# Why Do Pricing Rules Matter? Electricity Market Design with Electric Vehicle Participants

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## Abstract

**:**

## 1. Introduction

## 2. Related Literature

## 3. Preliminaries

## 4. Electricity Market Design

#### 4.1. Market Macrostructure

#### 4.2. Market Microstructure

#### 4.2.1. Bidding Languages

#### 4.2.2. Pricing Rules

#### 4.2.3. Congestion Management

#### 4.3. Pricing Properties

- 1.
- Market Clearing: this property ensures that grid stability is maintained, that is, supply and power inflows match demand and power outflows at any node and any time.
- 2.
- Financial Balance: this property demands that the market operator is revenue neutral. It is well known that some pricing schemes require money from outside the pool to pay for the uplifts. This raises questions about financing (e.g., [68,69,70,71]). The common suggestion is to collect money through fixed charges from customers. This may work for single-sided auctions but can cause problems with price-sensitive customers and prosumers such as EVs. The fees impact their actual surpluses and thus affect other properties, such as individual rationality (participation in the market only under non-negative profits).
- 3.
- Individual Rationality: this property requests that no market participant loses money by engaging in the market, so that suppliers and demanders are willing to participate and the TSO operates sustainably. Note that Property 3 is also termed revenue adequacy for suppliers [72]. Committed out-of-the-money bids causing market participants to suffer deficits are referred to as paradoxically accepted bids [44].
- 4.
- Competitive Equilibrium: this property postulates that the payment functions support a competitive equilibrium, which can be roughly defined as no supplier or demander wanting to deviate from the optimal allocation. This does not apply to the TSO because, as a monopoly, the TSO’s profits are strongly regulated, and hence there are hardly any incentives to deviate from the optimal allocation. This property also prevents paradoxically rejected bids, which are in-the-money bids that are not accepted [44]. it is worth mentioning that unlike in economic theory, where the concept of competitive equilibrium is formally defined, in electricity market design, this concept is treated slightly different from paper to paper (see Bichler et al. [71] for a discussion on this topic).
- 5.
- Economic Efficiency: in a single-sided auction (i.e., only for suppliers), economic efficiency is typically defined as minimal generation cost and/or minimal consumer payments. For double-sided auctions, the definition of maximal social welfare is more applicable.

#### 4.4. Pricing Schemes

- (i)
- solve the allocation problem;
- (ii)
- fix the binary variables to their optimal values and solve the resulting linear program;
- (iii)
- use the shadow prices of the balance constraints as uniform prices;
- (iv)
- use the dual variables associated to the optimality constraints as uplifts.

- (i)
- exchange the non-convex welfare function of the allocation problem and constraints with their convex hull;
- (ii)
- solve the resulting linear program;
- (iii)
- use the dual variables of the balance constraints as uniform prices;
- (iv)
- compute the lost opportunity costs, thus determining the uplift payments.

- (i)
- solve the continuous relaxation of the allocation problem;
- (ii)
- use the shadow price of the balance constraints as uniform prices;
- (iii)
- provide uplift payments to market participants to offset lost opportunity costs.

## 5. Market Model

#### 5.1. Generation Resources

#### 5.2. Demand Resources

#### 5.3. Electric Vehicles

#### 5.4. Transmission Network

#### 5.5. Allocation Problem

## 6. Numerical Experiments

- Scenario 1 (reference case): absence of EVs, absence of demand flexibility;
- Scenario 2: presence of EVs, absence of demand flexibility;
- Scenario 3: presence of EVs, presence of demand flexibility.

#### 6.1. Numerical Example

#### 6.2. Results

#### 6.2.1. Scenario 1

#### 6.2.2. Scenario 2

#### 6.2.3. Scenario 3

## 7. Discussion

- Participation of EV aggregators in a V2G model;
- Demanders that have a a fixed load that they want to fulfil regardless of the price, and another demand component that is only fulfilled when it is economically viable.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

EVs | Electric Vehicles |

V2G | Vehicle-to-Grid |

IP | Integer Programming |

SoC | State of Charge |

MC | Marginal Cost |

ISO | Independent System Operator |

TSO | Transmission System Operator |

LP | Linear Program |

ELM | Extended Locational Marginal |

CH | Convex Hull |

DMU | Direct Minimum Uplift |

## Appendix A

Symbol | Description |
---|---|

T | Set of time periods |

N | Set of network nodes |

${M}_{n}\subset N$ | Set of network nodes connected to node n |

G | Set of generation resources |

${G}_{n}\subset G$ | Set of generation resources located at node n |

D | Set of demand resources |

${D}_{n}\subset D$ | Set of demand resources located at node n |

V | Set of electric vehicles |

${V}_{n}\subset V$ | Set of electric vehicles located at node n |

Symbol | Unit | Description, Variable Type |
---|---|---|

${q}_{g,t}^{GEN}$ | (MWh) | Electricity generated by g in period t, non-negative |

${u}_{g,t}^{GEN}$ | (-) | commitment variable: 1 means g is online in period t and 0 offline, binary |

${q}_{g,t}^{ELA}$ | (MWh) | Flexible electricity demanded by d in period t, non-negative |

${u}_{g,t}^{DEM}$ | (-) | commitment variable: 1 means d is online in period t and 0 offline, binary |

${q}_{v,t}^{+}$ | (MWh) | Electricity charged by v in period t, non-negative |

${q}_{v,t}^{-}$ | (MWh) | Electricity discharged by v in period t, non-negative |

