1

Strategies for short-term intermittency

in long-term scenarios in the French power system

Rodica Loisel1,2

, Silvana Mima3, Lionel Lemiale

2 , Adrien Bidaud

4

Abstract

This paper depicts the flexibility provision with nuclear power in French energy scenarios.

The long-term energy model POLES is coupled with a power market module, EcoNUK, to

assess the interaction between nuclear and renewables. The paper addresses the issue of

optimal shares of nuclear and renewables that best regulate the system adequacy with concern

to nuclear ramping, minimum reactor stable power, and the share of the fleet needed to

operate load-following instead of baseload. Results show that depicting flexibility at half-hour

with EcoNUK results in more nuclear and gas power flows than in POLES, due mainly to

ramping constraints. Nuclear load-following is accounted in terms of cycling, with an annual

seasonality of cycles assessed by frequency and amplitude, and shows that by 2050 there are

more deep cycles than currently allowed by reactor’s license (250 instead of 200). A system

made of 25% nuclear and 65% renewables in 2050 needs deeper and longer flexibility than

frequent short oscillations observed in 2035, leading to excessive nuclear cycling. Policy

arbitrage is necessary among flexible nuclear and gas, both constrained by the French Energy

Law targets to reduce nuclear and carbon emissions. Coupling short-term operation with long-

term investment indicates that ultimately nuclear flexibility is a rigid long process with prior

organization, regulation and innovation; hence long-term scenarios need to comprehensively

include constraints to reach an informed decision on flexible nuclear fleet operation.

Keywords: scenarios, nuclear, load-following, long-term investment, short-term operation.

Highlights

• Long-term energy planning embeds short-term operation to assess flexibility

adequacy.

• Nuclear ramping and minimum rated power are the critical parameters of coupling.

• Power mix diversification needs to trade-off between nuclear energy and capacity.

• Excessive nuclear cycling indicates the need for faster reactors in the future.

• Revision of reactor transient limits would prevent early upgrading or retirement.

1 Corresponding author: rodica.loisel@univ-nantes.fr.

2 LEMNA Lab. of Economics, Univ. Nantes, 44000 Nantes, France.

3 GAEL, CNRS, Grenoble INP (Institute of Engineering), INRA, Univ. Grenoble Alpes, 38000 Grenoble, France

4 IN2P3, CNRS, Lab. of Physics, Univ. Grenoble Alpes, 38000, France

2

1. Introduction

Scenarios are typically defined as the description of the possible system evolution for

supporting near-term economic and political decision-making in front of an uncertain future

(Braunreiter and Blumer, 2018). The degree of complexity depends on the target audience,

e.g. policy advisors, citizens, industrials or researchers. While based on models, scenarios

understanding is key to deal with results and conclusions derived from the assumptions and

inputs on the socio-technical development in the long term (Pedde et al., 2020).

This study builds energy scenarios aiming at decarbonization with nuclear and renewables, as

part of the literature on energy transition modeling with exploratory exercises. Energy

scenarios are based on quite familiar modeling approaches, yet the way the uncertainty on the

evolution is modelled makes the reliability of results and conclusions critical. Scenarios in

general combine a soft part describing qualitatively the societal development, and a hard,

numerical representation of the energy system that simulates the technology interaction under

the constraint of the descriptive frame (Weimer-Jehle et al., 2016). The paper will combine

political targets on nuclear and renewables with market mechanisms to test the technical and

economic feasibility in a given power system.

Two types of scenarios are relevant for our assessment: normative scenarios (or backcasting)

which set bounds on the desired final state, such as targets on carbon and renewables, and let

open the question of trajectories to reach them; and exploratory scenarios, which analyze the

effects of an unconstrained indicator at final date by maintaining fixed the other drivers. The

combination of both approaches leads to a multitude of trajectories by exploring the possible

pathways which make feasible the target under different context conditions. The way the key

energy constraint is introduced (since the beginning or at final state) and maintained (all along

a trajectory) has consequences on the scenario results. This critical issue of understanding the

scenarios component interaction is next developed in the French context.

The French Energy Transition Act sets out a roadmap to mitigate climate change and

diversify the energy mix (ETA, 2015). The law includes ambitious targets by 2050 aiming at

reducing greenhouse gas emissions by 75% against a 1990 baseline, and cutting the energy

consumption by 50% related to 2012. In the power sector, the targets are to reduce the nuclear

power in favor of renewables, aiming to diversify the power mix and to decentralize the

power generation. This mix diversification has further picked up interest across researchers,

modelers and scenario builders. Among the long-term visions on the French power mix there

are scenarios of Ademe (Ademe, 2016; Ademe, 2020), the scenarios of the energy research

alliance (Ancre, 2013), the scenario Negawatt (2017), and studies of the French Transmission

System Operator (RTE, 2017), etc. They address the targets on carbon and nuclear by means

of different models, hypothesis and constraints, hence they are difficult to compare and to get

a collective overview of the French energy transition (Shift Project, 2019).

This paper develops in particular the flexibility needs of the power system in front of

increased variability of renewable energies. Models in general defend different views on the

power system adequacy, which strongly depends on the power mix and on the size of installed

capacities of nuclear reactors, gas turbines, hydro power plants and storage means (pumped

hydro, batteries, hydrogen). Therefore, a metrics of flexibility common to all models would be

difficult to set and irrelevant when isolated from the frame outside the power system, e.g. the

whole energy system, the demography, the growth rate, institutions, policies, etc. For

instance, Kraan et al. (2019) note that the common representation of scenarios with only

capacities installed by technology, along with the annual capacity factor, is unrepresentative

of the physical momentary potential of conventional technologies to fit the variability of

renewables.

3

Recent studies accurately embed policy targets and technology constraints. Alimou et al.

(2020) give a detailed representation of the adequacy needs in the French power system in

2050 by linking investment (TIMES) with dispatching (ANTARES), and carefully account

for technology constraints like ramping. Després et al. (2017) couple the energy planning

model (POLES, Prospective Outlook on Long-term Energy Systems) with dispatching

(EUCAD) to study the potential of storage to support renewables. POLES is further coupled

with a grid expansion module to evaluate the flexibility potential of the network (Allard et al.,

2020). Our study complements the literature on the way the scenarios integrate the nuclear

flexibility, with a focus on the management of the nuclear fleet, as baseload or mid and peak-

load, which influences the reactors’ fatigue and the future choice of investments.

Two time-frames are embedded by coupling long-term planning of capacities with short-term

operation of the power system. The technical-economic model POLES simulates the French

power system in 2050 under carbon emission constraint. Capacities installed, capacity factors

and demand and export-import flows are further integrated into a power market model

EcoNUK (Economic dispatching of NUClear reactors) to optimise the operation of the

nuclear power fleet. The market model tests the interaction between technologies at a detailed

time-scale, i.e. 30 minutes, such as to reproduce the final state of scenarios described by

POLES and to identify the link between societal carbon targets, physical reactor liability and

plant dispatching in deregulated markets. The infra-hourly loop shows for instance that

punctually nuclear reactors are cycling excessively and eventually substitute flexible gas-fired

units. Other technical provisions are needed to estimate flexibility, such as the gradients and

the amplitude of nuclear response, the minimum load limit, and the strategy of the uranium

management. Accounting for these parameters could ultimately change the portfolio

optimality for alternative paths of the transition while assessing the interaction between

renewables and nuclear.

In the following, Section 2 defines the nuclear load-following mode, Section 3 describes the

methodology reproducing the final state of a given scenario, Section 4 presents the main

results in support to the analysis of key parameters playing on scenarios’ inputs/outputs, and

the Final section concludes with policy design options.

2. Nuclear load-following

Load-following represents the change in the generation of electricity to match the expected

electricity demand as closely as possible (IAEA, 2018). Load-following covers predictable

events of large load variations, excluding small variations of primary and secondary

frequency control. Flexibility is supplied at the request of the Transmission System Operator

(in France RTE), in agreement with the plant operator (EDF), and the power output is set

manually at a lower level of the nominal power (Morilhat et al., 2019).

