Effect of Nuclear Energy Flexibility on Integrating Large-Scale Distributed Solar PV in an Existing Power Network

. This paper estimates the maximum integration level of residential rooftop solar photovoltaic (PV) capacity within the power network of the Duke Energy Progress (DEP) and Duke Energy Carolinas (DEC) under two scenarios embodying di ﬀ erent assumptions about the ﬂ exibility of nuclear power plant (NPP) operations. A mixed-integer optimization model was constructed and simulated to ﬁ nd out the maximum solar penetration level under each scenario and to calculate the expected total system ’ s electricity generation costs, energy mix, atmospheric emission reductions, and emission abatement costs. Analysis reveals that improving NPP operation maneuverability would increase the maximum solar PV penetration level in the DEP and DEC power networks by 39%, from 8.9% to 12.4% of the total system ’ s electricity generation. Consequently, it would further improve the electricity generations ’ unit costs and CO 2 emission reductions by 3% and 8% points, respectively. On the other hand, increasing the solar PV penetration limit under high ﬂ exible NPP operation scenario leads to increase in the CO 2 emission abatement costs by 8% points. The results of the study indicate that the ﬂ exibility of existing power system resources may present a barrier for a large uptake of solar energy.


Introduction
Nuclear energy is an important contributor to global clean energy supplies.Even though most clean energy plans focus on renewable resources to reduce GHG emissions, nuclear energy will continue to play a major role in meeting future clean energy goals alongside other forms of clean energy [1].Nuclear power plants (NPPs), particularly in the U.S., provide more than half of America's carbon-free electricity and are operated as baseload plants, which means that they are running most of the time at the rated capacity.On the other hand, flexible operation which allows NPPs to be operated in a load-following mode has been an important element of operations in several countries including, France, Germany, and Belgium [2,3].
The main motive behind the flexible operation of NPPs is the increased share of nuclear energy in the energy mix of these countries and, therefore, the need to vary their outputs to accommodate hourly, daily, and seasonal load variations.The other motive for flexible operation is the necessity for these large baseload NPPs to compensate for electricity generation fluctuations due to large-scale deployments of intermittent energy resources such as solar and wind, which have been observed in these European countries and multiple states across the United States.For instance, in the California Independent System Operator, the shares of solar and wind exceed 9.5% and 3.3% (as % of demand), respectively.Also, the Electric Reliability Council of Texas (ERCOT) has integrated about 0.3% of solar and 11% of wind energy [4].More generally, the plan is to rely more on variable renewable energy sources, e.g., to more than 60% in China and about 80% in United State by 2050 [5].This trend will require more resilient strategies, approaches, and technologies to maintain grid reliability and stability, and to ensure that it is run in a cost-effective manner as it integrates more intermittent renewable resources.
Pfeifer et al. [6] considered a high level of renewable penetration into the energy system of Bulgaria, including storage systems.The findings indicated that the increase of system flexibility will decrease the total annual cost of renewable energy systems.Jenkins et al. [7] found that increasing flexibility of nuclear power operations lowers total system operation costs, increases NPP revenue, and decreases the curtailment of renewable energy.Additionally, Denholm et al. [8] studied the influence of coupling a thermal energy storage system with nuclear power plants on levelized cost of electricity.It was found that levelized cost of energy decreases when wind and solar are integrated into an electric system that is largely supplied by a nuclear power source coupled with thermal storage system.
Recent studies presented the advantage of coupling nuclear power plants with a secondary power generator, including storage system, in order to increase the flexibility of nuclear share and to maximize the use of renewable energy source [9][10][11].During peak times, it was shown that those integrated systems were able to generate more power than the baseload power output.Al Kindi et al. [12] considered increasing the flexibility of a nuclear power plant by 32% of the nominal rated power through combining it with thermal energy storage systems and steam Rankine cycle systems.The integrated flexible system revealed an increase in the net benefits under low-carbon scenarios.
Thus, NPPs nowadays should be operated more flexibly to respond to hourly and daily variabilities caused by variable and intermittent renewable electricity generation [13] as well as to a seasonal variability (e.g., fluctuation in hydropower generation [14]).There are only very few NPPs in the U.S., which are able to reduce the power output to 50% [15] in order to respond to such variabilities while most of NPPs are only capable to maneuver and change their outputs from 100% to 70% and back to 100% during a day duration with a ramping rate of 0.5-2% per minute [16].
NPPs installed in North Carolina and South Carolina, mainly pressurized water reactors (PWRs), have historically been run as a baseload, since this has been the technically and economically preferred mode of operations [1].These NPPs produce around half of the electricity demand in North and South Carolina through Duke Energy Progress (DEP) and Duke Energy Carolinas (DEC) networks [17,18].The expected increase of solar energy deployment in the DEP&DEC network, due the enacted Renewable Energy and Energy Efficiency Portfolio Standard (REPS) [19] and the NC Clean Energy Plan (CEP), which aimed to decrease the statewide GHG emissions to 40% below the level of 2005 [20], motivates the researcher to evaluate the implications of such policies on the capability of the existing power network that is largely supplied by electricity generated by NPPs to accommodate large amount of solar energy which together with nuclear energy should displace considerable share of relatively flexible conventional fossil fuel resources such as coal-fired and natural gas power plants.
The previous works [21,22] show that the combination of sizable electricity generation capacity from inflexible base-load NPPs and the limited ramping capability of gas and coal-fired power plants set the penetration limit of rooftop solar PV systems to about 9% (10.8 GW).Here, we examine the economic and the environment merits of the power system when the penetration limit of rooftop solar PV systems and the flexibility of NPPs are increased.Therefore, the aim of this paper is to study the effect of different flexibility levels of NPPs' ramping capability on the maximum allowable integration of rooftop solar PV and consequently the implications on the DEP&DEC system's electricity generation costs, energy mix, and total CO 2 emission reductions and associated abatement costs.

