DP for UC

22 maio 2018, 11:00 • Luis Marcelino Ferreira

Review of previous class (per summary)

The many possible combinations of units

Six units yield 256 combinations, ten yield 1k

States and stages in an optimization grid

Each state is a combination, stages are hours

Arcs are transitions

Nodal costs (injected for being at that state); taken from the engineering curve of static commitment

Arc costs (cost of transition)

Initial state is known

Final state is unknown or pre-specified (unimportant)

Simple grid with numerical costs

Principle of Optimality by Bellman (’52)

Immediate solution even for very large grids (thousands of nodes, sparse branches)

Forward, backward, stochastic

State transition diagram for a single unit

Simplest case -- just startup and/or shutdown costs

Minimum uptime, minimum downtime, time-dependent startup cost

For eight units of 28 states each there is about a trillion possible combinations -- the curse of dimensionality

DP is very powerful, but there must be another way ...

Next: hydro resources

Practical class #12

17 maio 2018, 09:30 • Célia Maria Santos Cardoso de Jesus

Resolution of problem 11 (Questions 3,4 and5 )

Secure OPF and introduction to UC

17 maio 2018, 08:00 • Luis Marcelino Ferreira

Review of last class

Need for security: a simple example

Costs of security

Security is not remedial action, is healthy system

Formulating a secure OPF problem

Keep the decision u and insert new many constraints so as to ensure security against all specified contingencies

The art of which contingencies to consider and its resemblance with the active set strategy

What is still missing? Dynamics, motion -- OPF is still a picture

Ramp rates and ramp constraints -- where you are and where you want to go, constraints and costs, dynamics

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Chronological load profile

Hierarchy of decision and time discretization:

Real-time operation

Operations planning

Maintenance and resource management

Investment planning

Deterministic vs non-deterministic approaches

Unit commitment -- UC

Integer, binary variables -- integer programming and its inherent difficulties

Combination of units -- relationship to ED and OPF

Historical approach to UC

Static UC -- neglect dynamics

Prepare engineering computation: best combination (and cost) versus power demand -- optimum is a non-convex hull

How many combinations?

What about dynamics? Are they important?

Practical class #12

16 maio 2018, 09:00 • Célia Maria Santos Cardoso de Jesus

Resolution of problem 11 (Questions 3,4 and5 )

OPF by LP

15 maio 2018, 11:00 • Luis Marcelino Ferreira

Review of previous class (per summary)

Introducing linear programming (LP)

A simple example -- role of equality constraint and inequality in defining the polytope for the solution

Special case where A is incidence matrix and network flow problems

Simplex, Dantzig, NP complex or superlinear? Minos

Success of LP -- simplex method and interior methods

Is OPF suitable for LP -- is the objective linear, are the constarints linear?

Formal linearization and identification of all constants as needed for LP

The art of linearization -- tangent, secant, adequate region for the decision space

N-1 security and remedial action

Why one needs N-1 secure OPF -- planning, operations planning and dispatch