The effect of load variability has been investigated in the literature since a while for fossil fuel

power plants, yet the experience with nuclear load-following due to renewable intermittency

is limited. The topic has however been developed by operators and researchers from an

engineer point of view to analyze the physical and chemical consequences (Morilhat et al.,

2019; WNA, 2020), and to assess the market effect from technical-economic perspective

(Bruynooghe et al., 2010; OECD-NEA 2011, 2019; Bertsch et al., 2016; IAEA, 2018,

Mantripragada and Rubin, 2018). Among flexibility indicators there are the number of start

and shut down events (Cany et al., 2018), the loss or gains in profits (OCDE-NEA, 2015;

Ponciroli et al., 2017; Jenkins, 2018), the number of transients and the system cost (ANL,

2018; Loisel et al., 2018, etc). Results are method- and power-system dependent, function on

the way the residual demand is built, with or without load curtailment, and on the generation

4

mix and flexibility options such as trade flows, gas-fired units, storage means and demand

side measures.

Cycling. Load-following is measured by the transient from full power to minimum load and

back to full power. Technically, the modern light water nuclear reactors can operate flexibly

in the range of 100% to 50%-20% of the rated power in 30 minutes, with a ramp rate of up to

5% of rated power per minute (OECD-NEA, 2011). In practice, two situations occur: frequent

load-following over a small range of the rated thermal power, the so-called light cycles; and

less frequent cycling but over a large range of the rated power, or deep cycles (IAEA, 2018;

AREVA, 2009; EDF, 2013). Concerning design transients, some 12,000 load variations are

authorized over the 40 year license, and the regulation mentions that the frequency of deep

cycling should be at most once or twice per day (EUR, 2012; Persson et al., 2012). The

deepness of cycles depends on the refueling cycle: reactors are fully flexible at the beginning

of the cycle; less flexible at 65% of the fuel cycle and they run at steady power at the cycle

end (Morilhat et al., 2019).

Costs. Flexibility being included in the PWR design has no additional major costs until

reaching the maximum number of transients allowed by the license. For planned load-

following, no fuel cost adds for cycling, as the uranium fueled at the beginning of the

campaign adapts to flexibility based on EDF experience (EDF, 2013). Costs still occur due to

more maintenance for component upgrades, equipment life reduction and potential derating of

control rod drive mechanisms and of water and steam thermal cycle (IAEA, 2018), yet

compatible with vessel ageing.

Assumptions. Next the model considers free of cost ramping, and returns the solicitation type

and the frequency of cycling, differentiated by the deepness of load variations. The amplitude

is in the range of 0%-20% of the nominal power for light cycles (100%-80%-100%), up to

40% for mid-cycles (100%-60%-100%) and up to 70% for deep cycles (100%-30%-100%).

The budget of deep cycles is constrained by the license at 200 per year, and is set next for

mid-cycles at 300 cycles proportionately to the deepness, and to 3,000 cycles for light cycles

per year (see Ludwig et al. (2010) for comparable orders of magnitude).

Historically the nuclear power variation has remained since commissioning well below

allowed cycle-counting limits, hence an implicit respect of these values is assumed in

scenarios found in the literature while planning nuclear power. By explicitly looking at the

cycles’ profile, this study detects cases of excessive cycling and gives a normative vision on

the way the nuclear could adapt to increased intermittency in the future, beyond conservative

limits. We first formalize the problem and identify the market factors affecting the nuclear

operation, such as the capacity installed, the load factor and substitution possibilities, under

technological constraints and environmental regulation.

3. Modeling the power system

For nuclear load-following modeling, three types of assessments are identified in the

literature: (1) capacity expansion models for investment planning with cost-recovery approach

(JRC-EU-TIMES model; JRC, 2013); (2) technology studies where nuclear and renewables

match under physical and economic constraints including start-up costs (Jenkins et al., 2018);

and (3) power market models with plant dispatch based on marginal costs (Peng et al., 2018).

The framework developed here follows these trends and embeds capacity planning (POLES)

with technology constraints and market operation (EcoNUK): POLES provides the power

generation mix and EcoNUK depicts the nuclear operation over available technologies and

flows.

3.1. Model coupling

5

POLES model (Prospective Outlook on Long-term Energy Systems) is a long-term model

providing climate energy scenarios for the world, divided into 57 regions (Criqui et al., 2015;

Criqui and Mima, 2012). It is a bottom-up simulation model, representing the markets for oil,

gas, coal, biomass and hydrogen, with focus on the power sector module. Energy demand is

detailed for the main sectors such as industry, agriculture, service, residential, and transport,

each having its own demand profile. The electricity demand is endogenous and linked to the

GDP and population, and the supply is made of 41 technologies, of which ten are variable

renewables. With rich spatial and technology disaggregation, POLES limits the temporal

resolution to two-hour representative time-slices over 12 blocks by season, i.e. summer and

winter. POLES is simulated in Vensim language and is run annually from 2000 to 2100. For

renewable-conventional generator matching, the model ensures the capacity adequacy by

adding a ratio to renewable energies capacities.

EcoNUK dispatching model is run for three simulation years (2035, 2040 and 2050) with data

sent by POLES for the installed power generator and storage capacities, the total load, and

marginal costs by technology. EcoNUK uses the GAMS optimisation language with the Cplex

solver5, based on linear programming. The method has already been applied at a European

scale to the topic of nuclear load-following, with an hourly loop and more aggregated results

in terms of fatigue (Loisel et al., 2018). The version developed here follows similar dynamic

principles to describe the system operation over one year, with half-hour time slices and a

national loop.

The model simulates a centrally-dispatched market with the objective function of minimizing

the system short-term annual cost of operating generators, subject to satisfying the power

demand. The operating cost includes variable costs, the carbon price, and variable operation

and maintenance costs. When the system cannot absorb the natural inflow of fluctuating

renewables (wind, solar, marine energies and hydro run-of-river power), the energy in excess

is suppressed, the so-called load curtailment or lost load. Equations are listed in the Annex 1.

Within EcoNUK, the power plants are grouped into 12 technologies with similar technical

and economic characteristics as in POLES, yet some differences in specifications adapt to the

nuclear load-following description. There are two reactor types, used to operate either load-

following (called here Flexible, covering 2/3 of the fleet) or base-load (called Inflexible, 1/3

of the fleet). Although all reactors are technically capable to provide flexibility, the

management of the fleet is centralized, i.e. by the EDF operator, and some reactors, at the end

of the fuel cycle, are used as base-load units, and some others in flexible mode. The technical

constraints are minimum operational loads, maximum load factors, and ramping capability of

flexible technologies (see Annex 2).

Coupling. The EcoNUK model optimizes the power system for a given investment scenario

decided by POLES, together with the usage rate of power plants. A soft-linking one-direction

coupling is made to highlight the key characteristics of the nuclear planning. As no iteration is

further made, the flexibility obtained with the market operation model complements the long-

term planning with considerations on the short-term management of nuclear fleet, as an initial

step to long-term nuclear-renewable planning. Thus POLES captures the relevant properties

of the global energy system where the French power system integrates into, and EcoNUK

responds to the global model time-limitations by finely representing variable renewables and

nuclear dispatch. The two-model frame based on long-term energy planning (POLES) and

short-term operation (EcoNUK) is used to improve the understanding of the interaction

between technologies with some possible ways to use the nuclear power.

5 The General Algebraic Modeling System (GAMS) is suitable for modelling linear optimization

problems, being especially useful with large database (https://www.gams.com). The solver Cplex is

designed to solve large, difficult problems quickly (less than five minutes).

6

Fig 1. Diagram of soft-coupling of planning model (POLES) with power dispatch model

(EcoNUK)

Figure 1 shows the steps of core linking between the two models. On the top, there are the

legal targets of the French power mix in terms of renewables, nuclear and carbon emissions.

POLES is run for the key years 2035, 2040 and 2050 which are of high interest with concern

to high shares of each nuclear and renewables; it further transfers the power generation mix to

EcoNUK, with a given cost-effective adequacy in terms of installed capacity, storage and

demand use.

