Since 1970s, due to the rapid development of power electronic technology, various power electronic devices have been widely used in power system, industry, transportation and home, and the harm caused by harmonics has become increasingly serious. All countries in the world attach great importance to harmonic problems. Many international academic conferences on harmonics have been held, and many countries and international academic organizations have formulated standards and regulations to limit harmonics in power systems and electrical equipment.
The definition of harmonics in power supply system is to decompose periodic non-sinusoidal electric quantity by Fourier series, and get a series of components which are the same as the fundamental frequency of power grid, which are called harmonics. The ratio of harmonic frequency to fundamental frequency (n=fn/f 1) is called harmonic order. Sometimes, non-integer multiples of harmonics appear in the power grid, which is called anharmonic or fractional harmonics. Harmonic is actually a kind of interference, which has "pollution" to the power grid. The field of electrical technology mainly studies the generation, transmission, measurement, harm and suppression of harmonics, and its frequency range is generally 2≤n≤40.
How are harmonics generated?
Power grid harmonics come from three aspects:
First, the quality of power supply is not high, resulting in harmonics:
Because it is difficult to achieve absolute symmetry in the production of three-phase winding and absolute uniformity of iron core, the power supply will produce some harmonics, but generally speaking, it is rare.
Second, the power transmission and distribution system produces harmonics:
In power transmission and distribution system, harmonics are mainly generated by power transformers. Because of the saturation of transformer core, the nonlinearity of magnetization curve and the consideration of economy when designing transformer, the working magnetic field density is selected in the near saturation section of magnetization curve, which makes the magnetization current show a peak waveform, thus containing odd harmonics. Its size is related to the structure of magnetic circuit and the saturation of iron core. The higher the saturation of the iron core, the farther the transformer operating point deviates from linearity, and the greater the harmonic current, of which the third harmonic current can reach 0.5% of the rated current.
Third, the harmonics generated by electrical equipment:
Thyristor rectifier equipment. Thyristor rectifiers are widely used in electric locomotives, aluminum reduction cells, charging devices, switching power supplies and many other aspects, causing a lot of harmonics to the power grid. As we know, the thyristor rectifier adopts phase-shifting control to absorb the sine wave with missing angle from the power grid, thus leaving another sine wave with missing angle for the power grid, which obviously contains a lot of harmonics. If the rectifier is a single-phase rectifier circuit, it will contain odd harmonic current when it is connected to the inductive load, and the content of third harmonic can reach 30% of the fundamental wave; When connected with capacitive load, it contains odd harmonic voltage, and its harmonic content increases with the increase of capacitance value. If the rectifier device is a three-phase fully controlled bridge 6-pulse rectifier, the primary side of the transformer and the power supply line contain five or more odd harmonic currents;
If it is a 12 pulse rectifier, there are also odd harmonic currents of 1 1 and above. According to statistics, the harmonic generated by rectifier device accounts for nearly 40% of all harmonics, and it is the largest harmonic source.
Frequency conversion device. Frequency conversion devices are often used in fans, pumps, elevators and other equipment. Because of phase control, harmonic components are very complex, including integer harmonics and fractional harmonics. The power of this kind of equipment is usually high. With the development of variable frequency speed regulation, more and more harmonics are caused to the power grid.
Arc furnace, calcium carbide furnace. Because it is difficult for the three-phase electrodes of the electric furnace to contact uneven burden at the same time when heating raw materials, the combustion is unstable, resulting in unbalanced three-phase load and harmonic current, which is injected into the power grid through the triangular connecting coil of the transformer. Among them, the 27th harmonic is the main harmonic, with an average of 8% ~ 20% of the fundamental wave and a maximum of 45%.
Gas discharge electric light source. Fluorescent lamps, high-pressure mercury lamps, high-pressure sodium lamps and metal halide lamps belong to gas discharge electric light sources. Through the analysis and measurement of the volt-ampere characteristics of this kind of electric light sources, it is known that their nonlinearity is very serious, and some of them also contain negative volt-ampere characteristics, which will cause odd harmonic current to the power grid.
Household appliances. Television, video recorder, computer, dimming lamp, temperature regulating cooker, etc. With the voltage regulating and rectifying device, deep odd harmonics will be generated. In washing machines, electric fans, air conditioners and other equipment with windings, the waveform can also be changed due to the change of unbalanced current. Although these household appliances are small in power, they are huge in size and are also one of the main sources of harmonics.
Harm of harmonics
1. Harm to power supply and distribution lines
(1) affects the stable operation of the line.
