# Flexible Short-Term Electricity Certificates—An Analysis of Trading Strategies on the Continuous Intraday Market

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Literature Review

#### 1.3. Contribution and Paper Organization

## 2. The Flexible Certificate

- Offering Period: daily 12:40 to 3 p.m.;
- Fulfillment: next day;
- Granularity: hourly;
- Price: day-ahead auction price + premium P;
- Volume: to be fixed in advance.

## 3. Data and Descriptive Statistic

#### 3.1. Data

#### 3.2. Descriptive Statistics and Implications

- The concentration could be on a few individual contracts on a daily basis;
- The market is liquid only in the hours before expiration;
- Due to forecast errors, early available prices might still be more attractive (despite high bid–ask spread);
- Bid–ask spreads are usually based on low-volume orders, so larger volumes should be bought/sold split;
- There are differences between 2017 and 2018 regarding liquidity.

## 4. Strategies

#### 4.1. Definitions

- Up to 60 min before trading closes for a specific contract, the supplier buys (sells) any available volume (up to the required volume) at a price equal to or lower (higher) than the day-ahead auction price plus/minus an adjustment $\delta $.
- If the necessary volume has not been reached 60 min before the close of trading, this criteria is softened for buying (selling) strategies by increasing (decreasing) $\delta $ linearly with remaining time.
- As a final option, the remaining required volume is bought (sold) five minutes before the close of trading at any price.

- Up to 60 min before the close of trading, besides the known criterion related to the day-ahead price, the supplier only trades if the bid–ask spread is smaller than a level S.
- Analogous to Strategy I, S is increased linearly if there is missing volume 60 min before close.
- As with Strategy I, the remaining required volume is bought (sold) five minutes before the close of trading at any price.

- Up to 240 min before the close of trading, the supplier only trades according to the day-ahead price criterion, analogous to Strategy I.
- Within the last 240 min before the close of trading, the strategy is identical to Strategy II.

#### 4.2. Implementation

- We only consider orders where $Start\ne End$.
- If an order is executed, we remove any following orders with the same OrderID.
- The supplier of the certificate always buys (sells) at the best ask (bid) price for the quoted volume.
- We omit orders that would have been matched with another order that the supplier had previously executed.
- There are no transaction costs beyond the bid–ask spread.

## 5. Strategy Performance

#### 5.1. Average Premiums

#### 5.2. Risk

#### 5.3. Analysis of Hourly Contracts

## 6. Time-Series Characteristics and External Drivers

## 7. Limit Prices

#### 7.1. Methodology

#### 7.2. Results

#### 7.3. Relation to Strategy Premiums

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

P | Actual premium for the flexible certificate |

${P}_{B}$ | Base premium for intraday trading |

$\tilde{P}$ | Strategy premiums on the intraday market |

$Volum{e}_{ID}$ | Traded volume on the intraday market |

$Volum{e}_{DA}$ | Traded volume on the day-ahead market |

$\delta $ | Add-on to day-ahead price |

$Spr$ | Bid–ask spread |

S | Maximum bid–ask spread |

${p}_{da}$ | Day-ahead price |

$\sigma $ | Forecast error |

$L{P}_{neutral}$ | Maximum price that a risk-neutral buyer would pay for the flexible certificate |

$L{P}_{averse}$ | Maximum price that a risk/loss-averse buyer would pay for the flexible certificate |

