# Merit Order Effect Modeling: The Case of the Hellenic Electricity Market

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions, but the payment of consumers was increased for the examined years (2009 and 2011).

## 2. Merit Order Effect and the Hellenic Electricity Market

## 3. Day-Ahead Electricity Market Model

#### 3.1. Definition of the Merit Order Effect

#### 3.2. The Merit Order Curve

- ${\mathrm{S}}_{max}$ GWh/h the maximum feasible electricity supply;
- ${P}_{med}$ €/MWh the electricity price at half of maximum supply;
- $n$ - empirical shape constant.

_{2}emissions price, and the fuel price can be introduced in the parameters ${P}_{med}$ and$n$ through appropriate functions, but this is out of the scope of this paper.

#### 3.3. The Electricity Demand

- ${D}_{T}$ GWh/year the total electricity demand during the year;
- ${d}_{w}$ - the portion of the total annual demand for winter activities;
- ${d}_{s}$ - the portion of the total annual demand for summer activities;
- ${t}_{wo}$ days the time of the peak of winter activities;
- ${t}_{so}$ days the time of the peak of summer activities;
- $\Delta {t}_{w}$ days the typical duration of the winter activities;
- $\Delta {t}_{s}$ days the typical duration of the summer activities.

- ${d}_{n}$ - the portion of the total daily demand for noon activities;
- ${d}_{e}$ - the portion of the total daily demand for evening activities;
- ${t}_{no}$ hours the time of the peak of noon activities;
- ${t}_{eo}$ hours the time of the peak of evening activities;
- $\Delta {t}_{n}$ hours the typical duration of the noon activities;
- $\Delta {t}_{e}$ hours the typical duration of the evening activities.

#### 3.4. Renewable Electricity Production

- i days the day of the year (1, 2, …, 365);
- ${R}_{i}$ GWh/day the electricity generated from renewables during the day i;
- ${W}_{i}$ GWh/day the electricity generated from renewables except photovoltaics during the day i;
- $P{V}_{i}$ GWh/day the electricity generated from photovoltaics during the day i.

- ${W}_{T}$ GWh/year the total annual electricity generated by renewables except photovoltaics;
- $\Delta W$ GWh/day the seasonal variation amplitude of renewables except photovoltaics;
- ${i}_{Wo}$ days the day of minimum production for renewables except photovoltaics.

- $P{V}_{T}$ GWh/year the total annual electricity generated by photovoltaics;
- $\Delta PV$ GWh/day the seasonal variation amplitude of photovoltaics;
- ${i}_{PVo}$ days the day with the minimum production for photovoltaics.

- ${j}_{PVo}$ hours the hour with maximum production from photovoltaics.

#### 3.5. Regression Analysis

- Equations (2) and (3) are simultaneous fitted to real data of demand;
- Equations (5)–(8) are simultaneous fitted to real data of renewable electricity generation;
- Equation (1) is fitted to real data of system marginal price and virtual marginal price.

- ${D}_{ij}$ GWh/h Hourly electricity demand;
- ${R}_{ij}$ GWh/h Hourly renewables electricity;
- $SM{P}_{ij}$ €/MWh Hourly system marginal price;
- $VSM{P}_{ij}$ €/MWh Hourly virtual system marginal price.

- ${\mathrm{S}}_{max}$ GWh/h the maximum feasible electricity supply;
- ${W}_{T}$ GWh/year the total annual electricity generated by renewables except photovoltaics;
- $P{V}_{T}$ GWh/year the total annual electricity generated by photovoltaics;
- ${D}_{T}$ GWh/year the total electricity demand during the year.

## 4. Results and Discussion

#### 4.1. Statistical Analysis

#### 4.2. Regression Analysis

- ${\mathrm{S}}_{max}$ GWh/h the maximum feasible electricity supply;
- ${W}_{T}$ GWh/year the total annual electricity generated by renewables except photovoltaics;
- $P{V}_{T}$ GWh/year the total annual electricity generated by photovoltaics;
- ${D}_{T}$ GWh/year the total electricity demand during the year.

- Estimated values of ${D}_{T}$ and $P{V}_{T}$ are exactly as recorded 51.9 TWh/y and 3.72 TWh/y, respectively, while estimated value of ${W}_{T}$ is a little higher than recorded 5.84 TWh/y;
- S
_{max}of 9.88 GWh/h is a decline from the expected installed conventional power of 12 GW, because the total capacity does not participate continuously into the market.

#### 4.3. Sensitivity Analysis

- ${\mathrm{S}}_{max}$ GWh/h the maximum feasible electricity supply;
- ${W}_{T}$ GWh/year the total annual electricity generated by renewables except photovoltaics;
- $P{V}_{T}$ GWh/year the total annual electricity generated by photovoltaics;
- ${D}_{T}$ GWh/year the total electricity demand during the year.