Materials and Methods
The method used to carry out this study is explained in the following subsections, where we simulate the hourly operations of the DEP&DEC system throughout a year based on system information from 2020.
2.1.System Description and Assumptions.The DEP&DEC system covers a 53,000 square-mile service area in North Carolina and South Carolina and provides electricity services to about 4.3 million customers.Electricity demand is met through electricity generation from their power generation fleet with total capacity of 38,836 MW (summer capacity).The system's minimum and peak electricity demands were 10,172 MW and 30,969 MW, respectively [17,18].
Our model considers all existing power plants of DEP&-DEC network which are detailed in [17,18] and summarized in Table 1.The 3,854 MW solar resources generate about 4% of the system's total annual electricity demand, and it is assumed that the NPPs and hydropower plants (including pumped storage) produce 49% and 2%, respectively, of the total electricity generation.
The system hourly electrical load is assumed to be equal to that filed by DEP&DEC with the Federal Energy Regulatory Commission (FERC) [23].The total annual energy consumption of the system in 2020 was around 154 TWh with peak load of 30 GW.
Assuming that the new installations of the solar PV are connected to the distribution level of the system, the effect of their electricity generation will be mainly reducing the net power load (i.e., Net load = electricity consumption -PV generation).Thus, the simulation model ignores power transmission congestion because trimming the net load due to electricity generation by distributed PV system will reduce peak electricity demand and, therefore, will help relieving network congestion.
The NPPs are initially assumed to be able to change their power outputs between 70% and 100% of their maximum generation capacities within one hour [15].Then, under flexible operation scenario, as explained in Section 2.3, we consider that the NPP outputs are able to vary from 50% to 100% of their maximum generation capacities and vice versa within an hour [3].The maximum ramp rates for coal-fired generation units are assumed to be 85% of their rated maximum capacity per hour while combustion turbines and combined cycle power plants are assumed to have 2 International Journal of Energy Research hourly ramp rates of 100% of their rated maximum capacity as reported in [24,25].
While the NPPs are assumed to be running constantly as per the existing operational philosophy [17,18], the other generation resources have startup and shutdown constraints which are defined as follows: minimum run time, measured in hours, is defined by the minimum time that a generation unit once is started up must run before being turned off; minimum down time is the amount of time that once a unit is turned off must remain off before being turned on again.Hydropower plants are assumed to have a minimum down time and a minimum run time of no more than one hour, which allows them to turn on and off as needed with no restraints [26] while minimum run/down times for coal plants, combined cycle plants, and gas combustion plants are 9/15, 3/4, and 2/2 hours, respectively, as estimated by FERC [27].
The minimum operational output of a generator is the lowest generation level at which the generator can be operated.As estimated from the FERC dataset [27], the minimum operating capacity for coal-fired power plants varies between 40% of the nameplate capacity for the large units (i.e., ≥500 MW) and 35% of the nameplate capacity for smaller units, while all gas-fired power plants are assumed to have a minimum operating capacity of 25% of the design capacity according to the EPRI study findings [24].The fixed operations and maintenance costs of coal-fired, combined cycle, and combustion turbine power plants are set to 35, 10, and 9 $/kW/yr, respectively [28], while their startup costs are assumed to be 94, 35, and 36 $/MW, respectively, as found in [29,30].
The operational performance such as maximum generation capacity, average heat input, and air emissions was taken from the eGrid database [31].Gas and coal prices are based on the figures reported by the U.S. Energy Information Administration (EIA) [32].Thus, all costs and prices presented in this paper are in 2020 dollar values.

