Green Ammonia Production in Stochastic Power Markets
Abstract
:1. Introduction
2. Methodology
2.1. Power-to-NH3 Production Model
- N is the total number of hours in the optimization period
- is the power sold back to the grid at time t in MWh
- is the power provided through a PPA contract or off-grid connection to a generating asset at time t in MWh
- is the power bought from the grid at time t in MWh
- is the normalized electrical loss associated with the plant
- is the spot price when selling/buying power at time t in EUR/MWh
- is the price of electricity provided through the PPA in EUR/MWh
- is the quantity of NH3 produced at time t in tonnes of NH3
- T is the total time for the NH3 contract
- is the quantity of H2 produced at time t in tonnes of H2
- is selling price of NH3 at time t in EUR/tonnes of NH3
- is the minimal production capacity of the NH3 process (set to 0.2, i.e., the process cannot run at a lower load than 20% of the maximum load)
- is the maximal hourly capacity of the NH3 process in tonnes of NH3
- is the NH3 contract in tonnes of NH3
- is the total power used to produce NH3 at time t in MWh
- is the power used by the electrolyzer at time t in MWh
- is the power used for the water treatment at time t in MWh
- is the power used by the NH3 process at time t in MWh
- is the energy consumption for the electrolyzer to convert electricity into H2 in MWh/t of H2
- is the energy requirement for the water treatment in MWh/tonnes of H2
- is a binary variable for the production of NH3 at time t i.e., its value is 1 when NH3 is produced and 0 when not
- is the power consumed by the NH3 process when producing NH3 in MWh
- is the power consumed by the NH3 process when in standby in MWh
- is the mass balance between NH3 and H2
- is the mass balance between H2O and H2
- is the grid connection limit in MW.
- The power consumption of the electrolyzer is approximated to be linear with respect to the load. In reality, the load curve of an electrolyzer is not linear, as optimal working conditions are typically at 80% of full load. The results will be slightly more optimistic than reality, but the effect should be minimal and relatively constant throughout the different scenarios.
- The power consumption of the Haber–Bosch is modeled using two levels: when the unit is producing and when the unit is on standby. This simplistic modeling approach is more restrictive than realistic working conditions, as higher efficiency rates should be attainable as load increases.
- The plant cannot buy and sell power at the same t. This reflects what would happen in reality.
- Only the renewable power can be sold to the grid. As the plant cannot buy and sell at the same t, this means only the power produced by the renewable assets or the power provided through the PPA can be sold to the grid.
2.2. Electricity Prices Model
2.2.1. Electricity Price Model Calibration
- , , vector of observables,
- vector,
- vector,
- vector of serially uncorrelated disturbances with and .
- , serially uncorrelated disturbances with and .
2.2.2. Model Implementation
- We collect daily settlement prices of M1, Q1, Y1, Y2, Y3 Future contracts, where M1 refers to front month, Q1 front quarter, Y1 front year, Y2 front year +1, Y3 front year +2.
- The data period was 1 July 2002 to 18 April 2023. The entire available series was used to remove bias from choosing a specific calibration window, especially given the very volatile period of 2021 and 2022. As we are interested in the volatility and mean reversion speed of (log) returns, we considered using a long historical period as the most robust option, also to reduce sensitivity to localized market shocks, while still attributing more weight to recent observation thanks to the feature of the Kalman filter.
- We calibrate the state space model presented in Section 2.2.1 to estimate the parameters k and , used in Equation (9) to generate future electricity prices.
2.3. Ammonia Price Model
- A growing demand for green ammonia as a critical tool that will be adopted, for example, to decarbonize transport and agricultural industries.
- The premium currently charged to certify renewable energy (e.g., Guarantees of Origin in Europe) will be transferred to the price of ammonia produced from renewables.
- We collect Western Europe Ammonia CFR (Cost&Freight) [30] spot price historical data from 1 January 2020 to 31 January 2023 (constrained by availability). The data are only available on a weekly basis.
