# Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Reactor and Plant Assumptions

- better fuel utilization, lower waste production, and the capability to operate at higher temperatures with fast neutron spectrum operation;
- ability to operate coolant at atmospheric pressure with more compact infrastructure; and
- inherent safety mechanics due to high thermal inertia from thermal capacity and larger coolant mass, as well as retention of radioactive isotopes by lead in case of severe accident.

_{2}, confirming that the configuration is viable. It is also possible to configure a supercritical Rankine cycle in this manner, and analysis of this is ongoing at the University of Wisconsin–Madison. Indirect charging of the TES in this manner will naturally incur a ‘round trip’ efficiency penalty, which will somewhat penalize the desirability of the TES. However, the efficiency of the cycle at the design point is unaffected by the presence of the TES as the heat is transferred directly from the lead to the working fluid.

#### 2.2. Market Pricing and Economic Structure

`IRONMTN_2_N001`) node taken from 1 January to 31 December of 2019. The LMP are normalized in the same way as the SAM tariffs to not artificially inflate revenue values. Figure 2 shows weekly pricing curves from the CAISO data throughout the entire year. Prices range over more dramatic peaks compared to the SAM tariffs, with the added feature that they sometimes drop to negative values when excessive VRE is available and the Independent System Operators (ISOs) want to penalize further addition to the grid. A daily pattern with early morning and late afternoon peaks is evident from the normalized data.

#### 2.3. Mathematical Formulation of Dispatch Optimization Problem

#### 2.4. Implementation of Optimal Dispatch in Engineering Model

`cbc`(coin-or branch and cut) solver to solve the MILP in hourly timesteps for the two-day time horizon [29]. From that optimal schedule we keep solutions for the first 24 h, using these values as targets for the SAM engineering model. The SAM model solves system energy and mass balances and ensures component and plant operating feasibility to attempt activating those optimal operating modes. Using a system running Ubuntu 20.04.4 LTS with an Intel i5-10310U quad-core processor at 1.7 GHz and 16 GB of RAM, each time horizon solution for the combined MILP and SAM evaluation is solved within an average of 0.58 s. After converging on a solution, the Python interface logs the SAM results for the current day and creates a new instance of the MILP model starting at midnight of the next day. This rolling time horizon approach, where we alternate between MILP and engineering model calls, helps us anticipate any excessive ramping in market pricing or possible inhibiting weather conditions that may necessitate changes in energy storage levels overnight. Periodically refreshing the MILP initial conditions after calling on the engineering model also prevents the MILP model from drifting too far from the higher fidelity model representation.

## 3. Results

- the nominal generated electric power from the turbine;
- the capacity of the molten salt tanks; and
- the market pricing scenarios for the plant.

_{e}as this approximately matches the fixed nuclear core thermal output (the actual electrical output, with an assumed net efficiency of 48.9% [11], is closer to 465 MW

_{e}but here we choose a rounded number). Values of electrical output above the reference would require an oversized turbine relative to the reactor output, incurring excess costs which under some circumstances could be offset by increased dispatchability of stored energy. When choosing an oversized turbine output, any operation below that rated level (i.e., when only receiving nuclear output and no stored energy is dispatched) would incur an off-design penalty, calculated from the off-design data tables described in Section 2.1, on the overall efficiency. Power output values below the reference would not use thermal storage advantageously and so are not considered. We also assume the reference design point uses no thermal storage for comparison purposes. The energy capacity of the thermal storage tanks, when included in the design, is measured in equivalent hours of nominal turbine operation. Weather data for the plant, namely dry-bulb temperature, are used from collected hourly records hosted in SAM for a selection of sites. The records consist of weather data from different years that have been combined to represent a ’typical’ year. We use data for a tentative site in Phoenix, AZ though the simulation software is general to any weather data input.

