Optimal design and operations of a flexible oxyfuel natural gas plant

Accepted Manuscript Optimal design and operations of a flexible oxyfuel natural gas plant Holger Teichgraeber, Philip G. Brodrick, Adam R. Brandt PII:

S0360-5442(17)31606-7

DOI:

10.1016/j.energy.2017.09.087

Reference:

EGY 11581

To appear in:

Energy

Received Date: 29 June 2017 Revised Date:

18 September 2017

Accepted Date: 18 September 2017

Please cite this article as: Teichgraeber H, Brodrick PG, Brandt AR, Optimal design and operations of a flexible oxyfuel natural gas plant, Energy (2017), doi: 10.1016/j.energy.2017.09.087. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Optimal design and operations of a flexible oxyfuel natural gas plant Holger Teichgraebera,∗, Philip G Brodricka , Adam R Brandta Department of Energy Resources Engineering, Stanford University, Green Earth Sciences Building 065, 367 Panama St., Stanford, California, USA

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Abstract

We co-optimize the design and operations of a flexible semi-closed oxygen-combustion com-

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bined cycle (SCOC-CC) carbon capture plant under time-varying electricity prices. The system consists of a cryogenic air separation unit, liquid oxygen storage, a gas turbine, a heat-recovery steam generator, and a steam turbine. The gas turbine is modeled allowing part-load operation. Computational optimization is used to maximize net present value (NPV) in order to examine the potential benefits achievable through upfront investments in increased flexibility (i.e., allowing price arbitrage between times of low and high price).

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Case studies of Germany and California are examined. Flexible SCOC-CC systems are not profitable in either region under current electricity prices. With electricity prices ≈2 times current prices, we find systems with positive NPVs. Oxygen storage is used in days with

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extreme price variability. Optimal designs favor constant operation, without over- or undersizing system components and without additional oxygen storage. Sensitivity analyses show that external factors such as mean electricity price (± 200%), natural gas price (± 150%),

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and nominal discount rate (± 50%) have the strongest effect on NPV. Electricity price variability, which is thought to increase with increased penetration of renewables, does not strongly impact system design and profitability. Keywords: Nonlinear Optimization, Semi-closed oxygen-combustion combined cycle, Thermodynamic and cost modeling, Carbon capture, Gas turbine, Air separation unit

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Corresponding author. Tel: +1-650-725-0851 Email addresses: [email protected] (Holger Teichgraeber ), [email protected] (Philip G Brodrick), [email protected] (Adam R Brandt) Preprint submitted to Energy

September 18, 2017

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1. Introduction A low CO2 emission future will require electric grids with high fractions of renewable power. However, such electric grids are challenged by variable resources such as wind power.

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Solving the problems of variable, non-dispatchable power will likely require a suite of complementary solutions including responsive demand, electricity storage, and flexible generation that can be ramped to fill gaps. Different solutions will be required over different time scales, as supply gaps can be minutes to days long. Given the high costs of electricity storage, flex-

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ible generation may become an important part of future electric grids, and a low-carbon option for dispatchable power will be required. One choice is power generation from natural gas with carbon capture and storage (CCS)[1].

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Today, natural-gas-fired power plants are most commonly used to provide flexibility to power systems to support already-existing renewable energy, provide peak loads, or prevent disruption of the power supply. Many studies find that natural-gas-fired power plants, with and without CCS, will likely play an important role in managing variability and intermittency [2, 3].

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Three main types of CO2 capture exist: post-combustion capture, pre-combustion capture, and oxyfuel capture [4]. Oxyfuel cycles differ in two ways from conventional power cycles. First, fuel is combusted using pure O2 instead of air. This results in a flue gas with

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high concentrations of water and CO2 due to the lack of diluting N2 . Condensing moisture in the flue gas leads to an output stream of CO2 which can be stored or recirculated. Second,

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because of the high combustion temperatures of oxyfuel combustion alone, a recirculation fluid is used to moderate combustion. While CCS-enabled power plants to date have used amine-based post-combustion CO2 scrubbing, significant technical progress has been made on oxyfuel-combustion technology. Some have argued that oxyfuel-combustion technologies 25

are at similar levels of technological maturity as post-combustion scrubbing [5]. In oxyfuel-combustion, the recirculation fluid acts similar to N2 in a conventional gas turbine (GT). Depending on the specific oxyfuel cycle, the recirculation fluid consists of varying concentrations of CO2 , H2 O, Ar and N2 , with either CO2 or H2 O being the main 2

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component [6]. Depending on the dominant component, the corresponding cycles are called 30

CO2 -based and water-based, respectively. Stanger et al. [5] provide a detailed comparison of the leading oxyfuel GT cycles, which are the semi-closed oxygen-combustion combined cycle

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(SCOC-CC), the Allam cycle, the Clean Energy Systems cycle, and the GRAZ cycle. The SCOC-CC, first proposed by Bolland and Saether [7], is CO2 -based, and is most similar in design to the conventional combined cycle systems [8]. Franco et al. [9] found that SCOC-CC 35

systems are the most technically and economically promising oxyfuel systems.

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In this work, we evaluate the SCOC-CC for use in flexible power generation. We use computational optimization to jointly optimize system design and hourly operations. Our

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optimization objectives are economic rather than thermodynamic. We consider the design and operation of the complete system, including O2 production in the air separation unit, 40

power generation in the oxyfuel GT and the ST, and CO2 compression to pipeline pressure. We include liquid O2 storage to take advantage of intra-day electricity price changes. By jointly optimizing design and operations, we explore whether there are benefits in either over or undersizing some system components in order to increase operational flexibility.

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Several thermodynamic studies of the SCOC-CC have been conducted [8, 10, 11, 12]. All of these studies explore system design, but none of them address variable operation. Since oxyfuel carbon capture cycles produce lower purity CO2 streams than post-combustion

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capture, Posch and Haider [13] investigated optimal purification technologies for flue gas from coal and natural-gas-based oxyfuel cycles with the constraint of reaching at least 95% CO2 purity. Li et al. [14] considered an oxyfuel-based technology for peak shaving, and explored the production and storage of liquid N2 and O2 at times of low electricity prices. The

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authors used optimization to find thermodynamic system parameters but did not consider the optimization of system economics to value their peak shaving technology under variable electricity prices.