MWh | Megawatt hour |

GWh | Megawatt hour |

TWh | Terawatt hour |

C | Contract |

ES | Expected shortfall |

RA | Risk-neutral buyer |

RN | Risk/loss-averse buyer |

(A) | Arbitrary |

(C) | Consecutive |

## References

- Busse, J.; Rieck, J. Mid-term energy cost-oriented flow shop scheduling: Integration of electricity price forecasts, modeling, and solution procedures. Comput. Ind. Eng.
**2022**, 163, 107810. [Google Scholar] [CrossRef] - Braschczok, D.; Dellnitz, A.; Hilbert, M.; Kleine, A.; Ostmeyer, J. Energy costs vs. carbon dioxide emissions in short-term production planning. J. Bus. Econ.
**2020**, 90, 1383–1407. [Google Scholar] - Busse, J.; Windler, T.; Rieck, J. One month-ahead electricity price forecasting in the context of production planning. J. Clean. Prod.
**2019**, 238, 117910. [Google Scholar] - Braunreuther, S.; Keller, F.; Reinhart, G.; Schultz, C. Enabling energy-flexibility of manufacturing systems through new approaches within production planning and control. Procedia CIRP
**2016**, 57, 752–757. [Google Scholar] - Finnah, B.; Gönsch, J.; Ziel, F. Integrated day-ahead and intraday self-schedule bidding for energy storage systems using approximate dynamic programming. Eur. J. Oper. Res.
**2022**, 301, 726–746. [Google Scholar] [CrossRef] - Vahedipour-Dahraie, M.; Rashidizadeh-Kermani, H.; Anvari-Moghaddam, A.; Siano, P. Risk-averse probabilistic framework for scheduling of virtual power plants considering demand response and uncertainties. Int. J. Electr. Power Energy Syst.
**2020**, 121, 106126. [Google Scholar] [CrossRef] - Wozabal, D.; Rameseder, G. Optimal bidding of a virtual power plant on the Spanish day-ahead and intraday market for electricity. Eur. J. Oper. Res.
**2020**, 280, 639–655. [Google Scholar] [CrossRef] - Finnah, B. Optimal bidding functions for renewable energies in sequential electricity markets. OR Spectr.
**2022**, 44, 1–27. [Google Scholar] [CrossRef] - Finnah, B.; Gönsch, J. Optimizing trading decisions of wind power plants with hybrid energy storage systems using backwards approximate dynamic programming. Int. J. Prod. Econ.
**2021**, 238, 108155. [Google Scholar] [CrossRef] - Marijanovic, Z.; Theile, P.; Czock, B.H. Value of short-term heating system flexibility—A case study for residential heat pumps on the German intraday market. Energy
**2022**, 249, 123664. [Google Scholar] [CrossRef] - Busse, J.; Rieck, J. Electricity price-oriented scheduling within production planning stage. In Operations Research Proceedings; Springer: Berlin/Heidelberg, Germany, 2018; pp. 161–166. [Google Scholar]
- Erdmann, G.; Praktiknjo, A.; Zweifel, P. Energy Economics: Theory and Applications; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Henriot, A. Market design with centralized wind power management: Handling low-predictability in intraday markets. Energy J.
**2014**, 35, 99–117. [Google Scholar] [CrossRef] - Garnier, E.; Madlener, R. Balancing forecast errors in continuous-trade intraday markets. Energy Syst.
**2015**, 6, 362–388. [Google Scholar] [CrossRef] - Skajaa, A.; Edlund, K.; Morales, J. Intraday trading of wind energy. IEEE Trans. Power Syst.
**2015**, 30, 3181–3189. [Google Scholar] [CrossRef] - Gönsch, J.; Hassler, M. Sell or store? An ADP approach to marketing renewable energy. OR Spectr.
**2016**, 38, 633–660. [Google Scholar] [CrossRef] - Hassler, M. Heuristic decision rules for short-term trading of renewable energy with co-located energy storage. Comput. Oper. Res.
**2017**, 83, 199–213. [Google Scholar] [CrossRef] - Bertrand, G.; Papavasoliou, A. Adaptive Trading in Continuous Intraday Electricity Markets for a Storage Unit. IEEE Trans. Power Syst.
**2020**, 35, 2339–2350. [Google Scholar] [CrossRef] - Boukas, I.; Ernst, D.; Tháte, T.; Bolland, A.; Huynen, A.; Buchwald, M.; Wynants, C.; Cornélusse, B. A deep reinforcement learning framework for continuous intraday market bidding. Mach. Lang.
**2021**, 110, 2335–2387. [Google Scholar] [CrossRef] - Koch, C. Intraday imbalance optimization: Incentives and impact of strategic intraday bidding behavior. Energy Syst.
**2022**, 13, 409–435. [Google Scholar] [CrossRef] - Serafin, T.; Marcjasz, G.; Weron, R. Trading on short-term path forecasts of intraday electricity prices. Energy Econ.
**2022**, 112, 106125. [Google Scholar] [CrossRef] - Hagemann, S. Price determinants in the German intraday market for electricity: An empirical analysis. J. Energy Mark.
**2015**, 8, 21–45. [Google Scholar] [CrossRef] - Gianfreda, A.; Parisio, L.; Pelagatti, M. The Impact of RES in the Italian Day–Ahead and Balancing Markets. Energy J.
**2016**, 37, 161–184. [Google Scholar] [CrossRef] - Ziel, F. Modeling the impact of wind and solar power forecasting errors on intraday electricity prices. In Proceedings of the 14th International Conference on the European Energy Market, Dresden, Germany, 6–9 June 2017; IEEE: Piscataway, NJ, USA, 2017; pp. 1–5. [Google Scholar]
- Kulakov, S.; Ziel, F. The Impact of Renewable Energy Forecasts on Intraday Electricity Prices. Econ. Energy Environ. Policy
