【正文】 ad at the bus In figure 1, of all the Locational Marginal Price (LMP) bids for generation, the 600 MW @$10/MWh at bus E is pletely utilized before the 69 MW at bus A is employed. The transmission line flows that result from this dispatch are shown on the figure. The total operating cost is $6966/h. Fig. 1 Economic Dispatch for 669 MW Load to Utilize the Lowest Cost of Available Generation As the load on the system uniformly increases to 300 MW at busses B,C, and D, the LMP dispatch would attempt to use all the 210 MW of inexpensive power ( 110MW@$14/MWh and 100 MW@$15/MWh) at bus A before 90 MW of the $30/MWh power at bus D is used. The total cost would be $11,740/h. However, when 210 MW is dispatched at bus A, this results in 243 MW of flow on line ED to violate the constraint. As a result, only 166 MW of the inexpensive power at bus A is utilized and 124 MW at bus D is required. Total operation cost increases to $12,100/h because of the constraint. The dispatch is shown in figure 1a. If the transmission line ED has a ‘real world’ reactance of XED = *.0297, or in other words has a measured 25% more reactance than the database, the dispatch for 900 MW load utilizes all the low cost power because the power flow does not violate the ED line constraint. The transmission line power flows for this case are shown on figure 2. The total cost of the dispatch is $11,740/h. The example shown in figure 1 was employed by an Eastern USA power pool to demonstrate constraints in line flow. Figure 2 shows that power flows puted with correct line parameters are significantly different, to the point where large economic differences are present. Corrections are rarely made to transmission line parameters in order to match measured line flows because sources of measurement error are unknown. In a utility it also difficult to change parameters in the database because so many different groups within the utility, ., planning, relaying, security, etc., must change their values or settings of field equipment. III. ESTIMATION OF TRANSMISSION LINE PARAMETERS For short to medium length, pared to a 60 Hz wavelength, 3phase transmission lines are modeled by piequivalents calculated from ideal geometry and operated under balanced phase conditions. The voltage magnitudes at the line terminations are an average of the phase measurements, usually obtained with 1% to 2% accuracy stepdown transformer measurements.Fig. 1A Economic Dispatch for 900 MW Load Limited by Constraint on Line ED The real and reactive power flow for the piequivalent is a sum of flows on the 3 phases and obtained as an instantaneous product of 1% to 2% accurate current measurements with the voltage measurements. Neglecting the small contributions of A/D converters at the transducers and puter numerical word length, the overall accuracy of power flow measurements also is on the order of 1% to 2%. Figure 2 Economic Dispatch for 900 MW Load with XED =*.0297 Transmission Line Reactance (No line constraints violated) The Eastern power pool used for figure 1and 1a provided a SCADA ‘snapshot’ of power flow and voltage measurements for the 3bus network shown in figure 3. Data of the ‘snapshot’ is presented in figure 4. Notice more real power es out of line L1 than goes into it (S1 and S2), but this anomaly is due to measurement tolerance as the real power difference is ~2% of the absolute value. ‘Snapshot’ is State Estimator terminology for an almost synchronized set of measurements because a short time interval (milliseconds) exists from the initial measurement to the final measurement for a slowly changing load/generation. Fig. 3 SCADA Measurement Points on a 3 Bus Network Fig. 4 SCADA Measurements for Figure 3 A State Estimation putation ‘smoothes’ the data, detects bad transducers, and calculates the best estimate of the voltage and phase angle at busses of the network, ., the ‘state’ of the network. The calculated state is a weighted least squares estimate ‘best fit’ to the measurements using database values for the piequivalent transmission line parameters, R+jX for the series . impedance elements –jY/2 for the shunt . susceptance at both ends of the line. Analytical methods exist to estimate transmission line parameters from ‘snapshots’ in conjunction with the State Estimator. The first such method appeared soon after the start of State Estimation [2]. Many contributions were made around 1990 of which [3, 4] are typical, new techniques continue to evolve [5]. A recent summary is reference [6]. The data ‘snapshot’ of figure 4 was used to estimate the transmission line parameters of figure 3 by a method of propagating residual errors of State Estimation related to [5] and finding the worst ‘fit’ line. The results of the parameter estimation with this method are presented in figure 5. Only 2 transmission lines of the Figure 3 network could be estimated before residual errors ‘swamped out’ further detection. Lines BC and AB show 25% errors in line charging susceptance pared to the database. There is a 50% error in the estimated line resistance of line BC pared to the database value, which may be due to an operating temperature difference. Fig. 5 Results of Transmission Line Parameter Estimation for Network of Figure 3 with SCADA Data of Figure 4 The estimated values for line charging susceptance of transmission lines BC and AB affect reactive pensation in their vicinity. The 50% difference in resistance of line BC may affect the transmission loss coefficients in the vicinity. Power flow calculations with S1 to S6 data of figure 4 show that power flow on the network lines is much closer to measured values using the estimated parameters than with the database values. IV. VERIFICATION OF THE PARAMETER ESTIMATION METHOD It is difficult to prove that estimated transmission line parameters are true to the ‘real world’ values. Analytical cases using power flow putations from standard IEEE 5 bus, 14 bu