Several studies have investigated O2 supply specifically for oxyfuel processes [15, 16, 17, 55

18, 19, 20, 21]. Potential differences compared to conventional ASUs are the large amount of O2 needed, the relatively low O2 purity requirements (≈95%), possible heat integration opportunities, and ASU flexibility. To our knowledge, O2 storage has not yet been explored 3

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in the context of oxyfuel combustion. However, cryogenic energy storage (CES), in many ways similar to the O2 storage considered in oxyfuel ASU applications, has been recently 60

introduced and tested on a pilot scale demonstration plant by Morgan et al. [22, 23].

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Zhang et al. [24] optimized operations of an ASU and CES on an hour-to-hour basis over one week as an industrial scale demand response facility. Zhang et al. formulated a mixed-integer linear programming model and conducted a real-world case study based on industrial data, with the goal of meeting weekly gaseous demand of N2 and O2 , and liquid demand of N2 , O2 and Ar. The case study was conducted in the PJM electricity market with

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a plant utilization of around 60%. The optimal operation of the ASU leads to load shifting

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from high price to low price periods. Furthermore, the plant is shut down during the middle of the week. Zhang et al. added CES with 70% efficiency and observed shorter shutdown for the air separation unit, more load shifting, and power sales from the CES in times of high 70

electricity prices. The model was extended to account for uncertainty in electricity price and for the ASU to work as operating reserve with load reduction capacity [25, 26]. The Zhang et al. studies provide important insights into optimization of an ASU sys-

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tem. However, there are several differences between that work and possible optimization conducted on SCOC-CC systems that include the ASU. Zhang et al. had demand both for 75

liquid and gaseous products, whereas in the oxyfuel case, demand is only gaseous O2 . This

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leads to higher storage costs in the oxyfuel case because in this case, liquid O2 is not needed except for storage purpose, and if it is used for this purpose, liquid must be converted back to gaseous O2 . Furthermore, the O2 demand of the ASU for the oxyfuel system is determined

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by the operation of the GT. Since the GT yields increasing profit if operated at times of high electricity prices, the constraints on the ASU to operate within or close to these hours is stronger than in the case of industrial gas demand, which is not correlated with electricity prices. Thus, the value of storage for load shifting may be higher in the oxyfuel case. Carbon-capture-enabled NGCCs have been the subject of optimization studies with respect to system design [27, 28, 29, 30]. None of these studies included flexible power plant 85

operation due to variable electricity prices. Similarly, Kvamsdal et al. [31] optimized two NGCC reference cases for post-combustion capture. Kvamsdal et al. optimized integrated 4

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systems design and emphasize that the process modifications they suggest add complexity to the system, which makes the system more flexible but may result in more challenging operations. In studies of flexible capture, Cohen et al. [32] optimized a coal-fired post-combustion

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capture system for varying electricity prices, while Kang et al. [33] developed a detailed operational optimization model for a CCS unit powered with a GT or a wind park. Later Kang et al. added design optimization, included a detailed heat recovery steam generator (HRSG)

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model, and used a statistical proxy-model of the capture unit to reduce computational load [34, 35, 36]. These studies found that increased operating profits due to increased efficiency

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and flexibility come with higher capital costs. Joint design and operational optimization for net present value (NPV) was used in order to help make informed decisions regarding the trade-off between these two. The model was further expanded by Brodrick et al. [37] to include a solar thermal system, which necessitated the use of joint design and tempo100

rally explicit operations optimization. Brodrick et al. found trade-offs between operational flexibility and capital costs similarly to Kang et al.

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To the best of our knowledge, no study of joint design and operational optimization of NG oxyfuel systems has been performed. Key treatments considered in this work include: (1) we model an oxyfuel GT allowing part-load operation, (2) we include O2 storage to allow arbitrage across intra-day price differences, (3) we perform operational optimization

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of the SCOC-CC considering time-varying electricity prices, and (4) we perform joint design and operational optimization including economic objectives. This paper proceeds as follows:

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First, we describe the thermodynamic and economic modeling of the ASU and the SCOCCC. Then, the optimization formulation and search strategy are presented. In the results 110

section, two case studies situated in California and Germany are presented and sensitivities explored, key aspects of which are elaborated on in the concluding remarks. 2. Energy system model Our system model is built in a modular fashion and a system overview is shown in Fig. 1. System units include the air separation unit (ASU) and O2 storage tank, the oxyfuel 5

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GT (GT), and the heat recovery steam generator (HRSG) and ST (ST). Subsystems are connected by energy and mass flows modeled by a set of coupled algebraic equations. The different modules are implemented in C++, with exception for the gas turbine model,

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which is built in Matlab R2014a and included in the C++ model using lookup tables. The ASU produces O2 at 95%. The O2 is either gaseous (henceforth GOX), to be directly 120

used in the GT, or liquid (henceforth LOX), to be stored. The GT is modeled at full load and part load. Its exhaust gas stream flows through the HRSG, which transfers GT exhaust

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enthalpy to a steam stream which is then expanded in the ST. HRSG exhaust is cooled and recirculated to the GT, with a small fraction of the CO2 separated and stored.

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We design a power plant with 400 MW gross power output. Our base-case scenario is located in California, USA, while we examine a second implementation in Germany. These locations represent areas at the forefront of large-scale renewable power integration. 2.1. Air separation unit and O2 storage

Cryogenic air separation is the most widely established O2 production technology [38],

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and is the only currently practical process for oxyfuel systems because of the need for large quantities of O2 [1]. We model an ASU with a liquid O2 backup system, which consists of a liquid O2 storage tank and an evaporator.

