# Intraday Electricity Pricing of Night Contracts

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## Abstract

**:**

## 1. Introduction

## 2. Stylized Facts

#### 2.1. Data

#### 2.2. Hourly Seasonality

## 3. Methodology

#### 3.1. Econometric Model

- make a scatter plot of intraday auction prices ${P}^{\mathrm{Auc},\left(i\right)}$ versus expected demands ${\ell}^{\left(i\right)}$;
- fit the empirical merit-order-curve function $f(\ell )={\mathrm{e}}^{a\phantom{\rule{0.166667em}{0ex}}\ell +b}$ to the price–demand data;
- compute the derivative ${f}^{\prime}(\ell )$ of the fitted merit-order-curve function; and,
- substitute empirical demands ${\ell}^{\left(i\right)}$ to obtain merit-order-curve slopes ${\xi}^{\left(i\right)}={f}^{\prime}\left({\ell}^{\left(i\right)}\right)$.

#### 3.2. Threshold Regression

## 4. Estimation Results

#### 4.1. Threshold Regression

#### 4.2. Linear Regression

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Volume-weighted average transaction price (

**left**) and total trading volume (

**right**) of 15-min. contracts during off-peak hours averaged over summer (red) and winter (blue).

**Table 1.**Summary of explanatory variables, granularities, detailed descriptions and data sources. Variables indexed by t vary over the continuous intraday trading session of a 15-min. contract.

Variable [Unit] (Granularity) | Description | Source |
---|---|---|

Transaction price${P}_{t}$[EUR/MWh] (1-min.) | Transaction price of 15-min. contracts traded on the German continuous intraday power market at EPEX SPOT SE | European Energy Exchange AG [30] |

Trading volume${V}_{t}$ [MW] (1-min) | Trading volume of 15-min. contracts traded on the German continuous intraday power market at EPEX SPOT SE | European Energy Exchange AG [30] |

Auction price${P}^{\mathrm{Auc}}$ [EUR/MWh] (quarter-hourly) | Market clearing price of 15-min. contracts traded in the German 15-min. intraday auction at EPEX SPOT SE (published: daily after 3:10 PM) | European Energy Exchange AG [31] |

Wind power forecast${w}_{t}$ [GW] (quarter-hourly) | Intradaily updated forecast of wind power generation for each quarter-hour on the delivery day in Germany | EWE TRADING GmbH [32] |

Expected demandl [GW] (quarter-hourly) | Day-ahead total load forecast for each quarter-hour on the delivery day in Germany (published: daily at 10 AM) | European Network of Transmission System Operators for Electricity Transparency Platform [33] |

Expected conventional capacityc [GW] (daily) | Expected daily average of available generation capacity of conventional power plants on the delivery day in Germany (published: daily at 10 AM) | European Energy Exchange AG Transparency Platform [34] |

**Table 2.**Estimation results of the econometric model (1) for intraday price changes $\mathsf{\Delta}{P}_{t}$ of 15-min. contracts H1Q1–4.

H1Q1 | H1Q2 | ||||
---|---|---|---|---|---|

Variable | Estimate | Std Error | Variable | Estimate | Std Error |

Const | 0.160 | (0.808) | Const | −0.263 | (0.890) |

$\xi $ | −0.378 | (2.508) | $\xi $ | 2.251 | (3.204) |

$\mathsf{\Delta}{P}_{t-1}$ | −0.393 $***$ | (0.024) | $\mathsf{\Delta}{P}_{t-1}$ | −0.406 $***$ | (0.028) |

$\mathsf{\Delta}{P}_{t-2}$ | −0.201 $***$ | (0.020) | $\mathsf{\Delta}{P}_{t-2}$ | −0.196 $***$ | (0.022) |

$\mathsf{\Delta}{P}_{t-3}$ | −0.098 $***$ | (0.014) | $\mathsf{\Delta}{P}_{t-3}$ | −0.079 $***$ | (0.022) |

$\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.022 $*$ | (0.012) | $\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.014 | (0.010) |

$\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.014${}^{***}$ | (0.005) | $\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.124 $***$ | (0.023) |

$\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.157${}^{***}$ | (0.032) | $\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.119 $***$ | (0.017) |

$\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.033${}^{**}$ | (0.016) | $\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.011 | (0.013) |

${P}^{\mathrm{Auc}}$ | 0.020 $*$ | (0.016) | ${P}^{\mathrm{Auc}}$ | 0.003 | (0.017) |

${V}_{t}$ | −0.054 $***$ | (0.007) | ${V}_{t}$ | −0.050 $***$ | (0.013) |

$\mathsf{\Delta}{w}_{t}^{n}$ | −0.059 | (0.261) | $\mathsf{\Delta}{w}_{t}^{n}$ | −1.073 $***$ | (0.373) |

