Improved Fast Decoupled Power Flow

The index flow compend is a very important and tundamental tool in power schema analysis. Its results play the major role during the operational stages of every body for its suss off and economic schedule, as surface as during expansion and design stages The purpose of every load flow analysis is to compute punctilious steady-state electric potentials and electric potential burdens of tout ensemble private instructores in the ne iirk, the objective and activated power flows into every strain and transformer, under the arrogance of known generation and load.During the second half of the 20th century, and after the monstrous technological evelopments in the handle of digital computers and high-level programming talking tos, many methods for settlement the load flow problem have been developed, such as indirect Gauss-Siedel ( tutor admittance intercellular substance). direct Gauss-Siedel ( quite a little ohmic resistance intercellular substance).Newton-Raphson (NR) and its decoupled versions Nowadays, many Improvements have been added to in all in all these methods involving assumptions and approximations of the transmission lines and busbar information, base on real systems rails The unfaltering Decoupled mogul Flow system (FDPFM) is wizard of these rectifyd methods, which was based on a simplification of the Newton-Raphson method and describe by Stott and Alsac in 19744. This method and due to its calculations simplifications, lush adjoinnce and reliable results became the intimately widely utilise method in load flow analysis.However, FDPFM for both(prenominal) cases, where high RA ratios or heavy fill up (Low Voltage) at some buses argon present, does not converge well. For these cases, many efforts and developments have been made to overcome these overlap obstacles. some of them targeted the intersection of systems with hgh RIX ratios, others those with low electric potential buses However, single of the most rec ent developments is a Robust Fast Decoupled Power Flow developed by Wang and u it Is ased on heuristic justification and general potential normalization methods 171 and solves both high RIX ratios and low bus potential differences problems simultaneously.Though many efforts and elaborations have been achieved in order to improve the and simulations atomic figure of speech 18 becoming more than developed and are now able to handle and analyze large surface system. Today, and after r to for each one oneing processors do-nothingnonball alongs higher than 3 GHz, any improvement in the speed of convergency of the power flow method, provided it channels to reliable results, is of great value. This speed improvement is very important when baffling in operational stages of power distribution, where any illisecond preservation can hugely affix the probability of the right decision, of the control and dispatch computerized system.This paper works on providing reason bringings (in flops) and so higher speed of crossroad of the FDPFM based on the initial approximation in which real power changes are considered to be most sensitive to variations in voltage angle and very practically less(prenominal) to those of voltage order, as well as on the high sensitivity of reactive power changes to variations in voltage magnitude and much less to those of voltage angle. In this paper, the attention was focused on the update of the voltage angle (6) and oltage magnitude (V) in each iteration, based on the improvement of flops achieved, and plain on the results obtained.The results of these improvements and the comparative analysis with the Newton-Raphson and classical FDPFM provide be presented using the triad IEEE bus systems of 14, 30 and 57-bus, although the IFDPFM can be applied to any size bus system. II. Fast Decoupled Power Flow Method As the FDPFM is derived from the Newton-Raphson we pass on start from the intercellular substance means of NR, chi p in some simplifications and approximations, to overturn the equations of the FDPFM.The matrix theatrical work of the N-R method 17 is O APOOH Where I IVJI IYiJl +6) And -2 romaine lettuce microchip +2 cos -6i +6) Nii = I VI II YiJ I cos (B iJ- 6i + 6) Nil (7) -2 IYiil stn +2 IVJI IYiJl cos -6i +6) Now, for typical power system branches XIR and 200 (10) in the midst of AQ and A6, hence N and J entries of the initial matrix of (1) can be ignored leading to the pastime decoupled equations (12) Now, the precin one caseption elements of H according to Stott and Alsac 4 can be scripted as IVi12Bii (13) Where Bii = I Yill sin Bii is the conceptional part of the diagonal elements of the bus admittance matrix Ybus.Further simplifications can be applied to equation (12), by considering Bii Qi and I Vil 2 z I Vil yielding to the following simplified Hit Hii=- (14) Also, as under normal operating conditions 6 6i is quite small, thus Bii 6i + 6 Bit, and IVJI 1, the off-diagonal el ements of the matrix H can be written as HIJ I Vil (15) Similarly, the diagonal elements of the L matrix can be written as Lil (16) And its off- diagonal elements as LiJ=-lVll (17) Applying these assumptions to equations (11) and (12) we get =-BA6 I vil (18) (19) where B and B are the imaginary part of the bus admittance matrix Ybus , such thatB contains all buses admittances except those related to the quench bus, and B is B deprived from all voltage-controlled buses related admittances. Finally, all these approximations and simplifications lead to the following successive voltage magnitude and voltage angle modify equations (20) IVI (21) These equations formed the rump of the iteration scheme upon which the Matlab software written and because updated. Ill.Updated Algorithm The algorithmic programic program written according to the equations derived in the previous section is as follows look 1 initiation of the bus admittance Ybus according to the lines data given y the IEEE standard bus ladder systems. Step 2 Detection of all kinds and verse of buses according to the bus data given by the IEEE standard bus test systems, setting all bus voltages to an initial value of 1 pu, all voltage angles to O, and the iteration dealer iter to O.Step 3 Creation of the matrices B and B according to equations (18) and (19). Step 4 If exclusive (AP, AQ) accuracy thus Go to Step 6 else 1. weighing of the H and L elements of equations (14), (1 5), (16), (17). 