1.1 Development of the power system
In the early stage of the development of the power industry, electrical energy was directly produced in power stations (or power plants) near users, and each power station operated in isolation. With the development of industrial and agricultural production and cities, the demand for electrical energy has increased rapidly, and regions with rich thermal energy resources (such as coal fields) and hydropower resources are often far away from cities and industrial and mining areas where electricity is concentrated. Establish large-scale power stations in areas with abundant power resources, and then transmit electrical energy to power users over long distances. At the same time, in order to improve the reliability of power supply and the comprehensive economy of resource utilization, many scattered power stations of various forms are connected through transmission lines and substations. This kind of organically connected whole by generators, step-up and step-down substations, power transmission lines and electrical equipment is called the power system.
The power system plus the prime mover of the generator (such as steam turbine, water turbine), the power part of the prime mover (such as thermal boilers, reservoirs, and reactors of nuclear power plants), heating and heating equipment, are called power systems. Modern power systems put forward the concept of "flexible AC transmission and new DC transmission". Flexible AC transmission technology refers to the use of solid-state electronic devices and modern automatic control technology to perform real-time closed-loop control of the voltage, phase angle, impedance, power, and circuit on and off of the AC grid, thereby improving the transmission capacity of high-voltage transmission lines and the stability of the power system Level. New direct current transmission technology refers to the application of the latest achievements of current power electronic technology to improve and simplify the cost of converter stations.
1.2 Overview of MATLAB
MATLAB is an interactive, object-oriented programming language, widely used in industry and academia. It is mainly used for matrix operations. It also has advantages in numerical analysis, automatic control simulation, digital signal processing, dynamic analysis, drawing, etc. powerful functions.
In addition, MATLAB provides a special tool: TOOLBOXES. These toolboxes mainly include: signal processing (SIGNAL PROCESSING), control system (CONTROL SYSTEMS), neural network (NEURAL NETWORKS), fuzzy logic (FUZZY LOGIC) , Wavelet (WAVELETS) and simulation (SIMULATION) and so on. Users of different fields and levels can easily perform calculation, analysis and design work through the learning and application of corresponding tools. In MATLAB design, the filling format of the original data is a very critical link, which has a direct relationship with the convenience and flexibility of the program. The design of the original data input format should mainly be based on the perspective of use, the principle is simple and clear, and easy to modify.
The matrix is the basic unit of MATLAB data storage, and the operation of the matrix is the core of the MATLAB language. Almost all operations in the MATLAB language system are based on the operation of the matrix. The basic mathematical operations of the matrix include the four basic operations of the matrix, operations with constants, inverse operations, determinant operations, rank operations, eigenvalue operations and other basic function operations, which are briefly introduced here.
Chapter 3 Calculation of Related Parameters of Power Line Based on MATLAB
Power lines are mainly divided into transmission lines and distribution lines.
Transmission lines generally have higher voltage levels, high magnetic field strength, and long distances through air (arc). 35kV, 110kV, 220kV, 330kV (a few areas), 660kV (a few areas), DC/AC500kV, DC800kV and the newly built Shanghai 100kV are all transmission lines. After the power generated by the power plant is boosted by the booster station, it is transmitted to the various substations, and then the various substations are unified in series and parallel to form a transmission line network, which connects the "lines" between the various nodes on the "network" It is the transmission line.
Power distribution lines are mainly used for artificial lighting and electrical appliances, and they must be re-laid during the recent renovation. The general standard is:
(1) 2.5mm square copper wire is used for the main line.
(2) The air conditioner cable should be 4mm square, and each air conditioner should be routed separately.
(3) Signal lines such as telephone lines and TV lines cannot run parallel to the wires.
(4) Protective plastic boxes should be used for wires, rubber pipes (including PVC pipes) should be used for wires buried in the wall, and straight or elbow connections should be used. Where hoses cannot be used, metal hoses must be used for protection.
