电力系统导论实验报告.doc

Experiment Introduction to power systems 学生姓名：学生姓名： 学学 号：号： 专业班级：专业班级： 实验名称实验名称： 电力系统导论（双语）电力系统导论（双语） 20201414 年年 6 6 月月 5 5 日日 CONTENTS 1、EXPERIMENT 1.1 BUS ADMITTANCE MATRIX.1-6 2、EXPERIMENT 2.6 BUS IMPEDANCE MATRIX6-13 3、EXPERIMENT 3.13 GAUSS-SEIDEL AND NEWTON METHOD13-16 4、PERSENAL SUMMARY.16 0 Experiment 1 Bus Admittance Matrix 1. Objective To write a simple program in MATLAB for the algorithm of bus admittance matrix. 2. System Requirement Computer with MATLAB 6 or above installed. 3. Procedure 1.0 Launch the MATLAB program. 2.0 Go to FILE NEW M-file. 3.0 Write a function Y = The_Node_Admittance_Matrix(TopoStructureAndBranchPara) for the formation of the bus admittance matrix. 1 4.0 TopoStructureAndBranchPara is the transmission line, cable and transformer input data and contains five columns parameters. The first two columns are the line bus numbers and the remaining columns contain the line resistance and reactance in per-unit and transformer tap ratio or capacitor of transmission line. 5.0 The function should return the bus admittance matrix. 4. Exercises Use the written function, Y = The_Node_Admittance_Matrix (TopoStructureAndBranchPara) to obtain the Ybus of the following power system network: Q1. You are required to write the Ybus topological structure and parameter into a text file. (Hint: use the matlab text compiler to write down the table 1 data, using the comma to separate the parameters, and save it use the name of 4_Power_System_Data.dbf) Q2. You are required to write out the program flow figure of forming a nodal admittance matrix. Hint. You are required to compile a program to form the Ybus Matrix, the following program is a reference program to you. Figure : One-line diagram of power system For example ,from the textbook “power system analysis” No.2 edition 3 on page 6162 NodalAdmittanceMatrix = 1.0421 - 8.2429i -0.5882 + 2.3529i 0 + 3.6667i -0.4539 + 1.8911i -0.5882 + 2.3529i 1.0690 - 4.7274i 0 0 Table 1：Transformer and transmissssion Line data From Bus#To Bus#R(p.u)X(p.u)B(p.u)or ratio KOthers 120.10.4j0.01528 1300.31.1 140.120.5j0.01920 240.080.40J0.01413 2 0 + 3.6667i 0 0 - 3.3333i 0 -0.4539 + 1.8911i 0 0 0.9346 - 4.2616i 5.The flow chart Figure : The flow chart of Forming Nodal Admittance Matrix The program is: %function OutPut=The_Node_Admittance_Matrix(handles) %is a subroutine of PowerSystemCalculation function OutPut=The_Node_Admittance_Matrix(handles) %the following program is open a data file and get the Number of % Node and Branch data to form a nodal addmittance matrix %the following code is open a file and read the data of power system network fname,pname = uigetfile(*.dbf,Select the network parametre data-file); TopoStructureAndBranchPara= csvread(fname); NumberOfBranch,NumberOfPara=size(TopoStructureAndBranchPara); Temporary1=max(TopoStructureAndBranchPara(:,1); Temporary2=max(TopoStructureAndBranchPara(:,2); if Temporary1 Temporary2 NumberOfNode=Temporary1; else NumberOfNode=Temporary2; end %The following program is to form the Nodal Admittance Matrix % and the Topologic structure and Branch Parametres are arranged % I,J,R,X,C/K, and pay attention to the inpedence of transformer is in the % side of Node J and the ratio of transformer 1:K is in the side of Node I for CircleNumber1=1:NumberOfBranch for CircleNumber2=1:NumberOfBranch NodalAdmittanceMatrix(CircleNumber1,CircleNumber2)=0; end end for CircleNumber=1:NumberOfBranch if TopoStructureAndBranchPara(CircleNumber,5) 0.85 NodalAdmittanceMatrix(TopoStructureAndBranchPara(TopoStructureAndBranchPara(CircleNumber, 1),TopoStructureAndBranchPara(CircleNumber,1)=. 