Time-and-Level-of-Use (TLOU) is a recently proposed pricing policy for energy, extending Time-of-Use with the addition of a capacity that users can book for a given time frame, reducing their expected energy cost if they respect this self-determined capacity limit. We introduce a variant of the TLOU defined in the literature, aligned with the supplier interest to prevent unplanned over-consumption. The optimal price-setting problem of TLOU is defined as a bilevel, bi-objective problem anticipating user choices in the supplier decision. An efficient resolution scheme is developed, based on the specific discrete structure of the lower-level user problem. Computational experiments using consumption distributions estimated from historical data illustrate the effectiveness of the proposed framework.
The electricity grid is expected to require vast investments due to the decarbonization-by-electrification trend, calling for a change in grid tariff design which provides proper incentives for reducing peak loads. However, price signals from grid tariffs could be distorted from electricity spot prices which also represents a significant of the total consumer electricity bill. This paper attempts to identify whether there is a price signal conflict between grid tariffs and spot prices. Four different grid tariff designs are compared, using a generic demand response model as part of a cost-mini…
Joint Design of Time-of-Use Schedules and Price Levels: a Bilevel Model with Client Participation and Load Flexibility
École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；EDF Lab Paris-Saclay（法国电力集团萨克雷实验室）；Institut National de Recherche en Informatique et en Automatique (Inria)（法国国家信息与自动化研究所）
This two-part paper addresses the design of retail electricity tariffs for distribution systems with distributed energy resources such as solar power and storage. In particular, the optimal design of dynamic two-part tariffs for a regulated monopolistic retailer is considered, where the retailer faces exogenous wholesale electricity prices and fixed costs on the one hand and stochastic demands with inter-temporal price dependencies on the other. Part I presents a general framework and analysis for revenue adequate retail tariffs with advanced notification, dynamic prices and uniform connection…
Distributed renewable resources owned by prosumers can be an effective way of fortifying grid resilience and enhancing sustainability. However, prosumers serve their own interests and their objectives are unlikely to align with that of society. This paper develops a bilevel model to study the optimal design of retail electricity tariffs considering the balance between economic efficiency and energy equity. The retail tariff entails a fixed charge and a volumetric charge tied to electricity usage to recover utilities' fixed costs. We analyze solution properties of the bilevel problem and prove …
This paper presents a novel analysis of two feed-in tariffs (FIT) under market and regulatory uncertainty, namely a sliding premium with cap and floor and a minimum price guarantee. Regulatory uncertainty is modeled with a Poisson process, whereby a jump event may reduce the tariff before the signature of the contract. Using a semi-analytical real options framework, we derive the project value, the optimal investment threshold, and the value of the investment opportunity for these schemes. Taking into consideration the optimal investment threshold, we also compare the two aforementioned FITs w…
We propose a model of incentives for data pricing in large mobile networks, in which an operator wishes to balance the number of connections (active users) of different classes of users in the different cells and at different time instants, in order to ensure them a sufficient quality of service. We assume that each user has a given total demand per day for different types of applications, which he may assign to different time slots and locations, depending on his own mobility, on his preferences and on price discounts proposed by the operator. We show that this can be cast as a bilevel progra…
This two-part paper addresses the design of retail electricity tariffs for distribution systems with distributed energy resources (DERs). Part I presents a framework to optimize an ex-ante two-part tariff for a regulated monopolistic retailer who faces stochastic wholesale prices on the one hand and stochastic demand on the other. In Part II, the integration of DERs is addressed by analyzing their endogenous effect on the optimal two-part tariff and the induced welfare gains. Two DER integration models are considered: (i) a decentralized model involving behind-the-meter DERs in a net metering …
To guarantee the well-functioning of electricity distribution networks, it is crucial to constantly ensure the demand-supply balance. To do this, one can control the means of production, but also influence the demand: demand-side management becomes more and more popular as the demand keeps increasing and getting more chaotic. In this work, we propose a bilevel model involving an energy supplier and a smart grid operator (SGO): the supplier induces shifts of the load controlled by the SGO by offering time-dependent prices. We assume that the SGO has contracts with consumers and decides their co…
The death spiral hypothesis in electric utility represents a positive feedback phenomenon in which a regulated utility is driven to financial instability by rising prices and declining demand. We establish conditions for the existence of death spiral and conditions of stable adoption of distributed energy resources. We show in particular that linear tariffs always induce death spiral when the fixed operating cost of the utility rises beyond a certain threshold. For two-part tariffs with connection and volumetric charges, the Ramsey pricing that optimizes myopically social welfare subject to th…