7

Scenario building. The scenario generated with POLES is in line with the French Energy

Transition Act aiming at reducing the nuclear power while increasing renewables, under a

global constraint of keeping the temperature increase at 2°C by 2100. Trajectories are

endogenous in POLES, with intermediary targets to match the scenario Ampere of the French

TSO (RTE, 2017) in 2035 and to attain zero net emissions by 2050. Power mix diversification

is attained according to the French Law, by reducing the nuclear share from 75% to 50% by

2035, and by increasing renewables to 40% in 2030, and to more than 60% by 2050.

Fig. 2. Scenario generation with POLES for France under 2°C global climate constraint

subject to the French Energy Law

POLES energy plans build on the economic rationality of market mechanisms that minimize

the investment costs and operational expenditures. Political commitments for emissions

targets are supported by carbon signals which result from the model into taxes of 200

€2015/tCO2 in 2030 and more than 700 €2015/tCO2 in 2050 in Europe. The carbon price in

Poles is different by region and in the French case is closely related to the normative social

level used by the government to sustain clean projects. For the national low carbon strategy to

be in line with IPPC guidelines, France Strategie Commission (Quinet, 2019) recommends a

trajectory of social carbon value of 250 €2018/tCO2 in 2030, 500 €2018 in 2040 and of 775 €2018

en 2050, or a Hotelling rule at 4.5% discount rate.

The political target setting the share of nuclear power to 50% of the power generation by

2035, means that some 38 reactors from the current 56 will be in operation at that time.

Economic evaluations show that the balance between the cost of nuclear phase-out and the

cost of refurbishment of old plants (called carénage) is attained at 30 GW of nuclear capacity

(Ademe, 2018). Thus, nuclear power will continue to play a significant role for several

decades under increasingly stringent carbon limits and higher demand patterns of electricity in

transportation and industry.

The need to diversify the electricity mix by reducing nuclear is motivated by the end of the

license period but also by an overall need to decentralize the power mix. With large

economies of scale, the nuclear management remains highly centralized, at the opposite of

targets of governance transformation to locally deal with renewable variability. Economic

considerations add as well, such as the country full dependency on uranium imports, and the

ambiguous business model of a large nuclear fleet: the advantage of low cost carbon-free

uranium is balanced by the fact that locally French imports could be expensive while exports

could locally be very cheap. During the winter time, the French nuclear fleet does not cover

the peak load and the country needs expensive peaking imports. While over the year, it

81% 81% 79% 80%72% 72% 67%

60%

45% 45%

26%13% 10% 14% 16%

25%31%

43% 45%56%

58%71%

0%

20%

40%

60%

80%

0

50 000

100 000

150 000

200 000

250 000

300 000

350 000

2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050

Sh

are

in G

en

era

tion

, %Inst

alle

d C

apac

ity,

MW

France (National Targets + 2° C World)

Coal NUC Geothermal Wind on shore

Wind off shore Hydro Solar Biomass

Oil Gas Storage PHS Batteries

V2G DSM Nuclear share Oz axis RES share Oz axis

NUC%

RES%

8

produces excessively and exports power at a low cost, without inframarginal rents that cover

the nuclear cost estimated at 60 €/MWh by the Court of Auditors (2014).6

Figure 2 shows the scenarios generated with POLES and trends of reduced nuclear power and

increased renewables. Variable renewables (solar, wind, hydro run-of-river and marine

energies) reach 56 % of the total generation by 2050, 73% while including dispatchable

renewables (hydro-lake, geothermal and biomass). It should be noted that the model cannot

take into account the spatial complementarity among renewable sources to include the

correlation of regional wind or solar profiles (de Sisternes, 2014); therefore, the need for

back-up technologies could be overestimated due to reduced smoothing effect from spatial

aggregation of renewable inputs in POLES. The main substitutes to nuclear in the model are

storage (pumped hydro-storage, batteries, compressed-air and vehicle-to-grid), gas-fired units,

demand-load curtailment and grid interconnections.

Annex 3 describes scenarios in terms of capacity installed and projected power generation in

2035, 2040 and 2050 and shows statically the transition steps by comparing the final state

with the year 2017. The scenario returns high prices of carbon, gas and oil, which helps

building the merit order of plants’ entry in the power market; net export flows remain high by

the end of the period, due to high shares of nuclear and renewables with must-run power and

fatal nature respectively. Note that capacities installed are almost the double in 2050

compared to 2017, due to low capacity factors for solar power and for on-shore wind, related

to nuclear.

Outputs of the model EcoNUK. The market segment simulated is the wholesale market

where all plants bid and supply in real-time. The market model returns the power volume

generated by each technology, the half-hourly power clearing price, and derived indicators

such as actual load factors and curtailment rates. The reactors’ flexibility provision is

converted into light, mid and deep cycles which are further compared with the licensed design

to conclude on the nature of cycling and the flexibility needs. Interactions between nuclear

and the other technologies are analyzed from the status of complement or substitute for each

load-following and baseload operation mode. At the end, aggregated indicators obtained with

dispatching will support the long-term nuclear planning.

4. Results

4.1. Analysis of coupling matching

Results obtained with high temporal resolution models are in general different from results

obtained with long-term models due to the mismatch between data on constraints and on wind

and solar inflows (Poncelet et al., 2004; Alimou et al., 2020). Annual flows obtained with

POLES are different from half-hourly generation flows dispatched with the model EcoNUK,

in the way that more flexible flows are necessary in the later model, as shown in Table 1,

where gas flows increases from 2035 to 2050 along with the renewable penetration rate.

Simulations run with EcoNUK are built such as to respect the shares of nuclear and

renewables obtained with POLES. These targets being attained, the adjustment variables for

adequacy fulfillment are the usage of gas-fueled plants and storage, and load curtailment, e.g.

much higher in EcoNUK than in POLES.

6 The cost covers the investment cost, the operation of reactors, the maintenance and safety measures, the

dismantling provision and the investment for modernization and license extension program (the above-

mentioned grand carénage).

9

Table 1. Results with models POLES and EcoNUK; variations are computed as Δ = POLES-

EcoNUK

Nuclear flows being similar among the two models, the need for gas increases in time,

following the trend of increase in renewables and decrease in nuclear. The gas is higher with

5.6 TWh in the year 2035, and with 14 TWh in 2050 in EcoNUK than in POLES, revealing

challenges to dispatch flows informed by POLES. The three gas technologies (combined heat-

and-power, combined cycle and simple cycle turbines) cover the missing baseload, mid-

baseload and peak loads that the decrease in nuclear eventual induces when wind and solar

inflows are low. The additional gas supply in EcoNUK covers in this way the punctual lack of

capacity to ensure adequacy, and the need of positive flexibility when the system meets

technology constraints to ramp up generators.

For negative flexibility, all generators participate when demand is lower than supply; when all

possibilities are saturated, the system curtails the variable renewables in excess. The total

flow follows the same trend as the tensions from positive flexibility, i.e. the curtail increases

in time, with the deployment of renewables, as shown in Table 2. The detail by renewable

source shows the limits of the system to absorb the solar power in particular, with loss of

loads higher than for wind; the next to be curtailed is the hydro-power, due to higher variable

cost for operating turbines. The year 2035 represents a scenario mix made of 57% of nuclear

and 42% of renewables, showing that these ratios seem to be a convenient combination for

matching conventional generators with intermittent inflows: the curtailment of wind and solar

energy is zero.