- We calibrate the model to estimate using the historical volatility of the price return series described in the point above.
- The risk-free rate considered is 0.03, based on the 10-year US Treasury [28] on 17 April 2023.
- The net cost of storing ammonia (defined as the cost of storage minus pure benefit) is calculated by considering capital expenditure (CAPEX) and operational expenditure (OPEX), as identified in [31]. The resulting cost of storage, accounting for the benefit of holding the asset, is 2%. It should be mentioned that an alternative method to estimate is by utilizing the spot-forward relationship. However, due to the limited liquidity of ammonia-forward contracts, we have opted for the CAPEX/OPEX approach as it is considered more reliable.
- We simulate weekly prices to a 3-year horizon and 4000 Monte Carlo scenarios.
- Starting spot price is set at 350.70 EUR/tonne, as observed on 18 April 2023 [30].
3. Scenarios Definition
3.1. Co-Located Assets Configuration
3.2. Pay-as-Produced PPA Configuration
3.3. Baseload PPA Configuration
4. Discussion
- Solar energy generates less volatile revenues compared to wind energy. Furthermore, the lower load factor and production profile of solar results in a lower median P&L, as the generation is generally lower, and the system is forced to buy external electricity.
- Combining wind and solar power reduces the risk of cannibalization, therefore maximizing profit optimization activities for the electrolyzer but increasing volatility.
- Increased committed volumes of NH3 reduce revenues’ uncertainty, resulting in a lower P&L volatility but also lower median P&L.
- In a high-price environment, more energy through a BL PPA results in an improved median P&L, as it fixes the electricity price throughout the entire duration of the contract, thus significantly reducing price risk.
- However, we can see that a BL PPA generally hampers the system performance by restricting opportunities for profit optimization and NH3 production in the electricity market.
- Solar generation input enhances the P&L for electricity when compared to BL generation. However, there is still room for improvement based on the interplay between the solar profile and consumption patterns.
- Confirming the findings of the BL case, higher committed NH3 volumes, and increased electrolyzer capacity contribute to a reduction in volatility. However, these factors still have a negative impact on the P&L.
- Optimal P&L for solar is achieved by adopting lower NH3 commitments and a smaller electrolyzer capacity. This outcome can be attributed to the higher value of electricity relative to NH3, which is likely influenced by a lower procurement price. When buyers opt for a Pay-as-Produced approach, they receive a discount but also assume the risk of cannibalization associated with the solar profile. The ability to mitigate cannibalization risk using the electrolyzer as a form of storage (i.e., producing ammonia when market electricity prices are low) further supports the superior P&L of this configuration.
- Procuring the electricity via a Pay-as-Produced PPA featuring a mix of solar and wind generation. This allows one to buy electricity at a discount while minimizing the cannibalization risk, thanks to the negative correlation between wind and solar generation. The mixed input generation profile also allows great optimization, as the electrolyzer has more opportunities to choose from when to produce NH3.
- Committing lower volumes of NH3. We have observed that higher NH3 volume commitment results in lower volatility of the P&L but with a negative impact on the P&L distribution.
