Model description
We establish a linear optimization model to quantify the cost and emission intensity of hydrogen produced by hybrid grid-connected hydrogen production systems in Australia. In the following, we briefly describe the relevant features of the model. A full description is provided in the Supplementary Note 1, along with details of all technical and economic parameters. The model is operated with hourly time resolution over a one-year period and is constrained to deliver a constant supply of hydrogen (180 kg/hour) to industrial end-users throughout the year. This reflects the likely requirements of large, continuous industrial processes in refineries, ammonia plants, liquefaction facilities, and other industrial operations27. The optimization model minimizes the on-site hydrogen supply cost (OHSC), defined in Eq. (1), which consists of capital expenditure (\({CAPEX}\)) (annualized using the capital recovery factor \({CRF}\)), operation and maintenance costs (\(\mathrm{O\& M}\)) and annual electricity cost (\({C}^{e}\)). The \({CAPEX}\) and \(\mathrm{O\& M}\) are given by the sum of the costs associated with individual system components:
$${CAPEX}=\mathop{\sum }\limits_{k\in K}{C}^{k}{I}^{k}$$
(7)
$$O\& M=\mathop{\sum }\limits_{k\in K}{C}^{k}\left({{FOM}}^{k}+{{VOM}}^{k}\right)$$
(8)
where\(\,{C}^{k}\) represents the installed capacity of a component, \({I}^{k}\) is investment needed per unit installed capacity, \({{FOM}}^{k}\) and \({{VOM}}^{k}\) are the fixed and variable operation and maintenance cost of component \(k\), where \(K\) is the component set which includes wind, PV, electrolyser and \({H}_{2}\) storage facilities. The \({CRF}\) can be calculated according to the plant lifetime \(n\) and the interest rate \(i\) as:
$${CRF}=\frac{i{(1+i)}^{n}}{{(1+i)}^{n}-1}$$
(9)
The electricity cost \({C}^{e}\) over one year includes costs associated with buying electricity from the grid and negative “costs” from selling electricity to the grid in each time \(t\) and is given by,
$${C}^{e}=\mathop{\sum }\limits_{t=0}^{8759}({E}_{{out}}^{{grid}}(t)\times ({P}_{j}(t)+{TS})-{E}_{{in}}^{{grid}}(t)\times {P}_{j}(t))$$
(10)
where \({E}_{{out}}^{{grid}}\left(t\right)\) and \({E}_{{in}}^{{grid}}(t)\) are the amount of electricity bought or sold each hour, and \({P}_{j}(t)\) is the electricity spot price in state \(j\) at each time \(t\). In addition, the system pays an additional transmission use of system fee \({TS}\) when importing electricity48,49. The electricity into the electrolyser and the hydrogen storage level are both limited by the capacity of electrolyser \({C}^{{el}}\), and hydrogen storage \({C}^{S}\), respectively:
$${E}_{{in}}^{{el}}\left(t\right)\le {C}^{{el}}\,\forall t$$
(11)
$${H}^{{S}_{{level}}}\left(t\right)\le {C}^{S}\,\forall t$$
(12)
Constraints are placed on the size of the RE capacity to avoid unrealistic results. For example, in states with high electricity prices, the system may grossly oversize the local RE generation capacity to profit from selling electricity to the grid, in essence creating a second business to subsidize hydrogen production. This phenomenon does not align with practical constraints as the RE generation capacity is usually limited by the available land, project budget and the risk of investment48. Thus, we also constrain the \({CAPEX}\) of the on-grid system such that it does not exceed the \({CAPEX}\) of the optimized off-grid system without grid-connection.
The model simulates the operation of the production system by ensuring the equilibrium of electricity and hydrogen flows, as described in the following.
