# Optimal Participation of Heterogeneous, RES-Based Virtual Power Plants in Energy Markets

^{*}

## Abstract

**:**

## 1. Introduction

- A detailed STU model with storage capability. The model includes a linear formulation for the operation of STU that addresses conversion from thermal to electrical energy using a piece-wise linear efficiency function. It is noted that the thermal storage model proposed in this paper can be easily extended to other technologies (e.g., biomass CHP) without loss of generality.
- A demand model with two flexibility/response levels associated with different energy market trading sessions. In the first demand response level, the demand owner prepares different profiles with associated costs that the VPP manager can choose from in DAM. The second response level concerns IDM where tolerance around the DAM chosen profile is used in updating energy offers due to changes in forecasts of stochastic generating units or other causes;
- An operation model within a market structure that allows updates of energy offers. A network-constrained unit commitment model is used by the VPP to submit DAM auctions and then subsequently participate in IDM sessions to correct for deviations of its Non-Dispatchable Renewable Energy Source (ND-RES) forecasts.

## 2. Overview of Spanish Energy Market Structure

## 3. VPP Modeling

#### 3.1. Day-Ahead Market (DAM) Formulation

#### 3.1.1. Profit Maximization Objective

#### 3.1.2. Power Trades

#### 3.2. Intra-Day Market (IDM) Formulation

#### 3.2.1. Objective

#### 3.2.2. Power Trades

#### 3.3. Other Constraints

#### 3.3.1. Energy Balance

#### 3.3.2. Non-Dispatchable Renewable Energy Sources

#### 3.3.3. Network

#### 3.4. Solar Thermal Units

#### 3.5. Flexible Demands

#### 3.5.1. DAM Formulation

#### 3.5.2. IDM Formulation

## 4. Case Study

## 5. Results

- Base-case where generation or consumption units act individually (No Coordination);
- Coordinated VPP operation as formulated in Section 3.

#### 5.1. Traded Power and Output of Assets on a Clear Day

#### 5.2. Traded Power and Output of Assets on a Cloudy Day

#### 5.3. Effects of Non-Zero Cost on Demand Profile Choice

#### 5.4. Distribution of Profits among Assets

## 6. Conclusions

- The feasibility of RES-based VPP has been shown in this paper. From the purely economic perspective, BESSs can thus be excluded from RES-based VPPs when coupled with an appropriate operation model, thus avoiding the installation and operation costs of these devices. Additionally, this has to be accompanied with participation in markets that allow offer updates close to the energy delivery period;
- The VPP outperformed the case where the units are not coordinated by up to 20% during dam on cloudy days. This reveals one of the benefits of aggregation where the VPP, using the knowledge of every unit’s capability extends their operational flexibility. By doing so, the VPP’s overall profit is maximized;
- The profit distribution was shown to be impacted more by the STU in DAM participation. During IDM sessions, other units including the demand and ND-RESs play a bigger role by leveraging the flexibility provision of demands and updates of generation by the ND-RESs;
- The impact of the STU with its thermal storage was shown where the storage was charged at early periods while later discharging at higher capacity with higher efficiency. This led to higher profits of VPP over No Coordination in all conditions and especially during the cloudy days;
- The introduction of a more detailed STU model, while mirroring actual operation yielded an increased final objective value without leading to additional model complexity nor longer solver times;
- Flexible demands are advantageous in the provision of response/flexibility activities such as load shifting and deferring some energy volumes to other periods. Analysis of the results showed that VPPs incorporating flexible demand profiles with zero costs gave the most benefits compared to other configurations because the model selects the best profile that maximizes its profit;
- When the costs of demand profiles are non-zero, there are some thresholds that the VPP is willing to pay the demand owners until it becomes less profitable and they return to the default profile.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

DAM | Day-Ahead Market |

IDM | Intra-Day Market |

STU | Solar Thermal Unit |

ESS | Energy Storage System |

BESS | Battery Energy Storage System |

RES | Renewable Energy Source |

ND-RES | Non-Dispatchable Renewable Energy Source |

D-RES | Dispatchable Renewable Energy Source |

VPP | Virtual Power Plant |

PV | photovoltaic |

PHES | Pumped Hydro Energy Storage |

DC-PF | DC Power Flow |

PCC | Point of Common Coupling |

CPP | Conventional Power Plant |

Indexes and Sets | |

$b\in \mathcal{B}/{\mathcal{B}}^{m}$ | Network Buses/Network buses Connected to Main Grid |