Power lines and power transformers in power supply and distribution systems are generally detected and protected by electromagnetic relays, inductive relays or transistor relays to ensure the safety of lines and equipment in case of failure. However, electromagnetic relay and inductive relay can not be fully and effectively protected under the influence of harmonics because the content below 10% is as high as 40%, which leads to misoperation of relay protection. Although transistor relay has many advantages, it is easily affected by harmonics due to the adoption of rectifier sampling circuit, which leads to misoperation or refusal to operate. In this way, harmonics will seriously threaten the stability and safe operation of power supply and distribution system.
(2) affect the quality of power grid
The harmonics in the power system will distort the voltage and current waveforms of the power grid. For example, the neutral line in civil power distribution system will produce a large number of odd harmonics due to loads such as fluorescent lamps, dimming lamps and computers, among which the third harmonic content is more, up to 40%; In the three-phase distribution line, the integer multiple harmonics of 3 on the phase line will be superimposed on the neutral line, so that the current value of the neutral line may exceed the current on the phase line. In addition, harmonic voltage and harmonic current with the same frequency will produce active power and reactive power with the same harmonic, thus reducing the grid voltage and wasting the grid capacity.
2. Harm to power equipment
(1) Harm to Power Capacitors
When there are harmonics in the power grid, the terminal voltage of the capacitor rises after it is put into use, and the current flowing through the capacitor is larger, which increases the power loss of the capacitor. For the film-paper composite dielectric capacitor, although the loss power with harmonics is allowed to be 65438 0.38 times that without harmonics; For all-film capacitors, the allowable loss power with harmonics is 1.43 times that without harmonics. However, if the harmonic content is high and exceeds the allowable conditions of the capacitor, the capacitor will be over-current and overloaded, and the loss of power will exceed the above value, which will cause abnormal heating of the capacitor and accelerate the aging of the insulating medium under the action of electric field and temperature. Especially when the capacitor is put into the power grid with distorted voltage, it may also aggravate the harmonics of the power grid, that is, the phenomenon of harmonic expansion appears. In addition, the existence of harmonics often makes the voltage show a peak waveform, which is easy to induce partial discharge in the medium, and because of the large voltage change rate and strong partial discharge intensity, it can accelerate the aging of the insulating medium, thus shortening the service life of the capacitor. Generally speaking, every time the voltage increases by 10%, the life of the capacitor will be shortened by about 1/2. In addition, in the case of severe harmonics, the capacitor will expand, break down or explode.
(2) Harm to power transformer
Harmonic makes the copper loss of transformer increase, including resistance loss, eddy current loss and conductance in conductor.
The stray loss caused by external magnetic leakage will increase. Harmonic also increases the iron loss of transformer, which is mainly manifested in the increase of hysteresis loss of core. The worse the voltage waveform caused by harmonics, the greater the hysteresis loss. At the same time, due to the increase of losses in the above two aspects, the actual use capacity of the transformer should be reduced, or the harmonic content in the power grid should be considered when selecting the rated capacity of the transformer. In addition, harmonics will also lead to the increase of transformer noise. The vibration noise of transformer is mainly caused by the magnetostriction of iron core. With the increase of harmonic frequency, the mixed noise of components with vibration frequency around 1KHZ increases, and sometimes a metallic sound is emitted.
3) Harm to power cables
Because of the high harmonic frequency and the larger cross-sectional area of cable conductor, the skin effect is more obvious, which leads to the increase of AC resistance of conductor and the decrease of allowable current of cable. In addition, the resistance of the cable, the bus side of the system and the inductive reactance of the line are connected in series with the system, and the capacitor to improve the power factor and the capacitive reactance of the line are connected in parallel with the system, so resonance may occur under a certain inductance and capacitance value.
(4) Harm to electrical equipment
Damage to the motor
The influence of harmonics on asynchronous motor is mainly to increase the additional loss of motor, reduce efficiency, and even overheat the motor in severe cases. In particular, negative sequence harmonics generate negative sequence rotating magnetic field in the motor, forming torque opposite to the rotation direction of the motor, which plays a braking role, thus reducing the output of the motor. In addition, when the frequency of harmonic current in the motor is close to the natural frequency of a component, it will also cause mechanical vibration of the motor and produce great noise.
(5) Harm to low-voltage switchgear
For distribution circuit breakers, all-electromagnetic circuit breakers are easily affected by harmonic current, which increases iron consumption and generates heat. At the same time, it is difficult to trip because of the influence on electromagnet and eddy current, and the higher the harmonic frequency, the greater the influence. Thermomagnetic circuit breaker, due to the increase of conductor skin stress and iron loss, causes heat, reduces rated current and tripping current; The rated current of electronic circuit breakers should also reduce harmonics, especially for electronic circuit breakers that detect peaks. Therefore, the above three kinds of distribution circuit breakers may be caused by harmonics.