Price based demand response schemes may significantly improve power system efficiency. Additionally, it is desired that such schemes yield improved power operation, by reducing the peak consumption. This paper proposes the Intraday Block Pricing (IBP) scheme, aiming to promote effective demand response among consumers by charging their electricity usage based on intraday time-slots. To design the prices associated with the proposed scheme, we formulate a bilevel optimization problem that aims to minimize the Peak-to-Average Ratio (PAR) and simultaneously benefit the consumers and the utility c…
In the present work we tackle the problem of finding the optimal price tariff to be set by a risk-averse electric retailer participating in the pool and whose customers are price-sensitive. We assume that the retailer has access to a sufficiently large smart-meter dataset from which it can statistically characterize the relationship between the tariff price and the demand load of its clients. Three different models are analyzed to predict the aggregated load as a function of the electricity prices and other parameters, as humidity or temperature. More specifically, we train linear regression (…
This paper deals with the market-bidding problem of a cluster of price-responsive consumers of electricity. We develop an inverse optimization scheme that, recast as a bilevel programming problem, uses price-consumption data to estimate the complex market bid that best captures the price-response of the cluster. The complex market bid is defined as a series of marginal utility functions plus some constraints on demand, such as maximum pick-up and drop-off rates. The proposed modeling approach also leverages information on exogenous factors that may influence the consumption behavior of the clu…
Reduced installation and operating costs give energy storage systems an opportunity to participate actively and profitably in electricity markets. In addition to providing ancillary services, energy storage systems can also arbitrage temporal price differences. Congestion in the transmission network often accentuates these price differences and will under certain circumstances enhance the profitability of arbitrage. On the other hand, congestion may also limit the ability of a given storage device to take advantage of arbitrage opportunities. This paper analyzes how transmission congestion aff…
We consider an energy provider whose goal is to simultaneously set revenue-maximizing prices and meet a peak load constraint. In our bilevel setting, the provider acts as a leader (upper level) that takes into account a smart grid (lower level) that minimizes the sum of users' disutilities. The latter bases its decisions on the hourly prices set by the leader, as well as the schedule preferences set by the users for each task. Considering both the monopolistic and competitive situations, we illustrate numerically the validity of the approach, which achieves an 'optimal' trade-off between three…
In recent years, significant efforts for improving the technical and the economic performance of smart grids have been applied with the presence of different players making decisions in these grids. This paper proposes a bi-level hierarchical structure for designing and planning distributed energy resources in home microgrids (H-MGs). Such a small-scale grid inside the market environment permits energy exchange among distributed energy resources and home microgrids through a pool market. In this paper, each home microgrid's planner maximizes the performance of distributed energy resources whil…
A monopolist wishes to maximize her profits by finding an optimal price policy. After she announces a menu of products and prices, each agent $x$ will choose to buy that product $y(x)$ which maximizes his own utility, if positive. The principal's profits are the sum of the net earnings produced by each product sold. These are determined by the costs of production and the distribution of products sold, which in turn are based on the distribution of anonymous agents and the choices they make in response to the principal's price menu. In this paper, we provide a necessary and sufficient condition…
The European market clearing problem is characterized by a set of heterogeneous orders and rules that force the implementation of heuristic and iterative solving methods. In particular, curtailable block orders and the uniform purchase price (UPP) pose serious difficulties. A block is an order that spans over multiple hours, and can be either fully accepted or fully rejected. The UPP prescribes that all consumers pay a common price, i.e., the UPP, in all the zones, while producers receive zonal prices, which can differ from one zone to another. The market clearing problem in the presence of bo…
Energy storage is expected to play an increasingly important role in mitigating variations that come along with the growing penetration of renewable energy. In this paper, we study the optimal bidding of an energy storage unit in a semi-centralized market. The energy storage unit offers its available storage capacity and maximum charging/discharging rate to the operator; then the operator clears the real-time market by minimizing the total cost. The energy storage unit is paid/charged at locational marginal price (LMP). The problem casts down to a bilevel optimization problem with a mixed-inte…
