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1. 1. PRESENTED BY DEEPAK JOHN S1 M. Tech POWER SYSTEM
2. 2. CONTENTS INTRODUCTION DIFFERENT CONSTRAINTS IN ECONOMIC LOAD DISPATCH OPERATING COST OF THERMAL PLANT ECONOMIC DISPATCH NEGLECTING LOSSES ECONOMIC DISPATCH INCLUDING LOSSES REFERENCES
3. 3. INTRODUCTION In power generation our main aim is to generate the required amount of power with minimum cost. Economic load dispatch means that the generator’s real and reactive power are allowed to vary within certain limits so as to meet a particular load demand with minimum fuel cost This allocation of loads are based on some constraints.
4. 4. DIFFERENT CONSTRAINTS IN ECONOMIC LOAD DISPATCH INEQUALITY CONSTRAINTS  Voltage constraints Vmin ≤ V ≤ Vmax , δmin ≤ δ ≤ δmax  Generator constraints KVA loading of generator should not exceed prescribed value Pmin ≤ P ≤ Pmax Qmin ≤ Q ≤ Qmax
5. 5.  Running spare capacity constraints This constraints are needed to meet forced outage of one or more alternators in the system and also unexpected load on the system Transmission line constraints flow of power through transmission line should less than its thermal capacity Transformer tap setfor autotransformer tap t should between 0 & 1For two winding transformer – between 0& k
6. 6.  Equality constraints  Real power Pp= Vp Σ Ypq Vq cos(θpq-(δp+δq))  Reactive power Qp= Vp Σ Ypq Vq sin(θpq-(δp+δq))
7. 7. OPERATING COST OF THERMAL PLANT The factors influencing power generation at minimum cost are operating efficiencies of generators, fuel cost, and transmission losses. The most efficient generator in the system does not guarantee minimum cost as it may be located in an area where fuel cost is high. If the plant is located far from the load center, transmission losses may be considerably higher and hence the plant may be overly uneconomical.
8. 8.  The input to the thermal plant is generally measured in Btu/h, and the output is measured in MW In all practical cases, the fuel cost of generator can be represented as a quadratic function of real power generation a) Heat rate curve b) Fuel cost curve
9. 9. Incremental fuel-cost curve • By plotting the derivative of the fuel-cost curve versus the real power we get the incremental fuel-cost curve The incremental fuel-cost curve is a measure of how costly it will be to produce the next increment of power.
10. 10. ECONOMIC DISPATCH NEGLECTING LOSSES It is the simplest economic dispatch problem Assume that the system is only one bus with all generation and loads connected to it A cost function Ci is assumed to be known for each plant
11. 11.  The problem is to find the real power generation for each plant such that the objective function (i.e., total production cost) as defined by the equation Is minimum ,subjected to the constraints
12. 12.  when losses are neglected with no generator limits, for most economic operation. all plants must operate at equal incremental production cost Production from each plant can be found by This equation is known as the coordination equation For analytic solution we can find λ by
13. 13.  In an iterative technique, starting with a value of λ and the process is continued until ∆Pi is within a specified accuracy Corresponding to this λ , is calculated, and the power mismatch is calculated by Update value of λ by
14. 14. EXAMPLE
15. 15.  Above three eqn represent the eqn for straight line on plotting this line we will get
16. 16. ECONOMIC DISPATCH INCLUDING LOSSES When power is transmitted over long distances transmission losses are a major factor that affect the optimum dispatch of generation One common practice for including the effect of transmission losses is to express the total transmission loss as a quadratic function of the generator power outputs. The simplest quadratic form is
17. 17. Using the langrange multiplierMinimum of this function is fount at the points where thepartials of the function to it’s variables are zero
18. 18. Itration methodInitially assume a λ value. Then find out the generationfrom each plant using the equationCalculate the power mismatch calculate
19. 19. Update value of λ Repeat the procedure with new value of λ until the power mismatch is within the limit
20. 20. EXAMPLE
21. 21. SOLUTION
22. 22. REFERENCES Power System Analysis - Hadi Saadat power system analysis by nagrath and kothari
23. 23. THANKS