2. Calculation of the real and reactive power at each bus, and checking if Mvar of root buses re within the limits, otherwise update the voltage magnitude at these buses by ?2 3. Calculation of the power residuals, AP and AQ. 4.Calculation of the bus voltage and voltage angle updates AV and A6 according to equations (19) and (20). 5. Update of the voltage magnitude V and the voltage angle 6 at each bus. 6. Increment of the iteration counter iter = iter + 1 thus Go to Step 4 ingrain out Solution did not con verge and go to Step 6 Step 6 Print out of the power flow solution, computation and display of the line flow and losses. The update of this algorithm was based on the weak coupling surrounded by AP and AV, nd amid AQ and A6, explained in the previous section.Specifically, in the ivth office of Step 4 of the initial algorithm, and instead of modify the voltage magnitude and the voltage angle once and simultaneously in each iteration, the improved algorithm updated either the voltage angle or the voltage magnitude at each bus, Jumped to subroutine 1 to recalculate the real and reactive power and then updated the second variable based on what was updated rootage.Moreover, and for more speed improvements and convergence reliability, the update of one of the both variables was repeated several clock, holding the other ariable at its last calculated value, which reduced the proceeds of afloat(p) baksheesh operations of the algorithm and thus lead to the faster convergence of th e IFDPFM. IV. Numerical Analysis The performance of the IFDPFM was tested on IEEE 14, 30 and 57-bus systems with a convergence accuracy of 10-3 on a MVA base of nose candy or equivalently 10-1 MVA for both power residuals AP and AQ.This numerical analysis involved a speed comparison amidst the NR method, the FDPFM and the IFDPFM based on the government issue of flops (floating point operations) of each algorithm implementing each method, rather than on any other basis, because he flops count is independent from the central processor speed or the specific programming language used. In addition, as mentioned in the previous part, the algorithm of this paper updated the voltage angle several times before updating the voltage magnitude or vice versa which resulted in a antithetic flops count for each combination used for the same IEEE bus system.These combinations will be noted according to the number of loops of update of each variable. For instance, updating twice the voltage ang le (6) and then once the voltage magnitude (V) in the same iteration will be written as (21). Note that any flops number without the previous notation will be the one of the best case of the updated algorithm. Moreover, for any combination to be listed in this paper it should have satisfied the condition of no more than 3 % deviation of its results from that of the NR method.The blank out graph in see to it 1 shows a comparison based on the number of flops between the NR, FDPFM and the best case of IFDPFM for the three IEEE standard bus systems used in this paper. Number of flops per method per system 934. 573 305. 126 314. 925 157. 310 System 57 4,421. 752 2,841. 646 14 30. 823 56. 829 24. 574 1 ,ooo ,500 2,000 2,500 3,000 Flops IFDPFM FDPFM 4,000 4,500 (Thousands) Fig. 1 Flops Comparison between the 3 methods. It is clearly seen that the IFDPFM requires much less flops to converge as compared to FDPFM or NR.This flops saving is proportional to the system size and as shown, incre ases with the increase of the number of buses. Obviously, this improvement in the number of flops will make the IFDPFM converge much faster than the two other methods whatever CPU used. Numerically, and for the biggest system involved in this paper (IEEE 57-Bus System), the IFDPFM revealed a flops saving of or so 67 % when ompared with the FDPFM and about 78 % when compared with the NR.Normally, and as mentioned before, this saving goes down to the order of 50 % for the two little bus systems. In addition, and in order to reach the best case presented above, different strategies of updating the voltage angle (6) and the voltage magnitude (V) were tested and compared first with the FDPFM then with the NR. Figure 2 below the destiny of flops of IFDPFM versus that of the FDPFM, for 10 different updating strategies and for the three IEEE systems.Percentage Flops IFDPFM vs FDPFM 75 50 25 DeltaVoltage Loops IFDPFM14 IFDPFM30 IFDPFM57 Fig. 2 % of flops of IFDPFM vs. FDPFM for different voltage angle and voltage magnitude updating strategies. At the first look, it is seen that for the three systems, three duplicate curves are sketched with most values less then 75 % of the FDPFM. This parallel property of this graph shows the congruity of the algorithm in its number of flops variation for each strategy for each system studied.Also, it is seen that for low number of voltage magnitude and voltage angle loops the IFDPFM cant be more efficient than FDPFM, but for a just about higher number the IFDPFM shows great improvement in flops saving nd reaches the highest improvement at the point (43), where in each iteration, the voltage angle was updated four times while the voltage was unploughed at its initial value and then 6 was kept at its last value and V updated three times.Numerically, and for the best case of IFDPFM (43), the new algorithm showed a flops saving of 57 % for the 14-bus system, 50% for the 30-bus system, and 68% for the 57-bus system. Figure 3 below shows the percentage of flops of IFDPFM versus that of the NR, for 10 different updating strategies and for the three IEEE systems. IFDPFM vs NR 175 150 25 Fig. 3 % of flops of IFDPFM vs. NR for different voltage angle and voltage magnitude updating strategies.Basically, the same comments of the comparison of IFDPFM with FDPFM apply in this comparison. However, here the flops saving is much more significant and is proportional to the system size. Numerically, we have a 21 % flops saving for the 14-bus system, 49 % for the 30-bus system and 78% for the 57-bus system. Finally, it is remarked that when compared with NR, IFDPFM savings showed a high variation in their percentage, mainly because they are highly proportional to the