Project topics and materials
Get Complete Project Material File(s) Now! »
Electricity production management
Electricity production management aims at planning ahead which production levers to pull in order to satisfy demand in electricity as well as other requirements (as mentioned in 1.2.2: reliability, costs, scarce resources, etc.).
There is no unique framework to manage the production of electricity: levers and requirements vary considerably according to the setting considered. In this section, we will describe some aspects of the electricity production management at EDF that remain relevant for other generating companies.
Specificities of electricity
The electric system is basically composed of two intertwined layers: the physical exchanges of electricity and the related financial trades. At one end, producers – also commonly referred to as generating companies (GenCos) – own or lease physical generating assets – that is to say power plants – to produce electricity, physically provide it on the grid and sell it to end users that consume it at the other end of the grid. For a generating company, the distribution of production assets according to their types is called the energy bundle – or energy mix. For the demand side, the aggregation of all electric consumptions at a given time is called the load. The grid is a network of nodes – sometimes denoted buses – connected by transmission lines. Buses correspond to injection points for generating companies or consumption points for end users.
Safe and reliable operation of the electric system is ensured by Transmission System Operators (TSOs) and Distribution Network Operators (DNOs). The roles of and interactions between the major stakeholders involved in the electric system are presented in the Appendix A.2.
The electric system is demand-driven as the satisfaction of demand is essential: electricity is a good/service that is essential for human activity. It is interesting to note that electricity is an inevitable expense, thus its cheapness is also critical for the purchasing power of households and the bottom line of organizations. The satisfaction of the demand in electricity has to be instantaneous: end-users do not order it in advance nor are they willing to wait for a delayed delivery. The satisfaction of demand cannot be partial; for example, most electrical devices have technical specifications that forbid them to operate at half power. The satisfaction of demand is not flexible; a few end-users can curtail their consumption on demand, but, generally-speaking, there are less levers to control demand, compared to production. The electric system is subject to global requirements. Not only satisfying demand is essential for its usage, it is also necessary for the reliability of the network. Indeed, the electrical network is somewhat fragile: a surge or a shortage of supply compared to demand can cause disturbances and even damages to production/transmission/end-users appliances. Sometimes the last resort is load shedding, that is temporary shutdowns for parts of the network. The equilibrium of supply of producers and demand of consumers is the primary requirement the TSO must pursue. Safety and reliability of the network is subject to more elaborate requirements (congestion and capacity of lines, power losses, frequency adjustment, etc.) that we will not explain further. On the grid, electricity a non-differentiable good, therefore the overall equilibrium is satisfied if each producer meets the demand of its own clients. Note also that, compared to the number of end-users, there are few power plants, mainly due to economies of scale. Those plants are owned/operated by few prominent players on the production side; their responsibilities in guaranteeing the equilibrium is therefore paramount. In case of mismatch in production and demand on the network, prominent players are bound to provide all the leeway they have on demand of the TSO in order to counter-balance the disequilibrium.
Different stages of production management
We will now focus on the production management of electricity. Though not mentioned explicitly previously, an electricity producer – as a company – aims at using efficiently its resources to make a profit while staying within a given threshold of risk. Those financial requirements are supplemented by specific requirements related to the electric system – supply-demand equilibriu and stability of the network more generally – and related to complexity of the production process. The payoff of a generating company is derived as follows: revenues come from the sales to end users and on wholesale markets, costs come from investment, production and buying on wholesale markets.
A generating company must cope with several unknowns or risks: the regulatory context is likely to change over the lifetimes of facilities; markets prices and depths are uncertain; demandis uncertain; production is affected by uncertain factors such as technical failures, maintenance durations, and water precipitations into reservoirs of hydroelectric plants.
Decisions relative to production management can be decomposed according to the usua strategic/tactical/operational planning paradigm [2]. Though the demarcations are fuzzy, this paradigm coincides with the chain of long-term/mid-term/short-term planning horizons.