#### 3.1. Load Profiles for Plant with 700 MW_{e}, 2 h of TES, under SAM Tariff Rates

_{e}turbine design with 2 h of thermal storage operating in the generic peak market from SAM. The hourly generated power output of the power cycle and energy levels of the TES are tallied for a full simulated year. We then create a violin plot for both metrics, demonstrating the distribution in values for each hour of the day throughout the year. We further categorize the hourly distributions according to the seasonal and daily variations in SAM tariff levels shown in Figure 2: subplots distinguish between winter versus summer tariffs in the columns; each column is then subdivided between weekday versus weekend tariffs. Together, these subplots reveal the distributions in daily operating levels given pre-defined seasonal and weekly market variability.

_{e}contributions from the LFR and the rest coming from thermal storage. Tank energy levels decrease steadily between 8 a.m. and 8 p.m. as excess energy is dispatched to the power cycle; day-by-day variability in the targeted dispatch is based on anticipated outside dry temperatures and efficiency losses. Tank levels are mostly depleted by 8 p.m., after which the cycle runs with just the nuclear thermal contribution until midnight where the process is repeated.

_{e}and 2 h of thermal storage, but under the SAM market with exaggerated ramps. Across both winter and summer weekdays, the behavior is largely unchanged from the base tariff schedule. Winter weekend hourly distribution of both energy produced and energy dispatched have much less spread. The more uniform operating levels throughout the year imply less sensitivity to variable dry temperatures. The benefits of operating under more volatile pricing markets become more evident from the economics of the plant and are discussed in Section 3.4.

#### 3.2. Load Profiles for Plant wtih 800 MW_{e}, 6 h of TES, under SAM Tariff Rates

_{e}turbine with 6 h of thermal storage. With the extra storage capacity, power generation is more likely to shut-off during low pricing periods in order to focus more generation during higher pricing periods. Storage is particularly prioritized in the winter weekday mornings between 12 a.m. and 8 a.m. in anticipation of high daytime prices. Additional costs are incurred from power cycle shutdown and startup operations but are not prohibitive due to high daytime revenues. Generally, any pricing periods with multipliers greater than one are met with high power generation from both nuclear and thermal storage contributions regardless of season. This is best illustrated by the contrast between the winter and summer weekday distributions of this design compared with those of the smaller storage capacity design in Figure 4. In the smaller storage capacity case, the power generation scales more closely with each price multiplier increase due to the reduced energy capacity available for dispatch in the molten salt tanks, accentuated by the 5 h lag between complete tank fill-up and discharge ahead of the summer weekday noon price hike. In the 800 MW

_{e}design, with 6 h of thermal storage, the tanks can contribute more energy for longer.

_{e}and 6 h of storage plant but under the modified peak market from SAM with twice-amplified peaks and troughs. The plant behavior does not change dramatically except for some slightly faster ramping in power generation immediately preceding weekday daytime price increases. Weekend tank level distributions are also narrower similar to Figure 5.

#### 3.3. Load Profiles for Both Plant Cases under CAISO Market Conditions

_{e}turbine with 2 h of storage under CAISO market conditions. Power generation and storage charge level for both winter and summer have much more variable hourly distributions due to the increased volatility in market prices. However, it is evident that two charging periods occur on most days regardless of season: in the early morning and during midday hours. These charging periods precede higher peaks in energy pricing during morning and late afternoon hours. The charging periods also sometimes coincide with negative energy prices, giving the plant an alternative use for the nuclear thermal energy other than producing electricity at a loss. Winter and summer profiles differ mostly by the temporal location of the price peaks. Storage charging in the winter seems to start 1–2 h later than summer charging, likely due to a later sunrise which denotes the daily introduction of solar renewable energy into the grid and a subsequent lowering of prices. There are no notable differences between weekend and weekday behavior for the plant.

_{e}and 6 storage hours under the same CAISO market scenario. Figure 9 shows more uniform trends compared to the lower capacity case in Figure 8. With higher storage capacity, the optimized charge level profile follows a sinusoid with a single daily peak: rather than dispatch energy for both the morning and evening price peaks, it prioritizes the evening price peak with more lucrative prices. Midday generation is more likely to shut down during midday prices, regardless of season, to use all of the nuclear thermal availability for storage.