Electricity flow balance
The production system is powered by electricity which can be sourced from local RE generation or imported from the grid. At each time \(t\), local wind generation (\({E}_{{out}}^{{wind}}(t)\)) and solar generation (\({E}_{{out}}^{{PV}}\left(t\right)\)) are produced based on the local weather profile. RE can either be used to (i) power the electrolyser for hydrogen production (\({E}_{{in}}^{{el}}\left(t\right)\)) and the compressor for hydrogen transmission into either the pipeline (\({E}_{{in}}^{{comp}1}\left(t\right)\)) or storage facilities (\({E}_{{in}}^{{comp}2}\left(t\right)\)), (ii) exported to the grid (\({E}_{{in}}^{{grid}}(t)\)), or (iii) curtailed (\({E}_{{in}}^{C}(t)\)). If the local RE is insufficient to support the system’s operation, the system can choose to import electricity from the grid (\({E}_{{out}}^{{grid}}(t)\)). The decision of electricity dispatching is made by solving the flow balance equation given by
$$ {{E}_{{in}}^{{el}}\left(t\right)+{E}_{{in}}^{{comp}1}\left(t\right)+{E}_{{in}}^{{comp}2}\left(t\right)+{E}_{{in}}^{{grid}}\left(t\right)+{E}_{{in}}^{C}\left(t\right)=E}_{{out}}^{{wind}}\left(t\right)\\ +{E}_{{out}}^{{PV}}\left(t\right)+{E}_{{out}}^{{grid}}\left(t\right)\,\forall t$$
(13)
Hydrogen flow balance
The system converts electricity into hydrogen through electrolysis and then either pumps the hydrogen into the pipeline for direct transportation to the hydrogen load or stores it in the hydrogen storage equipment, which serves as a reserve for the load, storing hydrogen to supply when production by the electrolyser is insufficient to meet the demand. At each time \(t\), hydrogen is produced by the electrolyser with efficiency, \(\eta =70 \%\)30, as following:
$${H}_{{out}}^{{el}}\left(t\right)=\frac{{E}_{{in}}^{{el}}\left(t\right)\times \eta }{{HHV}}\,\forall t$$
(14)
where \({HHV}\) = 39.4 kWh/kgH250 is the higher heating value of hydrogen and \({H}_{{out}}^{{el}}(t)\) represents the hydrogen produced by electrolyser. This hydrogen is subsequently allocated by the system to either compressor 1 (\({H}_{{out}}^{{comp}1}\left(t\right)\)), which pumps it into the pipeline for direct transportation to end-users at a pressure of 100 bar, or to compressor 2 (\({H}_{{out}}^{{comp}2}\left(t\right)\)), where it is pressurized to 150 bar and then stored in the hydrogen storage:
$${H}_{{out}}^{{el}}\left(t\right)={H}_{{out}}^{{comp}1}\left(t\right)+{H}_{{out}}^{{comp}2}\left(t\right)\,\forall t$$
(15)
The hydrogen load in each time \(t\) (\({H}_{{in}}^{{Load}}\left(t\right)=180{kg}\)) is met either by hydrogen flow directly from the electrolyser via pipeline and/or hydrogen from storage (\({H}_{{out}}^{S}(t)\)) according to:
$${{H}_{{in}}^{{Load}}(t)=H}_{{pipe}}^{{comp}1}(t)+{H}_{{out}}^{S}(t)\,\forall t$$
(16)
Wind and solar generation
Local wind and PV generation at each time \(t\) depends on the optimized capacity of the generators. To enable the optimization, we define reference capacities for the onshore wind farm (\({C}_{{Ref}}^{{wind}}=320{\rm{MW}}\)) and PV field (\({C}_{{Ref}}^{{PV}}=1{\rm{MW}}\)), and calculate the hourly reference generation (\({E}_{\mathrm{Re}{f}_{{out}}}^{{wind}}\) and \({E}_{\mathrm{Re}{f}_{{out}}}^{{PV}}(t)\)) using NREL’s PySAM engine51 and historical local weather data from MERRA-2 dataset52. The actual generation is then calculated through linearly scaling the reference output based on the ratio of actual capacity to reference capacity:
$${E}_{{out}}^{{wind}}(t)=\frac{{C}^{{wind}}}{{C}_{{Ref}}^{{wind}}}\times {E}_{\mathrm{Re}{f}_{{out}}}^{{wind}}(t)\,\forall t$$
(17)
$${E}_{{out}}^{{PV}}(t)=\frac{{C}^{{PV}}}{{C}_{{Ref}}^{{PV}}}\times {E}_{\mathrm{Re}{f}_{{out}}}^{{PV}}(t)\,\forall t$$
(18)
where \({E}_{{out}}^{{wind}}(t)\) and \({E}_{{out}}^{{PV}}(t)\) represent the actual hourly generation of the wind farm and the PV field, respectively. \({C}^{{wind}}\) and \({C}^{{PV}}\) indicate the capacity for the wind farm and PV field, respectively.
Grid
We introduce the grid node to simulate the interaction between production system and the grid. The system can choose to import and export electricity from the grid node (the state in which it is located), defined by time and location dependent historical electricity prices and emissions factors (average and marginal), described in detail in section Modelling the Australian National Electricity Market below. Detailed information on the NEM data is provided in Supplementary Table 6 and Supplementary Fig. 7.