Table 2. Flows of curtailment of renewables in EcoNUK, by source

The EcoNUK model shows that the profile of different variable renewables combined with

the plant size results in a firm capacity (or capacity credit; Tapetado and Usaola, 2019)

which increases in time, meaning that at any moment there are at least 2.4 GW of capacity

available to supply in 2035, and at least 15 GW in 2050 (see Table 3). When variable

renewables can offer firm capacity over the year, they fully substitute conventional

dispatchable power at ratio 1 MW of renewables to 1 MW of nuclear or gas, provided that

ramping constraints do not inhibit the substitution. For higher inflows of renewables, the first

Generation, GWh

Technology POLES EcoNUK Δ POLES EcoNUK Δ POLES EcoNUK Δ

Nuclear 309 175 309 175 0 239 187 239 187 0 159 697 159 697 0

Coal - - 0 1 634 0 1 634 6 613 - 6 613

Oil - 0 0 0 13 -13 - 1 -1

Gas 3 212 5 936 -2 724 5 584 15 638 -10 054 17 578 31 912 -14 333

Hydro-Power 59 075 59 077 -2 59 718 56 708 3 010 60 927 56 988 3 939

Wind On-shore 130 080 130 080 0 171 823 171 734 90 192 293 192 218 74

Wind Off-shore 2 623 2 621 1 4 760 4 725 35 14 558 14 490 68

Solar 32 072 32 072 0 53 488 52 254 1 233 106 376 103 119 3 258

Other RES 7 279 7 279 0 20 267 20 267 0 81 484 81 485 0

Total 545 159 546 240 -1 081 558 213 560 526 -2 313 641 175 639 910 1 265

DSM 82 13 69 277 223 55 1 304 1 394 -90

Storage 1 644 2 150 -506 1 752 5 691 -3 940 1 647 10 475 -8 828

NUC / Generation 57% 57% 0% 43% 43% 0% 25% 25% 0%

RES / Generation 42% 42% 0% 56% 55% 1% 71% 70% 1%

vRES / Demand 47% 47% 0% 64% 65% -2% 88% 88% 1%

2035 2040 2050

Curtailment, GWh 2035 2040 2050

Wind On-shore 0 90 75

Wind Off-shore 0 34 69

Solar PV 0 1 233 3 258

Hydro Run-of-river 0.18 933 1 294

Total, GWh 0.18 2 291 4 695

10

to be phased-out of the market are the most expensive technologies, according to a descending

order of their marginal costs, ranked as follows: coal power plants, oil-fueled units, combined

cycles gas turbines, demand side management, simple gas turbines, combined heat-and-power

and nuclear, followed by renewables.

Table 3. Aggregated indicators related to adequacy obtained with EcoNUK

Surprisingly, the highest tension for adequacy is obtained in 2040, as shown by the indicator

Value of Lost Load (VOLL) measured in EcoNUK by the maximum shadow price of the

equilibrium between supply and demand. This reveals challenges in ramping up generators

and the need for an additional unit to meet the marginal MWh of demand; the value of this

tension is close to the cost of installing one more MW of the technology with the lowest fixed

cost, i.e. 16,000 €/MW for an open-cycle gas turbine (Jenkins et al., 2016). This represents a

signal of capacity adequacy issue showing that a mix in 2040 made of 43% nuclear and 49%

RES is not well enough calibrated for EcoNUK to easily meet the demand at any moment.

The average shadow price is however lower in 2040 than in 2050, when the mix made of 25%

nuclear and 65% renewables anticipates more DSM and storage means, along with a decrease

in exports.

The mix diversification through lower nuclear generally implies lower nuclear capacity, and

higher tensions to ensure adequacy. The alternative for a similar mix diversification is to keep

large capacities of nuclear fleet and to use less the reactors, ensuring in this way the adequacy

over high peak loads. The trade-off between power (GW) and energy (GWh) for mix

diversification significantly plays on the use of the nuclear plants and on reactors aging.

4.2. Nuclear operation

Scenarios obtained with POLES meet a cost-efficiency criterion at the system level with

respect to each technology investment and maintenance cost. Hence the trade-off between

investing in nuclear – gas – renewables defines an overall planning strategy further imposed

to EcoNUK through coupling. The strategy results in values of usage rates of nuclear around

75% over each period simulated (see Table 4). The annual usage rate is further depicted with

EcoNUK at half-hour time slices by each operating mode of nuclear, i.e. baseload and load-

following. Results show similar annual use of nuclear reactors among the two models in 2035,

but different in 2050; by that time, the system needs more flexible than mid- and base-load,

since firm capacity increases from renewables and substitutes to a more extent nuclear

baseload fleet.

Table 4. Usage rates of the nuclear fleet, by model and by operating mode

Cycling is therefore more challenging in 2050, as shown in Table 5 by the number of deep

cycles that are increasing from the year 2035 to 2050, when they account 228 events, largely

overpassing the currently licensed 200 deep cycles per year. As a trend, light and mid cycles

are decreasing over the period 2035-2050, while deep cycles are increasing, showing that

Year 2035 2040 2050

Firm Capacity of vRES, MW 2 600 5 491 14 969

max VOLL, €/MWh 456 16 207 639

Average shadow cost, €/MWh 173 210 276

DSM, frequency 27 279 642

Capacity Factor / Year 2035 2040 2050

Flexible Nuclear in EcoNUK 75% 75% 78%

Baseload Nuclear in EcoNUK 74% 76% 71%

All Fleet (POLES = EcoNUK) 75% 75% 76%

11

large deployment of variable renewables comes with the need for deeper and longer flexibility

than for frequent short oscillations such as obtained in 2035.

Table 5. The number of cycles of flexible nuclear fleet obtained with the model EcoNUK

Table reading. Cycle Type shows the amplitude of load-following: light cycles have an amplitude in

the range of 0%-20% of the nominal power (100%-80%-100%), mid cycles are up to 40% (100%-

60%-100%) and deep cycles are up to 70% of the reactor rated power (100%-30%-100%).

The budget for both light and mid cycles is respected over the period, provided that the

management follows the schedule set in the model EcoNUK with respect to three conditions:

- The dispatch of the fleet baseload – load-following occurs at the ratio of 1 : 2.

- The minimum rated power threshold is 30% of the nominal power.

- The speed of reaction of flexible reactors is 5%/half-hour.

Any change in these assumptions has consequences on the nuclear dispatch, on renewable

integration and curtailment, and on gas-originated flows. The influence of each key parameter

is next tested by changing each value while keeping the other indicators constant. Table 6

indicates the sensitivity of results to these parameters for the year 2050.

Table 6. Sensitivity of baseline to changes in ramping rates, minimum rated power and baseload

share

The speed of ramping. Faster reactors substitute gas supply and storage, and renewables are

better integrated as indicated by lower volume of curtailment. This suggests that storage in the

baseline supports technologies with ramping constraints, like nuclear reactors, rather than

storing intermittent renewable energy as expected. Increasing ramping rates makes decreasing

tensions on the equilibrium and the maximum VOLL slightly drops. At fixed total nuclear

flows, the split by operating mode is favorable to load-following compared to baseload: the

capacity factors increase for the load-following fleet. Ultimately, increased flexibility comes

with a cost in terms of reactors cycling, deep cycles in particular, which will further raise the

issue of compliance with the annual budget preventing earlier maintenance of ageing

components. At slower response of reactors, tested at 1%/half-hour speed, results show more

gas power needed and more curtailment, despite higher use of storage in support to flexibility.

The minimum rated power threshold. The indicator tested at rates of 20% and even 50% of the

nominal power shows results which are not too sensitive compared to the baseline, run at

minimum rate of 30%. Results vary however in the expected way: at lower minimum

Year Light Mid Deep

2035 1 411 279 83

2040 601 167 179

2050 161 95 228

Cycle Type

Baseline

Ramp 5%

Pmin 30%

BL 33%

1%/half-

hour

10%/half-

hour

20%/half-

hour20% 50% 10% 50%

Cycling

Light 161 267 195 246 152 179 183 140

Mid 95 88 67 74 90 92 92 81

Deep 228 11 296 311 229 231 225 239

Capacity factors

Baseload 71% 66% 68% 65% 73% 64% 62% 73%

Load-Following 78% 81% 80% 81% 78% 82% 77% 78%

Dispatching

Gas, GWh 31 912 36 834 29 817 28 683 31 818 33 049 29 751 33 609

Storage, GWh 10 475 12 099 9 175 8 039 10 494 10 231 9 690 10 993

Curtailment, GWh 4 695 7 606 3 747 3 392 4 598 5 775 3 417 5 745

max VOLL, €/MWh 639 639 639 621 639 639 639 639

Minimum rated power Baseload ShareRamping

12

threshold, nuclear is substituting the gas power as more flexible capacity is provided; while

ramping down at deeper level allows renewables to enter the market to a larger extent. At

higher minimum thresholds, the opposite effect occurs, e.g. higher gas supply, higher

curtailment as well.

