International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.5, pp. 1913-1916 ISSN 2078-2365 http://www.ieejournal.com/
Unit Commitment with Economic Dispatch M.S.Krishnarayalu Department of Electrical and Electronics Engineering, V.R Siddhartha Engineering College, Vijayawada, AP, 520007, India.
[email protected]
Abstract — Economic Dispatch (ED) in power systems is very important as it saves lot of money. There are two basic methods available. One is classical method where all units are committed and consumption of fuel is optimized by an optimization method. Second one is Unit Commitment (UC) method. In UC, units are committed based on their efficiency order and on load demand with most efficient unit committed first. Now a method called Unit Commitment with Economic Dispatch (UCED) is proposed combining these two methods. The efficacy of this new method is illustrated via a three unit thermal plant system. Index Terms — Fuel cost, Optimization, Economic Dispatch, Unit Commitment
Terminology: H– Heat input, MBtu/h h – Hour F– Fuel cost, `/h ` – Indian Rupees
I.
II.
TFC – Total fuel cost, `/h IFC– Incremental fuel cost, `/MWh – IFC of power system, `/MWh dFj/dPj– IFC of unit j, `/MWh Lj – Penalty factor of unit j UC – Unit Commitment ED – Economic Dispatch
INTRODUCTION
Economic Dispatch of power is one of the most important problems of power systems [1-9]. It is mainly tackled by two methods. Method one gives optimal power generation required to meet the load demand PD, with minimum total fuel cost, through a coordination equation. This is known as classical ED. In this method all units are turned on to meet the PD. The second method is Unit Commitment (UC). Here the most efficient unit is committed first followed by next efficient unit and so on. Here all units need not be committed. All units may be demanded (committed) only for large peak loads. There are many methods of UC are available in literature. However no UC solution is perfect. They have certain strengths and some weaknesses [5]. In this paper a new approach is presented mixing the ED and UC methods. BASIC METHODS
Here we discuss the two basic methods of economic dispatch namely Classical Economic Dispatch and Unit Commitment. Classical Economic Dispatch: This method minimizes total fuel cost (TFC) using Lagrange method resulting in a coordination equation that gives rise to optimum generations that minimize TFC. The objective is scheduling the output of each plant/unit such that the total fuel cost of all the plants/units is minimum for a given load demand PD. N = number of plants/units
1913 Krishnarayalu
Unit Commitment with Economic Dispatch
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.5, pp. 1913-1916 ISSN 2078-2365 http://www.ieejournal.com/ TFC = F1+ F2+…+ FN=∑𝑁 (1) 𝑗=1 𝐹𝑗 F1, F2,…,FN - fuel cost of individual plants/units PT = total power input to the network from all plants/units = P1+ P2+…+ PN=∑𝑁 (2) 𝑗=1 𝑃𝑗 P1, P2,…,PN - power outputs of individual plants/units PD = total power demanded by the loads of the entire system PL = total transmission loss Hence Ф = PD + PL- ∑𝑁 (3) 𝑗=1 𝑃𝑗 = 0 is the equality constraint for optimization. L = FT + Ф = Lagrange function = augmented cost function (4) - a constant called Lagrangian multiplier For minimum FT, L/Pj = 0, j This results in = (dFj/dPj) / [1- (PL /Pj)], = Lj (dFj/dPj), `/MWh j = 1, … N. (5) (5) is the coordination equation for finding optimum generation schedules that minimize TFC. Lj= 1/[1- (PL /Pj)] = penalty factor for plant j = 1 if transmission losses were neglected (zero). If transmission losses are included Lj will be more (penalty) and IFC of the power system will be high. If maximum and minimum generations are specified for each unit, some units will be unable to operate at the same IFC as others. Then dFj/dPj≥ , Pj = Pjmin dFj/dPj=, Pjmin