Optimization Formulation and Simulation Model.
A mixed-integer optimization model was constructed and sim-ulated using IBM CPLEX Optimization Studio (version 12.7) in the AMPL programming environment to determine the minimum cost unit commitment and economic dispatch of DEP&DEC network.The aim is to meet the DEP&DEC power system's net load which equals the total electrical demand minus solar PV generation.So, as presented in the following mathematical formulation, the optimization model's objective function is to minimize the total costs of electricity generation, including fuel costs, startup costs, no-load costs, spinning reserve costs, and various penalty costs, due to inadequate electricity generation and spinning reserves.The optimization model accounts for several technical and operational constraints such as generation units' maximum and minimum power outputs, minimum up and down times, and ramping up and down limits.Also, it accounts for the system's reliability performance standard by fulfilling the spinning reserve capacity requirements.Thus, the total electricity cost is expressed as (i) Electricity generation from all units meet total hourly demand: (ii) Available spinning reserve from all units meet system's total required hourly spinning reserve: (iii) Accounting for startup cost of all committed generation units: (iv) Generation and spinning reserve provided by each unit does not exceed its maximum generation capacity: (vi) The hourly output increase by each generation unit is bounded by its ramping up capability: (vii) The hourly output decrease by each generation unit is bounded by its ramping down capability: (viii) The hydropower plant only operates during peak time (according to the existing operational policy): (ix) Initializing generation, spinning reserve, and commitment parameters for the simulation: (x) All generating units meet their minimum up and down times: where where where where (xi) All decision variables are nonnegative: So, besides the forecasted total hourly demand and solar electricity generation, the key inputs to the model are the operational and cost parameters of the hydro, gas, coal, and nuclear power plants in the DEP&DEC system.The day-ahead hourly load forecast errors are assumed to follow a standard normal distribution having a mean of 0% and a standard deviation of 1% [33].
The hourly electricity generated from the distributed solar PV is estimated by the following PV generation model (PGM) assuming that the roof-top solar PV system is made of polycrystalline PV modules with an efficiency of 20%, rated at standard test conditions, 1000 W/m 2 , and the system output is derated to 77% to account for loss factors such as inverter losses, wiring losses, soiling of the modules, and module mismatch [34]: The hourly solar generation forecast errors are generated from actual historical data using a statistical method developed by the Pacific Northwest National Laboratory (PNNL).This method is based on observations which show that the accuracy of a day-ahead forecast depends on the clearness index (CI), which can be defined as the ratio of the hourly "actual" solar irradiance to the hourly "ideal" or "maximum" solar irradiance that corresponds to a clear sky condition.The method is well described in [15].
The output of the optimization model produces the optimal day-ahead hourly generator schedule and calculates the hourly and yearly electricity generation costs and CO 2 emissions to meet system's net load, hourly generation output and CO 2 emissions per generation unit, hourly spinning reserves, units' startup/shutdown events, and hourly system's generation and spinning reserve shortages.