3 NodalAdmittanceMatrix(TopoStructureAndBranchPara(TopoStructureAndBranchPara(CircleNumber, 1),TopoStructureAndBranchPara(CircleNumber,1)+. TopoStructureAndBranchPara(CircleNumber,5)2/. (TopoStructureAndBranchPara(CircleNumber,3)+. j*TopoStructureAndBranchPara(CircleNumber,4) ; NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,2),TopoStructureAndBranchPa ra(CircleNumber,2)=. NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,2),TopoStructureAndBranchPa ra(CircleNumber,2)+. 1/(TopoStructureAndBranchPara(CircleNumber,3)+j*TopoStructureAndBranchPara(CircleNumber,4 ); NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra(CircleNumber,2)=. NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra(CircleNumber,2). -TopoStructureAndBranchPara(CircleNumber,5)/. (TopoStructureAndBranchPara(CircleNumber,3)+j*TopoStructureAndBranchPara(CircleNumber,4) ); NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,2),TopoStructureAndBranchPa ra(CircleNumber,1)=. NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra(CircleNumber,2); else NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra(CircleNumber,1)=. NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra(CircleNumber,1)+. +1/(TopoStructureAndBranchPara(CircleNumber,3)+. Experiment 2 Bus Impedance Matrix 4 j*TopoStructureAndBranchPara(CircleNumber,4)+j*TopoStructureAndBranchPara(CircleNumber,5) ; NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,2),TopoStructureAndBranchPa ra(CircleNumber,2)=. NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,2),TopoStructureAndBranchPa ra(CircleNumber,2)+. +1/(TopoStructureAndBranchPara(CircleNumber,3)+. j*TopoStructureAndBranchPara(CircleNumber,4)+j*TopoStructureAndBranchPara(CircleNumber,5) NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra( CircleNumber,2)=. NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra( CircleNumber,2). -1/(TopoStructureAndBranchPara(CircleNumber,3)+. j*TopoStructureAndBranchPara(CircleNumber,4); NodalAdmittanceMatrix(TopoStructureAndBranchPara( CircleNumber,2),TopoStructureAndBranchPara(CircleNumber,1)=. NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPa ra( CircleNumber,2); end end The result is： NodalAdmittanceMatrix = 1.0421 - 8.2429i -0.5882 + 2.3529i 0 + 3.6667i -0.4539 + 1.8911i -0.5882 + 2.3529i 1.0690 - 4.7274i 0 0 0 + 3.6667i 0 0 - 3.3333i 0 -0.4539 + 1.8911i 0 0 0.9346 - 4.2616i 5 Experiment 2 Power Grid Bus Impedance Matrix 1. Objective To write a simple program in MATLAB for the algorithm of bus impedance matrix. 2. System Requirement Computer with MATLAB 6 or above installed. 3. Procedure 1.0 Launch the MATLAB program. 2.0 Go to FILE NEW M-file. Experiment 2 Bus Impedance Matrix 6 3.0 Write a function Z = znbus (z) for the formation of the bus impedance matrix. 4.0 z is the line input and contains three columns. The first two columns are the line bus numbers and the remaining columns contain the line resistance in per-unit. 5.0 The function should return the bus impedance matrix. 