31765: optimization in modern power systems - lecture 1: … · 2017-09-05 · s. boyd, l....

31765: Optimization in modern power systems

Lecture 1: Introduction

Spyros Chatzivasileiadis

Outline

• Welcome!

• Let’s introduce ourselves!

• My chance to get to know you better: Pre-course questionnaire

• What is optimization?

• Learning Objectives

• General info about the course

• Short introduction to linear optimization

• Economic dispatch

2 DTU Electrical Engineering 31765: Optimization in modern power systems Sep 5, 2017

Assistants to this course

Lejla [email protected]

Andreas [email protected]


[email protected]

[email protected]

What is optimization?


Outline

• Welcome!

• Let’s introduce ourselves!

• My chance to get to know you better: Pre-course questionnaire

• What is optimization?

• Learning Objectives

• General info about the course

• Short introduction to linear optimization

• Economic dispatch


Use of OPF in the industry: Utilities

• RTE, France: they invented the OPF! (Carpentier, EdF, 1962)

• RTE’s current efforts are on the convex relaxations of OPF (e.g. work ofCedric Josz with Dan Molzahn, initiated by Patrick Panciatici, and others)

• they divide their whole system in subsystems• the solve the optimization with convex relaxations for each subsystem, e.g.objectives are reactive power provision, unit commitment, etc. This givesthem an absolute minimum of the objective function for each subsystem

• then they gather these solutions in their non-convex master problem andsolve it. They iterate between subproblems and master problem until theyfind a feasible solution.

• CAISO, California, USA

• Use in Day-Ahead and Real-time markets• Energy and Ancillary services allocation• An OPF runs every day (Day-Ahead), every hour, every 15 minutes, andevery 5 minutes.

• Prices for energy, for ancillary services (primary and secondary frequencyreserves), and congestion revenue rights (participants that inducecongestion have to pay)

• Depending on the problem they run a DC-OPF with unit commitment, astandard DC-OPF, or just Economic Dispatch


Use of OPF in the industry: Utilities

• PJM, East Coast, USA

• Security-Constrained Economic Dispatch every5 minutes

• final test phase of optimal voltage control every5 minutes (they use AC-OPF as well)

• Day ahead market, etc.

• Energinet.dk: they don’t use OPF yet

• The US has cooptimization of the day-aheadmarket and the reserves


Use of OPF in the industry: Other companies

• OPF and optimization in general is used a lot in consultingcompanies, e.g. for investments, assessment of the market powerof participants, market design issues in order to ensuremaximization of the social welfare, etc.

• EUPHEMIA

• mandated by seven European Power Exchanges (APX, Belpex,EPEX SPOT, GME, Nord Pool Spot, OMIE and OTE)

• one common algorithm to calculate electricity prices acrossEurope, and allocate cross border capacity on a day-ahead basis

• 19 European countries, over 150 million EUR in matched tradesdaily

• PLEXOS

• June 2000: PLEXOS was first-to-market with electric powermarket simulation based entirely on mathematical programming

• Today PLEXOS is the most widely used integrated energymodel including the worlds largest and most sophisticatedutilities, regulators and system operators

• Features: generation capacity expansion planning, transmissionexpansion planning, hydro-thermal coordination, ancillaryservices8 DTU Electrical Engineering 31765: Optimization in modern power systems Sep 5, 2017

Linear Programming

• most widely used type of mathematical optimization

• many real-world applications can be modelled as a linear program• efficient techniques to solve large-scale programs

Example:


Linear Programming

Example of a linear program: Suppose a pro-duction manager is responsible for scheduling themonthly production levels xj of a certain product(pink flamingos) for a planning horizon of twelvemonths.