(5) When buying wires, switches, etc., you must buy good products. The only standard is to see whether they meet national standards. The dealer should indicate this when purchasing.
3.1 Rated voltage ( Nominal Voltage)
3.1.1 Introduction to Rated Voltage
The rated voltage is the best voltage applicable to the appliance when it works for a long time. In layman's terms, the voltage value at both ends of an electrical appliance when it is working normally. It is easy to burn out when it is high, and it does not work normally when it is low. At this time, the components in the electrical appliance are all working in the best condition. Only when they are working in the best condition, the performance of the electrical appliance is relatively stable, so that the life of the electrical appliance can be extended.
The so-called rated voltage is the voltage at which generators, transformers and electrical equipment have the greatest economic benefit during normal operation. The country has stipulated a series of standard voltage levels, which is conducive to the standardization and serialization of the electrical manufacturing industry, the standardization and selection of design, the interconnection and replacement of electrical appliances, and the production and maintenance of spare parts. The best choice should be made. Appropriate rated voltage level.
In order to facilitate the production standardization and serialization of the electrical appliance manufacturing industry, the state has stipulated a series of standard voltage levels. When designing, choose the most suitable rated voltage level. The so-called rated voltage is the voltage at which a certain receiver (motor, light, etc.), generator, and transformer has the greatest economic benefit during normal operation. my country has stipulated a unified voltage rating standard for power equipment. The voltage at each point in the power grid is different.
Electrical equipment: The rated voltage of the electrical equipment is consistent with the rated voltage of the grid. In fact, due to voltage loss in the power grid, the actual voltage at each point deviates from the rated value. In order to ensure the good operation of electrical equipment, the state has strict regulations on the deviation of the grid voltage at all levels. Obviously, electrical equipment should have a wider range of normal operating voltage than the allowable deviation of the grid voltage.
Generator: The rated voltage of the generator is 5% higher than the rated voltage of the grid at the same level to compensate for the voltage loss on the grid.
Transformer: The rated voltage of the transformer is divided into primary and secondary windings. For the primary winding, when the transformer is connected to the end of the power grid, it is essentially equivalent to a load on the power grid (such as a factory step-down transformer), so its rated voltage is consistent with the power grid. When the transformer is connected to the generator terminal (such as a power plant) Step-up transformer), the rated voltage should be the same as the rated voltage of the generator. For the secondary winding, the rated voltage refers to the no-load voltage. Taking into account the voltage loss of the transformer itself (calculated as 5%), the rated voltage of the transformer secondary winding should be 5% higher than the grid rated voltage. When the transmission distance of the secondary side is longer For a long time, the line voltage loss (calculated by 5%) should also be considered. At this time, the rated voltage of the secondary winding should be 10% higher than the rated voltage of the grid.
Table 3-1 Rated voltage description of power system
|
|
Power grid and electrical equipment Rated voltage |
generator Rated voltage |
Rated voltage of power transformer |
|
| Primary winding |
Secondary winding |
|||
| Low pressure V |
220/127 380/220 660/380 |
230 400 690 |
220/127 380/220 660/380 |
230/133 400/230 690/400 |
| high pressure kV |
3 6 10 － 35 63 110 220 330 500 750 |
3.15 6.3 10.5 13.8,15.75,18,20 － － － － － － － |
3 and 3.15 6 and 6.3 10 and 10.5 13.8,15.75,18,20 35 63 110 220 330 500 750 |
3.15 and 3.3 6.3 and 6.6 10.5 and 11 － 38.5 69 121 242 363 550 － |
This parameter is generally determined by relevant national regulations, so detailed calculations will not be made here.
3.2 Power frequency electric field
3.2.1 Introduction to power frequency electric field
Power transmission and transformation facilities have power frequency electric fields and power frequency magnetic fields during operation. The power frequency electric field strength of power transmission and transformation facilities is a measure of the strength of the electric field in a certain direction at a certain point in the space around the power transmission and transformation facilities. The unit of measurement is kilovolts/meter (kV/m). Electric field around power facilities. When the electrical equipment is connected to the power supply (that is, voltage is added or called live), a power frequency electric field is formed in the space around it.
