simulation of each combination of operating variables was run, allowing for the assessment of a range of realistic operating constraints. Without this treatment, it would not be possible to tell if an ISCC that is able to operate at, say, 11 a.m. on a partially cloudy day would also be able to operate at 2 p.m. on a sunny day. Furthermore, this method ensures that the ISCC will operate at a range of gas turbine part loads in the absence of solar irradiation. Careful examination of the validity of an ISCC includes the assessment of a full range of operating conditions. Future work will examine integrating these considerations into the optimization of ISCC design, and it will be demonstrated that considerably higher ASC values can be achieved by jointly optimizing the design and operations of the ISCC.

E E_

steam turbine total work [W]

FFR H h h hop m_ HTF m_ w

steam turbine full load net power output after N stages [W] fractional throttle flow rate set of all hours in the representative days enthalpy [J/kg] hour operating constraint vector heat transfer fluid mass flow rate [kg/s] water mass flow rate [kg/s]

ST N E_ ST

m_ des w npass NTU P PD PT Q_ Qneg

Acknowledgements Sm The authors thank Dr. Giovanni Manente for providing additional details regarding the heat exchanger design in Manente et al. [10] used here in the verification of the HyPPO ISCC model. The first author thanks the William H. Bourne Fellowship Fund for financial support. The Stanford Center for Computational Earth and Environmental Science provided the computational resources necessary for this work.

Spl Ssf T c THTF h THTF

Nomenclature

U um

Abbreviations ASC annual solar contribution HHV higher heating value HP high pressure (water stream) HRSG heat recovery steam generator HTF heat transfer fluid HyPPO Hybrid Power Plant Optimization IP intermediate pressure (water stream) ISCC integrated solar combined cycle LP low pressure (water stream) NGCC natural gas combined cycle SAM System Advisor Model

upl usf w

Variables

a

flue gas heat capacity fitting slope [J/kg-K2] heat transfer area [m2] proxy model coefficient [kg/s- C] proxy model coefficient [kg/s- C2] minimum heat capacity [W/K] flue gas heat capacity fitting coefficient [J/kg-K] flue gas heat capacity [J/kg-K] heat transfer fluid heat capacity [J/kg- C] minimum to maximum heat capacity ratio Dhgen steam turbine general part load efficiency Dhgov steam turbine governing stage part load efficiency Dp governing stage pitch diameter [inches] ðDTmin Þsol minimum feasible temperature difference between solar field inlet and outlet temperatures [ C] ε heat exchanger effectiveness

A c0 ðtÞ c1 ðtÞ Cmin c0p cp;fg cp;HTF Cr

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produced electricity [MWh]

design water mass flow rate [kg/s] number of pipe passes in a heat exchange element number of heat transfer units yearly profit [USD/year] steam turbine design exhaust pressure [Pa] steam turbine throttle pressure [Pa] heat transfer rate [W] largest inter-hour thermal gain or loss in the solar field throughout the day set of possible mass flow rates of the solar heat transfer fluid set of possible part loads of the gas turbine set of possible solar focus rates temperature [K or C] heat transfer fluid power block outlet (cold) temperature [ C] heat transfer fluid power block inlet (hot) temperature [ C] heat transfer coefficient [W/K-m2] mass flow rate of the solar heat transfer fluid (decision variable) [kg/s] part load of the gas turbine (decision variable) solar focus rate (decision variable) weight of modeled hour

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