Reactive Power allocation using Modified Y – Bus Matrix method

Reactive Power allocation using Modified Y – Bus Matrix method

S. Uma Mageswaran*, Dr.N.O.Guna Sekhar**

*Research Scholar, Bharat University

** Professor/EEE Dept, Easwari Engineering College

Abstract

Reactive power plays a vital role to transmit real power to the load or consumers. Generators produce real and reactive power to supply loads and transmission line losses. When reactive power demand is more than reactive power generation, power system voltage will reduce and it may lead to voltage collapse. Large distance between reactive power load and generation cause large transmission line reactive power loss. To earn consumer goodwill and reliability of power supply it needs to produce required reactive power and for economical operation distance between source and demand of reactive power has to be reduced. Modified Y – Bus matrix method is used to find reactive power path and amount of reactive power which flow from the source to load. This research paper explains modified Y – Bus method to find the reactive power supply from various generators to the load. To demonstrate this method IEEE 30 bus is considered for the research work.

Key Words: Reactive Power, Modified Y – Bus matrix, Reactive Power allocation.

1.  

           Introduction

Modified Y – Bus matrix is a straightforward method of allocating reactive power. This method uses basic circuit theory and partitions the Y-bus matrix to decompose the voltage of the load buses with a view to calculating the reactive power sharing [1], [2], [6]. This paper mainly discusses the allocation of the reactive power. However, it will not be concerned about the aspect of the real power because bilateral transactions of the real power will take place after the liberalization of the power industry as effective power transactions will be performed by fixed buyers and fixed sellers. Hence, the source and direction of the real power are already fixed, at least in the artificial assumption. By contrast, the reactive power is the result of the power system dispatching and does not exist in the bilateral transaction. The reactive power can be supplied by the synchronal generator, synchronal motor, and capacitor, so the reactive power supply certainly varies with suppliers and locations. Besides, the reactive power cannot transmit far off and will result in the loads with equal demand of reactive power. It is necessary to identify the reactive power sources of every load and calculate the reactive power allocation [3], [4]. Therefore, this paper mainly discusses the allocation of the cost of the reactive power. As for the matter of line losses, including real and reactive power, they are indeed to be shared by the users. The reactive power on load buses is the demand of consumers and the reactive power of line losses arises from the use of transmission lines, although both have the same physical properties. Only the reactive power of load demand is the focus of this paper. The allocation method proposed in this paper is based on one basic principle of circuit theory, which states that every load bus voltage is contributed by all source voltages in the circuit. Therefore, this paper will deduce the relationship function of the load voltage (VL) and the generator voltage (VG), to find out the quantity of the voltage component made up of all load voltages. Then it will use the voltage component of each load voltage and load current known from the results of the power flow analysis to obtain the reactive power that each load acquires from individual generators [5].

       Problem Formulation

The proposed methodology begins with the system node equation. For the convenience of explanation, it is assumed that the power system has a total number of nb -buses, ng - generators, nl - and loads, among which bus numbers 1 to ng are generation buses and bus numbers ng+1 to nb are load buses. Therefore, the Y bus of nb x nb dimension can be divided into four sub matrixes as given below 

Equation (1) can be briefly stated as follows in equation 2

The main goal is to deduce the load bus voltages as a function of the generator bus voltage, namely, V_L=f(V_G). The concept is based on the superposition of circuit theory, which states that each load voltage consists of individual source voltages in the circuit. However, it is required that all of the loads must be represented as admittances in the circuit if the theory is applied, but the loads in the form of injection current are derived from apparent power for performing power flow analysis. Therefore, the load must be transformed from the injection current into the equivalent admittance and the Y bus matrix must then be modified. The load can be transformed into the equivalent admittance by using the bus voltage known from the results of power flow analysis. Meanwhile, one thing that has to be emphasized here is that the power flow program should be executed to obtain the values of voltage, real power, and reactive power on each bus of the system studied before applying the proposed methodology. The relevant equation is as follows           

                                                                                                                     (3)

where S_Lj is the apparent power of load on bus j, Y_Lj is the equivalent admittance of load on bus j, and V_Lj is the resultant voltage of bus j of power flow analysis. We use (3) to calculate the equivalent admittance Y_Lj of every load and then modify the sub matrix [Y_LL] in the original Y bus matrix. The modification is executed by adding the corresponding YLj to the diagonal elements in the [YLL] matrix, so the original matrix [YLL] is replaced by matrix [Y_LL¹]. With the equivalent admittance of loads being represented, the load buses will have no injection current, thus reducing the sub-matrix [IL] to [0]. Hence equation (2) is changed as given below

                                                                                   (4)

Equation (4) on the lower half part of the matrix is used to arrive as

                                                      [Y_LG][V_G]+[Y_LL¹][V_L]=[0]                                                       (5)