#### 3.4. Plant Sizing Trade Studies

_{e}and hours of thermal storage, generating a full year simulation for each. Results of the parameter sweep over each market scenario are plotted as a heat map in their corresponding column within Figure 10. The color value of each 2-D plot represents a relative PPA price: the PPA price for each element is normalized by the PPA price of the reference design (having no storage and turbine matching the nuclear thermal output). Relative PPA prices lower than 1 represent design points more desirable than the reference case and therefore a subset of the parameter space where adding thermal storage to the nuclear plant is economically advantageous.

_{e}turbine strictly increases the PPA price as the power plant can never operate above nominal output and there is hence no price advantage to charging the TES. Separately, sizing up the power plant past the reference design point naturally worsens economic performance with increased turbine costs and no extra energy to sell from storage. Adding thermal storage to plants with output higher than 450 MW

_{e}does improve the performance relative to the respective case with no thermal storage; however, the improvements in the generic peak market are never better than the reference and have diminishing returns when adding more than 5 h of storage.

_{e}, a turbine oversized by 200%. Though many solutions exist that perform better than the reference, the optimal design point within this market for PPA price is at 700 MW

_{e}and 5 h of available thermal storage with 5% improvements in PPA price. Final PPA prices for all markets are shown in Table 4. We see that for a given turbine size above the nominal there exists an optimal TES size able to store enough energy to maximize turbine output over periods of peak pricing.

_{e}and 0 h of thermal storage design evaluated using CAISO tariff rates. The region of improved design points expands much further than even the twice amplified peaks in Figure 10; the improvements are greater in value as well. Only under certain cases does the plant perform worse than the reference design: heavily over-sized power outputs paired with low amounts of thermal storage and slightly over-sized power outputs paired with large amounts of thermal storage. In each case, any additional revenue from selling stored energy—even when dispatched optimally—does not offset costs incurred from oversizing the respective subsystem. The optimal design point for system performance in the CAISO market is similar to the twice amplified SAM generic peak market: a 750 MW

_{e}with 5 h of thermal storage results in 10% improvements in PPA price.

#### 3.5. Sensitivity Analysis on Thermal Storage Costs

_{e}turbine with 2 h of storage comes close to rivaling the reference design point when lowering the TES cost to $20 per kWt·h but ultimately does not cross the margins. The more volatile markets in the second and third row exhibit the same trend. Here, lower TES costs improve the relative PPA price past the reference. Increasing the TES cost reveals price points where thermal storage would no longer be advantageous. For the CAISO markets in the third row, all shown combinations outperform the plant with no storage except for the highest estimated cost with 7 h of storage.

`tshours`greater than 0 due to inclusion of an additional loop between the primary and the power conversion cycle with associated temperature losses. If the efficiency penalty were to drop by 1–2 percentage points this would correspond to roughly 2–5% reduction in the electrical power produced. Ultimately, this would introduce a step shift in PPA price for non-zero values of TES storage. Table 5 shows the sensitivity of the optimal design point when a performance penalty is imposed on the final PPA price (only for designs with storage). The optimal design for the SAM tariff rates is only affected by the TES efficiency penalty in markets where the tariff peak amplification factor is below two: adding performance penalties changes the optimal design to one without TES. The design point does not change for the twice-amplified SAM and the CAISO tariff schedules when imposing the additional TES efficiency penalty. However, improvements on PPA price from the additional TES in these markets are reduced with increasing performance penalties. They nevertheless still perform better than the reference no-storage design.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

