Short Answer:

The penalty factor in economic dispatch accounts for the effect of transmission losses when distributing load among generating units. It modifies the incremental cost of each generator so that the dispatch solution reflects the actual cost of delivering power, not just producing it.

A generator with a low fuel cost but high transmission loss may not be economical after applying the penalty factor. By including it, the dispatch becomes more accurate and ensures that power is delivered at the lowest total cost, including both generation and transmission effects.

Detailed Explanation:

Effect of penalty factor on economic dispatch

In power systems, Economic Dispatch (ED) aims to distribute the total load demand among different generators such that the total fuel cost is minimized. However, when transmission losses are considered, simply comparing the incremental fuel cost of each generator is not enough. Power lost during transmission must also be accounted for. This is where the penalty factor plays a vital role.

The penalty factor adjusts the incremental cost of each generating unit by considering the amount of power that gets lost while transmitting electricity from that generator to the load. It ensures that the true cost of delivering power — not just producing it — is minimized in the economic dispatch solution.

Understanding the Penalty Factor:

The penalty factor (denoted as λᵢ or PFᵢ) for a generator is a number greater than 1 that increases the generator’s incremental cost based on how much power is lost when using that unit. It is mathematically defined as:

PFᵢ = 1 / (1 – ∂PL / ∂Pᵢ)

Where:

• ∂PL / ∂Pᵢ is the rate at which transmission loss increases with an increase in generator output Pᵢ
• PFᵢ becomes larger if the generator contributes more to losses

Modified Economic Dispatch Condition with Penalty Factor:

In standard ELD without losses, the condition for optimal dispatch is:

dC₁/dP₁ = dC₂/dP₂ = … = dCn/dPn = λ

With transmission losses considered, the condition becomes:

(dC₁/dP₁) × PF₁ = (dC₂/dP₂) × PF₂ = … = (dCn/dPn) × PFn = λ

This means we now compare the adjusted incremental cost (also called penalized cost) for each unit.

Role and Impact in Economic Dispatch:

1. More Accurate Cost Calculation:
   The penalty factor gives a more realistic view of the true cost by including the effect of losses, especially for generators located far from the load centers.
2. Changes the Dispatch Order:
   A generator with a low fuel cost may end up having a higher adjusted cost if it causes high transmission losses, thus changing the optimal load distribution.
3. Reduces Overall System Losses:
   By considering losses, the dispatch shifts generation to units closer to loads or with lower loss impact, helping reduce total transmission losses.
4. Improves System Efficiency:
   The combination of fuel and loss cost ensures that the system operates in an economically and electrically efficient manner.
5. Supports Real-Time Operations:
   In modern systems with changing loads and conditions, penalty factors help operators adjust dispatch to current network conditions dynamically.

Conclusion:

The penalty factor in economic dispatch adjusts each generator’s incremental cost to include the effect of transmission losses. It ensures that the power is not only generated economically but also delivered efficiently. Including penalty factors makes the dispatch more practical and accurate, reduces losses, and improves overall system performance by ensuring the lowest total cost of generation and delivery.