"Technical Specification for Environmental Impact Assessment of Electromagnetic Radiation for 500kV Ultra-high Voltage Transmission and Transformation Projects (HJ/T24-1998)" is the current standard for evaluating the electromagnetic environment of power facilities in my country. It is also the technical basis for national environmental protection evaluation. The standard was drafted by Northern Jiaotong University commissioned by the State Environmental Protection Administration. (Beijing Jiaotong University has a national electromagnetic compatibility laboratory) promulgated and implemented in 1998. The standard was formulated based on the "Guidelines for Limiting Time-Varying Electric, Magnetic and Electromagnetic Field Exposure (below 300GHz)" issued by the International Commission for Non-Ionizing Radiation Protection (ICNIRP). The limit of "ICNIRP Guidelines" is 5kV/m of power frequency electric field and 0.1mT of magnetic induction. my country's "500kV Ultra-high Voltage Transmission and Distribution Engineering Electromagnetic Radiation Environmental Impact Assessment Technical Specification (HJ/T24-1998)" limits the power frequency electric field 4kV/m, and the magnetic induction intensity is 0.1mT.
2nd floor: According to research and related tests, transformers, ultra-high voltage power distribution devices and ultra-high voltage transmission lines will form a certain intensity of power frequency electromagnetic radiation during operation. According to relevant data, the power frequency electric field radiation of a 550KV transmission line can reach a height of 9.7KV/m at a distance of 1.5m from the ground. The power frequency magnetic field may cause serious interference to the deflection system of the computer monitor. The specific phenomenon is that the display screen of the monitor is jittered and colored spots may appear on the edge of the monitor. High-intensity power frequency electromagnetic radiation may also cause computer crashes.
The operation of high-voltage overhead power lines and substations will generate radio noise. When this kind of radio noise is severe, it will affect the radio reception (mainly medium and short wave broadcasting) of residents near the power lines and substations and the work of professional radio stations. . Because power lines and substations occupies a large area, especially the length of power lines may reach hundreds of kilometers, and the impact range is wide. Under normal circumstances, the radio noise of overhead power lines and substations has three types of root causes: respectively, on the wire and its metal surface Corona discharge in the air; insulators withstand high potential gradient areas and produce sparks; gap spark discharges caused by loose connections or poor contact. When the operating voltage is above 100KV (usually the wire surface potential gradient> 12KV/cm), the first root cause dominates and becomes inevitable, which is an inherent characteristic of the circuit.
Therefore, it is also very important to calculate the relevant data of the power frequency electric field for high-voltage lines in power lines.
3.2.2 MATLAB simulation of power frequency electric field
We can get the following simulation results:
Figure 3-1 Related simulation results of power frequency electric field (see Appendix 2 for the code)
3.3 Reactive power compensation capacity of high-voltage long-distance transmission lines
3.3.1 Introduction to reactive power compensation capacity of high-voltage long-distance transmission lines
In the power market environment, with the interconnection of regional power grids, power grid planning plays a vital role in alleviating the contradiction between power supply and demand, preventing power bottlenecks and transmission congestion, and ensuring the safe and stable operation of the power grid. Power system planning includes power supply planning and grid planning, but due to their respective complexity, they are often planned independently. Determine the type, capacity and installation location of reactive power compensation equipment in the power grid to ensure the voltage quality and stability of the grid under normal and faulty operation modes, and minimize the total investment and operating costs during the planning period.