**2021**, 10. [Google Scholar] [CrossRef] - Pape, C.; Hagemann, S.; Weber, C. Are fundamentals enough? Explaining price variations in the German day-ahead and intraday power market. Energy Econ.
**2016**, 54, 376–387. [Google Scholar] [CrossRef] - Kiesel, R.; Paraschiv, F. Econometric analysis of 15-minute intraday electricity price. Energy Econ.
**2017**, 64, 77–90. [Google Scholar] [CrossRef] - Karanfil, F.; Li, Y. The Role of Continuous Intraday Electricity Markets: The Integration of Large-Share Wind Power Generation in Denmark. Energy J.
**2017**, 38, 107–130. [Google Scholar] [CrossRef] - Scharff, R.; Amelin, M. Trading behaviour on the continuous intraday market Elbas. Energy Policy
**2016**, 88, 544–557. [Google Scholar] [CrossRef] - Narajewski, M.; Ziel, F. Econometric modelling and forecasting of intraday electricity prices. J. Commod. Mark.
**2020**, 19, 100107. [Google Scholar] [CrossRef] - Kath, C. Modeling intraday markets under the new advances of the cross-border intraday project (XBID): Evidence from the German intraday market. Energies
**2019**, 12, 4339. [Google Scholar] [CrossRef] - Baule, R.; Naumann, M. Volatility and Dispersion of Hourly Electricity Contracts on the German Continuous Intraday Market. Energies
**2021**, 14, 7531. [Google Scholar] [CrossRef] - Steinert, R.; Ziel, F. Electricity price forecasting using sale and purchase curves: The X-Model. Energy Econ.
**2016**, 59, 435–454. [Google Scholar] - Weron, R.; Ziel, F. Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks. Energy Econ.
**2018**, 70, 396–420. [Google Scholar] - Zhang, J.L.; Zhang, Y.J.; Li, D.Z.; Tan, Z.F.; Ji, J.F. Forecasting day-ahead electricity prices using a new integrated model. Int. J. Electr. Power Energy Syst.
**2019**, 105, 541–548. [Google Scholar] [CrossRef] - Maciejowska, K.; Nitka, W.; Weron, T. Enhancing load, wind and solar generation for day-ahead forecasting of electricity prices. Energy Econ.
**2021**, 99, 105273. [Google Scholar] [CrossRef] - Qussous, R.; Harder, N.; Weidlich, A. Understanding Power Market Dynamics by Reflecting Market Interrelations and Flexibility-Oriented Bidding Strategies. Energies
**2022**, 15, 494. [Google Scholar] [CrossRef] - Kuppelwieser, T.; Wozabal, D. Liquidity costs on intraday power markets: Continuous trading versus auctions. Energy Policy
**2021**, 154, 112299. [Google Scholar] [CrossRef] - Balardy, C. An Empirical Analysis of the Bid-ask Spread in the Continuous Intraday Trading of the German Power Market. Energy J.
**2022**, 43. [Google Scholar] [CrossRef] - Martin, H.; Otterson, S. German intraday electricity market analysis and modeling based on the limit order book. In Proceedings of the 15th International Conference on the European Energy Market, Lodz, Poland, 27–29 June 2018; IEEE: Piscataway, NJ, USA, 2018; pp. 639–644. [Google Scholar]
- Artzner, P.; Delbaen, F.; Eber, J.M.; Heath, D. Thinking coherently. Risk
**1997**, 10, 68–71. [Google Scholar] - Koch, C.; Maskos, P. Passive Balancing Through Intraday Trading: Whether Interactions Between Short-term Trading and Balancing Stabilize Germany’s Electricity System. Int. J. Energy Econ. Policy
**2020**, 10, 101–112. [Google Scholar] [CrossRef] - Newey, W.K.; West, K.D. Hypothesis testing with efficient method of moments estimation. Int. Econ. Rev.
**1987**, 28, 777–787. [Google Scholar] [CrossRef] - Kahneman, D.; Tversky, A. Prospect theory: An analysis of decision under risk. Econometrica
**1979**, 47, 263–292. [Google Scholar] [CrossRef] - Benartzi, S.; Thaler, R. Risk aversion or myopia? Choices in repeated gambles and retirement investmens. Manag. Sci.
**1999**, 45, 364–381. [Google Scholar] [CrossRef] - Thaler, R.H. Toward a positive theory of consumer choice. J. Econ. Behav. Organ.
**1980**, 1, 39–60. [Google Scholar] [CrossRef] - Thaler, R.H. Mental accounting and consumer choice. Mark. Sci.
**1985**, 4, 199–214. [Google Scholar] [CrossRef] - Müller, T.; Möst, D. Demand response potential: Available when needed? Energy Policy
**2018**, 115, 181–198. [Google Scholar] [CrossRef] - Pape, C. The impact of intraday markets on the market value of flexibility—Decomposing effects on profile and the imbalance costs. Energy Econ.
**2018**, 76, 186–201. [Google Scholar] [CrossRef]