Compressor 1 and Compressor 2
The electricity consumption of compressor 1, which pressurizes hydrogen produced by the electrolyser for pipeline injection, and compressor 2, which pressurises hydrogen for storage is given by
$${E}_{{in}}^{{comp}1}\left(t\right)={H}_{{out}}^{{comp}1}\left(t\right)\times {\mu }_{{out}}^{{comp}1}\,\forall t$$
(19)
$${E}_{{in}}^{{comp}2}\left(t\right)={H}_{{out}}^{{comp}2}\left(t\right)\times {\mu }_{{out}}^{{comp}2}\,\forall t$$
(20)
where \({\mu }_{{out}}^{{comp}1}\) and \({\mu }_{{out}}^{{comp}2}\) are the electricity consumption for each unit of hydrogen compressed by compressor 1 and compressor 2, respectively.
Hydrogen storage
The hydrogen storage level at each time \(t\) (\({H}^{{S\_level}}(t)\)) is updated according to:
$${H}^{{S}_{{level}}}\left(t\right)={H}^{{S}_{{leve}{l}_{0}}}+\mathop{\sum }\limits_{0}^{t}\left(-{H}_{{out}}^{S}\left(t\right)+{H}_{{out}}^{{comp}2}\left(t\right)\right)\,\forall t$$
(21)
where \({H}_{{out}}^{S}(t)\) represents the hydrogen sent out by the hydrogen storage to meet the load and \({H}^{{S\_level\_}0}\) is the initial level of hydrogen storage as we assume the system has been in trial operation for a period. The hydrogen storage level in the last time point should be equal to the initial level to ensure that all the hydrogen sent out is produced within the modelled year.
Modelling the Australian National Electricity Market
The NEM is made up of networks in five regions (roughly corresponding to the states) interconnected by a transmission network, including Queensland (QLD), New South Wales (NSW), South Australia (SA), Victoria (VIC) and Tasmania (TAS). Electricity is traded within and between states by the central dispatch engine run by the Australian Energy Market Operator (AEMO)53. The spot prices of electricity in each state are determined by the highest bid accepted by the AEMO from a generator to fulfill demand for each 5-minute interval. The historical data on spot prices and emission factors used in our study is from 2023 sourced from AEMO at five-minute intervals, and subsequently averaged to one-hour timesteps29, as described in the Supplementary Table 6. Here, a representative historical time series is shown in Fig. 6a, depicting hourly AEFs and MEFs for Queensland grid profile on 18 Feb 2023. The associated hourly spot prices for the same time and location are shown in Fig. 6b, along with a bar chart indicating how frequently each type of generator (coal, gas, renewables) becomes the marginal generator over the five-minute intervals in each hourly dataset.
a Shows marginal emissions factors (MEFs) (purple curve) and average emissions factors (AEFs) (green curve) in relation to the electricity generation of the grid (bars) in each hour. b Shows the frequency of each type of fuel generator becoming marginal (bars), along with electricity prices (blue curve) for each hour.
The graphs show that AEFs reflect the generation mix of the grid, with high AEFs during the early morning and evening peaks due to the reliance on fossil fuel-generated electricity, and lower AEFs during midday when the proportion of RE generation on the grid increases. In contrast, the MEF values are determined by the emissions intensity of the marginal generators and so can change rapidly across the day. The two emission factors can vary widely over some time periods. Further discussion about the comparison between MEFs and AEFs is given in Supplementary Note 5.
Yearly average AEFs and MEFs for each state are given in Supplementary Table 6, and the energy generation mix as quantified by the percentage contribution of different generators to annual generation is shown in Supplementary Fig. 8. Local grids in QLD, VIC and NSW are dominated by coal power (~60%)54, with RE meeting a major portion of the remaining demand, (also given in Supplementary Table 6 as 28%, 42%, 31% respectively) leading to average AEFs of 0.69, 0.73, and 0.63 kgCO2e/kWh in 2023. In contrast, 71% of SA electricity was provided by renewables in 2023, with the rest coming from gas power and imports from other states54, resulting in a much lower average AEF of 0.23 kgCO2e/kWh. The average AEF in TAS was lower still, at 0.12 kgCO2e/kWh, as over 90% of electricity generation was renewable, mostly from hydro (~70%), followed by wind (~20%).
The average MEF values vary much less between the states, from 0.4-0.52 kgCO2e/kWh, with the exception of TAS, which has a much lower average MEF of 0.19 kgCO2e/kWh. This is because the marginal generators that respond most frequently to increased demand in each state are similar: coal (33-50% of the time), followed by hydro (25-32%), as shown in Supplementary Fig. 8. Since TAS has abundant hydro, it is the marginal generator over 75% of the time. The high frequency of hydro as the marginal generator leads to MEFs that are lower than AEF in heavily coal-reliant states (QLD, NSW, VIC), while the fossil fuel technologies are marginal generators 45% of the time in SA, resulting in larger MEF than AEF.