Scenario Description.
In this study, three scenarios have been considered.Besides a baseline scenario, two scenarios have been examined for maximum distributed solar PV integration under different assumptions related to the flexibility of the nuclear power plants' ramping capabilities.These scenarios are described as follows: (A) Baseline scenario: it represents the existing system characteristics and the currently integrated share of the solar energy resources, in which it is assumed that DEP&DEC system has 4% solar penetration level and its NPPs capability to ramp up and down their power output is between only 70% and 100% within one hour.Under this scenario, we have calculated the total DEP&DEC system's electricity generation costs, generation mix, CO 2 emissions, and CO 2 abatement costs in order to be used as reference values compared to the new scenarios (B) Baseline+solar scenario: it examines the maximum allowable distributed solar PV integration without threating the reliability of the system.It also assumes no changes to the NPPs' ramping capabilities, and therefore, the NPPs are able to increase and reduce their power outputs between only 70% and 100% of the rated capacity within an hour (C) Flexible+solar scenario: it examines the maximum allowable distributed solar PV integration without threating the reliability of the system and assuming NPPs' ramping capabilities are improved and thus they will be able to increase and decrease their power outputs between 50% and 100% of the rate capacity within an hour

Results and Discussions
In this section, the simulation results are presented, focusing on the impacts of NPPs' load following capabilities on the total DEP&DEC system's maximum distributed solar PV penetration, electricity generation mix and costs, CO 2 emissions, and CO 2 abatement costs.The reported solar PV penetration figures are regarded as the percentage ratio of total electricity generated by solar PV systems to the total electricity generated by the DEP&DEC system.
3.1.Maximum Integrated Distributed PV Capacity.Under the baseline+solar scenario, the DEP&DEC power network was found to be able to accommodate only 8.6 GW solar PV that could supply 8.9% (13.8 TWh) of the entire systems' annual electricity generation.This constraint is mainly imposed by the limited operational flexibility of six large baseload NPPs that produce 49% of the annual total system electricity generation.These power plants have limited capability to ramp up and down their power outputs and also require a long time to startup and shutdown.Such constraints reduce the system's ability to accommodate the fluctuations caused by the variable solar generation and thus limit maximum penetration level to 8.9%.Integrating solar energy above to this level may result in inequalities between electricity supply and demand and consequently threaten the reliability of the network.Improving the NPPs' maneuverability under flexible +solar scenario, where the total NPP output can be reduced further by 2 GW, leads to an increase in the solar PV integration limit from 8.9% to 12.4% (19.2 TWh) where it allows the DEP&DEC network to integrate more solar PV electricity generation in the fall, summer, and spring seasons.While the low power output of the solar PV systems during winter does not require highly flexible system to manage output's fluctuation, the relatively high power output of the solar PV during spring and fall, which coincides with the relatively low-to-medium-demands in DEP&DEC system presents the need to have a highly flexible system to 5 International Journal of Energy Research accommodate significant fluctuations in the solar power output.Thus, it might be integrating new energy storage systems into DEP&DEC network to further enable the system to integrate more variable energy resources such as solar.

Total System Costs.
Figure 1 shows the DEP&DEC systems' electricity generation cost in 2020$/MWh under each scenario.These costs cover only the operational costs (i.e., fixed and variable generation costs) of conventional generators, and they exclude the costs of solar PV system installation, operations, and maintenance.The unit cost of the generation is calculated by dividing the total operational costs by the total amount of electricity generated by the con-ventional power plants only, and it excludes the electricity generated by solar PV.Thus, the system cost measures the impact of solar integration on the economic performance of the existing DEP&DEC's power generation fleet.The gray-colored bars represent the total system's operating of conventional electricity generation under all three scenarios.Under the baseline+solar scenario, the 8.9% solar penetration will reduce the total system's generation costs by 4% with respect to the baseline scenario while the flexible+solar scenario, at 12.4% solar penetration, achieves about 7% reduction with respect to the baseline scenario.These reductions are resulted from displacing expensive peaking gas and coal generation units by a large amount of solar PV generation.