We model the ASU using data provided by The Linde Group with a system similar to

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the one presented by Goloubev and Alekseev [20]. The data are summarized in Table 1 [39]. The coupled dual-column cryogenic air separation unit operates at two pressure levels, 5.7 bar and 1.3 bar. We assume an ambient cooling water temperature of 16◦ C and ambient air

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of 26◦ C and 1.0 bar. O2 produced by the ASU is 95% pure and is at 1.0 bar pressure, with the remaining 5% composed of N2 , Ar, and CO2 . The O2 stream can be produced either as GOX or LOX. We model an integrated liquefaction system, whereby LOX is extracted before it is used to cool incoming air. The specific 140

power consumption for GOX production has been reported in several studies, and falls in the range of 0.2 to 0.32 kWh nm−3 [18, 38, 40, 41, 42, 43]. In our study, the specific power demand is assumed to be 0.23 kWh nm−3 for production of GOX and 0.8 kWh nm−3 for pro6

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duction of LOX, with norm conditions given at 1.013 bar and 0 ◦ C. Clearly, LOX production and subsequent storage is energetically costly. We use a two compressor system with a load 145

range of 35% to 100%. Ramping rates reported in literature vary, but representative values

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are 2% min−1 for conventional systems, with up to 8% min−1 measured in small plants [39]. We assume that the ASU ramp rate can approach the upper limit, meaning that the system can ram up or down completely within the 1 hour discretization steps used in this work. In each hour, the operating conditions of the ASU and the GT determine if the LOX storage tank is charged, discharged, or unchanged. We assume that LOX can be used directly

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from storage at a sufficient rate so as to avoid additional operating constraints. The LOX

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vaporization enthalpy demand is not coupled to any other cold demand, which presents another opportunity for system integration in future studies. Due to imperfect insulation, some stored LOX becomes GOX in each time step and is vented. Reported losses are about 155

0.05% d−1 [22], and we assume a conservative 0.1% d−1 storage loss. 2.2. Oxyfuel GT

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To develop a robust oxyfuel GT model, we validate the GT full and part load model and adjust this validated model for oxyfuel combustion. The oxyfuel GT modeling workflow is as follows: (1) a conventional GT model is developed for full-load conditions, (2) the GT 160

model is modified to simulate part-load operation, (3) the GT model is modified for oxyfuel

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conditions. We use Matlab R2014a and the software toolkit Cantera [44] for thermodynamic modeling. The oxyfuel GT module is presolved and included in the overall C++ code using

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lookup tables. This is significantly faster than calling Cantera at every thermodynamic evaluation, and introduces only slight interpolation errors (≤ 0.5%). 165

2.2.1. GT full-load model

The GT consists of three parts: compressor, combustor and turbine. The compressor operates at pressure ratio PR. The compression is calculated using the polytropic efficiency ηp,comp (the ratio of actual work conducted to reversible work required between two states).

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It can also be seen as a differential version of the isentropic efficiency, written as ηp,comp =

δws , δw

(1)

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where δw is the work required over a differential step of the compression process and δws is the isentropic (adiabatic and reversible) work required over the same differential step. The polytropic efficiency is used because it has the advantage of staying almost constant over a wide range of PRs, unlike the isentropic efficiency, which changes over a range of PRs. After compression, the compressed air is mixed with fuel. The mixture then combusts, during

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which we assume a pressure loss of 5%. The combustion flue gas is then expanded through

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a turbine, modeled using polytropic efficiency in the same manner as the compressor. With the combination of the known state before the turbine and applying the polytropic efficiency for expansion to outlet pressure pturb,out = pamb , the outlet state is fully defined. 175

2.2.2. Full-load model validation

To validate our model we collected commercial specifications from 18 modern GTs for

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rep the following variables: power output (PGT ), efficiency (η rep ), PR (P Rrep ), mass flow rate rep (m ˙ rep turb,out ), and exhaust temperature (Tturb,out ) [45]. The data are listed in the supplementary

information. A 4% loss factor is applied to the heat rate for shell loss and other real-world 180

non-idealities. The state of the incoming air (ambient conditions) is fully defined. The fuel

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mass flow can be calculated from the data using the lower heating value of the fuel, the overall efficiency, and the rated power. The air inflow can be calculated from a mass balance

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of total mass outflow and inflow. The high pressure level is known through the PR. By assigning ηp,comp and ηp,turb , we arrive at a fully defined state which allows us to 185

calculate power output. We iteratively change the chosen ηp,comp and ηp,turb until we match rep reported commercial power output. As the reported exhaust temperature Tturb,out has not

been used in the modeling process, we compare our calculated Tturb,out to the reported value. Fig. 2a compares computed to reported Tturb,out . Relative errors are all ≤ 4%, and the mean absolute deviation is 10.1 K, indicating that our model predicts turbine operations 190

satisfactorily. 8

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2.3. Part-load model Several studies describe the modeling of part-load GT performance with different levels of detail [46, 47, 48, 49]. GT part-load performance test results have been reported by

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Jansen et al. [50]. Two part-load operational strategies are possible [49]: constant airflow with fuel flow modulation, and simultaneous airflow and fuel flow modulation. We use simultaneous airflow and fuel flow modulation as this enforces stoichiometric combustion, which is important for the oxyfuel turbine operation. Non-stoichiometric combustion would

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leave residual O2 in the injection stream, which is highly detrimental to subsurface storage systems, resulting in wellbore corrosion. We therefore allow part-load operation of 60%

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of the full-load mass flow rate, at which point we assume guide and stator vane closure is reached. To adjust the full-load model for part-load operation, we assume choked flow conditions at the turbine inlet [48, 51], which results in a constant reduced mass flow rate given as m ˙ red

p m ˙ turb,in Tturb,in = = const. pturb,in

(2)

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where m ˙ red is the reduced mass flow rate, m ˙ turb,in is the mass flow at turbine inlet, and Tturb,in and pturb,in are temperature and pressure at turbine inlet. The choked flow assumption is often used in literature. Nevertheless, it does not fully 195

reflect system behavior, and compressor maps are used for improved accuracy [49]. To

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address these additional effects we assume linear decreases in compressor and turbine polytropic efficiency, with 3% losses at 60% part load. This allows us to match reported values in

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efficiency while keeping turbine parameters within reasonable bounds. The PR is a variable at part-load conditions and is lower than it is at full-load operation. 200

We compare our model to results by Jansen et al. [50] by simulating the Siemens V64.3 GT. Fig. 2b compares model results of the relative efficiency at part-load conditions (with a reference efficiency of 35.8% at full power output) to measured data. We see consistently good agreement between our modeled results and these experimental data, with all deviations being less than 0.92% and mean absolute deviation of 0.44%.

