Short Answer:

The lambda-iteration method is a simple and widely used mathematical technique in Economic Load Dispatch (ELD) to determine the most cost-effective way to share electrical load among power-generating units. It helps in minimizing the total fuel cost while satisfying the total demand and generator limits.

The significance of this method lies in its ability to find the optimal value of lambda (λ), which represents the incremental fuel cost common to all generators at economic operation. Using this value, power outputs are adjusted so that all operating units have equal incremental costs, leading to the most economical generation schedule.

Detailed Explanation:

Significance of lambda-iteration method in ELD

In the operation of a power system, Economic Load Dispatch (ELD) is used to allocate total load demand among various power generating units in a way that minimizes the total fuel cost. The lambda-iteration method is a classical approach to solve the ELD problem for thermal generators with continuous, smooth, and convex cost functions.

The key idea behind this method is to ensure that all generators operating in the system have the same incremental fuel cost (λ). If this condition is met, the total fuel cost will be minimum. Lambda (λ) is a Lagrange multiplier used in optimization, and it helps in balancing the generation and demand under economic conditions.

Working of Lambda-Iteration Method:

1. Fuel Cost Function for Each Generator:
   Each generator has a cost function of the form:
   C(P) = a + bP + cP²
   where C(P) is the fuel cost and P is the power output.
2. Incremental Cost Calculation:
   For each generator, the incremental cost is calculated by differentiating the cost function:
   dC/dP = b + 2cP
3. Equalizing Incremental Costs:
   For optimal load distribution, the incremental cost of each generator must be equal to lambda (λ):
   λ = dC₁/dP₁ = dC₂/dP₂ = … = dCn/dPn
4. Power Balance Condition:
   The total generation must equal total load demand (plus transmission losses if considered):
   P₁ + P₂ + … + Pn = PD
5. Iteration Process:
   • Start with an initial guess of λ.
   • Compute power output for each unit using the formula:
     Pi = (λ – b) / 2c
   • Calculate total generated power and compare it with demand.
   • Adjust λ accordingly (increase if generation is less, decrease if it’s more).
   • Repeat the process until total generation matches the demand within an acceptable tolerance.

Significance in Power System Operation:

• Simple and Efficient:
  Lambda-iteration is a straightforward and fast method for solving small-to-medium scale ELD problems.
• Cost Minimization:
  Ensures minimum fuel cost by equalizing incremental cost across generators.
• Better Load Distribution:
  Helps in sharing the load among generators based on their fuel efficiency.
• Foundation for Advanced Methods:
  It forms the base for more complex and advanced optimization techniques used in modern systems.
• Useful for Educational and Practical Applications:
  Due to its simplicity, it’s widely taught and used for basic understanding of economic dispatch.

Limitations in Power System Operation:

• It assumes all cost functions are continuous and convex.
• Not suitable when there are constraints like ramp limits or prohibited zones.
• Difficult to apply in non-smooth or discontinuous cost problems.

Conclusion:

The lambda-iteration method is significant in ELD as it provides a simple and practical way to distribute load among generators economically. By ensuring equal incremental fuel cost (λ) across units, it minimizes total cost while meeting the demand. Though limited in handling complex constraints, it remains a fundamental and essential tool in power system optimization.