Operation analysis of ultra-high voltage and long-distance transmission lines:
For UHV long-distance transmission lines, it is not advisable to judge them as short, medium and long lines or long lines based on their physical length. For accurate analysis, the distributed parameter model should be used. The schematic diagram of the UHV long-distance transmission line is shown in Figure 3-2, and the parameter formula is as follows:
Figure 3-2 Schematic diagram of long-distance power lines
With the development of the power system, more and more large-capacity power plants far away from the load center have been put into operation one after another, and the large regional power grids are gradually interconnected to form a combined power system. The ultra-high-voltage long-distance transmission line is responsible for connecting the receiving end and the remote area. The task of capacity power plants or regional grids. Since reactive power cannot be transmitted over long distances, reactive power compensation devices must be used. Reactive power compensation is one of the important measures for the safe and economic operation of power systems. Reasonable reactive power compensation can improve the performance of the system.
3.4.1 Introduction to dynamic stable current
The rated dynamic stability current is also called the rated peak withstand current, which refers to the peak current of the first half wave of the rated short-time withstand current that the circuit breaker can withstand at the closing position, which is equal to the rated short-time closing current.
When the circuit breaker is in the closed position, the maximum short-circuit current that can pass is called dynamic stable current. Also known as the rated peak withstand current. It indicates the ability of the circuit breaker to withstand electromotive force under the action of short-circuit impulse current. The magnitude of this value is determined by the mechanical strength of conductive and insulating components.
In the design and assembly, firstly, consider the direction of the force of the busbar. It determines the arrangement of the three-phase busbar. If not necessary, try not to make the wide side of the busbar face each other, because the force is the worst at this time. Secondly, fully consider the spacing of the supporting insulators so as to meet the requirements without waste. At this point, many factories seem to have an unwritten rule that, no matter what the situation, the bus bar span is checked at 1000mm, which is wrong. Again, it is necessary to consider whether the strength of the busbar clamp can withstand the electric power of the busbar. I found that some manufacturers are contacting the busbar (when the wide sides are opposite, they use insulated splints. Visually, they are not strong enough to withstand the electric power of the busbar (not necessarily the most serious situation). At the same time, the busbar splint should not be formed. For circulating currents, non-magnetic materials must be considered. For systems above 31.5KA, our commonly used epoxy or polycarbonate materials are not strong enough. Finally, for systems with large short-circuit capacity, the supporting insulators must be verified. Although the manufacturer says how much its flexural (tensile) strength is, in fact, some products have bolts that cannot withstand the impact load of electrodynamic forces.
3.4.2 Introduction to thermally stable current
The thermally stable current is the maximum current allowed by the circuit breaker in a certain period of time. This indicator shows the ability of the circuit breaker to withstand the thermal effect of short-circuit current. During the specified period of time, these currents flowing through the device will not cause major damage to the device, and it can continue to be used after the current disappears. Therefore, the structural parts in the electrical structure should satisfy the heat generated by the current flowing in it for a specified period of time without causing damage.
These two parameters have to be inferred through actual observations, so we won't introduce them here.
3.5 wire diameter
3.5.1 Introduction to wire diameter
The wire diameter of the high-frequency transformer can be calculated according to the formula D=1.13(I/J)^1/2, J is the current density, and the wire diameter calculated by different values is different. Because the high-frequency current will be in the conductor Skin effect, so when determining the line length, the penetration depth of the conductor at different frequencies must be calculated. Formula: d=66.1/(f)^1/2 If the calculated line diameter D is greater than twice the penetration depth, You need to use multiple strands or litz wires.
For example: 1A current, 100K frequency. Suppose the current density is 4A/mm^2;
D=1.13*(1/4)^1/2=0.565mm Sc=0.25mm^2；
d=66.1/(f)^1/2=66.1/100000^1/2=0.209mm；
2d=0.418mm；
Use 0.4mm wire, single 0.4 cross-sectional area Sc=0.1256mm^2;
The cross-sectional area of two 0.4 pieces Sc=0.1256*2=0.2512mm^2;
It can be seen that the 2*0.4 scheme can meet the calculation requirements.