- D Demand is increased, all other factors are kept constant;
- D + R Demand and renewables are increased by the same rate and conventionals are kept constant;
- D + C Demand and conventionals are increased with the same rate and renewables are kept constant;
- A All factors are increased by the same rate;
- A − D All factors except Demand are increased by the same rate.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$cf$ | the correction factor (-) |

${d}_{e}$ | the portion of the total daily demand for evening activities (-) |

${D}_{i}$ | the electricity demand during the day i (GWh/day) |

${D}_{ij}$ | the electricity demand during the hour j of the day i (GWh/hour) |

${d}_{n}$ | the portion of the total daily demand for noon activities (-) |

${d}_{s}$ | the portion of the total annual demand for summer activities (-) |

${D}_{T}$ | the total electricity demand during the year (GWh/year) |

${d}_{w}$ | the portion of the total annual demand for winter activities (-) |

$i$ | the day of the year (1, 2, …, 365) (days) |

${i}_{PVo}$ | the day with the minimum production for photovoltaics (days) |

${i}_{Wo}$ | the day of minimum production for renewables except photovoltaics (days) |

$j$ | the hour with maximum production from photovoltaics (hours) |

${j}_{PVo}$ | the hour with maximum production from photovoltaics (hours) |

$n$ | empirical shape constant (-) |

$P$ | the supply price (€/MWh) |

$P{V}_{i}$ | the electricity generated from photovoltaics during the day i (GWh/day) |

$P{V}_{ij}$ | the electricity generated from photovoltaics during the hour j of the day i (GWh/hour) |

${P}_{med}$ | the electricity price at half of maximum supply (€/MWh) |

$P{V}_{T}$ | the total annual electricity generated by photovoltaics (GWh/year) |

${R}_{i}$ | the electricity generated from renewables during the day i (GWh/day) |

${R}_{ij}$ | the electricity generated from renewables during the hour j of the day i (GWh/hour) |

$S$ | the dispatchable electricity supply (GWh/h) |

${S}_{max}$ | the maximum feasible electricity supply (GWh/h) |

$SMP$ | the System Marginal Price (€/MWh) |

$SM{P}_{ij}$ | the System Marginal Price during the hour j of the day i (€/MWh) |

${\mathrm{t}}_{\mathrm{eo}}$ | the time of the peak of evening activities (hours) |

${t}_{no}$ | the time of the peak of noon activities (hours) |

${t}_{so}$ | the time of the peak of summer activities (days) |

${t}_{wo}$ | the time of the peak of winter activities (days) |

$VSMP$ | the Virtual System Marginal Price (€/MWh) |

$VSM{P}_{ij}$ | the Virtual System Marginal Price during the hour j of the day i (€/MWh) |

${W}_{i}$ | the electricity generated from renewables except photovoltaics during the day i (GWh/day) |

${W}_{ij}$ | the electricity generated from renewables except photovoltaics during the hour j of the day i (GWh/hour) |

${W}_{T}$ | the total annual electricity generated by renewables except photovoltaics (GWh/year) |

$\Delta PV$ | the seasonal variation amplitude of photovoltaics (GWh/day) |

$\Delta {t}_{e}$ | the typical duration of the evening activities (hours) |

$\Delta {t}_{n}$ | the typical duration of the noon activities (hours) |

$\Delta {t}_{s}$ | the typical duration of the summer activities (days) |

$\Delta {t}_{w}$ | the typical duration of the winter activities (days) |

$\Delta W$ | the seasonal variation amplitude of renewables except photovoltaics (GWh/day) |

## Abbreviations

A | all |

C | conventionals |

CO_{2} | carbon dioxide |

D | demand |

DAM | day-ahead market |

DR | demand minus renewables |

ETMEAR | surcharge on electricity price (Greek abbreviation) |

FIP | feed-in premium |

FIT | feed-in Tariff |

MOC | merit order curve |

MOE | merit order effect |

PVs | photovoltaics |

PXEFEL | merit order effect charge (Greek abbreviation) |

R | renewables |

RAE | regulatory authority of energy |

RES | renewable energy sources |

SMP | system marginal price |

VSMP | virtual system marginal price |

W | renewables except photovoltaics |

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**Figure 1.**Definition of the merit order effect (MOE) using the demand and supply curve (merit order curve) in the day-ahead electricity market.

**Figure 3.**Real data versus time along with the corresponding duration curves: D = demand, DR = demand renewables, R = renewables, VSMP = virtual system marginal price, SMP = system marginal price, MOE = merit order effect. Data from Hellenic electricity market operator [32] and the Hellenic energy exchange group [33].

**Figure 4.**Fitted normal distribution: D = demand, DR = demand renewables, R = renewables, VSMP = virtual system marginal price, SMP = system marginal price, MOE = merit order effect.

**Figure 5.**Seasonal variation using 24 hour moving averages: D = demand, DR = demand renewables, R = renewables, VSMP = virtual system marginal price, SMP = system marginal price, MOE = merit order effect.