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2.3.1. Oxyfuel GT model The oxyfuel GT model uses the above GT model with changes to fluid properties to account for oxyfuel cycles. We choose the Siemens SGT6-8000H as the base turbine to be

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modified [45]. We assume that the same amount of fuel is used but that, instead of air, an O2 -rich stream enters the compressor, and that additionally the recirculation fluid is added 210

as an input stream to the compressor. The recirculation fluid is extracted from the condenser downstream of the HRSG. A cooling water stream brings flue gas to low temperature and

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condenses H2 O, after which the flue gas stream is split into sequestered and recirculated streams. Recirculation fluid composition is adapted from Yang et al. [8]: 88.5% CO2 , 2%

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H2 O, 3% N2 , 6.5% Ar.

In order to implement this adaption of the Siemens SGT6-8000H GT, the condensation and thus recirculation fluid temperature, recycle mass ratio (RMR), and PR need to be assigned. We use a condenser exit temperature (and consequently a recirculation fluid compressor inlet temperature) of 18◦ C [8]. The PR in an oxyfuel GT is higher than in a conventional GT due to the changed working fluid properties of high CO2 mass-fraction blends. The isentropic coefficient is lower when CO2 replaces N2 , leading to the need for

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a higher PR to achieve the same efficiency. Mletzko and Kather [12] and Dahlquist and Denrup [52] explore this effect and show that feasible high PR compressor designs under

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these conditions exist.

We model a wide range of pressure ratios. Besides the fact that the polytropic efficiency accounts for changes in the isentropic efficiency with changing pressure ratio, we add a

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correction to the polytropic turbine efficiency similar to Yang et al. [8] based on the Smith chart [53]. We calculate the blade loading coefficient ψ as a function of the pressure ratio: ψ=

wst ∆hst = , 2 U U2

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where wst is the work per stage, ∆hst is the enthalpy change in the fluid per stage, and U is 225

the blade tip velocity [54]. We assume four turbine stages and correct the turbine efficiency based on a linear relationship of turbine efficiency to blade loading coefficient. Fig. 3 shows our modeling results with respect to varying PR and RMR. In the optimiza10

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tion model, the PR is a design decision variable and the RMR is an implicit variable that depends on the PR in order to match the temperature-constrained material limit (turbine 230

inlet temperature of the original GT without oxyfuel) at the turbine inlet.

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Varying the PR has significant influence on efficiency, and also influences temperature, as shown in Fig. 3a and 3c. The GT efficiency increases with increasing PR, with main gains in efficiency below a PR of 40, as is also reported by Stanger et al. [5]. Increasing the PR leads to higher efficiency and higher turbine inlet temperatures. In order to keep the turbine inlet temperature below material limits, the RMR needs to be increased for higher

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PRs. Stanger et al. report a commonly used range of PR 30-40 [5] based on thermodynamic

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studies.

Varying the RMR has significant influence on temperature, and very minor influence on efficiency, as shown in Fig. 3b and Fig. 3d. The GT efficiency decreases with increasing RMR 240

due to a higher ratio of compression work to turbine work. Thus, a RMR as small as possible is desirable. The turbine inlet temperature, however, decreases with increasing RMR while still being significantly above the turbine inlet temperature of the original turbine. For a

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PR of 40 and 1586 K as the upper limit for the turbine inlet temperature, we find a RMR of 9.01:1. The LHV efficiency at this point is 38.8%, which is lower than the 41.2% LHV 245

efficiency of the original turbine. The remaining energy is in the exhaust gas, which is at

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higher exhaust temperature. The RMR of 9.01:1 (90.0 % of the combustor inlet stream is recirculation fluid) matches well the RMRs of ≈ 90% of Stanger et al. [5]. Part-load operation of the oxyfuel GT is modeled by reducing the recycle stream mass

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flow rate through variable guide vanes (minimum load = 60%), similarly to what happens in the part-load operation of the conventional GT. We make similar assumptions regarding the conventional GT part-load behavior: choked flow at the turbine inlet and thus constant reduced mass flow rate additionally to the full load oxyfuel GT model, as well as 3% loss in polytropic compressor and turbine efficiencies linearly decreasing from 100% load to 60% load.

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2.4. Heat recovery steam generator and ST In this work, the HRSG and ST models are based on the model developed by Kang et al. and Brodrick et al. [34, 35, 37]. Kang et al. [35] perform detailed modeling and

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optimization of HRSG design and time-dependent operation. Heat transfer within each HRSG element is modeled using the effectiveness-number of transfer units method for heat 260

exchanger analysis. Brodrick et al. [37] added a “pre-optimization” procedure in order to reduce computational time enough to make design optimization of the overall system feasible

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within the limits of current computing resources. The part load performance of the ST is modeled based on relationships developed by Cannon et al. [55] as described in [56, 57]. We

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and Giannini [58]. 2.5. CO2 purification and compression

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choose a three-pressure HRSG design based on the optimized parameters found by Franco

The CO2 -rich stream that exits the condenser after the GT and HRSG is partly reused as recirculation fluid and partly sequestered. Sequestration is assumed to occur underground

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and is outside the bounds of this study. In order to store CO2 underground, the stream has to meet several requirements regarding the concentration of H2 O, O2 , Ar, N2 , SOx and NOx [59, 60, 61]. Designing purification and compression units for oxyfuel power plants has been discussed in many studies recently [13, 15, 59, 62]. We assume purification is done through

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separation that is integrated in the CO2 compression process. We use the work requirement reported by Pipitone and Bolland [59], which is 453 kJ kg−1 CO2 . This includes purification and compression to 110 bar.