Electricity Generation Mix.
Figure 2 shows the specific combination of various energy sources-nuclear, coal, gas, hydropower, and solar-used to meet the systems' total electricity demand.Each energy source is presented with a percentage of annual electricity generation in the system under all scenarios.In consistent with DEP&DEC operational strategy, the generation shares from the NPPs and hydro are constrained to 49% and 2% of total electricity, respectively, while maximum imported electricity from neighboring networks is kept at 3%.
As expected, under both baseline+solar and flexible+ solar scenarios, the electricity generated by solar PV reduces the electricity generation shares from the coal-fired and natural gas combustion turbine (NGCT) power plants by 2-7%.These plants are typically intermediate and peak load power plants.
While coal-fired power plants under the baseline scenario supply 29% of annual electricity generation, their share is reduced under baseline+solar and flexible+solar scenarios  4. The abatement cost (COA) is estimated by dividing the federal subsidy amount of solar PV installation costs by the total CO 2 emissions abated.The solar PV installation cost in the region is $2.67 per watt before applying 26% Federal Investment Tax Credit (ITC) [35].Under the baseline scenario, integrating 4% solar PV has reduced the total CO 2 emissions from 70 million tons to 66 million tons at COA of 307 (2020$/tCO 2 ).Integrating 8.9% solar PV under baseline+solar scenario would abate additional 10 million CO 2 tons at COA of 318 (2020$/tCO 2 ).However, increasing the solar PV penetration by 39% under flexible+solar scenario increases the CO 2 emission abatement by only 10% at COA of 342 (2020$/tCO 2 ).These COA values are relatively high compared with COA using other options of electricity generation technologies for carbon emission reductions including concentrated solar power (CSP), integrated solar combined cycle (ISCC), and NGCC [36].For the distributed solar PV to reach to the social cost of carbon, which is estimated to be $75 per ton CO 2 at 2.5% discount rate [37], its installation cost should be reduced by 75%, or by $0.6 per watt.

Conclusions
This paper examines the impact of the operational flexibility of the large DEP&DEC's baseload nuclear power plants on solar PV integration limits and, consequently, the implications system's generation costs and mix, CO 2 emission rate, and emission abatement costs.
The study's findings indicate that the inflexible baseload nuclear power generation units inflict a major constraint on integrating large amounts of residential solar PV into the DEP&DEC system and thus place a significant impact on the systems' marginal cost of electricity generation, carbon emission rates, and abatement costs.
The results suggest that a maximum of 8.9% of DEP&-DEC network's electricity demand can be provided by rooftop solar PV units under the low flexible NPP scenario (baseline+solar).Upgrading the existing old NPPs with a more flexible operation system would increase the maximum allowable solar PV integration by 39%, to reach up to 12.4% of the systems' total electricity consumption.This increase in the solar PV penetration limit under such a scenario (flexible+solar) would lead to 23% reduction in the system's total CO 2 emissions, compared with only 17% emission reduction under inflexible NPP operations.The study reveals that integrating large solar PV is less costeffective option to abate systems' carbon emissions.The outcomes of this study emphasize the importance of assessing renewable energy-related policies and regulations in a real setting of power system operations.The interaction between various energy resources due their distinct operational characteristics may deliver lower economic and environmental benefits than expected.
As nuclear power will continue to play a vital role in the future sustainable, balanced energy mix since it is the only efficient source of electricity that delivers reliable, carbonfree electricity at a very high capacity factor (>90%), this study provides valuable insights for policymakers and other decision-makers on the implication of integrating large amount of rooftop solar PV into a real power network that is heavily supplied by electricity from large baseload nuclear power plants with limited flexible operations.It also helps them understand the economic and environmental merits of adopting more flexible nuclear energy resources taking into account that the age of existing NPPs ranges from 32 to 48 years.

Figure 1 :
Figure 1: System cost results by scenario.The unit is $/MWh.The % value inside the bar represents the change in the cost relative to the baseline scenario.
Figure 2: Electricity generation mix by scenario.An increase of solar PV penetration reduces the share of coal-fired, NGCC, and NGCT generations.
MinDn 0u : Initial down time of unit u (intervals) MinD nu : Minimum down time of unit u (intervals) MinG u : Minimum generation of unit u (MW) MinUp 0u : Initial uptime of unit u (intervals) MinUp u : Minimum uptime of unit u (intervals) NlC u : No-load cost of operating unit u ($/interval) OG t : Surplus of generation in interval t (MW) pv C : Nameplate solar PV capacity (W) RampDn u : Maximum ramp-down rate of generator u (MW/hr) RampUp u : Maximum ramp-up rate of generator u (MW/ StartC u,t : Startup cost of unit u in interval t ($) T: Number of intervals in time horizon T a : Ambient temperature ( °C) T c : PV module's temperature ( °C) U: Number of generation units in the system USr t : Shortage of spinning reserve in interval t (MW) UGP: System under generation penalty ($/MWh).Dispatchable generator unit, u ∈ 1 ⟶ U t: Time interval hour, t ∈ 0 ⟶ T n: Time interval index used for minimum up and down time requirements, n ∈ t ⟶ T.
t : Spinning reserves required in interval t (MW) StartC u : Cost of starting unit u ($)