Definition of Prosumer: General and in Electricity Markets

Introduction

The concept of a prosumer has gained significant attention in economics, finance, and technology due to the evolving nature of production and consumption patterns. The term combines producer and consumer, reflecting individuals or entities that both produce and consume goods or services. In the context of electricity markets, Prosumers play a crucial role by generating electricity, often from renewable sources, and consuming it, potentially supplying excess generation back to the grid.

This article seeks a comprehensive definition of a prosumer both generally and specifically within electricity markets. It includes mathematical models, logical explanations, and references to economic, finance, scientific, and technical literature.

General definition of a prosumer

A Prosumer is an individual or entity that both produces and consumes goods or services. The term reflects the blurring of roles between producers and consumers, where consumers actively participate in the production process, often for their own use or for exchange with others.

Alvin Toffler introduced the term “Prosumer” to describe the merging roles of producers and consumers in the post-industrial society. He predicted a shift where individuals would become more involved in producing goods and services for their own consumption.¹

Don Tapscott expanded on the concept in the context of the digital economy, where technology empowers consumers to participate in production processes, for example, user-generated content.²

Characteristics of prosumers

Prosumers are actively involved in the creation or customization of products and services. They often produce goods tailored to their specific needs. Advances in technology enable consumers to produce goods and services that were previously the domain of specialized producers, for example 3D printing.

Prosumers can disrupt traditional market structures by reducing the distinction between producers and consumers. They contribute to the value creation process, influencing product development and innovation. Prosumers can affect supply by adding their own production and influence demand through consumption patterns.

Definition of prosumer in electricity markets

In electricity markets, a Prosumer is an individual, household, or entity that both produces electricity, often through renewable energy sources like solar photovoltaic panels or wind turbines, and consumes electricity for their own use. They can supply excess electricity back to the grid, becoming both consumers and suppliers within the energy system.

Characteristics of electricity prosumers

They generate electricity at or near the point of use. They both draw electricity from the grid and feed electricity into it. Prosumers may engage in net metering, feed-in tariffs, or sell electricity on energy markets. Utilize technologies such as solar panels, energy storage systems, and smart meters.

Mathematical models in prosumer behavior

Energy balance equation

A prosumer’s energy balance over a time period t is given as:

$$E_{\text{consumed}, t} = E_{\text{produced}, t} + E_{\text{imported}, t} - E_{\text{exported}, t} \pm E_{\text{stored}, t} \label{eq:PEBE}$$
Where:

• $E_{\text{consumed}, t}$: Energy consumed by the prosumer

• $E_{\text{produced}, t}$: Energy generated by the prosumer

• $E_{\text{imported}, t}$: Energy imported from the grid

• $E_{\text{exported}, t}$: Energy exported to the grid

• $E_{\text{stored}, t}$: Change in energy stored (positive when charging storage, negative when discharging).

Optimization problem for a prosumer

Optimization requires that we minimize total energy cost or maximize net profit over a time horizon $T$, subject to several constraints.

$$\min_{\{E_{\text{imported}, t}, E_{\text{exported}, t}, E_{\text{stored}, t}\}} \sum_{t=1}^{T} \left[ P_{\text{buy}, t} \cdot E_{\text{imported}, t} - P_{\text{sell}, t} \cdot E_{\text{exported}, t} + C_{\text{storage}, t} \right] \label{eq:ProsumerOpt}$$

Energy balance constraints

$$E_{\text{consumed}, t} = E_{\text{produced}, t} + E_{\text{imported}, t} - E_{\text{exported}, t} \pm E_{\text{stored}, t} \label{eq:EBC}$$

Technical constraints

Generation capacity limits

$$0 \leq E_{\text{produced}, t} \leq E_{\text{produced}, t}^{\text{max}} \label{eq:GCL}$$

Storage capacity limits

$$E_{\text{stored}, t}^{\text{min}} \leq E_{\text{stored}, t} \leq E_{\text{stored}, t}^{\text{max}} \label{eq:SCL}$$

Grid import and export limits

$$0 \leq E_{\text{imported}, t} \leq E_{\text{imported}, t}^{\text{max}} 0 \leq E_{\text{exported}, t} \leq E_{\text{exported}, t}^{\text{max}} \label{eq:}$$

Regulatory constraints

Net metering policies, feed-in tariffs, or other market rules that affect prices $P_{\text{buy}, t}$ and $P_{\text{sell}, t}$.

Variables

• $E_{\text{imported}, t}$

• $E_{\text{exported}, t}$

• $E_{\text{stored}, t}$

Parameters

• $P_{\text{buy}, t}$: Price of electricity purchased from the grid

• $P_{\text{sell}, t}$: Price of electricity sold to the grid

• $C_{\text{storage}, t}$: Cost associated with charging/discharging storage (includes efficiency losses).