**Figure 6.**Daily variation using monthly-averaged hourly data: D = demand, DR = demand renewables, R = renewables. Horizontal axis = hour of the day, vertical axis = energy in GWh/h.

**Figure 7.**Daily variation using monthly-averaged hourly data: VSMP = virtual system marginal price, SMP = system marginal price, MOE = merit order effect. Horizontal axis = hour of the day, vertical axis = price in €/MWh.

**Figure 8.**Seasonal variation: Comparison between real (grey lines) and model calculated (black lines) values. D = demand, R = renewables, SMP = system marginal price, MOE = merit order effect.

**Figure 9.**Daily variation: Comparison between real (points) and model calculated (lines) values. D = demand, DR = demand renewables, R = renewables, VSMP = virtual system marginal price, SMP = system marginal price, MOE = merit order effect.

**Figure 11.**Merit order curve: Comparison between real and model calculated values. Monthly averaged values.

**Figure 12.**Sensitivity analysis (one factor at a time): Effect of crucial market factors on the merit order effect. D = demand, W = renewables except photovoltaics, PV = photovoltaics, and S

_{max}= conventional.

**Figure 13.**Scenario analysis (simultaneous factor variation): D + R = demand and renewables are increased by the same rate, conventionals are kept constant; D = demand is increased, all other factors are kept constant; A = all factors are increased by the same rate; D + C = demand and conventionals are increased with the same rate, renewables are kept constant; and A − D = all factors, except demand, are increased by the same rate.

Variable | Symbol | St Dev | Mean | Median | Min | Max | Units |
---|---|---|---|---|---|---|---|

Demand | D | 1.13 | 5.89 | 5.84 | 3.24 | 9.61 | GWh/h |

Demand renewables | DR | 1.09 | 4.84 | 4.70 | 1.81 | 8.48 | GWh/h |

Renewables | R | 0.64 | 1.05 | 0.91 | 0.12 | 3.29 | GWh/h |

Virtual system marginal price | VSMP | 33.9 | 68.8 | 57.6 | 37.8 | >150 | €/MWh |

System marginal price | SMP | 16.8 | 54.7 | 51.7 | 0.0 | >150 | €/MWh |

Merit order effect | MOE | 24.5 | 14.2 | 6.9 | 0.0 | >150 | €/MWh |

Merit Order Curve Parameters | Equation (1) | Units | |

Price at half of maximum supply | P_{med} | 55.2 | €/MWh |

Maximum feasible electricity supply | S_{max} | 9.88 | GWh/h |

Empirical shape constant | n | 0.412 | - |

Demand Seasonal Variation Parameters | Equation (2) | ||

Annual demand | D_{T} | 51.6 | TWh/y |

Winter activities fraction | d_{w} | 0.099 | - |

Winter activities peak day | t_{wo} | 13.1 | days |

Winter activities standard period | Δt_{w} | 44.5 | days |

Summer activities fraction | d_{s} | 0.085 | - |

Summer activities peak day | t_{so} | 205 | days |

Summer activities standard period | Δt_{s} | 33.3 | days |

Demand Daily Variation Parameters | Equation (3) | ||

Noon activities fraction | d_{n} | 0.147 | - |

Noon activities peak hour | t_{no} | 12.5 | h |

Noon activities standard period | Δt_{n} | 3.38 | h |

Evening activities fraction | d_{e} | 0.127 | - |

Evening activities peak hour | t_{eo} | 21.1 | h |

Evening activities standard period | Δt_{e} | 3.03 | h |

Renewable Electricity Variation Parameters | Equations (5)–(8) | ||

Annual production of other renewables | W_{T} | 5.48 | TWh/y |

Seasonal relative variation of other renewables | ΔW | 0.00 | - |

Other renewables generation peak day | i_{wo} | 0.00 | days |

Annual production of photovoltaics | PV_{T} | 3.71 | TWh/y |

Seasonal relative variation of photovoltaics | ΔPV | 0.294 | - |

Photovoltaics production minimum day | i_{PVo} | 3.58 | days |

Photovoltaic production peak hour | j_{PVo} | 13.7 | h |

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**MDPI and ACS Style**

Loumakis, S.; Giannini, E.; Maroulis, Z.
Merit Order Effect Modeling: The Case of the Hellenic Electricity Market. *Energies* **2019**, *12*, 3869.
https://doi.org/10.3390/en12203869

**AMA Style**

Loumakis S, Giannini E, Maroulis Z.
Merit Order Effect Modeling: The Case of the Hellenic Electricity Market. *Energies*. 2019; 12(20):3869.
https://doi.org/10.3390/en12203869

**Chicago/Turabian Style**

Loumakis, Stelios, Eugenia Giannini, and Zacharias Maroulis.
2019. "Merit Order Effect Modeling: The Case of the Hellenic Electricity Market" *Energies* 12, no. 20: 3869.
https://doi.org/10.3390/en12203869