For the earth leakage circuit breaker, due to the action of harmonic leakage current, the circuit breaker may generate abnormal heat, resulting in misoperation or non-operation. For the electromagnetic corner connector, the harmonic current increases the temperature rise of the magnet part, which affects the contact, and the coil temperature rise reduces the rated current. For thermal relays, the rated current should also be reduced due to the influence of harmonic current. It may cause misoperation in the work.
(6) Interference with weak current system equipment
For computer network, communication, cable TV, alarm, building automation and other weak current equipment, the harmonics in the power system are coupled into these systems through electromagnetic induction, electrostatic induction and conduction, resulting in interference. Among them, the coupling strength of inductance and electrostatic induction is proportional to the interference frequency, and the conduction is coupled through the common ground, and a large amount of unbalanced current flows into the ground electrode, thus interfering with the weak current system.
(7) Affect the accuracy of power measurement.
At present, there are magnetoelectric and inductive power measuring instruments, which are greatly affected by harmonics. Especially for electric energy meters (mostly inductive), when the harmonics are large, the measurement will be chaotic and inaccurate.
(8) Harmonics have an impact on human body.
Physiologically speaking, when human cells are stimulated and excited, they will undergo rapid electric fluctuation or reversible inversion based on the resting potential of the cell membrane. If the frequency is close to the harmonic frequency, the electromagnetic radiation of power grid harmonics will directly affect the human brain magnetic field and the cardiac magnetic field.
When the harmonic pollution degree of power grid is less than the national standard, it usually does not affect the system. With the increase of pollution, the influence of harmonics gradually appears. In the case of serious harmonic exceeding the standard, if harmonic control is not carried out, it will often cause very serious consequences.
The characteristics of harmonic sources are very complicated, because the generation of harmonics depends not only on the load that generates harmonics, but also on the short-circuit capacity of power grid, the composition of power grid and the properties of other loads in power grid. Therefore, the filter screen cannot be made into a shaped product, and it must go through our company.
Technicians test the field situation of harmonic source, and then carry out special design according to the field test results.
Working principle of harmonic control
Passive filter is mainly composed of filter capacitor and filter reactor. They are appropriately combined into an LC filter device. In addition to filtering, the filter also plays the role of reactive power compensation. LC filters mainly include tuned sum filters, double tuned sum filters, high-pass filters and C-type filters. In practical application, according to the distribution and size of harmonic current and reactive power demand, several groups of filters are designed, and each group of filters has low impedance corresponding to a certain harmonic. High-pass filter has low impedance to harmonics above cut-off frequency, and C-type filter has the characteristics of tunable bandwidth and low loss. The grouping of filters needs accurate calculation, which not only filters out the main harmonic current, but also meets the requirements of reactive power compensation, and at the same time prevents harmonic current amplification caused by parallel resonance of filters and system impedance at integer frequency. The passive filter harmonic elimination and reactive power compensation device successfully developed by our company can provide accurate filter design quickly and reasonably according to the specific characteristics of each user.
The main features of the product
1. It is specially designed and manufactured for user systems, and can simultaneously filter out 2-60 times of harmonic current, with obvious filtering effect (the average harmonic current elimination rate can reach over 70-80%).
2. It can not only control harmonics, but also compensate reactive power. After harmonic control, it meets the requirements of national standards and saves electricity 10-30%.
3. The power consumption quality can be obviously improved after the filter device is put into use, which can improve the current impact caused by the impact load, reduce the voltage fluctuation, restrain the voltage flicker, improve the stability and improve the voltage quality. The power factor can be increased to above 0.96, which can reduce the line loss of users and improve the on-load efficiency of distribution transformers, with obvious economic benefits.
4. Each filter branch switch adopts high-performance vacuum contactor, with perfect control system and complete protection functions, such as short circuit protection, overvoltage protection and overcurrent protection. , reliable operation and simple operation.
Benefits of harmonic control
1. After installing the harmonic control device, the harmonic current is effectively reduced, the effective capacity of the transformer is increased, the corresponding load capacity can be increased, and the investment required for capacity expansion is reduced.
2. After installing the harmonic control device, the loss of the transformer can be effectively reduced, the safe operation coefficient of the transformer can be improved, and the protection device and the harmonic-sensitive device can be ensured not to misoperate. Thereby saving energy and reducing consumption.
3. Energy saving rate 10% ~ 30%, harmonic filtering rate 70% ~ 80%, reducing skin effect, greatly reducing heat loss, copper loss, iron loss, magnetic loss and noise, meeting the national energy saving and consumption reduction instructions and sustainable development requirements.