The impedance of a wire is directly proportional to its length and inversely proportional to its wire diameter. Please pay special attention to the wire material and diameter of the input and output wires when using the power supply. To prevent accidents caused by overheating of the wires due to excessive current. Commonly used starting from 1 square millimeter: 1, 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240 square millimeters; less commonly used are: 0.5, 0.75 , 300, 400, 500 square millimeters, etc. The following is a table of the maximum current that the copper wire can withstand at different temperatures.
Table 3-1 Wire diameter query table
| Wire diameter (Large about the value) (Square millimeter) |
Copper wire temperature (Celsius) |
|||
| 60℃ |
75℃ |
85℃ |
90℃ |
|
| Current ( A ) |
||||
| 2．5 |
20 |
20 |
25 |
25 |
| 4．0 |
25 |
25 |
30 |
30 |
| 6．0 |
30 |
35 |
40 |
40 |
| 8．0 |
40 |
50 |
55 |
55 |
| 14 |
55 |
65 |
70 |
75 |
| 22 |
70 |
85 |
95 |
95 |
| 30 |
85 |
100 |
100 |
110 |
| 38 |
95 |
115 |
125 |
130 |
| 50 |
110 |
130 |
145 |
150 |
| 60 |
125 |
150 |
165 |
170 |
| 70 |
145 |
175 |
190 |
195 |
| 80 |
165 |
200 |
215 |
225 |
| 100 |
195 |
230 |
250 |
260 |
3.5.2 Matlab calculation of wire diameter
The wire diameter of power lines is generally calculated according to the following formula:
Copper wire: S= I*L / 54.4*U`
Aluminum wire: S= I*L / 34*U`
In the formula: I——the maximum current passing through the wire (A)
L——The length of the wire (m)
U`——allowable power drop (V)
S——The cross-sectional area of the wire (mm2)
3.6.2 Matlab calculation of power system flow
Appendix 1: Rated voltage
附录二：工频电场
clear;
clc;
close all;
x=-40:0.5:40;
a=13.72;b=12.19;
y=1.5;
c=8.85e-12;
QR=2*pi*c*[54705 -73523 24287];
Qi=2*pi*c*[46378 19701 -67517];
Q=QR+Qi*j;
A=[(y-b)./sqrt((a-x).^2+(b-1.5).^2)-(y-b)./sqrt((a-x).^2+(-b-1.5).^2);(y-b)./sqrt(x.^2+(b-1.5).^2)-(y-b)./sqrt(x.^2+(-b-1.5).^2);
(y-b)./sqrt((-a-x).^2+(b-1.5).^2)-(y-b)./sqrt((-a-x).^2+(-b-1.5).^2)];
Ey=abs(Q*A./2*pi*c)*1e21;
subplot(3,2,1);
y=1.5;
plot(x,y)
hold on;
plot([0 a -a -a 0 a],[b b b -b -b -b],'o')
ylabel('离地面高度');
xlabel('水平距离');
subplot(3,2,2);
plot(x,Ey);
title('电场强度曲线');
xlabel('x(m)');
ylabel('E(V/m)');
