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Optimal Power Flow (DC-OPF and AC-OPF)

DTU Summer School 2017

Spyros Chatzivasileiadis

What is optimal power flow?

Use of OPF in the industry

 (^) RTE, France: they invented the OPF! (Carpentier,

• Their focus is mostly on the optimization of the system operation and not so much on markets
• They are working on the application of convex relaxations of OPF on their system (see Dan Molzahn's talk!)

 CAISO, California, USA

• Electricity markets: An OPF runs every day (Day-Ahead), every hour, every 15 minutes, and every 5 minutes.
• (^) Depending on the problem they run a DC-OPF with unit commitment, a standard DC-OPF, or just Economic Dispatch

Use of OPF in the industry

 PJM, East Coast, USA

• Security-Constrained Economic Dispatch every 5 minutes
• nal test phase of optimal voltage control every 5 minutes (they use AC-OPF as well)

 EUPHEMIA

• one common algorithm to calculate electricity prices across Europe, and allocate cross border capacity on a day-ahead basis
• 19 European countries, over 150 million EUR in matched trades daily

 PLEXOS

• June 2000: PLEXOS was rst-to-market with electric power market simulation based entirely on mathematical programming
• Features: generation capacity expansion planning, transmission expansion planning, hydro-thermal coordination, ancillary services

Outline

 Economic Dispatch

 (^) DC-OPF

 AC-OPF

Outline

 Economic Dispatch

• (^) used in power exchanges, e.g. EPEX, etc.
• Supply must meet demand
• (^) Generator limits

Outline

 Economic Dispatch

• (^) used in power exchanges, e.g. EPEX, etc.
• Supply must meet demand
• (^) Generator limits

 DC-OPF

• extends Economic Dispatch
• (^) considers the power ows! (in a linearized form)
• includes the power ow limits of the lines
• (^) only active power; no losses

 AC-OPF

• full AC power ow equations
• (^) active and reactive power ow
• (^) current, voltage
• losses

Economic Dispatch

min

i

ciPGi

subject to:

P Gmini  PGi  P Gmaxi

i

PGi = PD

Economic Dispatch

min

i

ciPGi

subject to:

P Gmini  PGi  P Gmaxi

i

PGi = PD

 (^) The Economic Dispatch does not consider any network ows or network constraints!

 (^) We assume a copperplate network, i.e. a lossless and unrestricted ow of electricity from A to B.

Can we solve the economic dispatch problem without using an

optimization solver?

The Merit-Order Curve

0 A B C D

cG 1

cG 2

cG 3

cG 4

price

power

A = P (^) Gmax 1

B = A + P (^) Gmax 2

C = B + P (^) Gmax 3

D = C + P (^) Gmax 4

The Merit-Order Curve

0 A B C D

cG 1

cG 2

cG 3

cG 4

price

power PD

A = P (^) Gmax 1

B = A + P (^) Gmax 2

C = B + P (^) Gmax 3

D = C + P (^) Gmax 4

The Merit-Order Curve: An Example

Merit-Order of the German conventional generation in 2008. Source: Forschungsstelle fur Energiewirtschaft e. V.

Merit-Order Curve, Marginal Generators,

and Line Congestion

0 A B C D

cG 1

cG 2

cG 3

cG 4

price

power PD

 (^) Although G3 has enough capacity, it cannot produce enough to cover the demand due to line congestion

 (^) Instead G4, a more expensive gen that does not contribute to the line congestion, must produce the missing power

 (^) In a DC-OPF context, there is no longer a single system marginal price

14 (we will observe different nodal prices in different nodes)DTU Electrical Engineering Optimal Power Flow (DC-OPF and AC-OPF) Jun 12, 2017