4. Effectively suppress the harmonic current, and the 10KV side conforms to the national standard GB/T 14549-93 to optimize the power supply quality, so as to avoid being fined by the local power supply department for the distortion of AC waveform caused by harmonics.
National standard of power grid harmonics
GB/T 14549-93 harmonic standard for public power grid
Voltage (KV) Total Harmonic Content% Odd Content% Even Content%
0.38 5 4 2
6 4.0 3.2 1.6
10 4.0 3.2 1.6
35 3.0 2.4 1.2
66 3.0 2.4 1.2
1 10 2.0 1.6 0.8
Fourier series
Fourier series
A special kind of trigonometric series. French mathematician J.-B.-J. Fourier proposed it when studying the boundary value problem of partial differential equations. Thus greatly promoting the development of the theory of partial differential equations. At home, Cheng Minde first systematically studied multivariate trigonometric series and multivariate Fourier series. He first proved the uniqueness theorem of spherical sum of multivariate trigonometric series and revealed many characteristics of Riess-Bochner spherical average of multivariate Fourier series. Fourier series has greatly promoted the development of the theory of partial differential equations. It has important applications in mathematics, physics and engineering.
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Fourier series formula
Given a function x(t) with a period t, it can be expressed as an infinite series:
& lt Math & gtx(t)= \ sum _ {k =-\ infty} a _ k \ cdote e {JK (\ frac {2 \ pi}) t} < /math & gt； (j is an imaginary unit) (1)
Among them,
& lt Mathematics & GTA _ k = \ frac \ int _ x (t) \ cdote e {-JK (\ frac {2 \ pi}) t} < /math & gt； (2)
take notice of
Convergence of Fourier series
Convergence of Fourier series: Fourier series represented by periodic functions satisfying Dirichlet condition are convergent. Dilihri conditions are as follows:
X(t) must be absolutely integrable in any period;
In any finite interval, x(t) can only take a finite number of maxima or minima;
In any finite interval, x(t) can only have a finite number of discontinuous points of the first kind.
Gibbs phenomenon: at the nondifferentiable points of x(t), if only the finite items in the infinite series on the right side of (1) are taken as the sum of X(t), then X(t) will fluctuate at these points. A simple example is a square wave signal.
Orthogonality of trigonometric function families
The orthogonality of two different vectors means that their inner product is 0, that is, there is no correlation between the two vectors. For example, in three-dimensional Euclidean space, mutually perpendicular vectors are orthogonal. In fact, orthogonality is the abstraction and generalization of verticality in mathematics. A set of n mutually orthogonal vectors must be linearly independent, so it must be an n-dimensional space, that is, any vector in the space can be expressed linearly by them. The orthogonality of trigonometric function family is expressed by formula:
& lt Mathematics & gt \ int _ {2 \ pi} \ sin (NX) \ cos (MX) \, dx = 0；; & lt/math & gt；
& lt Mathematics & gt \ int _ {2 \ pi} \ sin (MX) \ sin (MX) \, dx = 0；; (m \ ne n)& lt； /math & gt；
& lt Mathematics & gt \ int _ {2 \ pi} \ cos (MX) \ cos (MX) \, dx = 0；; (m \ ne n)& lt； /math & gt；
& lt Math & gt \ int _ {2 \ pi} \ sin (NX) \ sin (NX) \, dx = \ pi& lt/math & gt；;
& lt Mathematics & gt \ int _ {2 \ pi} \ cos (NX) \ cos (NX) \, dx = \ pi& lt/math & gt；;
Odd and even functions
Odd number function < math > f _ o (x) <; /math & gt； It can be expressed as a sine series or even a function.
& lt Mathematics & GTF _ o (x) = \ sum _ {-\ infty} {+\ infty} b _ k \ sin (kx); & lt/math & gt；
& lt Mathematics & GTF _ e (x) = \ frac+\ sum _ {-\ infty} a _ k \ cos (kx); & lt/math & gt； Just pay attention to Euler's formula:
Generalized Fourier series
Any orthogonal function system
& lt Mathematics & gt \ int _ f 2 (x) \, dx = \ sum _ {k =1} {\ infty} c _ < /math & gt； (4),
Then the series.
& lt Mathematics & GTC _ n = \ int _ f (x) \ phi _ n (x) \, dx < /math & gt； (6)。
In fact, whether (5) converges or not, we always have:
& lt Mathematics & gt \ int _ f 2 (x) \, dx \ ge \ sum _ {k =1} {\ infty} c _ < /math & gt； This is the so-called Bessel inequality. In addition, formula (6) can be easily deduced from orthogonality, because for any unit orthogonal basis,