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2.6. Cost calculations

The capital cost calculations of the GT, HRSG and ST are based on Kang et al. [35] and Brodrick et al. [37]. The cost data is obtained from Ulrich and Vasudevan [63]. Gas turbine and condenser costs scale exponentially [63], while the HRSG costs scale linearly [64]. We make one modification to model GT capital cost, implementing a GT capital cost estimate that is a function of the GT PR, which is a decision variable in the optimization 12

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algorithm. We use tabulated data from 91 modern commercial GTs, including capital cost, PR, and turbine size [45]. Multivariate linear regression is used to obtain a relationship between capital cost and PR as  P α GT Coxy,BM,0 (γ + β P R) , PGT,0

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Coxy,BM =

(4)

where the first part is the bare module cost of the gas turbine based on the power law with PGT and PGT,0 as the gas turbine size and reference size, α = 0.77394, and a bare module

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cost basis of Coxy,BM,0 at P R = 20 and PGT = 200 MW. We assume no economies of scale above 250 MW gas turbine capacity. γ=0.939608 and β=0.00302 are the linear regression

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coefficients to include the PR. This shows that the capital cost increases with increasing PR, which is due to increased design complexity. With PRs in the range of 20-80, the orders of magnitude of γ and β show that the GT size has a higher impact on capital cost than the PR. We obtain p-values ≤ 10−7 for capital cost and PR, suggesting that both features are 285

statistically significant. Operations and maintenance cost data for the GT, HRSG, and ST are also based on Kang et al. [35] and Brodrick et al. [37].

relating cost is

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The ASU and storage capital costs are modeled based on reported data. The equation

CASU,BM

P αˆ ASU = CASU,BM,0 , PASU,0

(5)

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where PASU is the power input to the ASU at maximum capacity. We assume CASU,BM,0 is 1500 $/kW at a capacity PASU,0 of 250 MW.

Annual ASU operations and maintenance

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costs are 3% of the plant’s capital expenditures. 2.7. Statistically representative days Available computing resources do not allow combined design and operations optimization with a full set of 365 days of input data, even given access to large-scale computing clusters. We therefore use k-means clustering following the methodology introduced by Brodrick et al. [37] to find representative days of electricity prices . Such an approach was also used by 295

Bahl et al. [65] for k-means clustering, and Nahmmacher et al. [66] for hierarchical clustering. We z-normalize the data before clustering. Fig. 4 shows the NPV for different numbers of 13

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representative days, illustrating that large changes are observed up to cluster size k=5, but that five days are sufficient to capture the properties of the objective function. We therefore choose to use five representative days. Fig. 5 shows these days and their respective weights for Northern California and Germany. We can observe that extreme days carry low weight

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due to their limited number of occurrences. California has two days with peak prices, and Germany has a number of days that include some hours of negative prices.

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3. Optimization problem formulation

In our model, decision variables are categorized as design variables and operational variables. Design variables specify component characteristics as designed when the plant is

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built (e.g., gas turbine size and PR), while operational variables specify the hourly usage of the components (e.g., hourly mass and energy flows). Design variables affect capital costs, while operational variables affect operating profit. NPV is computed from capital costs and operating profit streams and used as the optimization function. Design variables (x) and operational variables (u) are jointly optimized. We maximize

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NPV in a nonlinear programming problem: max

x∈X,u∈U

NPV(x, u) (6)

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s.t.

hdes (x) ≤ 0, hop (x, u) ≤ 0

where X and U define the range of values that the design variables x and operational

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variables u can take. hdes and hop are the design and operational constraint violations. The NPV includes both capital requirements C(x) (design of the system) and yearly operating profit P (x, u) (operations of the system) over an investment time of Nyears =25. Nyears

NPV = −C(x) +

X P (x, u) . τ (1 + r) τ =1

(7)

Since the NPV can be segmented into two parts (design and operational), the problem in equation 6 is reformulated and solved in two levels similar to the approach described by 14

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Brodrick et al. [37]: max max NPV(x, u) x∈X u∈U

Nyears

= max − C(x) + max x∈X

u∈U

|

315

s.t. hop (x,u)≤0

{z

s.t. hdes (x)≤0, hop (x,u)≤0

(8)

}

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|

X P (x, u)
 (1 + r)τ τ =1 {z }

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The outer level is the design optimization, and the inner level is the operational optimization. A candidate design is chosen by the design optimization algorithm. Optimal operations

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for this particular candidate design are then determined subject to operational constraints. Given these operations, design constraints are evaluated, and the objective function and constraint violations returned to the design optimization algorithm. The design optimiza320

tion algorithm then chooses another candidate design, and this process continues until the design space is explored. Each candidate design is evaluated by the operational optimiza-

parallel. 3.1. Design optimization

The design variables x and their bounds are shown in Table 3. The design problem

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tion algorithm independently, which allows for multiple candidate designs to be assessed in

is nonlinear and is solved using the Mixed Integer Distributed Ant Colony Optimization

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(MIDACO) solver [67]. This algorithm is based on an extended Ant Colony Optimization algorithm that samples iterates from multi-kernel Gaussian probability density functions. Constraints are handled by the oracle penalty method [68]. MIDACO carries the important 330

property, for this problem, of being derivative free. Convergence to the global optimum in general nonlinear optimization cannot be formally proved, but MIDACO performs well on benchmark problems [69] and tends in our case to repeatedly converge to similar optimal designs given different starting values.

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3.2. Operational optimization The operational optimization algorithm chooses optimal hourly operations for a given

Nop operational variables: ˆop , Nop = 24 × k × N

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ˆop =4 types of operational variables exist for each hour. We thus have a total of design. N

(9)

where k is the number of representative days. The operational variables u and their bounds are shown in Table 2. Both GT and ASU can either be turned off, or operate in a range

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between 60%-100% and 35%-100%, respectively. Up to 20% of the oxygen can be produced

for a given candidate design:

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in liquid form. The optimal operational variables are found by maximizing operating profit

max P(x, u) = max (R(x, u) − E(x, u)), u∈U

335

u∈U

(10)

where R is the revenue of the power plant and E are the expenses for one year. We selected SNOPT as the operational optimization algorithm [70]. SNOPT is a se-

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quential quadratic programming algorithm that is well suited for smooth nonlinear objective functions and constraints. It makes successive quadratic estimates of the Lagrangian function. In this work the gradient is constructed using numerical finite differences. The 340

Hessian is then calculated with a quasi-Newton method. The operations problem is non-

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convex; hence, only local solutions can be found. Thus, different random initial points are used within the bounds of the operational variables, and the best solution in terms of the

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objective function value that satisfies all constraints is chosen. Each SNOPT operational optimization run is seeded with 300 initial points chosen from the operations space. 345

3.3. Constraints

The overall gross power output of the entire oxyfuel plant, meaning GT and ST power output, is constrained to 400 MW to prevent the design optimization algorithm from choosing an infinitely large gas turbine at positive NPV. HRSG constraints ensure that the HRSG design is physically valid [35]. These constraints include number and ordering of HRSG com350

ponents and pressure levels, pressure drop in HRSG, steam quality minimums, pinch tem16

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peratures, approach temperatures, and overall temperature bounds. Details on the HRSG constraints can be found in Brodrick [56].