4. Exercises Use the written function, Z = znbus(z) to obtain the Ybus of the following power system network: Example 1 Figure 3: One-line diagram of power system For example ,from the textbook “power system analysis” No.2 edition 3 on page 6162 Table 1：Transformer and transmissssion Line data From Bus#To Bus#R(p.u)X(p.u)B(p.u)or ratio KOthers 120.10.4j0.01528 1300.31.1 7 140.120.5j0.01920 240.080.40J0.01413 Q2. You are required to write the Zbus into a text file. (Hint: use the matlab text compiler) Example 2 For the system shown, form Zbus matrix using the building algorithm Solution A line list Experiment 2 Bus Impedance Matrix 8 Apply Kron reduction to eliminate the last row Hint. You are required to compile a program to form the Zbus Matrix.the following program is a reference program to you. The program is: %function OutPut=The_Node_impedance_Matrix(handles) %is a subroutine of PowerSystemCalculation function OutPut=The_Node_impedance_Matrix(handles) %the following program is open a data file and get the Number of % Node and Branch data to form a nodal impedance matrix %the following code is open a file and read the data of power system network fname,pname = uigetfile(*.dbf,Select the network parametre data-file); Topo_Structure_And_Branch_Para= csvread(fname); %get the electric power system the number of branch and the parametre of % elements 9 NumberOfBranch,NumberOfPara=size(Topo_Structure_And_Branch_Para); %Temporary1-temporary variable 1 %Temporary2-temporary variable 2 Temporary1=max(Topo_Structure_And_Branch_Para(:,1); Temporary2=max(Topo_Structure_And_Branch_Para(:,2); if Temporary1 Temporary2 NumberOfNode=Temporary1; else NumberOfNode=Temporary2; end % The following program is to form the Nodal impedance Matrix % and the Topologic structure and Branch Parametres are arranged % I,J,R,X,C/K, and pay attention to the inpedence of transformer is in the % side of Node J and the ratio of transformer 1:K is in the side of Node % % set the initial value of Nodal Admittance Matrix to zero for CircleNumber1=1:NumberOfNode for CircleNumber2=1:NumberOfNode Nodal_impedance_Matrix(CircleNumber1,CircleNumber2)=0; end end for CircleNumber=1:NumberOfBranch if Topo_Structure_And_Branch_Para(CircleNumber,5) 0.85 Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(Topo_Structure_And_Branch_Para(Cir cleNumber,1),Topo_Structure_And_Branch_Para(CircleNumber,1)=. Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(Topo_Structure_And_Branch_Para(Cir cleNumber,1),Topo_Structure_And_Branch_Para(CircleNumber,1)+Topo_Structure_And_Branch_ Para(CircleNumber,5)2/(Topo_Structure_And_Branch_Para(CircleNumber,3)+. j*Topo_Structure_And_Branch_Para(CircleNumber,4) ; Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,2),Topo_Structure_And _Branch_Para(CircleNumber,2)=. Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,2),Topo_Structure_And _Branch_Para(CircleNumber,2)+. 1/(Topo_Structure_And_Branch_Para(CircleNumber,3)+j*Topo_Structure_And_Branch_Para(Circle Number,4); Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para(CircleNumber,2)=. Experiment 2 Bus Impedance Matrix 10 Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para(CircleNumber,2). -Topo_Structure_And_Branch_Para(CircleNumber,5)/. (Topo_Structure_And_Branch_Para(CircleNumber,3)+j*Topo_Structure_And_Branch_Para(CircleN umber,4); Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,2),Topo_Structure_And _Branch_Para(CircleNumber,1)=. Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para(CircleNumber,2); else Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para(CircleNumber,1)=. Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para(CircleNumber,1)+. +1/(Topo_Structure_And_Branch_Para(CircleNumber,3)+. j*Topo_Structure_And_Branch_Para(CircleNumber,4)+j*Topo_Structure_And_Branch_Para(Circle Number,5); Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,2),Topo_Structure_And _Branch_Para(CircleNumber,2)=. Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,2),Topo_Structure_And _Branch_Para(CircleNumber,2)+. +1/(Topo_Structure_And_Branch_Para(CircleNumber,3)+. j*Topo_Structure_And_Branch_Para(CircleNumber,4)+j*Topo_Structure_And_Branch_Para(Circle Number,5) Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para( CircleNumber,2)=. Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para( CircleNumber,2). -1/(Topo_Structure_And_Branch_Para(CircleNumber,3)+. 11 j*Topo_Structure_And_Branch_Para(CircleNumber,4); Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para( CircleNumber,2),Topo_Structure_And_Branch_Para(CircleNumber,1)=. Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1),Topo_Structure_And _Branch_Para( CircleNumber,2); end end format short Nodal_impedance_Matrix*inv(Nodal_impedance_Matrix) 运行结果运行结果： Nodal_impedance_Matrix = 1.0421e+000 -8.2429e+000i -5.8824e-001 +2.3529e+000i 0 +3.6667e+000i 0 -5.8824e-001 +2.3529e+000i 5.8824e-001 -2.3377e+000i 0 0 0 +3.6667e+000i 0 0 -3.3333e+000i 0 0 0 0 4.5386e-001 -1.8719e+000i Nodal_impedance_Matrix = 1.0421e+000 -8.2429e+000i -5.8824e-001 +2.3529e+000i 0 +3.6667e+000i - 4.5386e-001 +1.8911e+000i -5.8824e-001 +2.3529e+000i 1.0690e+000 -4.7274e+000i 0 0 0 +3.6667e+000i 0 0 -3.3333e+000i 0 -4.5386e-001 +1.8911e+000i 0 0 9.3463e-001 -4.2616e+000i ans = 1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 1.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i Experiment 2 Bus Impedance Matrix 12 -0.0000 - 0.0000i -0.0000 - 0.0000i 1.0000 - 0.0000i -0.0000 0 - 0.0000i 0 + 0.0000i 0.0000 - 0.0000i 1.0000 + 0.0000i 以上就是对阻抗矩阵的验证，其和其逆相乘为单位对角矩阵 ExperimentExperiment 3 3 Gauss-Seidel Method 1. Objective To write a simple program in MATLAB for the algorithm to solution of nonlinear algebraic equations; Known as the method of successive displacements. 2. Discussion The most common methods for solving nonlinear algebraic equations are Gauss-Seidel, Newtow-Rahpson, and quasi-Newton-Raphson methods. We start with one dimensional equations and then generalize to n-dimensional equations. 3. Mathmatics model Consider the nonlinear equation .The equation is broken into two parts thus:. We 0)(xf)(xgx assume is an initial “guess“ of the solution, then “refine“ the solution using: )0( x )( )0()1( xgx This process is repeated thus )( )1()2( xgx and on the iteration we have: th n)( )1()( nn xgx . If this process is convergent, then the successive solutions approach a value which is declared as the solution. Thus if at some step we have: 1k 13 )()1(kk xx where e is the desired “accuracy“, then we claim the solution has been found to the accuracy specified. 4. System Requirement Computer with MATLAB 6 or above installed. 5. Procedure 1.0 Launch the MATLAB program. 2.0 Go to FILE NEW M-file. 3.0 Write a function program of Gauss Seidel Method. 6. Exercises Example: Using the Gauss-Seidel method to obtain the roots of the equation: 0496)( 23 xxxxf First the equation is expressed in a different form thus )(46 9 1 23 xgxxx Experiment 2 Bus Impedance Matrix 14 And the iteration can proceed. Take a good look at the shape of the iterations! Below is the program showing the process graphically (later showing how to do it iteratively). 7.The flow chart of Gauss Seidel method (Omitted) 8.Reference Program and result. 程序是：程序是： clear all clc x0=0.5; n=0; while (abs(x03-6*x02+9*x0-4)0.00001) x0=-(x03-6*x02-4)/9; y=x0; n=n+1; end 结果是结果是：n=1627 y=x0=0.99818 clear all clc x0=2.5; n=0; while (abs(x03-6*x02+9*x0-4)0.00001) x0=-(x03-6*x02-4)/9; y=x0; n=n+1; end 结果是结果是：n=7 y=x0=4 仿照高斯-赛德尔法，我们可以写