Long-term planning deals with equipment investment decisions to ensure the energy bundle is adapted to offer enough capacity and maneuvrability to satisfy future demand. The installed production facilities are then considered frozen for the mid-term and the short-term planning horizons. Mid-term planning deals with the design of management policies such as deciding on maintenance campaigns for plants, stock policies – that are enforced either with guide-curves or through opportunity cost indicators – and hedging policies. Such policies then bind or at least influence the possible courses of actions for the short-term horizon. Short-term planning deals with actual scheduling of power plants and is described in further details in Section 1.3.3.
Table of contents :
1 Introduction
1.1 Problem statement and contributions
1.1.1 Case study 1: a real-world hydropower unit commitment problem
1.1.2 Case study 2: a heuristic for MINLP
1.2 Hydropower and hydroelectricity
1.2.1 Basics of hydropower
1.2.2 Electricity technology comparison
1.3 Electricity production management
1.3.1 Specificities of electricity
1.3.2 Different stages of production management
1.3.3 Short-term electricity production scheduling
1.3.4 Short-term hydroelectricity production scheduling
1.4 Optimization for electricity production scheduling
1.4.1 State of the art of unit commitment
1.4.2 The unit commitment problem at EDF
1.4.3 Challenges
2 Real-world hydropower unit commitment: data and model pre-processing for infeasibilities
2.1 Model description
2.1.1 Notation
2.1.2 MILP formulation of the complete model
2.2First computational tests
2.2.1 Test set and configuration
2.2.2 Test results
2.2.3 Problem statement
2.3 LP formulation of a simple model
2.4 Numerical errors
2.5 Scaling to deal with floating-point errors
2.5.1 Tolerances, scaling, and floating-point-based solvers
2.5.2 Computational tests
2.6 Corrective relaxation to deal with data errors
2.6.1 Corrective relaxations
2.6.2 Computational tests
2.7 Extensions of results to the complete model
2.8 Infeasibility classification
2.8.1 Approach
2.8.2 Computational results and interpretation
2.9 Target volume reformulation for feasibility recovery
2.9.1 Minimization of target volume deviations
2.9.2 Optimization of the original problem within deviations
2.9.3 Computational tests
2.10 Conclusion
3 A multiplicative weights update heuristic for mixed-integer non-linear programming – an application to a hydropower unit commitment problem
3.1 The MWU framework
3.1.1 Original MWU framework
3.1.2 The MWU approximation guarantee
3.1.3 The intuition of the MWU for MINLP
3.1.4 The MWU as a metaheuristic for MINLP
3.2 Pointwise reformulations
3.2.1 Concept and definition
3.2.2 Properties
3.3 MWU adaptation for pointwise reformulated MINLP
3.3.1 Sampling parameters
3.3.2 Solution and refinement
3.3.3 Computing the MWU costs
CONTENTS 5
3.4 MWU for an NLP HUC
3.4.1 Model description
3.4.2 Pointwise reformulation
3.4.3 MWU adaptation for the HUC
3.5 Computational results
3.5.1 Test configuration
3.5.2 Comparative results on solution quality and CPU time
3.5.3 Sensitivity to instance size
3.5.4 Comparative results on primal integral
3.5.5 Sensitivity to varying initializations
3.5.6 Importance of the pointwise and refinement steps
3.6 Conclusion
4 Conclusion and perspectives
A Electricity production management
A.1 Hydroelectric structures
A.2 Stakeholders of the electric system
A.3 Unit-commitment settings
B Mathematical optimization
B.1 Brief background
B.2 Basic notions
B.2.1 Variables
B.2.2 Bounds and constraints
B.2.3 Objective function
B.2.4 Optimal solution
B.3 Problem types
B.3.1 Properties
B.3.2 Problems of interest
B.3.3 Complexity
B.4 Algorithms and solutions
B.4.1 Properties
B.4.2 Algorithms related to Mixed-Integer Linear Programming
B.5 Computations and solvers
B.5.1 Use cases
B.5.2 Advantages
B.5.3 Solvers of interests
B.5.4 Challenges
C Data
C.1 Parameter values for the NLP HUC
List of Tables
Bibliography