Prosumer impact on electricity markets

Prosumers can alter local supply and demand conditions, affecting electricity prices and grid stability. Aggregate prosumer generation can reduce peak demand, influencing market clearing prices. With peer-to-peer (P2P) trading, prosumers can trade electricity directly with other consumers or prosumers using platforms or microgrids. Considering the possibility of Virtual Power Plants (VPPs), aggregated prosumer resources can allow a group of prosumers to participate in wholesale markets.

Mathematical modeling of prosumer market participation

A prosumer’s net supply to the grid can be modeled as:

$$S_{\text{Prosumer}, t}(P_t) = E_{\text{exported}, t}(P_t) - E_{\text{imported}, t(P_t)} \label{eq:PSF}$$
Where $P_t$ is the electricity price at time $t$.

Including prosumers in the market supply function gives:

$$\sum_{j} S_{\text{Producer}, j, t}(P_t) + \sum_{k} S_{\text{Prosumer}, k, t}(P_t) = \sum_{i} D_{\text{Consumer}, i, t}(P_t) \label{eq:PMSF}$$
Where $S_{\text{Producer}, j, t}(P_t)$ is the supply from traditional producers, $S_{\text{Prosumer}, k, t}(P_t)$ is the net supply from prosumers $k$, and $D_{\text{Consumer}, i, t}(P_t)$ represents demand from consumers.

Impact of prosumers on electricity markets

Variability in prosumer generation introduces uncertainty in supply. Reverse power flows can affect voltage levels and grid infrastructure. Smart grids and advanced control systems can solve this by managing distributed generation and maintaining grid stability. Energy storage systems can further mitigate variability and enhance reliability.

Increased supply from prosumers can lead to lower wholesale electricity prices, especially during peak generation periods, such as the midday solar production period. Traditional generators may face reduced revenues, impacting investment in new capacity. This can incentivize innovation in the demand response and flexibility services.

Policies must be developed that determine compensation for excess energy supplied by prosumers and ensure that prosumers can participate fairly in energy markets, including access to real-time pricing and ancillary services markets. Prosumers may contribute to reducing greenhouse gas emissions by generating renewable energy. However, if system stability is provided by coal, oil or gas this assumption may not hold. Policy makers should incentivize the move away from fossil fuels and promote energy autonomy, which enhances energy security and resilience at the local level.

Mathematical proofs and models

We can model prosumers maximizing net profit $\pi$ over a time horizon $T$ as:

$$\max_{\{E_{\text{exported}, t}, E_{\text{stored}, t}\}} \pi = \sum_{t=1}^{T} \left[ P_{\text{sell}, t} \cdot E_{\text{exported}, t} - P_{\text{buy}, t} \cdot E_{\text{imported}, t} - C_{\text{generation}, t} - C_{\text{storage}, t} \right] \label{eq:PPM}$$
This is subject to the energy balance and technical constraints as previously defined.

For optimality, the marginal revenue from exporting electricity should equal the marginal cost, considering storage and generation costs.

$$P_{\text{sell}, t} = \frac{\partial C_{\text{generation}, t}}{\partial E_{\text{produced}, t}} + \frac{\partial C_{\text{storage}, t}}{\partial E_{\text{stored}, t}} \label{eq:MRO}$$

Similarly, for importing electricity:

$$P_{\text{buy}, t} = \text{Marginal Utility of Consuming Additional Electricity} \label{eq:EI}$$

With these considerations, aggregate market supply curve shifts outward with the inclusion of prosumers’ net supply, potentially lowering market prices.

Conclusion

Prosumers represent a significant evolution in both general economic activity and specifically within electricity markets. They embody the convergence of production and consumption roles, facilitated by technological advancements and changing market dynamics.

In electricity markets, prosumers impact supply and demand, influence prices, and contribute to grid operations and energy sustainability. Mathematical models illustrate how prosumers optimize their energy production and consumption, participate in markets, and affect overall market equilibrium.

Understanding the role of prosumers is essential for designing policies, market mechanisms, and technologies that harness their potential benefits while addressing challenges related to grid integration, market fairness, and regulatory frameworks.

The definitions and explanations provided are consistent with principles in economics, finance, and technical literature. The mathematical models are standard representations used to analyze prosumer behavior in both general contexts and specifically in electricity markets.

Bibliography

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References

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1. Alvin Toffler. The Third Wave. New York: William Morrow and Company (1980).↩︎

2. Don Tapscott. The Digital Economy: Promise and Peril in the Age of Networked Intelligence. New York: McGraw-Hill (1995).↩︎