ECE4053 Chap.2 Alternative Power Flow and Economic Dispatch
Alternative Power Flow and Economic Dispatch
This chapter compares power-flow methods by the outputs they preserve. Full AC Newton-Raphson keeps coupled active and reactive balances. Decoupled and fast-decoupled methods use transmission-network sensitivity structure. DC power flow linearises active-power and angle relations, while forward-backward sweep exploits radial feeder topology.
Economic dispatch then allocates demand among committed generators.
Constant marginal costs support a merit order, while differentiable cost curves lead to equal incremental cost for units that are free to move. Capacity, losses and network constraints determine which unit is actually marginal.
What this chapter covers
- 01
AC Newton-Raphson as the reference model
- 02
Decoupled and fast-decoupled sensitivity blocks
- 03
DC power-flow assumptions
- 04
Forward-backward sweep for radial feeders
- 05
Marginal and average generation cost
- 06
Merit-order dispatch
- 07
Incremental-cost equalisation
- 08
Equality and inequality constraints
Worked example · free
Dispatch three units in merit order
- +1Rank the units A, B, C by ascending marginal cost.
- +1Dispatch A at its 80 MW maximum, leaving 50 MW.
- +1Dispatch B at 50 MW and C at 0 MW.
- +1Check 80 + 50 = 130 MW.
- +1Calculate cost as 80×22 + 50×35 = $3,510 per hour.
- +1Identify B as the marginal unit at $35/MWh because it can still increase.
Key terms
- Decoupled Power Flow
- An AC solution approach that treats active-power and voltage-angle sensitivity separately from reactive-power and voltage-magnitude sensitivity.
- DC Power Flow
- A linear active-power and angle approximation that omits voltage-magnitude and reactive-power behaviour.
- Forward-Backward Sweep
- A radial-network method that accumulates downstream quantities toward the source and then updates voltages outward.
- Marginal Cost
- The cost of producing one additional unit of electrical energy at the current operating point.
- Merit Order
- A ranking that dispatches available generation by increasing marginal cost under a simple constant-cost model.
- Unit Commitment
- The scheduling decision that determines which generating units are on or off before output is economically dispatched.
Alternative Power Flow and Economic Dispatch FAQ
When is DC power flow useful?
It is useful for rapid active-power transfer and contingency screening when voltage magnitudes remain near nominal, angles are small and resistance and reactive detail are not central. It is unsuitable for voltage or reactive-limit studies because those variables are omitted.
Why can fast-decoupled power flow be quicker?
It separates weak cross-couplings and reuses simplified sensitivity matrices instead of rebuilding and refactorising a full Jacobian every iteration. The speed comes from assumptions that can weaken in resistive or heavily stressed networks.
What does equal incremental cost mean?
For differentiable costs and an unconstrained lossless optimum, any small transfer of output between free units should not reduce total cost. Their incremental costs must therefore be equal. Units at a minimum or maximum are exceptions because they cannot move freely.
What is the difference between average and marginal cost?
Average cost divides total cost by total output. Marginal cost is the cost of the next small output increment. A dispatch can have a low average because cheap units produce much of the energy while a dearer partially loaded unit sets the marginal value.
Exam move
Make method choice a scored decision in your own practice. For each network study, write the required outputs, the topology and the approximation you are willing to accept. If voltage magnitudes, reactive limits or losses matter, retain an AC model. If only broad active transfers are needed and assumptions are defensible, test the DC approximation.
If the network is radial, rehearse the backward accumulation and forward voltage update of a feeder sweep. Compare methods on identical base data and stopping rules so differences reflect the method rather than a changed model. Build a one-page assumption ledger. For decoupling, write why active power mainly follows angle and reactive power mainly follows magnitude in the intended network.
For DC power flow, list nominal magnitudes, small angle differences, negligible resistance and omitted Q. Beside each assumption, write the failure mode it hides. This turns comparison into reasoning rather than a table of names. For dispatch, begin with feasibility: total available capacity must meet demand plus any losses.
Rank constant marginal costs, apply minimum and maximum outputs, close the balance and identify the unit that can move next. With curved costs, practise equal incremental-cost reasoning while separating free units from those fixed at bounds. Always recompute total cost from printed dispatch values. Keep unit commitment separate from dispatch.
An on/off schedule changes the feasible set; dispatch allocates output within that set. If a transmission limit or loss model is introduced, say how it can make a more expensive local unit necessary. Finish with one sentence naming the active constraint and marginal unit.
The practical solutions show priority lists and optimisation sequences but publish no mark allocation, so use ordering, feasibility, balance, cost and marginal interpretation as method checks rather than claimed official marks.
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