**Figure 1.**Descriptive statistics of the prices of the day-ahead auction: (

**a**) mean prices and standard deviations separated by individual hourly contracts; (

**b**) relative share of the daily most-favorable contracts separated by lowest price, second-lowest price, and third-lowest price contracts.

**Figure 2.**Descriptive statistics of the continuous intraday order book for individual contracts: (

**a**) Mean number of all buy and sell orders for individual contracts. The lower dashed lines indicate the mean number for 2017 only, and the upper lines indicate the mean number for 2018 only. (

**b**) Total average volume of all buy and sell orders for individual contracts, as well as the average volume actually traded (national).

**Figure 3.**Bid–ask spreads in the continuous intraday market: (

**a**) mean bid–ask spreads and realized standard deviation as a function of remaining time to expiration for the 00–01 h contract for 2017, 2018, and for the entire period; (

**b**) empirical probability of movement of the bid–ask spread for different contracts as a function of remaining time to expiration.

**Figure 4.**Trading rules for Strategies I–III (buying). When the respective criterion is met, available volume is purchased at the offered ask price: ${p}_{s}$ is the price of a sell order, ${p}_{da}$ is the price of the day-ahead auction, $Spr$ is the bid–ask spread, and T is the maturity of a contract in minutes. The factor $\lambda $ is fixed at 1 EUR/min for Strategy I and at 0.50 EUR/min for Strategies II and III because the impact of the bid–ask spread is greater compared to the adjustment in Strategy I.

**Figure 5.**Mean strategy premiums $\tilde{P}$ across all contracts for different strategies as a function of $\delta $ for different volumes: (

**a**–

**c**) buying strategies; (

**d**–

**f**) selling strategies; (

**a**) buying mean 0.1 MWh; (

**b**) buying mean 10 MWh; (

**c**) buying mean 100 MWh; (

**d**) selling mean 0.1 MWh; (

**e**) selling mean 10 MWh; (

**f**) selling mean 100 MWh.

**Figure 6.**Strategy risk measured by 90% expected shortfall across all contracts for different strategies as a function of $\delta $ for different volumes: (

**a**–

**c**) buying strategies; (

**d**–

**f**) selling strategies; (

**a**) buying ES 90% 0.1 MWh; (

**b**) buying ES 90% 10 MWh; (

**c**) buying ES 90% 100 MWh; (

**d**) selling ES 90% 0.1 MWh; (

**e**) selling ES 90% 10 MWh; (

**f**) selling ES 90% 100 MWh.

**Figure 7.**Boxplots for the premiums $\tilde{P}$ of the 24 individual contracts at 100 MWh separately for buying (

**a**) and selling strategies (

**b**). Strategy III, $\delta =\pm 4$ and $S=0.50$, is applied in both cases.

**Figure 8.**Autocorrelations of the strategy premium $\tilde{P}$ for 100 MWh determined with Strategy III, $\delta =\pm 4$ and $S=0.50$: results of the corresponding (

