Figure 1.
Gas storage unit schema.
Figure 1.
Gas storage unit schema.
Figure 2.
Decision-framework structure.
Figure 2.
Decision-framework structure.
Figure 3.
Decision-making framework.
Figure 3.
Decision-making framework.
Figure 4.
Example of three-block piecewise linear approximation of the heat rate curve.
Figure 4.
Example of three-block piecewise linear approximation of the heat rate curve.
Figure 5.
Injection and withdrawal curves of the gas storage unit.
Figure 5.
Injection and withdrawal curves of the gas storage unit.
Figure 6.
Fit of the entire historical data set of electricity price with a relative error equal to 3.71%.
Figure 6.
Fit of the entire historical data set of electricity price with a relative error equal to 3.71%.
Figure 7.
Electricity actual price time series, forecasts, and one hundred scenarios.
Figure 7.
Electricity actual price time series, forecasts, and one hundred scenarios.
Figure 8.
Initial set of electricity price scenarios and the five most representative scenarios.
Figure 8.
Initial set of electricity price scenarios and the five most representative scenarios.
Figure 9.
Fit the entire historical data set of gas price with a relative error equal to 3.93%.
Figure 9.
Fit the entire historical data set of gas price with a relative error equal to 3.93%.
Figure 10.
Gas price time series forecast and 100 scenarios.
Figure 10.
Gas price time series forecast and 100 scenarios.
Figure 11.
One hundred gas price scenarios and the most significant five scenarios.
Figure 11.
One hundred gas price scenarios and the most significant five scenarios.
Figure 12.
Expected spark price and expected prices of electricity and natural gas.
Figure 12.
Expected spark price and expected prices of electricity and natural gas.
Figure 13.
Bilateral contracts selected. (a) Natural gas purchases per day and per bilateral contract with storage; (b) natural gas purchases per day and per bilateral contract without storage; (c) electricity sold per hour and per bilateral contract with gas storage; (d) electricity sold per hour and per bilateral contract without gas storage.
Figure 13.
Bilateral contracts selected. (a) Natural gas purchases per day and per bilateral contract with storage; (b) natural gas purchases per day and per bilateral contract without storage; (c) electricity sold per hour and per bilateral contract with gas storage; (d) electricity sold per hour and per bilateral contract without gas storage.
Figure 14.
Relationship among spot natural gas product and access capacity (a) with a gas storage and (b) without gas storage.
Figure 14.
Relationship among spot natural gas product and access capacity (a) with a gas storage and (b) without gas storage.
Figure 15.
The expected gas procurement. (a) Natural used per day to feed the combined-cycle gas turbine (CCGT) using the gas storage; (b) natural used per day to feed the CCGT without gas storage.
Figure 15.
The expected gas procurement. (a) Natural used per day to feed the combined-cycle gas turbine (CCGT) using the gas storage; (b) natural used per day to feed the CCGT without gas storage.
Figure 16.
The expected energy produced, (a) with gas storage, and (b) without gas storage.
Figure 16.
The expected energy produced, (a) with gas storage, and (b) without gas storage.
Figure 17.
Storage operation per scenario. (a) Energy stored; (b) energy injected, and (c) energy withdrawn.
Figure 17.
Storage operation per scenario. (a) Energy stored; (b) energy injected, and (c) energy withdrawn.
Figure 18.
Sensitivity analysis: gas storage size.
Figure 18.
Sensitivity analysis: gas storage size.
Figure 19.
Sensitivity analysis: spark price. (a) Expected profit considering storage, (b) difference between the profits of cases with and without storage.
Figure 19.
Sensitivity analysis: spark price. (a) Expected profit considering storage, (b) difference between the profits of cases with and without storage.
Figure 20.
Out-of-sample scenarios. (a) Electricity price scenarios; (b) gas price scenarios.
Figure 20.
Out-of-sample scenarios. (a) Electricity price scenarios; (b) gas price scenarios.
Figure 21.
