Maximum Utility under fairness constraints, ahead-of-time

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From load following to load shaping

A key rule in maintaining power system stability is to balance generation and consumption at all times. This is traditionally done by controlling generation sources that should have a power output that matches demand shape. However, with the introduction of renewable energy, generation is becoming less controllable. This gave rise to Demand Response as a way of shaping demand to overcome generation flexibility shortage. We now give an overview of traditional system control, new trends with the deployment of renewable energy sources and possible ways to deal with demand shape through DR.

Traditional generation sources control

As stated previously, in traditional power systems, generation should be controlled to always match demand. This is denoted by load following. In order to have enough available generation sources capable of following the load curve, system planning is done on different timescales. These timescales are related with existing markets that determine unit commitment for each production source. These markets are designed to adjust generation in order to fulfill predicted demand or correct demand prediction errors. Indeed, some demands can be predicted with high certainty a long time in advance which allows an early reservation of generators. These demands correspond to base load and usually take advantage of (somewhat cheap) slow ramping sources like nuclear.
For more uncertain demands, power generation required to fulfill them can be decided on markets of faster timescales namely wholesale spot markets and Ancillary Services (A/S) market. For wholesale spot markets, each production source will know how much it should generate at each hour of the next day. These markets are usually designed to decide the price of energy depending on the marginal cost function of generation. Let us suppose hourly markets. The cost function shape depends particularly on the generation mix available at a given hour on the grid. It usually grows exponentially with the amount of energy that need to be generated (see Figure 2.1 that represents the mix for a given hour). In addition to generation mix, this cost function will depend on production capacity and ramping capability of generation sources supposing the supply outcome at the previous hour. So for a certain hour, settlement price for energy is equal to the marginal cost at the point where demand curve and supply curve intersect. The amount of energy that should be generated is given by the abscissa of the intersection point. Most generation sources of average cost (e.g., nuclear) have slow ramping capability. So, when a peak in demand occurs costly flexible generators (e.g., gas and oil power plants) need to be used. This will yield in a higher price for energy. Wholesale energy markets can, however, be insufficient to maintain the balance since demand prediction is never perfect and unpredicted events may occur (e.g., bad control of a generator output). This requires sources that can react on a faster time scales to imbalances (in the order of minutes to seconds). Services targeting to solve fast imbalances are referred to by A/S. There is mainly three types of A/S, namely primary, secondary and tertiary regulation [83]. Imbalances in generation and consumption will make the frequency of the grid deviate from its nominal value (i.e., 50 Hz or 60Hz depending on the country). This nominal value corresponds to balanced generation and consumption.
When an imbalance occurs, primary regulation is used to stabilize grid frequency fluctuations. This should be done in matters of seconds (e.g., in less than 30 seconds in France). Following primary reserves, secondary and tertiary reserves are consecutively used in order to bring back frequency to its nominal value (in matters of minutes). This is done by producing more or reducing generation in a way that equates consumption and production on the grid. Indeed, secondary reserves are immediately automatically dispatched. Tertiary are called for when secondary reserves are insufficient or to preserve flexible capacity of sources participating to secondary regulation. Generation sources providing A/S need to have required capacity and enough ramping flexibility to follow adequately the load curve.

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New renewable intermittent sources

Maintaining balanced generation and demand is made more complex with the introduction of renewable energy sources and the willingness of governments to go towards clean energy.
With the increasing deployment of renewable energy sources and particularly highly volatile ones like wind turbines and PhotoVoltaics (PV) cells, flexible resources that can help maintaining the bal- ance between generation and consumption, is becoming more needed. One example of potential effects of high penetration of renewable energy sources can be illustrated by the “duck shape” (see Figure 2.2 from California Independent System Operator (CAISO)) of the net load curve that may appear in certain times of the year2. Net load is the difference between forecasted load and expected generation from renewable energy sources. It corresponds to the energy that should be produced by classical generation sources in order to maintain a consumption and generation balance. The observed shape can be explained by taking the example of solar generation. Indeed, solar generation will be concentrated during some sunny hours of the day. During these hours, the net load curve will have very low values which produces the shape of a belly. The belly will be more pronounced with the increased penetration of the energy source (i.e., solar in this case) and may sometimes result in negative values of the net load (i.e., over generation). In this case, enough flexible resources should be available particularly to cope with steep ramps (e.g., on the tail and the neck of the duck).

Table of contents :

1 Introduction 
1 Motivation
2 Thesis contributions and outline
2 Demand Response: Overview 
1 History
2 From load following to shaping
2.1 Traditional generation sources control
2.2 New renewable intermittent sources
2.3 Main objectives of Demand Response
3 Objectives and approaches
3.1 Main actors
3.2 Implicit versus explicit services
3.3 Control timescale
3.4 Evolution of energy markets
3.5 Power grid operation constraints
4 First classification
4.1 Pricing-based DR
4.2 Direct Load Control
5 Control of heterogeneous loads
6 Summary and thesis motivation
3 Framework and utility functions 
1 Framework
1.1 General architecture
1.2 DR solutions
2 Appliances taxonomy
2.1 Overview
2.2 Proposed taxonomy
3 System model
3.1 Utility functions and constraints
3.2 Optimization problem
4 Case study
4.1 Lighting System
4.2 Heater System
4.3 Washing machine
4.4 Summary
4 Fine-grained centralized control 
1 Motivation
2 Related work
3 System architecture
4 Proposed control schemes
4.1 Maximum Utility
4.2 Fairness constraints
4.3 Decision time
5 Model
5.1 Maximum Utility, ahead-of-time
5.2 Maximum Utility, real-time
5.3 Maximum Utility under fairness constraints, ahead-of-time
5.4 Maximum Utility under fairness constraints, real-time
6 Solving the problem
6.1 Exact resolution
6.2 Greedy heuristics
7 Numerical analysis
7.1 Settings
7.2 Use case 1
7.3 Use case 2
8 Conclusion
5 Partially distributed control 
1 Related work
2 Proposed schemes
2.1 One-way hierarchical schemes
2.2 Greedient approach
3 Considered Use cases
4 Performance analysis
4.1 Use case: Lights and heaters
4.2 Use case: Lights, heaters and washing machines
5 Conclusion
6 Distributed control 
1 Motivation
2 Related work
3 System architecture
4 Problem formulation
4.1 Local constraints
4.2 Scheduling
4.3 Excess management
5 Numerical analysis
5.1 Use Case: Lights and heaters
5.2 Use Case: Lights, heaters and washing machines
6 Conclusion
7 Demand dispatch 
1 Motivation and related work
2 A Distributed Control Problem
2.1 Grid dynamics
2.2 Actuator dynamics
2.3 Grid disturbance
2.4 Control design
2.5 Cost of heterogeneity
3 Risk & Cost using Demand Dispatch
3.1 Actuator block
3.2 Load models and pre-filter design
3.3 Transfer functions to model risk & performance
3.4 Mean-square cost
3.5 Disturbance rejection
4 Conclusion
8 Conclusion 
1 Future work


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