**a**) buying and (

**b**) selling strategies.

**Figure 9.**Limit prices for a risk-neutral (

**a**) and a risk/loss-averse (

**b**) agent. The figures show the limits for different forecast errors $\sigma $ as a function of the number of contracts (for the same volume). Regarding the number of contracts, we differentiate between arbitrary (A) and consecutive (C) contracts. Arbitrary means that the contracts can be distributed over the day, while consecutive means that the contracts must follow one another in time.

**Figure 10.**Premiums P for 100 MWh for different quantities acquired on the day-ahead auction and on the continuous intraday market for different basic premiums ${P}_{B}$. For the base premium ${P}_{B}$, different values of the strategy premiums (mean as well the 90% quantile) were applied as determined by buying strategy III with $\delta =-4$ and $S=0.50$. The lines indicate the limit prices for a risk-neutral buyer (RN) for $\sigma =1.00$ (for 1 and 8 contracts (A)), $\sigma =$2.50 (for 1 contract), and for a risk/loss-averse buyer (RA) for $\sigma =$5.00 (for 1 contract).

**Table 1.**Descriptive statistics of the continuous intraday order book. The statistics include information on the number of buy orders, volume of buy orders, volume-weighted average price of buy orders, number of sell orders, volume of sell orders, volume-weighted average price of sell orders, the volume actually traded (national), and the number of hourly contracts observed. The results are presented for the different quarters of 2017 and 2018 and in total. Orders with the same OrderID due to partial executions were only considered once.

2017 | 2018 | Total | |||||||
---|---|---|---|---|---|---|---|---|---|

Q1 | Q2 | Q3 | Q4 | Q1 | Q2 | Q3 | Q4 | ||

# Buy (Mio.) | 3.15 | 3.03 | 2.96 | 3.58 | 4.31 | 4.77 | 5.16 | 7.49 | 34.45 |

Vol. Buy (TWh) | 40.61 | 34.00 | 34.67 | 42.06 | 43.82 | 45.11 | 40.14 | 50.70 | 331.11 |

$\overline{p}$ Buy (EUR) | 29.32 | 20.35 | 20.44 | 14.82 | 28.79 | 23.59 | 30.54 | 14.14 | 22.74 |

# Sell (Mio) | 2.46 | 2.41 | 2.62 | 3.22 | 3.88 | 4.34 | 4.78 | 7.65 | 31.37 |

Vol. Sell (TWh) | 31.66 | 27.43 | 30.13 | 36.64 | 37.87 | 40.37 | 36.30 | 50.04 | 290.43 |

$\overline{p}$ Sell (EUR) | 58.82 | 40.70 | 45.66 | 56.85 | 44.78 | 49.23 | 93.92 | 94.58 | 60.53 |

Tr. Vol. (TWh) | 7.55 | 7.52 | 7.33 | 7.65 | 7.97 | 8.58 | 7.88 | 8.10 | 62.57 |

# Contracts | 2073 | 2158 | 2176 | 2114 | 2066 | 2119 | 2159 | 2085 | 16,950 |

**Table 2.**Descriptive statistics for strategy premiums $\tilde{P}$ for Strategy III with a volume of 100 MWh, separated into buying and selling strategies for different $\delta $ and different S.

Buying Strategy | Selling Strategy | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

$\mathbf{\delta}\mathbf{=}\mathbf{-}\mathbf{\infty}$ | $\mathbf{\delta}\mathbf{=}\mathbf{-}\mathbf{10}$ | $\mathbf{\delta}\mathbf{=}\mathbf{-}\mathbf{4}$ | $\mathbf{\delta}\mathbf{=}\mathbf{0}$ | $\mathbf{\delta}\mathbf{=}\mathbf{4}$ | $\mathbf{\delta}\mathbf{=}\mathbf{-}\mathbf{4}$ | $\mathbf{\delta}\mathbf{=}\mathbf{0}$ | $\mathbf{\delta}\mathbf{=}\mathbf{4}$ | $\mathbf{\delta}\mathbf{=}\mathbf{10}$ | $\mathbf{\delta}\mathbf{=}\mathbf{\infty}$ | ||