The schedule of flexible nuclear fleet. A lower share of baseload means that more flexible

nuclear capacity is made available to the system; load-following does not necessarily occur

more often, but it is the magnitude of flexibility which varies, having an eviction effect of the

gas supply on the market. A higher share of baseload puts more pressure on the remaining

flexible capacity which has to cycle more; the direct effect from lower flexible capacity is

similar to the above tests, i.e. higher gas supply, higher curtailment, and more storage use.

Crossing indicators allows concluding that the highest sensitivity of results is obtained while

varying the ramping speed, with effects at both levels, on the nuclear fleet with concern to

cycling, and on the system in terms of gas supply and renewables integration. The value of a

flexible fleet is next revealed into two ways: 1) in relative terms, by supposing that the fleet

operates baseload instead of load-following; and 2) in absolute terms, supposing that one

reactor is out of operation over the entire year, here 2050 for test purposes.

1) Load-following versus Baseload operation reveals the support of flexible nuclear to the

system, avoiding thus curtailment of renewables and reducing gas power generation. Figure

3 shows that solar power in particular induces large inflows at mid-day and flows are partly

lost if nuclear operates baseload (upper graph) or and it is smoothly integrated when nuclear

acts load-following (bottom graph).

Fig. 3. Comparison of load-following with baseload nuclear over one day in January 2050

2) Having one reactor out of operation for technical reasons. This test allows measuring the

value of one reactor and the margins that the system has to hedge against potential technology

risk of unavailability. Results show that the system has the necessary capacity in 2050, since

there is no increase in the shadow cost for eventual lack of supply. The equivalent of the

0

10 000

20 000

30 000

40 000

50 000

60 000

70 000

80 000

90 000

100 000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

MW

Scenario Base-Load Nuclear

NucInfl Nuc Flex Wind Hydro RES GsCC CHP GsGT PV Storage

0

10 000

20 000

30 000

40 000

50 000

60 000

70 000

80 000

90 000

100 000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

MW

Scenario Load-Following Nuclear

NucInfl Nuc Flex Wind Hydro RES GsCC CHP GsGT PV Storage

13

marginal reactor phased-out is 700 GWh of additional gas over the year, and 400 GWh of

renewable flows curtailed. The period where gas substitutes the missing reactor are in general

the hours without solar power; by seasonality, these events are more frequent during winter.

The number of hours where the reactor would need a dispatchable substitute is around 4,000

hours, i.e. 46% of the year. Interestingly, the substitution does not occur 1 MWh of nuclear

(less) to 1 MWh of gas (more), as less than 1 MWh of gas is needed. The reactor phased-out

is replaced by another operational reactor with spare capacity; hence, the remaining reactors

run more, attaining capacity factors from 71% initially to 80% in the stress test for Base-Load

and from 78% to 79% for Flexible fleet.

In terms of power, the maximum gas supply over the year is 1740 MW, showing that

removing 1,000 MW of nuclear would need more dispatchable capacity, due to ramping

constraints of the remaining fleet to attain full power during positive flexibility requirements.

The model assumes that the flexibility provision is uniformly distributed among reactors,

therefore one reactor less means eventually issues to provide flexibility to the same extent as

initially.

Scenarios matching among the two models has been based on the constraint that the total

nuclear power is similar over the year; results have shown constraints to attain the same

amount of gas power flows, largely overpassing the outputs of POLES, e.g. 14 TWh of gas

more in EcoNUK in 2050. Therefore, next we analyze the requirements from nuclear power

for constant gas supply among the two models.

Alternative paths for keeping gas similar while coupling. In 2050, the French power

system is dominated by renewables (71%), followed by nuclear power (25%) with punctual

inflows of gas (3%). These aggregated indicators obtained with POLES modify the mix

power obtained with EcoNUK: renewables (70%), nuclear (28%), gas (3%) and storage (2%).

Consequently, keeping the gas constant requires more flexible nuclear power, i.e. 18 TWh of

additional nuclear compared to POLES outputs.

Fig. 4. Flexible nuclear supply with model EcoNUK in 2050 in Scenario Gas_constant

(Sce_Gas) and Scenario Nuclear_constant (Sce_NUC)

More nuclear is necessary to supply both positive and negative flexibility, as shown by Figure

4, where nuclear load-following is represented in August which records high inflows of solar

power and large load variations. Results show similar trends among the two scenarios, with

gas constant and alternatively nuclear flows constant; however the scenario where gas is

constant shows deeper ramping down and upper ramping replacing gas and eventually DSM

measures. The number of light cycles increases by 8% and of deep cycles by 3% compared to

the constant nuclear scenario, leading to even higher budget of transient necessary to comply

with the license.

4.4. Long-term planning options

Results obtained with the dispatching model EcoNUK are overall consistent with POLES

scenarios, showing the robustness of our linking exercise. Yet, technical constraints of

0

2 000

4 000

6 000

8 000

10 000

12 000

14 000

16 000

18 000

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 10

1

10

6

11

1

11

6

12

1

12

6

13

1

13

6

14

1

14

6

15

1

15

6

16

1

16

6

17

1

17

6

18

1

18

6

19

1

19

6

20

1

20

6

21

1

21

6

22

1

22

6

23

1

23

6

24

1

24

6

25

1

25

6

26

1

26

6

27

1

27

6

28

1

28

6

29

1

29

6

30

1

MW

hour

Nuclear Load-Following over 6 days in August

Sce_GAS Sce_NUC

14

ramping and minimum rated power seem to be the critical parameters for obtaining similar

generation flows among the two models. In the absence of hourly technical constraints, long-

term energy models usually need less flexibility than time-disaggregated models. Similarly,

our dispatching model needs more flexible flows and tends to select flexible nuclear power

rather than gas-fired units, due to high costs of gas and carbon. Fulfilling nuclear reduced

share target counterbalances the respect of carbon emissions limit, as more gas is necessary to

ensure flexibility. Uncertainty on the development of gas issued from hydrogen and on gas

plant with carbon capture and storage system, makes us suppose that higher gas use in the

future might increase the green-house gases, from carbon and methane emissions. Therefore

the trade-off for an energy planner is between the nuclear policy and the carbon emission

target.

Admitting the urgency of climate change actions, deviations from nuclear target shares should

be the policy to adopt. Under long-term targets from POLES, the market model EcoNUK

shows some details on the way the nuclear operation should be anticipated, by depicting the

schedule of nuclear power obtained in the Scenario Gas-constant.

1°. Anticipation of the uranium use. Capacity factors obtained with EcoNUK show high

usage rates of both baseload (90%) and flexible fleets (82%), higher than historical values

which are around 75%. Well defining the capacity factors allows planning the refueling

campaign, since the material flow inventory takes into account the percentage of the reactor

use over one cycle. National targets aim at stabilizing the nuclear waste, plutonium in

particular (PNGMDR, 2018). By 2022, some more 15% of plutonium will add to the current

deposit (350 tons), if no recycling is made, i.e. MOx processing7, thus coping with the target

of inventory stabilization. According to the Court of Auditors (2019), the balance between the

deposit of waste and its reprocessing cannot be guaranteed in the future unless a large number

of reactors use MOx as input. Anticipating the waste infrastructure, such as pools for spent

fuel pending reprocessing or reutilization, is critical for scenario building as new facilities are

necessary at 2025-2035 horizon.