Then the relationship function can be obtained as follows

                                                      [Y_LL¹][V_L] = - [Y_LG][V_G]                                                          (6)

and                                                [V_L] = - [Y_LL¹]^-1[Y_LG][V_G]                                            (7)

Equation (7) can be rewritten as

                                                            [V_L]=[Y_A][V_G]                                                                   (8)

Where,                                                 [Y_A]= - [Y_LL¹]^-1[Y_LG]                                                          (9)

The voltage of each load bus consisting of the voltages contributed by individual generators is expanded as shown in the following equation:

                                                                                                                      (10)

And it is assumed that

                                                                                                                    (11)

Where ∆V_{L i,j} is the voltage contribution that load j acquires from generator i, equation (10) may also be expressed as

                                                                                                                        (12)

Voltage contribution of each load bus received from individual generators is ∆V_L. The reactive power contribution that load j acquires from generator i is as follows

                                                            Q_{L i,j} = Imag{∆V_{L i,j} * I_Lj^*}                                              (13)

Where I_Lj is the load current which is to divide the power of the load by known load bus voltage and take the conjugate of the complex number on load bus j.

In the modified Y Bus method all generators in the systems is rearranged and connected first ng buses. Loads are connected to remaining buses. Formulate network equation (1), calculate equivalent admittance value of the loads and modified Y_LL¹ sub-matrix. From this network matrix ∆V_L and Q_L contribution of each generator to the load is calculated. The procedure is given as a flowchart below.

1.      Solution Methodology

1.      Simulation Result

For the simulation test case IEEE 30 bus is considered, this system has 6 generators, 4 transformers and 41 transmission lines. In this modified Y bus technique the generator connected to buses are shifted to first 6 places, so buses 1 to 6 is a generator bus remaining 7 to 30 buses are taken as load buses. Newton Raphson power flow is executed to find voltage magnitude, phase angle, real power and reactive power of each bus. This power flow solution is used to find ∆V_L and Q_L contribution of each generator to the load. Table 1, shows the reactive demand of all load buses and the proportional reactive power supply by all 6 generators.

Table 1: Reactive Power Allocation of IEEE 30-BUS System

1.      Conclusion

This paper uses network theory to find reactive power allocation by each generator to the load. This modified Y – Bus method is a straight forward and simple method to calculate the reactive power contribution of all generators to the load of the particular load bus. Test case IEEE 30 bus system is considered to demonstrate the proposed modified Y- bus method. Future work of the proposed method is to extend modified Y- Bus method to find reactive power cost allocation to the sources of reactive power.  

References

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[2]   J.Janusz Bialek, “Topological generation and load distribution factors for supplement charge allocation in transmission open access,” IEEETrans. Power Syst., vol. 12, pp. 1185–1193, Aug. 1997.

[3]   D.Daniel Kirschen, R.Ron Allan, and G.Goran Strbac, “Contributions of individual generators to loads and flows,” IEEE Trans. Power Syst., vol. 12, pp. 52–60, Feb. 1997.

[4]   G.Goran Strbac, D.Daniel Kirschen, and S.Syed Ahmed, “Allocation transmission system usage on the basis of traceable contributions of generators and loads to flows,” IEEE Trans. Power Syst., vol. 13, pp. 527–532, May 1998.

[5]   F. F.Felix F. Wu, Y.Yixin Ni, and P.Ping Wei, “Power transfer allocation for open access using graph theory—fundamentals and applications in systems without loopflow,” IEEE Trans. Power Syst., vol. 15, pp. 923–929, Aug. 2000.

[6]   Wen-Chen Chu, Member, IEEE, Bin-Kwie Chen, Member, IEEE, and Chung-Hsien Liao, “Allocating the Costs of Reactive Power Purchased in an Ancillary Service Market by Modified Y-Bus Matrix Method”, IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 1, FEBRUARY 2004, pp. 174 – 179.

BIOGRAPHIES

 S. Uma Mageswaran was born in 1980, he completed B.E (Electrical and Electronics Engineering) in Thirumalai Engineering college, Anna University tamil nadu in 2005, M.E (Power Systems Engineering) in B.S.A. Crescent Engineering College, Anna University, Chennai, in the year 2007. He is working as Assistant Professor in Velammal Institute of Technology, Anna University, Chennai. His research area is reactive power allocation, power system optimization, and smart grid.

Dr.N.O.Guna Sekhar was born in 1944, completed Engineering in the year 1967 at REC, Warrangal (AP), M.Sc(Engg) at College of Engineering, Guindy in 1973 and Ph.D in the year 1987 at Indian Institute of Science (IISc) Bangalore. He is presently working as Professor in Easwari Engineering College, Anna University, Chennai. His research area is wind energy conversion, power system optimization and Solar energy