Panel A: Strategy III with $S=0.5$ | |||||||||||

min | −47.92 | −24.46 | −26.03 | −26.12 | −25.33 | −17.29 | −21.36 | −21.36 | −23.47 | −48.29 | |

median | 0.28 | 0.25 | −0.01 | −0.28 | 2.59 | 2.69 | −0.24 | 0.14 | 0.38 | 0.44 | |

mean | 0.48 | 0.50 | 0.59 | 1.07 | 2.66 | 2.72 | 1.16 | 0.67 | 0.57 | 0.51 | |

max | 182.84 | 182.84 | 182.84 | 154.13 | 122.36 | 84.52 | 84.52 | 84.52 | 84.52 | 84.52 | |

sd | 7.19 | 6.78 | 6.23 | 4.99 | 3.44 | 2.86 | 4.24 | 5.28 | 5.88 | 6.62 | |

skewness | 4.15 | 5.59 | 7.21 | 8.92 | 14.20 | 8.98 | 4.87 | 2.78 | 1.81 | 0.10 | |

kurtosis | 78.63 | 95.74 | 131.31 | 156.83 | 341.04 | 158.75 | 48.42 | 21.67 | 14.98 | 16.52 | |

$E{S}_{90\%}$ | 12.68 | 12.55 | 12.20 | 10.96 | 7.21 | 7.09 | 10.44 | 11.37 | 11.70 | 11.96 | |

Panel B: Strategy III with $S=1$ | |||||||||||

min | −45.33 | −26.03 | −26.03 | −26.12 | −25.33 | −17.29 | −21.36 | −21.36 | −23.47 | −48.23 | |

median | 0.43 | 0.40 | 0.22 | −0.25 | 2.59 | 2.69 | −0.21 | 0.36 | 0.52 | 0.56 | |

mean | 0.56 | 0.58 | 0.67 | 1.08 | 2.65 | 2.71 | 1.17 | 0.74 | 0.66 | 0.60 | |

max | 160.04 | 160.04 | 160.04 | 160.04 | 118.79 | 74.49 | 74.49 | 74.49 | 74.49 | 74.49 | |

sd | 6.65 | 6.30 | 5.82 | 4.69 | 3.24 | 2.75 | 3.97 | 4.89 | 5.41 | 6.09 | |

skewness | 4.35 | 5.74 | 7.23 | 8.94 | 13.27 | 8.87 | 4.64 | 2.57 | 1.66 | −0.12 | |

kurtosis | 85.41 | 102.18 | 135.61 | 171.07 | 310.02 | 161.58 | 48.27 | 21.63 | 15.51 | 18.39 | |

$E{S}_{90\%}$ | 11.68 | 11.57 | 11.32 | 10.30 | 7.10 | 7.01 | 9.75 | 10.43 | 10.69 | 10.89 | |

Panel C: Strategy III with $S=2$ | |||||||||||

min | −43.55 | −24.46 | −24.46 | −24.46 | −22.83 | −17.29 | −21.36 | −21.36 | −23.47 | −48.23 | |

median | 0.77 | 0.75 | 0.62 | −0.21 | 2.59 | 2.69 | −0.16 | 0.79 | 0.90 | 0.92 | |

mean | 0.88 | 0.89 | 0.92 | 1.18 | 2.65 | 2.72 | 1.30 | 1.02 | 0.99 | 0.94 | |

max | 155.29 | 155.29 | 155.29 | 105.20 | 91.00 | 68.07 | 68.07 | 68.07 | 68.07 | 68.07 | |

sd | 6.02 | 5.77 | 5.37 | 4.32 | 2.98 | 2.58 | 3.81 | 4.65 | 5.06 | 5.64 | |

skewness | 3.42 | 4.50 | 5.51 | 6.60 | 10.58 | 7.15 | 3.71 | 1.98 | 1.18 | −0.53 | |

kurtosis | 65.10 | 73.64 | 92.45 | 96.06 | 212.19 | 123.47 | 34.49 | 15.84 | 12.04 | 17.89 | |