$\mathsf{\Delta}{w}_{t}^{p}$ | −2.085 $***$ | (0.246) | $\mathsf{\Delta}{w}_{t}^{p}$ | −1.177 $***$ | (0.250) |

c | 0.000 | (0.021) | c | −0.009 | (0.021) |

$\mathsf{\Delta}t$ | 0.071$**$ | (0.032) | $\mathsf{\Delta}t$ | 0.002 | (0.040) |

#Obs | 6649 | #Obs | 6421 | ||

${R}_{\mathrm{adj}}^{2}$ | 0.224 | ${R}_{\mathrm{adj}}^{2}$ | 0.203 | ||

H1Q3 | H1Q4 | ||||

Variable | Estimate | Std Error | Variable | Estimate | Std Error |

Const | −5.207 | (4.508) | Const | −2.601 | (1.632) |

$\xi $ | 39.743 | (45.309) | $\xi $ | 10.180 | (11.879) |

$\mathsf{\Delta}{P}_{t-1}$ | −0.358 $***$ | (0.025) | $\mathsf{\Delta}{P}_{t-1}$ | −0.608 $***$ | (0.084) |

$\mathsf{\Delta}{P}_{t-2}$ | −0.177 $***$ | (0.018) | $\mathsf{\Delta}{P}_{t-2}$ | −0.351 $***$ | (0.086) |

$\mathsf{\Delta}{P}_{t-3}$ | −0.101 $***$ | (0.013) | $\mathsf{\Delta}{P}_{t-3}$ | −0.157 $***$ | (0.045) |

$\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.023 | (0.014) | $\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.047 $**$ | (0.021) |

$\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.078 $***$ | (0.020) | $\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.170 $***$ | (0.024) |

$\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.223 $***$ | (0.021) | $\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.169 $*$ | (0.094) |

$\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.033 $*$ | (0.018) | $\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.041 | (0.027) |

${P}^{\mathrm{Auc}}$ | 0.016 | (0.012) | ${P}^{\mathrm{Auc}}$ | 0.027 $*$ | (0.016) |

${V}_{t}$ | 0.030 $***$ | (0.010) | ${V}_{t}$ | 0.011 | (0.013) |

$\mathsf{\Delta}{w}_{t}^{n}$ | −1.032 $**$ | (0.492) | $\mathsf{\Delta}{w}_{t}^{n}$ | −1.291 $***$ | (0.435) |

$\mathsf{\Delta}{w}_{t}^{p}$ | −1.090 $***$ | (0.229) | $\mathsf{\Delta}{w}_{t}^{p}$ | −0.621 $**$ | (0.270) |

c | 0.006 | (0.024) | c | 0.004 | (0.029) |

$\mathsf{\Delta}t$ | −0.078${}^{*}$ | (0.040) | $\mathsf{\Delta}t$ | −0.180${}^{***}$ | (0.061) |

#Obs | 7075 | #Obs | 7914 | ||

${R}_{\mathrm{adj}}^{2}$ | 0.207 | ${R}_{\mathrm{adj}}^{2}$ | 0.290 |

**Table 3.**Estimation results of the econometric model (1) for intraday price changes $\mathsf{\Delta}{P}_{t}$ of 15-min. contracts H3Q1–4.

H3Q1 | H3Q2 | ||||

Variable | Estimate | Std Error | Variable | Estimate | Std Error |

Const | −1.352 | (0.881) | Const | 0.865 | (0.810) |

$\xi $ | −3.468 | (4.834) | $\xi $ | −2.496 | (1.742) |

$\mathsf{\Delta}{P}_{t-1}$ | −0.399 $***$ | (0.020) | $\mathsf{\Delta}{P}_{t-1}$ | −0.365 $***$ | (0.024) |

$\mathsf{\Delta}{P}_{t-2}$ | −0.214 $***$ | (0.017) | $\mathsf{\Delta}{P}_{t-2}$ | −0.190 $***$ | (0.019) |

$\mathsf{\Delta}{P}_{t-3}$ | −0.076 $***$ | (0.015) | $\mathsf{\Delta}{P}_{t-3}$ | −0.102 $***$ | (0.016) |

$\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.039 $**$ | (0.018) | $\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.017 | (0.014) |

$\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.014 | (0.016) | $\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.119 $***$ | (0.017) |

$\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.140 $***$ | (0.020) | $\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.139 $***$ | (0.024) |

$\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.037 $**$ | (0.017) | $\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.069 $***$ | (0.017) |