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4. Results The optimization results strongly depend on the mean electricity price, natural gas price, 355

and the discount rate. These external parameters depend on the economic environment that the power plant operates in, which the power plant has relatively little impact on. We first

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present two base case scenarios, which are later expanded with sensitivity analyses.

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4.1. Base case

The base case uses data from Northern California for 2015. Using California 2015 elec360

tricity prices directly, the system never achieves positive NPV. We therefore multiply each hour’s price by 2.0, which leads to positive NPV in base case assumptions. This results in mean electricity price µ of 60.8 $ MWh−1 . The natural gas price is 4 $ GJ−1 . An additional base case study is conducted with data from Germany for 2015. In this case, each hour’s

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price is multiplied by 2.2, which leads to a mean electricity price µ of 69.6 EUR MWh−1 . The natural gas price is 6.8 EUR GJ−1 . The nominal discount rate in both cases is 8%. The exchange rate for the year 2015 is: 1 EUR = 1.10973 USD.

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Table 3 shows the optimal values of the decision variables for both the Northern California and Germany cases. The optimal design is the same for both the Northern California and Germany case. The optimal design indicates that capital expenditures for enhanced flexibility do not pay off in the base case. The ASU is sized exactly to provide O2 for

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370

full-load operation of the GT. Furthermore, the O2 storage tank is sized at the minimum constraint of 200 m3 . Note that if the minimum constraint was reduced to 0 m3 , the optimal result would likely not include any storage. The overall capacity constraint of 400 MW is binding with a GT size of 260.2 MW and a ST size of 139.8 MW. Determining the optimal 375

GT PR is a function of both thermodynamic and economic factors and leads to PR = 40.2 in the base case. A more detailed analysis of the PR is given below. The optimal design results in a NPV of 226.4 million USD for the Northern California case, and in a NPV of 17

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72.7 million EUR for the Germany case. A cost breakdown is provided in Table 4. Note that the systems share the same optimal base case design, with the same cost, but in different 380

currencies. We observe that the ratio of operating cost to revenue is higher in the Germany

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case, which reduces operating profit and thus results in a lower NPV in the Germany case. The operating cost are higher in Germany because of higher natural gas prices.

The operating profile of the GT and ASU for the California case are shown in Fig. 6 for the five representative days. We observe that the GT and ASU are operated at full load for the majority of hours. Note that the shown net power output at full load is 337 MW

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385

which includes 37 MW power consumption of the ASU and 26 MW power consumption of

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the CO2 compression unit and leads to a gross power output of 400 MW. In a few low price situations, the GT and ASU are turned off simultaneously. One representative day has high evening prices. At low prices in the morning, the ASU runs at full load, but produces some 390

of its O2 in liquid form for storage, while the GT is turned down to part load. The stored O2 is used at the high price hour in order to turn the ASU down to part load, reducing parasitic power and thus increasing net power output. These high variability events occur

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only rarely during the year in our base case and have small weights associated with them. Thus, the increased operating profit by storing O2 is outweighed by the capital expenditure 395

of building larger O2 storage tanks.

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The operating profile shown in Fig. 7 for the German case study shows a similar behavior, with more time where the GT and ASU are completely turned off. The GT and ASU are either at full load or turned off, with only one day where storage is used. During this

400

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day, the storage tank is charged at negative electricity prices in the beginning of the day and discharged later at positive electricity prices. However, negative prices do not occur frequently enough to make a larger O2 storage tank economic in the base case. 4.2. Sensitivity analysis

The results of the base case are strongly influenced by assumptions made for the parameters. Fig. 8 shows the effect on NPV for Northern California when changing parameter 405

values individually. The results are obtained by running a full design and operations op18

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timization for each of the sensitivity cases while keeping the other parameters constant at the base case value. External parameters such as mean electricity price, natural gas price and nominal discount rate have a strong impact on NPV. At a low mean electricity price

410

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or a high natural gas price, the NPV becomes negative. In this case, the design variables that size the system all take on the value of the minimum constraint. Because capital expenditures exceed operating profit in this case, this minimizes overall losses in profit. A high mean electricity price or a low natural gas price leads to no change in design variables,

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but to higher profits due to higher margins during operations. This is similar for the other sensitivity studies if not noted otherwise. Increasing or decreasing ASU capital cost has only a minor effect on NPV. In the base case, gaseous O2 is vented when the ASU produces

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415

more gaseous O2 than the GT uses. Two of the sensitivity cases assume that we can sell O2 , while the base case corresponds to selling the gaseous O2 at price 0 $ t−1 . O2 prices can vary significantly based on location and O2 availability [71]. Here, we assume two cases with prices of 20 $ t−1 and 50 $ t−1 . While the lower O2 price only leads to minimal increase 420

in NPV, the higher price case leads to significant increases in NPV. In this case, the ASU

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is oversized to its maximum constraint value. This indicates that there is a price threshold above which the design and thus the operational profile is adjusted, and additional revenue can be generated at low electricity prices by selling gaseous O2 . However, it is not clear

425

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what industries would be willing to take gaseous O2 in flexible manner. Additionally, we carried out a sensitivity study reducing the energetic penalty on LOX production by successively examining the cost of LOX production from 0.8 kWh nm−3 to