$E{S}_{90\%}$ | 11.15 | 11.10 | 10.92 | 10.00 | 7.10 | 7.05 | 9.58 | 10.11 | 10.29 | 10.40 |

**Table 3.**Strategy premiums by subset $\tilde{P}$ (mean and quantiles) for separate buying or selling strategies. Premiums are based on Strategy III, $\delta =\pm 4$ and $S=0.50$. Panel A distinguishes between the two years 2017 and 2018. In Panel B, subsets of realized strategy premiums are formed according to the daily realized prices of the day-ahead auction. Thus, the contracts of the day-ahead auction are sorted by their prices on a daily basis, and the subsets contain the corresponding strategy premiums separated by the cheapest and most-expensive daily contracts. In addition, a subset was provided containing all strategy premiums associated with the day-ahead contracts that achieved a negative price.

Buying Strategy | Selling Strategy | ||||||
---|---|---|---|---|---|---|---|

Mean | 90% | 95% | Mean | 90% | 95% | $\#\mathit{obs}.$ | |

Panel A: Years | |||||||

2017 | 0.63 | 6.08 | 8.95 | 0.95 | 6.70 | 9.89 | 8521 |

2018 | 0.55 | 6.06 | 8.76 | 0.38 | 5.75 | 8.29 | 8429 |

Panel B: Day-ahead auction prices | |||||||

lowest ${p}_{da,t}$ | 1.88 | 8.18 | 11.95 | −0.35 | 4.69 | 8.71 | 707 |

2 lowest ${p}_{da,t}$ | 1.58 | 7.57 | 11.53 | −0.11 | 4.90 | 8.28 | 1417 |

3 lowest ${p}_{da,t}$ | 1.34 | 7.16 | 10.72 | −0.05 | 4.90 | 8.32 | 2118 |

4 lowest ${p}_{da,t}$ | 1.18 | 6.69 | 10.18 | 0.09 | 5.11 | 8.40 | 2821 |

5 lowest ${p}_{da,t}$ | 1.08 | 6.31 | 10.00 | 0.21 | 5.18 | 8.50 | 3513 |

6 lowest ${p}_{da,t}$ | 0.96 | 6.23 | 9.65 | 0.33 | 5.39 | 8.74 | 4220 |

highest ${p}_{da,t}$ | −0.19 | 5.59 | 8.19 | 1.83 | 7.97 | 11.86 | 717 |

2 highest ${p}_{da,t}$ | −0.02 | 5.57 | 8.33 | 1.52 | 7.64 | 11.35 | 1426 |

3 highest ${p}_{da,t}$ | 0.03 | 5.56 | 8.34 | 1.45 | 7.43 | 10.82 | 2141 |

4 highest ${p}_{da,t}$ | 0.13 | 5.58 | 8.19 | 1.36 | 7.34 | 10.36 | 2851 |

5 highest ${p}_{da,t}$ | 0.15 | 5.59 | 8.11 | 1.24 | 7.27 | 9.96 | 3547 |

6 highest ${p}_{da,t}$ | 0.16 | 5.69 | 8.17 | 1.20 | 7.14 | 9.81 | 4267 |

${p}_{da}<0$ | 8.77 | 27.39 | 36.25 | −2.33 | 5.47 | 18.69 | 254 |

**Table 4.**Descriptive statistics of the explanatory variables. $\Delta Wind$ is the difference between realized wind energy and forecast wind energy in GWh; $Wind$ is the relative wind share of total consumption. $\Delta Solar$ and $Solar$ are analogously defined as the difference between realized solar energy in GWh and forecast solar energy, respectively. $\Delta Wind$ is the difference between realized other energies and forecast other energies in GWh, and $\Delta Load$ is the difference between realized consumption and forecast consumption in GWh.