NPP | Nuclear power plants |

VRE | Variable renewable energy |

CAISO | California Independent System Operator |

TES | Thermal energy storage |

CSP | Concentrated solar power |

LFR | Lead-cooled fast reactor |

SAM | System Advisor Model |

sCO${}_{2}$ | Supercritical CO${}_{2}$ |

EES | Engineering Equation Solver |

OASIS | Open Access Same-time Information System |

LMP | Locational marginal prices |

ISO | Independent System Operator |

PPA | Power purchase agreement |

MILP | Mixed-integer linear program |

SSC | SAM Simulation Core |

## Appendix A

#### Appendix A.1. Nuclear Supply and Demand Constraints

#### Appendix A.2. Nuclear Start-Up Constraints

#### Appendix A.3. Nuclear Logic Constraints

#### Appendix A.4. Energy Balance Constraints

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**Figure 1.**Schematic of LFR-molten salt flow loop. LFR heats (via secondary steam loop) the molten salt that flows from the cold to hot storage tanks. The hot tank can then discharge heat to the power cycle leading up to the steam turbine.

**Figure 2.**Price multipliers used to simulate different market conditions: (

**top**) generic peak pricing schedule from SAM and (

**bottom**) normalized locational marginal price from CAISO. Some negative pricing outliers for CAISO are not directly shown in the axis but are annotated in the graph.

**Figure 4.**Hourly violin plot distributions for a year of simulated electric power and stored energy levels. Computed for a 700 MW

_{e}turbine with 2 h of TES under SAM generic peak market prices. Median value for each hour is shown as a white circle and the black vertical rectangle demarcates 25th and 75th percentiles. Distributions are split between winter and summer price schedules as well as weekday and weekend prices; price multipliers are shown on the right axis of each subplot.

**Figure 5.**Hourly violin plot distributions for a year of simulated electric power and stored energy levels. Computed for a 700 MW

_{e}turbine with 2 h of TES under twice-amplified SAM generic peak market prices. Median value for each hour is shown as a white circle and the black vertical rectangle demarcates 25th and 75th percentiles. Distributions are split between winter and summer price schedules as well as weekday and weekend prices; price multipliers are shown on the right axis.

**Figure 6.**Hourly violin plot distributions for a year of simulated electric power and stored energy levels. Computed for a 800 MW

_{e}turbine with 6 h of TES under SAM generic peak market prices. Median value for each hour is shown as a white circle and the black vertical rectangle demarcates 25th and 75th percentiles. Distributions are split between winter and summer price schedules as well as weekday and weekend prices; price multipliers are shown on the right axis of each subplot.

**Figure 7.**Hourly violin plot distributions for a year of simulated electric power and stored energy levels. Computed for an 800 MW

_{e}turbine with 6 h of TES under twice-amplified SAM generic peak market prices. Median value for each hour is shown as a white circle and the black vertical rectangle demarcates 25th and 75th percentiles. Distributions are split between winter and summer price schedules as well as weekday and weekend prices; price multipliers are shown on the right axis.

**Figure 8.**(Top row) Hourly ranges in normalized CAISO energy price multipliers for a full year. Mean price and standard deviation are shown in a darker shade. (Rows 2–5) Hourly violin plot distributions for a year of simulated electric power and stored energy levels. Computed for a 700 MW

_{e}turbine with 2 h of TES under normalized CAISO energy prices. Median value for each hour is shown as a white circle and the black vertical rectangle demarcates 25th and 75th percentiles. Distributions are split between winter and summer price schedules as well as weekday and weekend prices.

**Figure 9.**(Top row) Hourly ranges in normalized CAISO energy price multipliers for a full year. Mean price and standard deviation are shown in a darker shade. (Rows 2–5) Hourly violin plot distributions for a year of simulated electric power and stored energy levels. Computed for an 800 MW

_{e}turbine with 6 h of TES under normalized CAISO energy prices. Median value for each hour is shown as a white circle and the black vertical rectangle demarcates 25th and 75th percentiles. Distributions are split between Winter and Summer price schedules as well as weekday and weekend prices.