- Lower electrolyzer capacity. In the cases analyzed, the result was a higher median profit, as the electrolyzer improved profits by optimizing between the cheap electricity purchased via the PPA and the market prices.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Correction Statement
Abbreviations
BL | Baseload |
CFR | Cost&Freight |
CAPEX | Capital expenditure |
EEX | European Energy Exchange |
GBM | Geometric Brownian Motion |
GW | Gigawatts |
IEA | International Energy Agency |
ktonnes | kilo tonnes |
Mtonnes | Mega tonnes |
MW | Megawatts |
MWhr | Megawatts hour |
OPEX | Operational expenditure |
OU | Ornstein-Ulenbeck |
PaP | Pay as Produced |
P&L | Profit and Loss |
PPA | Power Purchase Agreement |
PtX | Power-to-X |
Appendix A
Parameter | Variables Optimized |
---|---|
Electrical losses, | Power sold, |
Price of electricity provided through the PPA, | Power bought, |
Spot price of the power modeled, | Power used, |
Power procured through the PPA, | Ammonia produced, |
Selling price of NH3, | Power used by the electrolyzer, |
Minimal production capacity of the NH3 process, | Power used for the water treatment, |
Maximal hourly capacity of the NH3 process, | Power used by the NH3 process, |
NH3 contract, | H2 produced, |
Energy consumption for the electrolyzer, | Binary variable for NH3 production, |
Energy requirement for the water treatment, | |
Power consumed by the NH3 process when producing NH3, | |
Power consumed by the NH3 process when in standby, | |
Mass balance between NH3 and H2, | |
Mass balance between H2O and H2, | |
Grid connection limit, |
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Parameter | Unit | Symbol | Value |
---|---|---|---|
Electrical losses | % | 3.0 | |
Energy requirement for the water treatment | MWh/tH2O | 0.002 | |
Energy requirement for the electrolyzer | MWh/tH2 | 53.4 | |
Grid connection limit | MW | 280 | |
Capacity of the electrolyzer | MW | 100 | |
Capacity of the Haber–Bosch unit | tNH3/h | 13 | |
NH3 annual contract | tNH3/week | 600 | |
Power consumption of the Haber–Bosch unit in operation mode | - | 0.52 | |
Power consumption of the Haber–Bosch unit in standby mode | - | 0.1755 | |
Solar installed capacity 1 | MW | 250 | |
Mixed installed capacity 2 | MW | 250 | |
PPA baseload price | EUR/MWh | 130.61 | |
PPA solar PaP price | EUR/MWh | 102.91 | |
PPA mixed PaP price | EUR/MWh | 100.39 |
Data | Source | Description | Reference |
---|---|---|---|
Wind production | Co-located | Historical wind production for 2020 in Germany | [37,38] |
Solar production | Co-located | Historical solar production for 2020 in Germany | [37,38] |
Forward electricity settlement prices | European Power Exchange | Daily closing settlement prices for the forward contracts M1, Q1, Y1, Y2 and Y3 | [27] |
Spot price for ammonia | Western Europe Ammonia CFR (Cost&Freight) | Historical spot price for ammonia from 1 January 2020 to 31 January 2023 | [30] |
Scenario | Procurement | Technology | Renewable Capacity [MW] | Electrolyzer Capacity [MW] | NH3 Contract [t/Week] | P50 P&L M€ | Std P&L M€ |
---|---|---|---|---|---|---|---|
i | Co-located | Solar | 250 | 100 | 300 | 92 | 15 |
ii | Co-located | Mixed | 250 | 100 | 300 | 169 | 37 |
iii | BL | - | 30 | 100 | 600 | −52 | 5.5 |
iv | BL | - | 30 | 50 | 300 | −18 | 13 |
v | BL | - | 60 | 100 | 300 | −22 | 37 |
vi | PaP | Solar | 250 | 100 | 600 | −34 | 5 |
vii | PaP | Solar | 250 | 100 | 300 | −7 | 15 |
viii | PaP | Solar | 250 | 50 | 300 | 0.3 | 17 |
ix | PaP | Mixed | 250 | 50 | 300 | 26 | 38 |
x | PaP | Mixed | 250 | 100 | 300 | 20 | 37 |
xi | PaP | Mixed | 250 | 100 | 600 | −4 | 23 |
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Lauro, E.; Têtu, A.; Geman, H. Green Ammonia Production in Stochastic Power Markets. Commodities 2024, 3, 98-114. https://doi.org/10.3390/commodities3010007
Lauro E, Têtu A, Geman H. Green Ammonia Production in Stochastic Power Markets. Commodities. 2024; 3(1):98-114. https://doi.org/10.3390/commodities3010007
Chicago/Turabian StyleLauro, Ezio, Amélie Têtu, and Hélyette Geman. 2024. "Green Ammonia Production in Stochastic Power Markets" Commodities 3, no. 1: 98-114. https://doi.org/10.3390/commodities3010007