$\mathbf{\Delta}\mathit{Wind}$ | $\mathbf{\Delta}\mathit{Solar}$ | $\mathbf{\Delta}\mathit{Other}$ | $\mathbf{\Delta}\mathit{Load}$ | $\mathit{Wind}$ | $\mathit{Solar}$ | |
---|---|---|---|---|---|---|

min | −9.697 | −4.698 | −24.00 | −15.84 | 0.003 | 0.000 |

25% | −0.597 | −0.019 | −8.249 | −0.248 | 0.089 | 0.000 |

median | 0.047 | 0.000 | −4.823 | 0.970 | 0.175 | 0.002 |

mean | 0.138 | 0.004 | −5.381 | 1.081 | 0.214 | 0.072 |

75% | 0.841 | 0.008 | −2.217 | 2.351 | 0.306 | 0.113 |

max | 10.78 | 4.662 | 19.42 | 10.26 | 0.848 | 0.584 |

sd | 1.434 | 0.669 | 4.680 | 2.006 | 0.157 | 0.112 |

**Table 5.**Regression results for Strategy III, $\delta =\pm 4$ and $S=0.50$, for different volumes. The coefficients of the explanatory variables, the adjusted ${R}^{2}$, and the number of observations are given. $\Delta Wind$ is the difference between realized and forecast wind energy in GWh; $Wind$ is the relative wind share of the total consumption. $\Delta Solar$, $Solar$, and $\Delta Other$ are analogously defined for solar energy and other energy, respectively. $\Delta Load$ is the difference between realized consumption and forecast consumption in GWh. The asterisks denote the significance level, with *** = 0.1%, ** = 1%, and * = 5%.

Panel A: Buying Strategy | Panel B: Selling Strategy | |||||
---|---|---|---|---|---|---|

0.1 MWh | 10 MWh | 100 MWh | 0.1 MWh | 10 MWh | 100 MWh | |

$Intercept$ | −1.878 ** | −1.287 * | −1.178 | 0.348 | 1.148 * | 1.575 ** |

(0.642) | (0.632) | (0.644) | (0.541) | (0.49) | (0.497) | |

$\Delta Wind$ | −1.152 *** | −1.234 *** | −1.477 *** | 1.143 *** | 1.217 *** | 1.410 *** |

(0.088) | (0.085) | (0.079) | (0.074) | (0.069) | (0.069) | |

$\Delta Solar$ | −0.948 *** | -0.942 *** | −1.210 *** | 0.892 *** | 0.936 *** | 1.192 *** |

(0.116) | (0.115) | (0.13) | (0.119) | (0.116) | (0.112) | |

$\Delta Other$ | 0.024 | 0.001 | 0.004 | −0.046 | −0.032 | −0.007 |

(0.036) | (0.035) | (0.038) | (0.038) | (0.035) | (0.035) | |

$\Delta Load$ | 0.234 *** | 0.263 *** | 0.299 *** | −0.184 ** | −0.235 *** | −0.255*** |

(0.052) | (0.052) | (0.054) | (0.063) | (0.061) | (0.058) | |

$Wind$ | 2.424 * | 2.327 * | 3.356 ** | −2.223 * | −1.494 | −0.919 |

(1.13) | (1.13) | (1.214) | (1.006) | (0.984) | (1.08) | |

$Solar$ | 2.715 | 2.345 | 2.445 | −5.226 ** | −4.195 * | −2.05 |

(1.58) | (1.51) | (1.681) | (1.717) | (1.697) | (1.788) | |

fixed effects | yes | yes | yes | yes | yes | yes |

adj. ${R}^{2}$ | 0.092 | 0.111 | 0.154 | 0.120 | 0.144 | 0.184 |

Observations | 16,631 | 16,631 | 16,631 | 16,631 | 16,631 | 16,631 |

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**MDPI and ACS Style**

Baule, R.; Naumann, M. Flexible Short-Term Electricity Certificates—An Analysis of Trading Strategies on the Continuous Intraday Market. *Energies* **2022**, *15*, 6344.
https://doi.org/10.3390/en15176344

**AMA Style**

Baule R, Naumann M. Flexible Short-Term Electricity Certificates—An Analysis of Trading Strategies on the Continuous Intraday Market. *Energies*. 2022; 15(17):6344.
https://doi.org/10.3390/en15176344

**Chicago/Turabian Style**

Baule, Rainer, and Michael Naumann. 2022. "Flexible Short-Term Electricity Certificates—An Analysis of Trading Strategies on the Continuous Intraday Market" *Energies* 15, no. 17: 6344.
https://doi.org/10.3390/en15176344