**Figure 10.**Effect of increased price ramping on final PPA price. Each column represents PPA price results for the SAM generic tariff rates with increasing peak-amplification from left to right. Heatmaps show PPA prices relative to the reference design at 450 MW

_{e}and 0 h of storage for each market scenario. Contours are generated using interpolated data to highlight key regions: values higher than 1 perform worse than the reference; values lower than 1 perform better. Values higher than 1.1 are not shown for clarity. Corresponding tariff rates shown in bottom row for each column.

**Figure 11.**Performance of LFR and TES plant in a simulated CAISO market using normalized price multipliers. Heatmap plots PPA price values relative to the reference design at 450 MW

_{e}and 0 h of thermal storage. Contours are generated using interpolated data to highlight key regions: values higher than 1 perform worse than the reference; values lower than 1 perform better. Values higher than 1.1 are not shown for clarity.

**Figure 12.**Sensitivity of PPA price to TES cost. Plots are arranged by different market scenarios in the rows and power cycle outputs in the columns. Individual plots show PPA price relative to the reference design performance (marked as a horizontal line at a value of 1.0) as a function of thermal storage hours. Multiple lines are shown per plot for varying TES cost. Optimal design points are highlighted for each market scenario: the optimal electrical output column is highlighted by face color and the corresponding storage size is marked by a vertical line.

Symbol | Value | Units | Description | Source |
---|---|---|---|---|

Dispatch Optimization Parameters | ||||

${C}^{pc}$ | 0.00875 | $\$/{\mathrm{kW}}_{e}\xb7\mathrm{h}$ | Operating cost of power cycle | Scaled SAM parameters [23,26,27] |

${C}^{csu}$ | 27,345 | $\$/\mathrm{start}$ | Penalty for power cycle cold start-up | “1 |

${C}^{chsp}$ | 5470 | $\$/\mathrm{start}$ | Penalty for power cycle hot start-up | “ |

${C}^{csb}$ | 0.00175 | $\$/{\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Operating cost of power cycle standby operation | “ |

${C}^{{\Delta}_{w}}$ | 0.04375 | $\$/\Delta {\mathrm{kW}}_{e}$ | Penalty for power cycle production change | “ |

${C}^{{v}_{w}}$ | 1.75 | $\$/\Delta {\mathrm{kW}}_{e}$ | Penalty for power cycle production change past design | “ |

${C}^{nop}$ | 0.00734 | $\$/{\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Operating cost of nuclear plant | Westinghouse estimates |

Engineering Model Financial Parameters | ||||

${r}^{fin}$ | 7 | % | Interest rate on financing loan | General assumption |

${\tau}^{con}$ | 4 | yr | Construction time | “ |

${C}^{tes}$ | 29.8 | $\$/{\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Thermal energy storage cost | Scaled SAM parameters [23,26,27] |

${C}^{nuc}$ | 4150 | $\$/{\mathrm{kW}}_{e}\xb7\mathrm{h}$ | Nuclear plant cost including fuel over analysis period | Westinghouse estimates |

^{1}Tables elements annotated with (“) are equivalent to the element in the row above.

Symbol | Units | Description |
---|---|---|

Sets | ||

$\mathcal{T}$ | Set of all time steps within time horizon | |

Time-Indexed Parameters | ||

${Q}_{t}^{in,nuc}$ | ${\mathrm{kW}}_{t}$ | Available thermal power generated by the nuclear plant in time t |

${\delta}_{t}^{ns}$ | - | Estimated fraction of time t required for nuclear start-up |

${\eta}_{t}^{amb}$ | - | Cycle efficiency ambient temperature adjustment factor in time t |

${\eta}_{t}^{c}$ | - | Normalized condenser parasitic loss in time t |

${P}_{t}$ | $\$/{\mathrm{kW}}_{e}\xb7\mathrm{h}$ | Electricity sales price in time t |

${Q}_{t}^{c}$ | ${\mathrm{kW}}_{t}$ | Allowable power per period for cycle start-up in time t |