${P}^{\mathrm{Auc}}$ | 0.029 $***$ | (0.009) | ${P}^{\mathrm{Auc}}$ | 0.011 | (0.015) |

${V}_{t}$ | 0.024 $**$ | (0.010) | ${V}_{t}$ | 0.037 $***$ | (0.011) |

$\mathsf{\Delta}{w}_{t}^{n}$ | −1.012 $*$ | (0.360) | $\mathsf{\Delta}{w}_{t}^{n}$ | −0.702 $**$ | (0.283) |

$\mathsf{\Delta}{w}_{t}^{p}$ | −1.669 $***$ | (0.275) | $\mathsf{\Delta}{w}_{t}^{p}$ | −1.289 $***$ | (0.181) |

c | 0.031 | (0.023) | c | 0.009 | (0.020) |

$\mathsf{\Delta}t$ | 0.038 | (0.036) | $\mathsf{\Delta}t$ | −0.050 | (0.033) |

#Obs | 6357 | #Obs | 6309 | ||

${R}_{\mathrm{adj}}^{2}$ | 0.208 | ${R}_{\mathrm{adj}}^{2}$ | 0.191 | ||

H3Q3 | H3Q4 | ||||

Variable | Estimate | Std Error | Variable | Estimate | Std Error |

Const | −0.227 | (1.475) | Const | −1.199 | (0.913) |

$\xi $ | 4.497 | (8.890) | $\xi $ | −1.381 | (2.122) |

$\mathsf{\Delta}{P}_{t-1}$ | −0.428 $***$ | (0.027) | $\mathsf{\Delta}{P}_{t-1}$ | −0.370 $***$ | (0.021) |

$\mathsf{\Delta}{P}_{t-2}$ | −0.174 $***$ | (0.016) | $\mathsf{\Delta}{P}_{t-2}$ | −0.166 $***$ | (0.018) |

$\mathsf{\Delta}{P}_{t-3}$ | −0.053 $**$ | (0.021) | $\mathsf{\Delta}{P}_{t-3}$ | −0.057 $***$ | (0.013) |

$\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.053${}^{***}$ | (0.015) | $\mathsf{\Delta}{P}_{t}^{(i-2)}$ | 0.023 $*$ | (0.014) |

$\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.072 $***$ | (0.017) | $\mathsf{\Delta}{P}_{t}^{(i-1)}$ | 0.183 $***$ | (0.015) |

$\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.210 $***$ | (0.020) | $\mathsf{\Delta}{P}_{t}^{(i+1)}$ | 0.049 $***$ | (0.016) |

$\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.075 $***$ | (0.028) | $\mathsf{\Delta}{P}_{t}^{(i+2)}$ | 0.035 $**$ | (0.016) |

${P}^{\mathrm{Auc}}$ | 0.005 | (0.011) | ${P}^{\mathrm{Auc}}$ | 0.021 $*$ | (0.011) |

${V}_{t}$ | 0.015 | (0.010) | ${V}_{t}$ | −0.010 | (0.008) |

$\mathsf{\Delta}{w}_{t}^{n}$ | −0.711 $***$ | (0.242) | $\mathsf{\Delta}{w}_{t}^{n}$ | −0.809 $***$ | (0.280) |

$\mathsf{\Delta}{w}_{t}^{p}$ | −1.063 $***$ | (0.167) | $\mathsf{\Delta}{w}_{t}^{p}$ | −0.981 $***$ | (0.223) |

c | −0.015 | (0.020) | c | 0.030 | (0.024) |

$\mathsf{\Delta}t$ | −0.042 | (0.030) | $\mathsf{\Delta}t$ | −0.027 | (0.033) |

#Obs | 6610 | #Obs | 7337 | ||

${R}_{\mathrm{adj}}^{2}$ | 0.219 | ${R}_{\mathrm{adj}}^{2}$ | 0.174 |

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## Share and Cite

**MDPI and ACS Style**

Kremer, M.; Kiesel, R.; Paraschiv, F. Intraday Electricity Pricing of Night Contracts. *Energies* **2020**, *13*, 4501.
https://doi.org/10.3390/en13174501

**AMA Style**

Kremer M, Kiesel R, Paraschiv F. Intraday Electricity Pricing of Night Contracts. *Energies*. 2020; 13(17):4501.
https://doi.org/10.3390/en13174501

**Chicago/Turabian Style**

Kremer, Marcel, Rüdiger Kiesel, and Florentina Paraschiv. 2020. "Intraday Electricity Pricing of Night Contracts" *Energies* 13, no. 17: 4501.
https://doi.org/10.3390/en13174501