$so{c}_{v,t}$ | (MWh) | State of charge of v in period t, non-negative |

${m}_{v,t}$ | (-) | Charging mode:1 v is charging in period t and 0 discharging, binary |

${q}_{nm,t}^{TRN}$ | (MWh) | Power flow on transmission line $nm$ in period t, continuous |

${\delta}_{n,t}$ | (rad) | Phase angle value at node n in period t, continuous |

Symbol | Unit | Description |
---|---|---|

${C}_{g,t}^{{Q}^{GEN}}$ | (USD/MWh) | Marginal cost for electricity generation of resource g in period t |

${C}_{g,t}^{U}$ | (USD) | Commitment cost of resource g in period t |

${\underline{Q}}_{g,t}^{GEN}$ | (MWh) | Minimum capacity requirement of resource g in period t |

${\overline{Q}}_{g,t}^{GEN}$ | (MWh) | Maximum capacity of resource g in period t |

${C}_{d,t}^{{Q}^{ELA}}$ | (USD/MWh) | Marginal value for flexible electricity demand of resource d in period t |

${\underline{Q}}_{d,t}^{DEM}$ | (MWh) | Minimum capacity requirement of resource d in period t |

${\overline{Q}}_{d,t}^{DEM}$ | (MWh) | Maximum capacity of resource d in period t |

${\underline{SOC}}_{v,t}$ | (MWh) | Minimum capacity requirement of resource v in period t |

${\overline{SOC}}_{v,t}$ | (MWh) | Maximum capacity of resource v in period t |

$\mathsf{\Delta}SO{C}_{v,t}$ | (MWh) | Unscheduled change in SOC of resource v in period t (i.e., electricity for driving) |

${\overline{Q}}_{v,t}^{CHR}$ | (MWh) | Maximum (dis-)charging power of resource v in period t |

${\eta}^{+}$ | (%) | charging efficiency |

${\eta}^{-}$ | (%) | discharging efficiency |

${Q}_{d,t}^{FIX}$ | (MWh) | Electricity demanded by resource d in period t |

${B}_{nm}$ | (MWh) | Susceptance of transmission line $nm$ |

${\overline{Q}}_{l,t}^{TRN}$ | (MWh) | Transmission capacity of transmission line l in period t |

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Generation | Demand | |||||||
---|---|---|---|---|---|---|---|---|

Type | Symbol | Unit | G1 | G2 | G3 | D1 | D2 | D3 |

Marginal cost/value | ${C}_{i}^{Q}$ | (USD/MWh) | 65.00 | 100.00 | 125.00 | 145.00 | 120.00 | 90.00 |

Capacity | ${\overline{Q}}_{i}^{GEN}$,${\overline{Q}}_{i}^{DEM}$ | (MW) | 16.00 | 13.00 | 12.00 | 10.00 | 14.00 | 15.00 |

Minimum production | ${\underline{Q}}_{i}^{GEN}$ | (MW) | - | 13.00 | - | - | - | - |

Type | Unit | Symbol | G1 | G2 | G3 |
---|---|---|---|---|---|

Capacity | (MWh) | ${\overline{Q}}_{g}^{GEN}$ | 450.00 | 60.00 | 100.00 |

Minimum output | (MWh) | ${\underline{Q}}_{g}^{GEN}$ | 100.00 | 5.00 | 50.00 |

Marginal cost | (USD/MWh) | ${C}_{g}^{{Q}^{GEN}}$ | 10.00 | 23.00 | 22.00 |

Commitment cost | (USD) | ${C}_{g}^{U}$ | 210.00 | 60.00 | 120.00 |

Type | Unit | Symbol | EV1 | EV2 | EV3 | EV4 | EV5 | EV6 |
---|---|---|---|---|---|---|---|---|

Hours where plugged | (-) | - | 18-5 | 20-7 | 19-6 | 17-7 | 18-5 | 0-23 |

Driving energy | (MWh) | $\mathsf{\Delta}SO{C}_{v}$ | 16.94 | 21.17 | 36.00 | 21.17 | 10.59 | 0.00 |

Battery capacity | (MWh) | ${\overline{SOC}}_{v}$ | 43.84 | 54.80 | 65.76 | 54.80 | 27.40 | 49.32 |

Battery minimum output | (MWh) | ${\underline{SOC}}_{v}$ | 8.768 | 10.96 | 13.152 | 10.96 | 5.48 | 9.864 |

Maximum (dis-)charge | (MWh) | ${\overline{Q}}_{v}^{CHR}$ | 11.67 | 14.58 | 24.80 | 14.58 | 7.29 | 14.58 |

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**MDPI and ACS Style**

Maldonado, F.; Saumweber, A.
Why Do Pricing Rules Matter? Electricity Market Design with Electric Vehicle Participants. *World Electr. Veh. J.* **2022**, *13*, 143.
https://doi.org/10.3390/wevj13080143

**AMA Style**

Maldonado F, Saumweber A.
Why Do Pricing Rules Matter? Electricity Market Design with Electric Vehicle Participants. *World Electric Vehicle Journal*. 2022; 13(8):143.
https://doi.org/10.3390/wevj13080143

**Chicago/Turabian Style**

Maldonado, Felipe, and Andrea Saumweber.
2022. "Why Do Pricing Rules Matter? Electricity Market Design with Electric Vehicle Participants" *World Electric Vehicle Journal* 13, no. 8: 143.
https://doi.org/10.3390/wevj13080143