${W}_{t}^{u+}$ | ${\mathrm{kW}}_{e}$ | Maximum power production when starting generation in time t |

${W}_{t}^{u-}$ | ${\mathrm{kW}}_{e}$ | Maximum power production in time t when stopping generation in time $t+1$ |

Steady-State Parameters | ||

$\alpha $ | $ | Conversion factor between unitless and monetary values |

${E}^{c}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Required energy expended to start cycle |

${\eta}^{des}$ | - | Cycle nominal efficiency |

${E}^{u}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Thermal energy storage capacity |

${\eta}^{p}$ | ${\mathrm{kW}}_{e}/{\mathrm{kW}}_{t}$ | Slope of linear approximation of power cycle performance curve |

${L}^{c}$ | ${\mathrm{kW}}_{e}/{\mathrm{kW}}_{t}$ | Cycle heat transfer fluid pumping power per unit energy expended |

${Q}^{b}$ | ${\mathrm{kW}}_{t}$ | Cycle standby thermal power consumption per period |

${Q}^{l}$ | ${\mathrm{kW}}_{t}$ | Minimum operational thermal power input to cycle |

${Q}^{u}$ | ${\mathrm{kW}}_{t}$ | Cycle thermal power capacity |

${W}^{b}$ | ${\mathrm{kW}}_{e}$ | Power cycle standby operation parasitic load |

${\dot{W}}^{l}$ | ${\mathrm{kW}}_{e}$ | Minimum cycle electric power output |

${\dot{W}}^{u}$ | ${\mathrm{kW}}_{e}$ | Cycle electric power rated capacity |

${W}^{\Delta +}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-up designed limit |

${W}^{\Delta -}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-down designed limit |

${W}^{v+}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-up violation limit |

${W}^{v-}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-down violation limit |

${\delta}^{nl}$ | h | Minimum time to start the nuclear plant |

${E}^{n}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Required energy expended to start nuclear plant |

${L}^{n}$ | ${\mathrm{kW}}_{e}/{\mathrm{kW}}_{t}$ | Nuclear pumping power per unit power produced |

${Q}^{nl}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Minimum operational thermal power delivered by nuclear |

${Q}^{nsb}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Required thermal power for nuclear standby |

${Q}^{nsd}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Required thermal power for nuclear shut down |

${Q}^{nu}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Allowable power per period for nuclear start-up |

${W}^{nht}$ | ${\mathrm{kW}}_{e}\xb7\mathrm{h}$ | Nuclear piping heat trace parasitic loss |

Symbols | Units | Description |
---|---|---|

Continuous Variables | ||

${x}_{t}$ | ${\mathrm{kW}}_{t}$ | Cycle thermal power utilization at t |

${x}_{t}^{n}$ | ${\mathrm{kW}}_{t}$ | Thermal power delivered by the nuclear at t |

${x}_{t}^{nsu}$ | ${\mathrm{kW}}_{t}$ | Nuclear start-up power consumption at t |

$\dot{w}$ | ${\mathrm{kW}}_{e}$ | Power cycle electricity generation at t |

${\dot{w}}^{\Delta +}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-up at t |

${\dot{w}}^{\Delta -}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-down at t |

${\dot{w}}^{v+}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-up beyond designed limit at t |

${\dot{w}}^{v-}$ | ${\mathrm{kW}}_{e}/\mathrm{h}$ | Power cycle ramp-down beyond designed limit at t |

${\dot{w}}^{s}$ | ${\mathrm{kW}}_{e}$ | Energy sold to the grid at t |

${\dot{w}}^{p}$ | ${\mathrm{kW}}_{e}$ | Energy purchased from the grid at t |

${u}_{t}^{csu}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Cycle start-up energy inventory at t |

${u}_{t}^{nsu}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | Nuclear start-up energy inventory at t |