$c\in \mathcal{C}/{\mathcal{C}}_{b}$ | Dispatchable Renewable Energy Source (D-RES)/D-RES connected to bus b |

$d\in \mathcal{D}/{\mathcal{D}}_{b}$ | Demand/Demand connected to bus b |

$i(\ell )/j(\ell )$ | Sending-/receiving-end bus of line ℓ |

$\ell \in \mathcal{L}/{\mathcal{L}}_{b}$ | Network lines/network lines connected to bus b |

$k\in \mathcal{K}$ | IDM sessions |

$p\in \mathcal{P}$ | Demand profiles for DAM auctions |

$r\in \mathcal{R}/{\mathcal{R}}_{b}$ | Non-Dispatchable Renewable Energy Source (ND-RES)/ND-RES connected |

to bus b | |

$t\in \mathcal{T}$ | Time periods |

$\theta \in \mathsf{\Theta}/{\mathsf{\Theta}}_{b}$ | Solar Thermal Unit (STU)/STU connected to bus b |

Parameters | ||

${C}_{c}^{0}/{C}_{c}^{1}$ | Shut-down/start-up cost of D-RESs | [] |

${C}_{c}^{\mathrm{V}}$ | Variable production cost of D-RESs | [/MWh] |

${C}_{d,p}$ | Cost of load profile p of demand | [] |

${\underset{\overline{}}{E}}_{d}$ | Minimum energy consumption of demand d throughout the planning horizon | [MWh] |

${\underset{\overline{}}{E}}_{\theta ,t}/{\overline{E}}_{\theta ,t}$ | Lower/upper bound of the energy stored in STU storage $\theta $ in time t | [MWh] |

${K}_{\theta}$ | STU $\theta $ output multiplier at startup | [−] |

${\underset{\overline{}}{P}}_{\theta}/{\overline{P}}_{\theta}$ | Minimum/Maximum production capacity of STU $\theta $ | [MW] |

${\underset{\overline{}}{P}}_{\theta}^{-}/{\overline{P}}_{\theta}^{-}$ | Lower/upper bound of discharging capacity of STU storage $\theta $ | [MW] |

${\underset{\overline{}}{P}}_{c}/{\overline{P}}_{c}$ | Minimum/Maximum power production of D-RESs | [MW] |

${\underset{\overline{}}{P}}_{\theta}^{+}/{\overline{P}}_{\theta}^{+}$ | Lower/upper bound of charging capacity of STU storage $\theta $ | [MW] |

${\underset{\overline{}}{P}}_{d,t}/{\overline{P}}_{d,t}$ | Lower/upper bound of the power consumption of demand d in time t | [%] |

${\underset{\overline{}}{P}}_{r,t}$ | Minimum production of ND-RES in time t | [MW] |

${P}_{d,p,t}$ | Maximum hourly consumption of profile p of demand d | [MW] |

${\stackrel{\u02c7}{P}}_{\theta ,t}$ | Available generation of STU in time t | [MW] |

${\stackrel{\u02c7}{P}}_{r,t}$ | Available generation of ND-RES in time t | [MW] |

${\overline{P}}_{b}^{m}$ | Maximum power that can be traded with the main grid at bus b | [MW] |

${\overline{P}}_{l}$ | Maximum power flow through line ℓ | [MW] |

${\underset{\overline{}}{R}}_{d}/{\overline{R}}_{d}$ | Down/up ramping limit of demand d | [MW/h] |

T | Last period of schedule | [−] |

${X}_{\ell}$ | Reactance of network line ℓ | [pu$\left(\Omega \right)$] |

${\underset{\overline{}}{\alpha}}_{\theta}/{\overline{\alpha}}_{\theta}$ | Lower/upper bound multiplier of STU storage $\theta $ at last period in schedule | [−] |

$\Delta t$ | Duration of time periods | [h] |

${\eta}_{\theta}^{+}/{\eta}_{\theta}^{-}$ | Charging/discharging efficiency of STU storage | [%] |

${\eta}_{\theta}^{n}$ | Conversion between thermal and electrical power in the PB of STU $\theta $ in segment $n\in \{1,2,3,4\}$ | [%] |

${\lambda}_{t}^{\mathrm{DA}}$ | DAM price in time t | [/MWh] |

${\lambda}_{k,t}^{\mathrm{ID}}$ | Price of IDM session k in time t | [/MWh] |

Variables | ||

${e}_{\theta ,t}$ | Energy stored in STU storage $\theta $ in time t | [MWh] |

${p}_{t}^{\mathrm{DA}}$ | Total power traded in the DAM in time t | [MW] |

${p}_{\ell ,t}$ | Power flow through network of line ℓ in time t | [MW] |

${p}_{\theta ,t}$ | Electrical power generation of STU in time t | [MW] |

${p}_{\theta ,t}^{+}/{p}_{\theta ,t}^{-}$ | Charging/discharging thermal power level of STU storage $\theta $ in time t | [MW${}_{t}$] |