Production+Storage cost per month min∑j

(cjxj +

j−1∑k=1

skxk

)subject to:

total annual demand D x1 + . . .+ x12 = D

max. prod. capacity per month mj 0 ≤ xj ≤ mj


Learning Objectives

• Recognize and formulate problems for operation and investments in power systems

• Basic principles of

• Linear programming• Quadratic programming• Nonlinear programming, and• Semidefinite programming

• Formulate the dual of an optimization problem and the optimality conditions (KKT)

• Explain what locational marginal price is in electricity markets

• Design and solve:

• DC-OPF• AC-OPF

• Understand and apply convex relaxations (e.g. semidefinite programming)

• Describe three advantages and disadvantages of each formulation

• Organize, plan, and carry out work in a group project

• Analyze and present the results in front of an audience


General Info About the Course

• Lectures

• Location: Building 325, Room H009• Time: 8:00-10:00, every Tuesday(as we agreed, classes will start at 8.15am)

• Working on assignments (with the support of a teaching assistant)

• Location: Building 325, Room 153• Time: 10:00-12:00, every Tuesday

• According to DTU rules, 5 ECTS credits correspond to about 10-11hours of work per week during the 13-week period. This means you areexpected to continue working on the assignments during the afternoon.


General Info About the Course

• Necessary for the class

• A laptop or a PC with Matlab installed• Please see the instructions ”Setup Matlab Optimization Environment”on how to setup all the necessary software tools on Campusnet.

• Course Material:

• please see the list of links on Campusnet• you can also check www.chatziva.com/teaching/2017/31765.html

for some supplementary material• Examples:

• R.D. Christie, B.F. Wollenberg, I. Wangesteen, Transmission Management in theDeregulated Environment. Proceedings of the IEEE, vol. 88, no. 2, pp. 170-195,Feb. 2000.

• S. Boyd, L. Vandenberghe, Convex Optimization. Cambridge University Press(Chapters 4 and 5).

• H. Glavitsch, R. Bacher, Optimal Power Flow Algorithms. ETH Zurich, (around1999).


www.chatziva.com/teaching/2017/31765.html

Guest Lecture!

• Who: Patrick Panciatici, RTE France

• Title: Optimization in power systems: current state and perspectives

• When: Tue, Oct 24

You wouldn’t want to miss it!


Assignments

• Groups of 3 persons

• Random allocation in groups

Three assignments:

1 Economic Dispatch, DC-OPF, and Nodal Prices

2

AC-OPF andor AC-OPF with convex relaxations

OPF-based project of your choice

3 Solution methods of optimization problems

• Study in groups the principles of different solution methods• prepare a presentation to present at end of the class• peer-reviewing: review the presentation with another group beforepresenting in front of class


Evaluation

• 45% Assignments

• 55% Oral Exam

• Assignment 1 is already on Campusnet!

• Deadline for Assignment 1: Tue, Oct 3, 2017


Linear Program

Linear Programming

min c · x

subject to:

ai · x = bi, i = 1, . . . ,m

x ≥0, x ∈ Rn

• LP: Optimization variables in the form of a vector x.


Economic Dispatch and Optimal Power Flow:Short Introduction on the Board

1 2

3


Economic Dispatch

min∑i

ciPGi(1)

subject to:PminGi

≤ PGi≤ Pmax

Gi(2)

and ∑i

PGi= PD (3)


Economic Dispatch

min∑i

ciPGi(4)

subject to:PminGi

≤ PGi≤ Pmax

Gi(5)

and ∑i

PGi= PD (6)

How do you interpret these constraints for a 2-generator system on thecartesian plane?


Graphical representation of the 2-generatorEconomic Dispatch

PG1

PG2

PG1 + PG2 = PD•

100

200 Assumptions

PD = 150 MW

0 ≤ PG1 ≤ 100 MW

0 ≤ PG2 ≤ 200 MW


DC-OPF

min∑i

ciPGi(7)

subject to:PminGi

≤ PGi≤ Pmax

Gi(8)

andB · θ = PG −PD (9)

and1

xij

(θi − θj) ≤ Pij,max (10)


31765: optimization in modern power systems - lecture 1: … · 2017-09-05 · s. boyd, l....

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