2°. New design of reactors. The future design of reactors is triggered by new flexibility

requirements. Few evidence is generally revealed by scenarios on the flexibility provided with

nuclear power. Yet, this information is key to determine the system needs in terms of ramping

speed and transient reliability. Our results show that the system will need faster reactors and

longer and deeper cycling technologies. Within the current design and license, complying

with carbon targets would imply in the future that reactors perform excessive cycling and bear

additional fatigue. This will call for two solutions: refurbishment or early decommissioning,

with additional cost in the first case for plant upgrading; and sunk costs in the latter case.

Alternatively, regulation could adapt the limit of deep cycles admitted per year to new system

needs, e.g. from currently 200 cycles to some 250 per year.

New types of solicitation will change the reactor design, for both new reactors and those

under modernization, and should integrate at their early stage of design the capability to

operate more flexibly. Scenarios should be able to inform on new gradients of the load

variations and manoeuvers, like the waiting time before starting a new cycle (or the

stabilization of the power output after ramping due to xenon oscillations), the boundary of

operation like minimum core power at which a reactor can safely generate, the solicitations

from the grid in term of frequency restoring, and cycling periodicity, etc. Two constraints will

7 Nuclear reactors have three input options: natural uranium, used uranium, and MOx fuel, which is

mixed oxide based on recycled plutonium. France is one of the few countries having adopted what is

called a partially closed cycle due to recycling phase of the plutonium, which is the element with the

highest radiotoxicity. In the nuclear power plants in France, MOx fuel represents approximately 10%

of total fuel and it is used in some 20 reactors of the French fleet (Thiollière et al. 2018).

15

add to nuclear industry, one related to the technology capability to increase the speed and to

decrease the security threshold to some 20% of the rated power; and one related to economic

considerations including the cost of design change which could give priority to speed over the

minimum rated power in terms of opportunity cost.

3°. Nuclear planning: energy versus power. The Energy Transition Act mentions that 14

reactors should be phased-out by 2035, and distribute the effort by closing one reactor per

power plant (ETA, 2015). This would limit the economic and social cost in terms of

employment, regional dependency of industrial sites, and geographical power mix equilibria.

Considerations being mostly political and social, the discussion on the future power system

could be oriented towards capacities instead of flows, i.e. maintaining as many reactors but

using them less, as mix diversification is attained in both cases, yet with varying capacity

factors. The need of the power system for low-carbon supply in EcoNUK is translated into

large capacity needs over some hundreds hours per year, in particular during winter and night

time, with large load variations over short seasons, like days. Decreasing therefore the nuclear

share could review the schedule of reactors’ closure subject to the additional stress put on the

remaining reactors. This further requires to better anticipate the substitution with storage,

demand side management and green gas supply, as locally perfect substitutes to nuclear

power, in order to avoid “unfeasible” solutions as returned by the model EcoNUK, over-

constrained by reduced both nuclear capacity and gas flows.

4°. Flexibilty provision: a market-based mechanism and a matter of central planning

The power mix operation optimized with EcoNUK has showed excessive cycling in 2050 and

however low shadow cost in 2050, raising the issue on the market incentives to supply

flexibility in the future. Methodologically, prices derived from a dispatching problem cover

the short-run operation, and make signals coincide with long-run capital cost, including

refurbishment. Yet, irregular non-convexities due to ramping and costs for upgrading deviate

from long-term cost, hence, the marginal cost-based mechanism, specific to liberalized

electricity markets, can discourage the investment in flexible technologies.

Incentivizing operators to supply flexibility might need additional regulatory provisions, such

as binding obligations to operate load-following at the request of the system operator. The

issue is even more challenging in front of reduced capacity of nuclear power in the future and

of limited output of flexible gas due to carbon emissions. In France, the market redesign

includes the forward capacity market, which is operational since 2017, but has a limited

horizon of four years. Other projects are contracts for differences which will concern the new

plants during the first seven years of their operation and are meant to secure the investor

incomes (CRE, 2018).

Nuclear load-following requires central planning at the plant level as well. Beyond technical

requirements, flexibility with nuclear reactors needs new O&M plant specifications, new

safety analysis, codes and standards, and mostly needs human resources for special controls

and monitoring (IAEA, 2018). As any innovative work and organization process, the timespan

will cover not only the human resource training, but would face inertial phases of the

historical load-following experience and instrumentation (Tillement and Hayes, 2019). New

managerial routines will be necessary for frequent maneuvering of reactors, such as to address

the periodicity of power calibration and surveillance.

The entities involved in the flexible operation of nuclear power plants are mainly the national

regulator body (ASN), the reactors operator (EDF), and the transmission system operator

(RTE).

The Nuclear Safety Authority (ASN) has the critical and primary role in the flexible operation

and its main responsibilities are to authorize, maintain and review regulatory requirements

16

governing safe operation, and maintenance of the plant design and license, including the

flexible operation aspect, such as to ensure public health and safety.

The operator, EDF, has the ultimate responsibility for safe operation of nuclear power

plants, ensuring compliance with the plant’s license, and deciding the modes of flexible

operation (IAEA, 2018).

It works closely with the grid operator, RTE, which sets the technical and commercial

requirements for frequency control, reduced load and power ramping in line with grid codes.8

A common understanding is therefore key to ensure the compliance between grid

requirements and plant capability of power control, leading to well established protocols that

optimally ensure flexibility.

This analysis concludes that flexibility is not restricted to a momentary power adjustment, but

it is a long decision process which needs prior organization of the work and staff training, the

coordination between regulators, plant operator, grid operator and waste reprocessing facility,

along with the support and the expertise of scientists, general public and policy-makers.

Nuclear flexibility provision seems ultimately a rigid long process with prior organization,

regulation and innovation, hence long-term scenarios should more comprehensively include

all stakeholders to reach an informed decision on the need of nuclear flexible operation.

5. Concluding remarks

Decarbonization of the French electricity system will massively be based on renewables,

nuclear and carbon sequestration, yet it be built on lasting inertial conventional power

systems. Coupling long-term planning with short-term operation showed that including

nuclear detailed constraints on load-following is the linking necessary approach to assess the

French power system flexibility. The combination between renewables, gas and nuclear-based

capacities and flows multiplies the number of scenarios while testing the applicability of

carbon targets in particular in power systems with high shares of baseload and mid-merit load

generators.

The technological capability of power systems to face the instantaneous variability of

renewables makes in general energy scenarios ambiguous and new metrics to assess their

feasibility are necessary. The one-direction model coupling has transferred the planning

strategy from POLES to the market model EcoNUK to make a loop on the load-following

with nuclear power. More specifically we showed that high shares of intermittent renewables

in France by 2050 could add pressure on nuclear power plants in terms of ramping and

cycling, and according to the current license provision, could push nuclear reactors to retire

earlier. New metrics on the system flexibility and technology fatigue are necessary to steer

climate policy and investment decisions based on high-fidelity short-term representation of

the energy system. The study conclusions could be exploratory in understanding the way that

scenarios impacting the nuclear pathway choices fuel the scientific and societal debates.

The issue of flexibility and security of the supply is extensively discussed in the energy

system community; this study complements existing assessments with power generation

adequacy in the operational stage and how this could influence back the energy planning for

long-term investments. This paper has been motivated by several methodological issues raised

by the power sector planning practice: (1) scenarios on the power mix implicitly use the

nuclear power as flexible option to support massive integration of variable renewables; (2) the

measure of flexibility is often a matter of capacity adequacy, and need to be complemented by

the transient of reactors cycling and load variation types (short/ long, light/ deep cycles); (3)

the indicators which evaluate the feasibility of carbon targets vary in general with the

audience: a policy-maker use capacities installed (unit measure: MW), a policy planner

8 https://clients.rte-france.com/lang/fr/clients_traders_fournisseurs/services_clients/reglement_sogl.jsp

17

looking at the energy balance is using the total primary energy (tons oil equivalent), a

physicist looks at the amount of joules generated, and an economist at the flows sold on the

market (MWh). Our approach integrates these perspectives as political bounds and

technological constraints, and builds the bridge between the energy planning and the

operational stage to conclude on the use of the nuclear fleet.

