Using Kirchmayer’s Method for Short Term Hydro-thermal Scheduling

The hydro plants require less starting time and take a load in a very short time as compared to thermal plants which take several time to make the boilers, superheater and turbine system ready to take the load. Hydro plants have the capability to handle fast-changing loads but thermal plants are slow in response. Due to this, hydro plants are preferred to operate at peak load plants and thermal plants as baseload plant. In order to utilize energy efficiently, the cost must be as minimum as possible. So the main aim of operation of the power system is to generate and transmit power to meet the system load demand at minimum fuel cost and minimum environmental pollution.

Hence, hydrothermal scheduling is necessary. The objective of optimum hydrothermal scheduling is to minimize fuel cost of thermal plants under constraints of water availability for hydro plants over a given period of time.

Long-term Coordination is extended from one week to one year or several years. This is used for long-term minimization of the cost of the whole system. The long-term coordination problem becomes very difficult to solve due to its size, time span (several years) and randomness of water inflows for a long time.

Short-term Scheduling is required for one day or one week. In the short-term problem, the head of water is assumed to be constant as there will not be any appreciable change in the water level in the reservoirs.

So, this is quite easy to solve due to its size, time span (one week). Short-term scheduling is required for one day or one week involving the hour-by-hour scheduling of both hydro and thermal plants to get minimum production cost for the given time. In this scheduling problem, the load, the hydraulic inflows, and unit availability are assumed to be known.

In addition, the generating unit limits and the load demand over the scheduling interval are known. In the short-term problem, the head of water is assumed to be constant as there will not be any appreciable change in the water level in the reservoirs. Several mathematical optimization techniques have been used to solve short-term hydrothermal scheduling problems[4]. Load cycle, expected water inflow, water head, and generation in a hydro plant, the incremental fuel cost of thermal plant and incremental transmission loss are the various factors on which the economic operation of hydro-thermal scheduling depends. The various methods used for hydro-thermal scheduling are constant hydro generation method, constant thermal generation method, maximum hydro-efficiency method and Kirchmayer’s method. A large number of researchers have extensively investigated the short-term hydro scheduling problem. Main computational techniques that have been employed are maximum principal, variational calculus , dynamic programming and nonlinear programming. In this paper, Kirchmayer’s method for short-term scheduling is presented.

The proposed method is one of the effective methods for solving the short-term hydro-thermal scheduling problem. The objective is to minimize the operating cost of the plant. A two-plant system having a steam plant near load and hydro plant at a remote location as shown in fig1. Fig 1:- Typical Hydro-thermal system The characteristics of units are C = 130 + 50 PGT + 0.1P2GT (1) W = 0.00300 P2GT + 0.8PGT (2) Loss coefficient, BHH =0.001 MW-1 ?j is the constant to convert the incremental water rate of hydro plant j into an incremental cost and must be selected in such a way that the specified amount of water is used during its operation period. Table I represents load demand for a day. In this paper, generation schedule, daily water used by the hydro plant and the daily operating cost of the thermal plant is obtain using Kirchmayer’s method for short-term scheduling. Kirchmayer’s method is a conventional approach for short-term scheduling. This approach is the simplest approach for hydro-thermal scheduling. Since it is a short-term problem, there will not be any appreciable change in the water level in the reservoirs during the rainfall.

So, the head of water is assumed to be constant[10]. Coordination equation for thermal unit is dC/dPGT = 50+0.2PGT (3) Condition for optimal scheduling is (dC/dPGT)LT = ?j (dW/d PGH)[1/1-0.002 PGH] = ? (4) and power balance equation is PGT + PGH = PD + PL (5) where PGH is the power generation at hydro plant(MW), PGT is the power generation at thermal plant(MW), PD is the power demand(MW), PL be the power losses(MW), dC/dPGT be the incremental fuel cost of thermal plant, (Rs./MWh), dW/dPGH be the incremental water rate of hydro plant, (m3/s/MW), ?j is the constant to convert the incremental water rate of hydro plant j into an incremental cost, ? be the Lagrangian multipliers and LT =1/(1-dPL/dPGT)=1 Since the load is near to thermal plant, the transmission loss is only due to hydro plant. Therefore, BTT = BTH = BHT =0 Loss Coefficient, BHH=0.001 MW-1 (given) PL = BHHP2GH (6) For PD= 450 MW and PD =300 MW, using equations (3),(4),(5) and (6), the following data are shown in the table is obtained. TABLE II:- shows hydro-thermal scheduling for two different load demand. S.N0. PD = 450MW PD = 300MW 1. PGH =82.5MW PGH =52.24MW 2. PGT =374.306MW PGT=250.48MW 3. PL =6.806MW PL=2.72MW The daily operating cost of the thermal plant is obtained using equation(1) for two different load demands is shown in table III and the daily water used by the hydro plant is obtained using equation(2) for two different load demands is shown in Table IV. Daily operating cost of the thermal plant is equal to operating cost of thermal plant for meeting 450 MW of load for 16 hours plus the operating cost of thermal plant for meeting 300 MW of load for 8 hours. Also, the daily water used by the hydro plant is equal to daily water quantity used for 450 MW of load for 16 hours plus the daily water quantity used for 300 MW of load for 8 hours. Table III:- Daily operating cost of thermal plant For PD= 450MW and PD = 300MW Daily operating cost of thermal plant C=677116.95 per day Table IV:- Daily water used by the hydro plant.

For PD= 450MW and PD = 300MW Daily water used by the hydro plant. W=6417000 m3 The paper presented an effective method for solving short-term hydro-thermal scheduling problem by using Kirchmayer’s method to minimize fuel cost of thermal plants under constraints of water availability for hydro plants over a given period of time. Generation schedule, daily water used by the hydro plant and the daily operating cost of the thermal plant are obtained for two different power demands. Thus, the proposed method is one of the effective methods for solving the short-term hydrothermal scheduling problem.