${p}_{\theta ,t}^{\mathrm{PB}}$ | Thermal power delivered to the STU power block | [MW${}_{t}$] |

${p}_{\theta ,t}^{\mathrm{SF}}$ | Thermal power generated by the solar field | [MW${}_{t}$] |

${p}_{b,t}^{m}$ | Power scheduled to be bought from/sold to the DAM and IDM markets at bus b in time t | [MW] |

${p}_{c,t}$ | Power generation of D-RESs in time t | [MW] |

${p}_{d,t}$ | Power consumption of demand in time t | [MW] |

${p}_{k,t}^{\mathrm{ID}}$ | Total power traded in IDM session k in time t | [MW] |

${p}_{r,t}$ | Power generation of ND-RES in time t | [MW] |

${u}_{\theta ,t}$ | Binary variable to control STU PB operation | [$0/1$] |

${u}_{\theta ,t}^{+}$ | Binary variable to control STU storage charging | [$0/1$] |

${u}_{d,p}$ | Binary variable to select demand profile | [$0/1$] |

${v}_{\theta ,t}^{1}$ | Binary variable to control startup of STU PB $\theta $ | [$0/1$] |

$\Delta {p}_{k,c,t}$ | Change in energy offers by D-RES c between market windows in time t | [MWh] |

${\delta}_{b,t}$ | Voltage angle at bus b in time t | [rad] |

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**Figure 8.**Traded power on a clear day at DAM and IDM in: (

**a**) No Coordination; (

**b**) VPP with default load profile; (

**c**) VPP with three load profiles at zero cost.

**Figure 9.**Output of assets at DAM on a clear day: (

**a**) No Coordination; (

**b**) VPP with default load profile; (

**c**) VPP with three load profiles at zero cost.

**Figure 10.**Traded power on a cloudy day at DAM and IDM: (

**a**) No Coordination; (

**b**) VPP with default load profile; (

**c**) VPP with three load profiles at zero cost.

**Figure 11.**Output of assets at DAM on a cloudy day: (

**a**) No Coordination; (

**b**) VPP with default load profile; (

**c**) VPP with three load profiles at zero cost.

References | CPP | RES | Storage | Load | STU | ||
---|---|---|---|---|---|---|---|

WPP | PV | PHSP | BESS | ||||

[4,5] | ✓ | ✓ | ✓ | ✓ | |||

[6] | ✓ | ✓ | ✓ | ||||

[7] | ✓ | ✓ | ✓ | ||||

[8] | ✓ | ✓ | ✓ | ✓ | |||

[9,10] | ✓ | ✓ | ✓ | ||||

[11,12] | ✓ | ✓ | ✓ | ||||

[13] | ✓ | ✓ | |||||

[14,15,16] | ✓ | ✓ | ✓ |

Demand | Base-Case | Early Peak | Late Peak |
---|---|---|---|

Industrial | chosen when cost > €320/day | optimal | ✘ |

Residential | chosen when cost > €180/day | ✘ | optimal |

Airport | chosen when cost > €500/day | optimal | suboptimal-chosen when cost > €305/day |

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## Share and Cite

**MDPI and ACS Style**

Oladimeji, O.; Ortega, Á.; Sigrist, L.; Rouco, L.; Sánchez-Martín, P.; Lobato, E.
Optimal Participation of Heterogeneous, RES-Based Virtual Power Plants in Energy Markets. *Energies* **2022**, *15*, 3207.
https://doi.org/10.3390/en15093207

**AMA Style**

Oladimeji O, Ortega Á, Sigrist L, Rouco L, Sánchez-Martín P, Lobato E.
Optimal Participation of Heterogeneous, RES-Based Virtual Power Plants in Energy Markets. *Energies*. 2022; 15(9):3207.
https://doi.org/10.3390/en15093207

**Chicago/Turabian Style**

Oladimeji, Oluwaseun, Álvaro Ortega, Lukas Sigrist, Luis Rouco, Pedro Sánchez-Martín, and Enrique Lobato.
2022. "Optimal Participation of Heterogeneous, RES-Based Virtual Power Plants in Energy Markets" *Energies* 15, no. 9: 3207.
https://doi.org/10.3390/en15093207