Further developments should cover the normalization of cycling for modern reactors by

means of physics tools and expertise, and to develop the managerial aspects of work

organization to operate flexible reactors in a safe and reliable way. Scenarios, as static

pictures of the future energy mix, might ignore physical material energy principles, making

some scenarios infeasible; and from sociological and managerial perspectives, ignoring the

human resource component and the large spectrum of stakeholders involved in the nuclear

flexibility provision would somehow underestimate the length of the process. The balance

between renewables and nuclear should integrate the nuclear load-following accounting in

terms of cycles even in cases with reduced nuclear share, such as to dispatch a diversified

power mix in a well-coordinated and cost-efficient way.

Acknowledgment. We appreciate the financial support from the French National Centre for

Scientific Research CNRS Energy unit (Cellule Energie) through the project PEPS 2020 SCANNER

(SCenario Assessment of Nexus Nuclear Energy & Renewables).

References

Ademe 2020, Scenarios Energy-Climate 2035-2050, updated. In French. Report 010305.

Ademe 2018, Paths of the power mix to 2020-2060. In French. Report 010655.

Ademe 2016, Power mix with 100% renewables. In French. Report 8891.

Alimou Y., Maïzi N., Bourmaud J-Y., Li M., 2020. Assessing the security of electricity supply

through multi-scale modeling:The TIMES-ANTARES linking approach, Applied Energy 279:

115717.

Allard S., Mima S., Debusschere V., Quoc T-T., Criqui P., Hadjsaid N., 2020. European transmission

grid expansion as a flexibility option in a scenario of large scale variable renewable energies

integration. Energy Economics 87: 104733.

ANCRE, 2013. National Alliance for the Coordination of Research for Energy. Scenarios for energy

transition. In French. At http://scenarios.allianceenergie.fr/?app=ancre

ANL, Aragonne National Laboratory, 2018. Balancing nuclear and renewable energy. Press release.

AREVA-EdF, 2009, Preconstruction Safety Report, Sub-chapter 1.2, General description of the unit,

UKEPR Issue 01.

Bertsch, J., Growitsch, C., Lorenczik, S., Nagl, S., 2016. Flexibility in Europe's power sector — An

additional requirement or an automatic complement?. Energy Economics 53: 118–131.

Braunreiter L., Blumer Y.B. 2018. Of sailors and divers: How researchers use energy scenarios,

Energy Research & Social Science 40: 118-126. 2018.

Bruynooghe C, Eriksson A, Fulli G. 2010. Load-following operating mode at Nuclear Power Plants

(NPPs) and incidence on Operation and Maintenance (O&M) costs.Compatibility with wind power

variability, JRC, European Commission.

Cany, C., Mansilla, C., Mathonniere, G., da Costa, P., 2018. Nuclear contribution to the penetration of

variable renewable energy sources in a French decarbonised power mix, Energy 150:544-555.

Court of Auditors, 2014. The cost of nuclear power generation. Update. In French. At

https://www.ccomptes.fr/sites/default/files/EzPublish/20140527_rapport_cout_production_electricite_

nucleaire.pdf

18

Court of Auditors, 2019. The upstream of the nuclear fuel cycle. In French. At

https://www.ccomptes.fr/system/files/2019-07/20190704-synthese-aval-cycle-combustible-nucleaire-

2.pdf

CRE, French Energy Regulatory Commission. 2018. Thesis on the market design of the electricity

sector. In French. Report E-cube. http://fichiers.cre.fr/Etude-perspectives-

strategiques/3Theses/3_These_MarketDesign.pdf

Criqui, P., Mima, S., 2012. European climate—energy security nexus: a model based scenario

analysis. Energy Policy 41, 827–842. https://doi.org/10.1016/j.enpol.2011.11.061.

Criqui, P., Mima, S., Menanteau, P., Kitous, A., 2015. Mitigation strategies and energy technology

learning: an assessment with the POLES model. Technol. Forecast. Soc. Change

90, 119–136. https://doi.org/10.1016/j.techfore.2014.05.005

de Sisternes FJ. 2014. Risk Implications of the Deployment of Renewables for Investments in

Electricity Generation. PhD Thesis MIT.

Després J., Mima S., Kitous A., Criqui P., Nouredine Hadjsaid N., Noirot I., 2017. Storage as a

flexibility option in power systems with high shares of variable renewable energy sources: a POLES-

based analysis, Energy Economics 64: 638–650.

EDF, 2013. Load following. EDF experience feedback. IAEA technical meeting, Paris. At

http://www.iaea.org/NuclearPower/Downloadable/Meetings/2013/2013-09-04-09-06-TM-

NPE/8.feutry_france.pdf

ETA, 2015. French Energy Transition Act, at https://www.gouvernement.fr/en/energy-transition.

EUR, 2012. European Utility Requirements for LWR Nuclear Power Plants. Volume 2, Generic

Nuclear Island Requirements. www.europeanutilityrequirements.org .

IAEA, 2018. Non-baseload operations in nuclear power plants: load-following and frequency control

flexible operations, Report NP-T-3.23.

JRC, 2013. European Commission – Joint Research Centre. The JRC-EU-TIMES model - Assessing

the long-term role of the SET Plan Energy technologies, Report EUR 26292 EN.

Jenkins J.D., Z. Zhou, R. Ponciroli, R.B. Vilim, F. Ganda, F. de Sisternes et al., 2018. The benefits of

nuclear flexibility in power system operations with renewable energy, Applied Energy 222:872–884.

Kraan O., Chappin E, Kramer GJ, Nikolic I., 2019. The influence of the energy transition on the

significance of key energy metrics. Renewable and Sustainable Energy Reviews 111:215–223.

Loisel R, Alexeeva V, Zucker A, Shropshire D., 2018. Load-following with nuclear power: market

effects and welfare implications, Progress in Nuclear Energy 109: 280-292.

Ludwig H., Salnikova T., Stockman A., Waas U., 2010. Load cycling capabilities of German nuclear

power plants, International Journal for Nuclear Power 55(8/9).

Mantripragada H, Rubin ES., 2018. Techno-Economic Analysis Methods for Nuclear Power Plants.

SSRN Electronic Journal. Doi: 10.2139/ssrn.3198421.

Morilhat, P., Feutry, S., Le Maitre, C., Favennec, J.M., 2019. Nuclear Power Plant flexibility at EDF,

hal-01977209.

Negawatt Association, 2017. Scenario Negawatt 2017-2050. In French. Report 170126a.

OECD-NEA Nuclear Energy Agency, 2019. The Costs of Decarbonisation: System Costs with High

Shares of Nuclear and Renewables. Report 7299.

OECD-NEA, 2015, Projected costs of generating electricity, https://www.oecd-nea.org/ndd/egc/2015/

OECD-NEA Nuclear Energy Agency, 2011. Technical and Economic Aspects of Load Following with

Nuclear Power Plants, http://www.oecd-nea.org/ndd/reports/2011/load-following-npp.pdf

Pedde, S., Harrison P.A., Holman I.P., Powney G.D., Stephen L., Schmucki R., et al., 2020. Enriching

the Shared Socioeconomic Pathways to co-create consistent multi-sector scenarios for the UK. Science

of The Total Environment. 143172. In Press.

Peng F, Zhou W, Sui X, Hu S, Sun H, Yu P. 2018. Equivalent Peak Load Regulation of Nuclear

Power Plant Considering Benefits of Different Power Generation Groups. Energy Procedia 152: 227-

232.

19

Persson J. et al., 2012, Additional Costs for Load-following Nuclear Power Plants. Experiences from

Swedish, Finnish, German, and French nuclear power plants. Elforsk rapport.

PNGMDR, 2018. French National Plan for the management of the Radioactive Materials and Waste

2016-2018. Report of the Ministry of Energy Transition. At https://www.ecologique-

solidaire.gouv.fr/sites/default/files/16308-GB_PNGMDR_2016-

2018_DEF_Web_pap_1%20ao%C3%BBt%2017_0.pdf

Poncelet K., Delarue E., Duerinck J., Six D, D’haeseleer W., 2014. The importance of integrating the

variability of renewables in long-term energy planning models. Rome, Italy.