Out-of-sample results. (a) Profit per scenario considering storage; (b) difference between the profits of cases with and without storage, (c) histogram of the difference between profits of cases with and without storage.
Figure 21.
Out-of-sample results. (a) Profit per scenario considering storage; (b) difference between the profits of cases with and without storage, (c) histogram of the difference between profits of cases with and without storage.
Table 1.
Characteristics of the heat-rate blocks.
Table 1.
Characteristics of the heat-rate blocks.
Breakpoint | Heat Rate Slope | Power Output (MWh) | Gas Consumption (MWh) |
---|
Minimum 1 | - | 120.00 | 267.95 |
1 | 1.39 | 280.00 | 489.87 |
2 | 1.45 | 360.00 | 605.87 |
3 | 1.52 | 400.00 | 666.51 |
Table 2.
Electricity bilateral contracts—energy and prices.
Table 2.
Electricity bilateral contracts—energy and prices.
Bilateral Contract | Energy Sold (MWh) | Prices (€/MWh) |
---|
1 | 20.00 | 38.35 |
2 | 40.00 | 42.78 |
3 | 100.00 | 55.00 |
4 | 120.00 | 59.21 |
Table 3.
Seasonal Autoregressive Integrated Moving Average model (SARIMA) coefficients. Electricity price.
Table 3.
Seasonal Autoregressive Integrated Moving Average model (SARIMA) coefficients. Electricity price.
Coefficient |
---|
Nonseasonal | Seasonal |
---|
| 0.953392686 | | −0.689749350 |
| −0.537356443 |
Constant K | 0.0000814540 | | −0.307308537 |
| −0.154635954 |
Table 4.
Average 10, 50, and 90 percentiles of the probability distribution of electricity spot price for different reduced sets of scenarios.
Table 4.
Average 10, 50, and 90 percentiles of the probability distribution of electricity spot price for different reduced sets of scenarios.
Number of Scenarios | Electricity Spot Prices (euro/MWh) |
---|
Perc. 10% | Perc. 50% | Perc. 90% |
---|
100 | 37.34 | 54.73 | 61.17 |
80 | 37.36 | 54.73 | 61.17 |
60 | 37.36 | 54.79 | 61.17 |
40 | 37.11 | 54.79 | 61.17 |
20 | 35.13 | 54.79 | 60.76 |
10 | 35.13 | 54.79 | 62.66 |
5 | 35.12 | 54.79 | 62.66 |
3 | 41.70 | 54.79 | 54.79 |
1 | 54.79 | 54.79 | 54.79 |
Table 5.
Probabilities and average price of the five electricity price scenarios.
Table 5.
Probabilities and average price of the five electricity price scenarios.
Scenario | Probability | Average Price (€/MWh) |
---|
1 | 0.44 | 54.79 |
2 | 0.03 | 28.85 |
3 | 0.19 | 41.70 |
4 | 0.25 | 62.66 |
5 | 0.09 | 35.13 |
Table 6.
Natural gas bilateral contracts—quantity and prices.
Table 6.
Natural gas bilateral contracts—quantity and prices.
Bilateral Contract | Quantity Purchased (MWh/day) | Prices (€/MWh) |
---|
1 | 6430.80 | 15.23 |
2 | 5326.08 | 12.39 |
3 | 2784.00 | 14.85 |
4 | 1455.36 | 13.50 |
Table 7.
Natural gas spot market—quantity by daily products.
Table 7.
Natural gas spot market—quantity by daily products.
Product | Quantity (MWh/day) |
---|
1 | 130 |
2 | 1000 |
3 | 2000 |
4 | 2100 |
5 | 3200 |
6 | 4000 |
7 | 5200 |
8 | 7050 |
Total per day | 24,680 |
Table 8.
SARIMA coefficients. Gas price.
Table 8.
SARIMA coefficients. Gas price.
Coefficient |
---|
Nonseasonal | Seasonal |
---|
| 0.000000000 | | 0.119851759 |
| −0.095659720 | | −0.003820293 |
Constant K | −0.000010676 | | |
Table 9.