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0.23 kWh nm−3 , the cost of GOX production. In both cases, California and Germany, this does slightly impact operations, but does not impact system design, because in order to take advantage of price spreads, the ASU would have to be oversized and produce excess 430

oxygen in times of low prices. The capital costs of oversizing the ASU turn out to not pay off operationally, even with small LOX energy penalties. Fig. 9 shows the results of the sensitivity analysis for the German case study with sensitivities carried out in similar proportions. We generally see similar results to the California case. The NPV for the case with a low natural gas price increases strongly. This is because 19

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435

the natural gas price for the base case in Germany is high, and while the overall plant is turned off for parts of several days in the base case (see Fig. 7), lowering the natural gas price allows the plant to operate and generate additional revenue in these hours. Since the base

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case NPV in the Germany case is lower than in the California case, small changes in nominal discount rate (in this case from 8% to 10%) can make the overall system unprofitable. 440

The original set of representative days of the electricity price has mean µ and and standard deviation σ. We perform sensitivity analysis on these two parameters. To change the

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mean independently from the standard deviation, each hourly price pt is increased by µ such ˆ = µ + µ while that the new price is pˆt = pt + µ and the new mean of the electricity price is µ

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the standard deviation σ stays constant.

To change the standard deviation independently from the mean such that the new standard deviation is σ ˆ = σ σ, the price pt is modified by a factor σ, N 1 X pˆt = µ + σ(pt − µ) − σ(pi − µ), N i=1

where the second term is a correction for the bias in the deviation from the mean in order to keep the original mean.

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445

(11)

Both methods, which change either mean or standard deviation of the electricity price independently from each other, are combined and lead to Fig. 10 for California. Each point

450

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in Fig. 10 corresponds to a full optimization run with the adjusted electricity prices. We observe that increasing the mean electricity price impacts the NPV more than increasing the standard deviation of the electricity price. Especially when the NPV is positive, the

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standard deviation does not have a large impact on NPV. The base case shows that the optimization algorithm does not choose to build storage in order to increase flexibility and gain money during operations through arbitrage. Even increasing the standard deviation 455

significantly (and thus possible profit through arbitrage) does not lead to increased storage size due to its capital cost. Thus, even if electricity prices were to become significantly more volatile in the future, building O2 storage to take advantage of arbitrage opportunities is not profitable. However, a price on carbon that would increase mean electricity prices would have positive impacts on the profitability of the SCOC-CC. The impact of increasing mean 20

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460

and standard deviation for the German case study have a qualitatively similar effect on NPV like the one shown in Fig. 10, but are not shown. We further studied the sensitivity to GT PR by running several cases and in each con-

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straining the optimization run to the specific PR. We observe the maximum NPV at a PR of 40.2, the base case. While the net efficiency increases with increasing PR over the range of 465

PRs considered, the maximum in NPV at a lower PR is due to the minimum approach temperature constraint of the HRSG. This constraint ensures that the fluid in the economizer

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does not reach the boiling point. At low PRs, the GT efficiency increases with increasing PR and the turbine outlet temperature decreases and thus the enthalpy of the exhaust

470

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stream decreases. Thus, the optimization algorithm tries to choose smaller heat exchanger area sizes (lower cost). At some point (P R = 40.2), the economizer area size cannot be decreased because the minimum approach temperature is reached. At PRs higher than this point, the economizer’s area size has to be increased (higher cost), explaining the maximum in NPV.

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5. Concluding remarks

In this work, we developed a thermodynamic and cost model and optimized design and operations of a semi-closed oxygen-combustion combined cycle power plant including the air

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separation unit. The objective was to maximize NPV with respect to design and operating constraints. The problem was formulated as a two-level optimization problem, with an outer level (design optimization) and an inner level (operational optimization). Sensitivity analysis was carried out on several economic parameters in order to obtain design knowledge

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480

based on different scenarios. Our analysis shows that including liquid O2 storage for the purpose of load shifting is not economical based on current price spreads in electricity prices in the day-ahead market, and that this holds even for much higher price volatility. Please note that O2 storage 485

may be useful to support fast ramp-up of the ASU. Modern GTs have fast ramp rates, and O2 storage could support fast ramp-up of the ASU in order to provide fast SCOC-CC ramp-up capability. However, this requires sub-hourly time discretization and is beyond 21

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the scope of this work. Overall, external factors such as mean electricity price, natural gas price, and discount rate influence the overall system design and profitability significantly 490

more than thermodynamic factors. This indicates that the design of appropriate policies

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to support zero-emissions technologies is important to the adoption of oxyfuel natural gas plants. Policies that penalize carbon dioxide emissions such as a price on carbon or that reduce the cost of capital could make oxyfuel natural gas plants profitable in future electricity markets.

There are multiple opportunities to extend this work. While we consider time steps on

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495

the order one hour, increasing time resolution could lead to interesting insights concerning

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markets other than the day-ahead market. Sub-hourly time discretization could also lead to interesting insights concerning O2 storage to support fast SCOC-CC ramp-up capability. Another topic of interest when doing integrated design and operations could be thermody500

namic integration of the ASU and the combined cycle. Here, one could analyze the trade-off between efficiency gains through integration and the flexibility constraints imposed by such

the SCOC-CC. 6. Acknowledgements

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integration. Lastly, this analysis could be done considering another oxyfuel cycle besides

This work was supported by the Wells Family Stanford Graduate Fellowship for HT. The

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Stanford Center for Computational Earth and Environmental Science (CEES) provided the

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computational resources used in this work. Nomenclature

510

α

component scaling factor

β

linear regression coefficient

δw

work (differential step)

δws

isentropic work (differential step) 22

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m ˙ red reduced mass flow rate m ˙ turb,in GT turbine inlet mass flow rate m ˙ rep turb,out reported GT exhaust mass flow rate η rep

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515

reported GT efficiency

ηp,comp polytropic GT compressor efficiency

hdes

constraint violations of the design optimization

hop

constraint violations of the operations optimization

µ

mean electricity price

σ

electricity price standard deviation

nm3

cubic meter at norm conditions

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linear regression coefficient

CASU,BM ASU bare module cost

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525

γ

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520

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ηp,turb polytropic GT turbine efficiency