Ponciroli R., Wang Y., Zhou Z., Botterud A., Jenkins J., Vilim R.B., Ganda F., 2017. Profitability

Evaluation of Load-Following Nuclear Units with Physics-Induced Operational Constraints, Nuclear

Technology, DOI: 10.1080/00295450.2017.1388668.

Quinet A, 2019. The value of social action. The social value of carbon to sustain the public

investments. In French at https://www.strategie.gouv.fr/sites/strategie.gouv.fr/files/atoms/files/fs-

2019-rapport-la-valeur-de-laction-pour-le-climat_0.pdf

RTE, 2017. Generation Adequacy Report of the electricity supply-demand balance. In French.

Weimer-Jehle W, Buchgeister J, Hauser W, Kosow H, Naegler T, Poganietz WR et al. 2016. Context

scenarios and their usage for the construction of socio-technical energy scenarios. Energy 111 (15):

956-970.

Shift Project, 2018. The carbon transition think tank. Future studies on the energy transition 2050.

Tapetado P., Usaola J., 2019. Capacity credits of wind and solar generation: The Spanish case.

Renewable Energy 143 :164-175.

Thiollière N., Clavel J.B., Courtin F., Doligez X., Ernoult M., Issoufou Z., et al., 2018. A methodology

for performing sensitivity analysis in dynamic fuel cycle simulation studies applied to a PWR fleet

simulated with the CLASS tool. EPJ Nuclear Sci. Technol. 4, 13 (2018)

https://doi.org/10.1051/epjn/2018009

Tillement S., Hayes J., 2019. Maintenance schedules as boundary objects for improved organizational

reliability. Cognition, Technology and Work, Springer Verlag. doi: 10.1007/s10111-018-0530-y.

WNA, 2020. Nuclear Power in France. Last accessed at 16 december 2020. At https://www.world-

nuclear.org/information-library/country-profiles/countries-a-f/france.aspx

Annex 1. Model equations

Symbols

NPP – nuclear power plants

Index

tech – technology type (1 to 12)

h – half-hours over one year (1 to 8760 x 2)

Fixed Variables (Inputs)

Cvom – variable cost of operation and maintenance (€/MWh_output)

Cfuel – cost of fuel (€/MWh_input)

Ktech – capacity installed by technology (MW)

PM – price of imports (€/MWh)

TaxCO2 – carbon tax (€/t CO2)

Variables (Outputs)

CostFuel – annual fuel cost of NPP operators (€)

CostVOM – annual variable costs of NPP operators (€)

Cycle_uph – the amplitude of positive flexibility of NPP at hour h (MW∙h)

Cycle_downh – the amplitude of negative flexibility of NPP at hour h (MW∙h)

Dh – hourly power demand (MW∙h)

20

EG – annual energy sale of nuclear power (MW∙h)

– total annual carbon emissions (t)

Fobj – the objective function of the system operator (€)

Gentech – power generation by technology (MW∙h)

Curth – output suppression (MW∙h)

Mh – hourly power imports (MW∙h)

REV – annual revenue of the nuclear operator from the sale of energy (€)

South – hourly power generated with the storage system (MW∙h)

Sinh – hourly power filled in the storage technology at hour h (MW∙h)

Sth – cumulated energy stored at hour h (MW∙h)

Sth-1 – cumulated energy stored at hour h-1(MW∙h)

Xh – hourly power exports (MW∙h)

Parameters

AFtech – plant availability annual factor (%)

cftech – carbon emission coefficient by technology (tCO2/MWh_input)

Effs – efficiency of storage technology (%)

Efftech – efficiency of power generation by technology (%)

MinLoadh,tech – minimum generation level (%)

LFh,tech – hourly load factors of variable renewables (in the range 0-1)

– transport and distribution loss rate (%)

– ramp up rate, by technology (%)

– ramp down rate, by technology (%)

Eq 1. The objective function = System costs minimisation:

Eq 2. Hourly power market equilibrium Supply = Demand:

Eq 3. Ramping constraints:

Eq 4. Used capacities are lower than installed capacities times the annual availability factor

and the natural input inflows for renewable energy technologies:

Eq 5. Minimum load condition = hourly generation has a minimum level of production:

Eq 6. Storage dynamics:

Eq 7. Power discharged is lower than the power charged over the year:

Eq 8. Total system CO2 emissions:

21

Eq 9. Total curtailment of on and off-shore wind power, hydro power and solar power:

Eq 10. Cycling accounting:

, if >0

if <0

Annex 2. Inputs of the model, by technology type in 2050

Note. Max Availability is the maximum load factors and defines the maximum use of a technology

due to a limited natural resource inflow, to the power plant unavailability, or to political will to limit

the use of imported fuels.

Annex 3. Scenarios obtained with the model POLES for the years 2035, 2040 and 2050

EfficiencyMax

AvailabilityRamp

VOM

CO2= 767 €/t

% %/year %/half-

hour €/MWh

Nuclear Inflexible 36% 90% 0.1% 22

Nuclear Flexible 36% 90% 5% 22

Hydro River 100% 42% 100% 3

Hydro Lake 100% 28% 100% 3

Coal 40% 70% 25% 509

Oil steam turbine 41% 70% 50% 639

CCGT (Combined cycles gas 55% 80% 10% 324

NGGT (Natural gas gas turbines) 40% 100% 90% 452

CHP (Combined heat and power) 70% 70% 10% 258

Wind On-shore 100% 24% 100% 1

Wind Off-shore 100% 38% 100% 1

Solar 100% 13% 100% 1

Other RES 100% 25% 100% 1

Technology

Capacity Generation CF Capacity Generation CF Capacity Generation CF Capacity Generation CF

MW GWh % MW GWh % MW GWh % MW GWh %

Nuclear 63 130 382 320 69% 47 225 309 175 75% 36 353 239 187 75% 24 030 159 697 76%

Coal 2 930 5 310 21% 1 572 - - 1 928 1 634 10% 1 369 6 613 55%

Oil 6 550 5 310 9% 2 955 - - 2 815 - - 4 330 - 0%

Gas 12 120 30 207 28% 13 660 3 212 3% 14 458 5 584 4% 16 301 17 578 12%

Hydro River 10 327 42 000 46% 5 727 21 152 42% 5 741 21 205 42% 5 766 21 297 42%

Hydro Lake 8 231 16 410 23% 15 393 37 923 28% 15 632 38 513 28% 16 085 39 630 28%

Wind On-shore 11 790 21 210 21% 89 039 130 080 17% 99 832 171 823 20% 91 929 192 293 24%

Wind Off-shore 10 30 34% 1 114 2 623 27% 1 716 4 760 32% 4 355 14 558 38%

Solar 6 550 10 620 19% 35 598 32 072 10% 53 033 53 488 12% 94 240 106 376 13%

Other RES 4 397 12 270 32% 8 265 7 279 10% 14 478 20 267 16% 37 289 81 484 25%

Total 126 035 525 687 48% 220 549 545 159 28% 245 987 558 213 26% 295 694 641 175 25%

DSM 873 82 1% 1 270 277 2.5% 3 979 1 304 4%

Storage (PHS + CAES +

Batteries)4 965 5 310 12% 3 940 1 644 5% 3 518 1 752 5.7% 7 599 1 647 2%

Connections Imports, MW 11 000 23 000 25 000 27 000

Connections Exports, MW 17 000 28 000 31 000 34 000

National Demand, GWh 480 000 413 276 427 420 471 478

Net Exports, GWh 38 000 60 084 55 524 54 611

Losses, GWh 7 687 1.5% 71 800 13.2% 75 268 13.5% 115 085 17.9%

NUC / Total Generation 73% 57% 43% 25%

NUC / Demand 80% 75% 56% 34%

RES/ Generation 16% 35% 49% 65%

Variable RES / Demand 7% 40% 54% 66%

Scenario POLES 2050Scenario POLES 2040Scenario POLES 2035Actual mix, 2017

Technology

22