Average 10, 50, and 90 percentiles of the probability distribution of gas spot price for different reduced sets of scenarios.
Table 9.
Average 10, 50, and 90 percentiles of the probability distribution of gas spot price for different reduced sets of scenarios.
Number of Scenarios | Gas Spot Prices (euro/MWh) |
---|
Perc. 10% | Perc. 50% | Perc. 90% |
---|
100 | 11.58 | 14.59 | 15.95 |
80 | 11.58 | 14.58 | 15.95 |
60 | 11.59 | 14.58 | 15.95 |
40 | 11.57 | 14.61 | 15.95 |
20 | 11.57 | 14.61 | 16.00 |
10 | 11.44 | 14.61 | 16.20 |
5 | 11.44 | 14.61 | 16.20 |
3 | 12.55 | 14.61 | 14.61 |
1 | 14.61 | 14.61 | 14.61 |
Table 10.
Probabilities of the most significant five gas price scenarios.
Table 10.
Probabilities of the most significant five gas price scenarios.
Scenario | Probability | Average Price (€/MWh) |
---|
1 | 0.48 | 14.65 |
2 | 0.05 | 10.34 |
3 | 0.16 | 12.53 |
4 | 0.24 | 16.20 |
5 | 0.07 | 11.44 |
Table 11.
Open access capacity market—fixed term coefficients by duration type and day.
Table 11.
Open access capacity market—fixed term coefficients by duration type and day.
Product | Type | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 |
---|
1 | Monthly | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.20 | 1.20 |
2 | Monthly | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.20 | 1.20 |
3 | Daily | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 |
4 | Monthly | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.20 | 1.20 |
5 | Quarterly | 1.21 | 1.21 | 1.21 | 1.21 | 1.21 | 1.08 | 1.08 |
6 | Quarterly | 1.21 | 1.21 | 1.21 | 1.21 | 1.21 | 1.08 | 1.08 |
7 | Daily | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 |
8 | Daily | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 |
Table 12.
Bilateral contracts—fixed term coefficients by duration type and day.
Table 12.
Bilateral contracts—fixed term coefficients by duration type and day.
Bilateral Contract | Type | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 |
---|
1 | Monthly | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.20 | 1.20 |
2 | Daily | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 |
3 | Monthly | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.20 | 1.20 |
4 | Daily | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 |
Table 13.
Open access capacity market—quantity by products, and auction premium.
Table 13.
Open access capacity market—quantity by products, and auction premium.
Product | Quantity (GWh/day) | Premium (€/MWh) |
---|
Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 |
---|
1 | 0.10 | 0.10 | 0.10 | 0.10 | 0.10 | 0.13 | 0.13 | 0.100 |
2 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 0.001 |
3 | 3.20 | 3.20 | 3.20 | 3.20 | 3.20 | 2.00 | 2.00 | 0.100 |
4 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 2,10 | 2,10 | 0.100 |
5 | 1.13 | 1.13 | 1.13 | 1.13 | 1.13 | 3.20 | 3.20 | 0.100 |
6 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 0.100 |
7 | 7.05 | 7.05 | 7.05 | 7.05 | 7.05 | 5.20 | 5.20 | 0.100 |
8 | 3.25 | 3.25 | 3.25 | 3.25 | 3.25 | 7.05 | 7.05 | 0.010 |
Total per day | 24.73 | 24.73 | 24.73 | 24.73 | 24.73 | 24.68 | 24.68 | -- |
Table 14.
Computational issues.
Table 14.
Computational issues.
Item | Value |
---|
binary variables (×103) | 7.183 |
continuous variables (×103) | 45.984 |
constraints (×103) | 54.282 |
Computing time (h) | 2.863 |
Number of threads | 10 |
Table 15.
Expected profit.
Table 15.
Expected profit.
Item | With Storage | Without Storage |
---|
Expected value (k €) | 1849.2 | 1812.3 |