CASU,BM reference ASU bare module cost

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Coxy,BM,0 reference bare module cost oxyfuel GT Coxy,BM bare module cost oxyfuel GT

530

pt

hourly electricity price

pamb

ambient pressure

PASU,0 reference ASU maximum power input PASU ASU maximum power input 23

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PGT,0 reference GT power rep PGT

pturb,in GT turbine inlet pressure

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535

reported GT power

pturb,out GT exhaust pressure P Rrep reported GT pressure ratio

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Tturb,in GT turbine inlet temperature

540

rep Tturb,out reported GT exhaust temperature

u

operational decision variables

x

design decision variables

C

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ASU air separation unit capital cost

CCS CO2 capture and storage

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Tturb,out GT exhaust temperature

CES cryogenic energy storage yearly expenses

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E

GOX gaseous oxygen GT 550

gas turbine

HRSG heat recovery steam generator k

number of representative days

LHV lower heating value 24

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LOX liquid oxygen NGCC natural gas combined cycle

560

yearly profit

PR

GT pressure ratio

R

yearly revenue

r

real discount rate

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P

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NPV net present value

RMR oxyfuel GT recycle mass ratio

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555

SCOC-CC semi-closed oxygen-combustion combined cycle ST

steam turbine

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Symposium. Banlf, Alberta, Calgary: Brimstone Engineering Services, Inc.; 2002,.

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System overview. The air separation unit (including O2 storage), the oxyfuel GT, and the HRSG and ST are modeled as independent components linked together with mass and energy flows. . . . . . . . . . . . . . . . . . . . . . . GT model validation for (a) full-load turbine exhaust temperature verification using 18 different GTs, and (b) part-load relative efficiency verification, using GT V64.3 parameters [50]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oxyfuel GT modeling results at full load. (a & b): efficiency changes with (a) parameter PR at fixed RMR and (b) parameter RMR at fixed PR. (c & d): inlet and outlet temperature changes with (c) parameter PR at fixed RMR and (d) parameter RMR at fixed PR. Dashed lines are temperatures of original GT without oxyfuel for reference. . . . . . . . . . . . . . . . . . . . NPV for different number of clusters. . . . . . . . . . . . . . . . . . . . . . . California and Germany electricity prices from 2015 clustered into 5 representative days. Cluster centroids for California (a) and Germany (c), and each day labeled with its respective cluster color for California (b) and Germany (d). The percentages in the legend show the fraction of the year that each day represents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal operations of the SCOC-CC in the base case for five representative days in California. The GT and ASU operate at full load for the majority of hours, and load shifting occurs only rarely. . . . . . . . . . . . . . . . . . . . Optimal operations of the SCOC-CC in the base case for five representative days in Germany. The GT and ASU operate at full load for the majority of hours, or are turned off. LOX production for storage purposes occurs in the case of negative electricity prices. . . . . . . . . . . . . . . . . . . . . . . . . California: Effect of changing parameters individually. The results are obtained by running a full design and operations optimization for each of the sensitivity cases while keeping the other parameters constant at the base case value. The dotted line in the middle indicates the base case. . . . . . . . . . Germany: Effect of changing parameters individually. The results are obtained by running a full design and operations optimization for each of the sensitivity cases while keeping the other parameters constant at the base case value. The dotted line in the middle indicates the base case. . . . . . . . . . Influence of increasing the mean electricity price µ on NPV for different scenarios of standard deviation σ for the California case. . . . . . . . . . . . . .

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HRSG and Steam Turbine

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Air Separation Unit

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Figure 1: System overview. The air separation unit (including O2 storage), the oxyfuel GT, and the HRSG and ST are modeled as independent components linked together with mass and energy flows.

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Figure 2: GT model validation for (a) full-load turbine exhaust temperature verification using 18 different GTs, and (b) part-load relative efficiency verification, using GT V64.3 parameters [50].

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Figure 3: Oxyfuel GT modeling results at full load. (a & b): efficiency changes with (a) parameter PR at fixed RMR and (b) parameter RMR at fixed PR. (c & d): inlet and outlet temperature changes with (c) parameter PR at fixed RMR and (d) parameter RMR at fixed PR. Dashed lines are temperatures of original GT without oxyfuel for reference.

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Figure 5: California and Germany electricity prices from 2015 clustered into 5 representative days. Cluster centroids for California (a) and Germany (c), and each day labeled with its respective cluster color for California (b) and Germany (d). The percentages in the legend show the fraction of the year that each day represents.

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Figure 6: Optimal operations of the SCOC-CC in the base case for five representative days in California. The GT and ASU operate at full load for the majority of hours, and load shifting occurs only rarely.

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Figure 7: Optimal operations of the SCOC-CC in the base case for five representative days in Germany. The GT and ASU operate at full load for the majority of hours, or are turned off. LOX production for storage purposes occurs in the case of negative electricity prices.

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Figure 8: California: Effect of changing parameters individually. The results are obtained by running a full design and operations optimization for each of the sensitivity cases while keeping the other parameters constant at the base case value. The dotted line in the middle indicates the base case.

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Figure 9: Germany: Effect of changing parameters individually. The results are obtained by running a full design and operations optimization for each of the sensitivity cases while keeping the other parameters constant at the base case value. The dotted line in the middle indicates the base case.

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List of Tables

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Operational data for the ASU [39] . . . . . . . . . . . . . . . . . . . . . . . . Operational decision variable types and bounds. . . . . . . . . . . . . . . . . Base case results: optimal design decision variables and their constraints . . Base case results for both California and Germany cases: revenue, cost, and profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Table 1: Operational data for the ASU [39]

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Table 2: Operational decision variable types and bounds.

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Table 3: Base case results: optimal design decision variables and their constraints

Design variable

Unit

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GT MW HRSG nondim. area size Relative ASU size O2 storage size m3 GT PR -

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Table 4: Base case results for both California and Germany cases: revenue, cost, and profit

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Highlights

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Thermodynamic and cost modeling of an oxyfuel natural gas plant Computational optimization of combined design and operations Operations reduction through clustering to representative days Constant operation designs are found to be favorable Oxygen storage is only used in days with extreme price variability

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