${s}_{t}$ | ${\mathrm{kW}}_{t}\xb7\mathrm{h}$ | TES reserve quantity at t |

Binary Variables | ||

${y}_{t}^{n}$ | - | 1 if nuclear is generating “usable” thermal power at t; 0 otherwise |

${y}_{t}^{nsb}$ | - | 1 if nuclear is in standby mode at t; 0 otherwise |

${y}_{t}^{nsd}$ | - | 1 if nuclear is shutting down at t; 0 otherwise |

${y}_{t}^{nsu}$ | - | 1 if nuclear is starting up at t; 0 otherwise |

${y}_{t}^{nsup}$ | - | 1 if nuclear is starting up at t from off; 0 otherwise |

${y}_{t}^{nhsp}$ | - | 1 if nuclear is starting up at t from standby; 0 otherwise |

${y}_{t}$ | - | 1 if cycle is generating electric power at t; 0 otherwise |

${y}_{t}^{csb}$ | - | 1 if cycle is in standby mode at t; 0 otherwise |

${y}_{t}^{csd}$ | - | 1 if cycle is shutting down at t; 0 otherwise |

${y}_{t}^{csu}$ | - | 1 if cycle is starting up at t; 0 otherwise |

${y}_{t}^{csup}$ | - | 1 if cycle is starting up at t from off; 0 otherwise |

${y}_{t}^{chsp}$ | - | 1 if cycle is starting up at t from standby; 0 otherwise |

${y}_{t}^{cgb}$ | - | 1 if cycle begins electric power generation at t; 0 otherwise |

${y}_{t}^{cge}$ | - | 1 if cycle stops electric power generation at t; 0 otherwise |

Market Scenario | Optimal Turbine Size (MW _{e}) | Optimal TES Size (h) | Optimal PPA Price (¢/kWe·h) |
---|---|---|---|

SAM Generic Peak ×1.0 | 450 | 0 | 6.54 |

SAM Generic Peak ×1.5 | 600 | 3 | 6.49 |

SAM Generic Peak ×2.0 | 700 | 5 | 6.26 |

CAISO | 750 | 5 | 5.63 |

**Table 5.**Sensitivity of optimal design point to efficiency penalty incurred by implementing TES. PPA price improvements are calculated relative to reference design performance in the respective market.

Market Scenario | Optimal Turbine Size (MW _{e}) | Optimal TES Size (h) | PPA Price Improvement (%, Relative to Reference) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Performance Penalties: | 0% | 1% | 2.5% | 5% | 0% | 1% | 2.5% | 5% | 0% | 1% | 2.5% | 5% |

SAM Generic Peak × 1.0 | 450 | ←1 | ← | ← | 0 | ← | ← | ← | 0 | ← | ← | ← |

SAM Generic Peak × 1.5 | 600 | ← | 450 | ← | 3 | ← | 0 | ← | 1.05 | 0.06 | 0 | ← |

SAM Generic Peak × 2.0 | 700 | ← | ← | ← | 5 | ← | ← | ← | 4.88 | 3.93 | 2.50 | 0.13 |

CAISO | 750 | ← | ← | ← | 5 | ← | ← | ← | 10.06 | 9.16 | 7.81 | 5.57 |

^{1}A left arrow (←) denotes a table element equivalent to the value of its left-adjacent column.

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**MDPI and ACS Style**

Soto, G.J.; Lindley, B.; Neises, T.; Stansbury, C.; Wagner, M.J. Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage. *Energies* **2022**, *15*, 3599.
https://doi.org/10.3390/en15103599

**AMA Style**

Soto GJ, Lindley B, Neises T, Stansbury C, Wagner MJ. Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage. *Energies*. 2022; 15(10):3599.
https://doi.org/10.3390/en15103599

**Chicago/Turabian Style**

Soto, Gabriel J., Ben Lindley, Ty Neises, Cory Stansbury, and Michael J. Wagner. 2022. "Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage" *Energies* 15, no. 10: 3599.
https://doi.org/10.3390/en15103599