axis([-40 40 0 12000]);
a1=20;b1=8;c1=25;
QR=2*pi*c*[75864 -40753 -31074];
Qi=2*pi*c*[-7926 70575 -69662];
Q=QR+Qi*j;
A=[(y-b1)./sqrt((a1-x).^2+(b1-1.5).^2)-(y-b1)./sqrt((a1-x).^2+(-b1-1.5).^2);(y-c1)./sqrt(x.^2+(b1-1.5).^2)-(y-c1)./sqrt(x.^2+(-b1-1.5).^2);
(y-b1)./sqrt((-a1-x).^2+(b1-1.5).^2)-(y-b1)./sqrt((-a1-x).^2+(-b1-1.5).^2)];
B=[(x-a1)./sqrt((a1-x).^2+(b1-1.5).^2)-(x-a1)./sqrt((a1-x).^2+(-b1-1.5).^2);(x)./sqrt(x.^2+(b1-1.5).^2)-(x)./sqrt(x.^2+(-b1-1.5).^2);
(x+a1)./sqrt((-a1-x).^2+(b1-1.5).^2)-(x+a1)./sqrt((-a1-x).^2+(-b1-1.5).^2)];
Ey1=abs(Q*A./2*pi*c)*1e20;
Ey2=abs(Q*B./2*pi*c)*1e20;
Ey3=sqrt(Ey1.^2+Ey2.^2);
subplot(3,2,3);
y=1.5;
plot(x,y)
hold on;
plot([0 a1 -a1 -a1 0 a1],[c1 b1 b1 -b1 -c1 -b1],'o')
ylabel('离地面高度');
xlabel('水平距离');
subplot(3,2,4);
plot(x,Ey1);
title('算例二的电场强度曲线');
xlabel('x(m)');
ylabel('E(V/m)');
subplot(3,2,5);
plot(x,Ey2)
subplot(3,2,6);
plot(x,Ey3)
附录三：无功补偿容量
clc;
clear;
f=50;
u=380;
p=4000e3;
w1=0.83138;
w2=0.86;
C1=p*(((1-w1*w1)^0.5)/w1-((1-w2*w2)^0.5)/w2)
C2=1000000*C1/(2*pi*f*u*u)
附录四：线径
I=0;
L=0;
U=0;
S1=I*L/(54.4*U)
S2=I*L/(34*U)
附录五：潮流
clear;
clc;
close all;
n=5;%节点数
b=4;%b支路数
Sb=100;
Ub=10;
Zb=Ub^2/Sb;
%第一列存支路号，第二列存首节点号，第三列存尾节点号，第四列存支路自阻抗,第五列存尾节点给定功率
Z=[1 ,0 ,1 ,0.075/Zb+i*0.1/Zb ,2.00/Sb+i*1.6/Sb
2 ,1 ,2 ,0.09/Zb+i*0.18/Zb ,2.0/Sb+i*0.18/Sb
3 ,1 ,3 ,0.08/Zb+i*0.11/Zb ,3.0/Sb+i*1.5/Sb
4 ,2 ,4 ,0.04/Zb+i*0.04/Zb ,1.5/Sb+i*1.20/Sb
];
k=0;
V=ones(n,1);
t=0;
while t<b & k<10
x1=Z(b,3);x=x1-n;%注入电流
for l=1:b
j=Z(l,3);
ua=V(j+1,1);
I(j,1)=conj(Z(j,5)/ua);
end
J=zeros(b,1);
l=b;
J(l)=J(l)+I(l);
for jj=1:b-1
l=l-1;
for m=l+1:b
if Z(m,2)==Z(l,3)
J(l)=J(l)+J(m);
end
end
J(l)=J(l)+I(l);
end
%前推算节点电压
for l=1:b
j=Z(l,3)+1;
i=Z(l,2)+1;
V(j,1)=V(i,1)-Z(l,4)*J(l,1);
end
%收敛判定
t=0;
for j=2:n
SS=V(j,1)*conj(I(j-1,1));
dp=real(SS-Z(j-1,5));
dq=imag(SS-Z(j-1,5));
S(j-1,1)=SS;
ddp=abs(dp);
ddq=abs(dq);
L1=(ddp<0.000001)&(ddq<0.000001);
F(j-1,1)=L1;
if L1==1
t=t+1;
end
end
k=k+1;
end
disp('输出直角坐标各节点电压');
disp(V);
disp('显示迭代次数');
disp(k);
disp('显示收敛节点情况,"1"表示收敛，"0"表示不收敛');
disp(F);
for j=1:b
if F(j,1)==0
disp('显示不收敛节点号、计算功率');
disp(j);disp(S(j,1));
end
end
for j=1:n
Vm(j,1)=abs(V(j,1));Va(j,1)=angle(V(j,1));
end
disp('输出各节点电压幅值');
disp(Vm);
disp('输出各节点电压相角');
disp(Va)