1、电气专业本科毕业设计英文翻译学院(部) ： 电气与信息工程学院专业班级： 电气 09-6 班 学生姓名： 李 鼎 指导教师： 李红月副教授 年 月 日POWER FACTORThe power factor of an AC electric power system is defined as the ratio of the real power flowing to the load to the apparent power in the circuit, and is a dimensionless number between 0 and 1 (frequently express
2、ed as a percentage, e.g. 0.5 pf = 50% pf). Real power is the capacity of the circuit for performing work in a particular time. Apparent power is the product of the current and voltage of the circuit. Due to energy stored in the load and returned to the source, or due to a non-linear load that distor
3、ts the wave shape of the current drawn from the source, the apparent power will be greater than the real power. In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents inc
4、rease the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.Linear loads with
5、 low power factor (such as induction motors) can be corrected with a passive network of capacitors or inductors. Non-linear loads, such as rectifiers, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and rais
6、e the power factor. The devices for correction of the power factor may be at a central substation, spread out over a distribution system, or built into power-consuming equipment.Power factor in linear circuits .Instantaneous and average power calculated from AC voltage and current with a unity power
7、 factor (=0, cos=1). Since the blue line is above the axis, all power is real power consumed by the load. Instantaneous and average power calculated from AC voltage and current with a zero power factor (=90, cos=0). The blue line shows all the power is stored temporarily in the load during the first
8、 quarter cycle and returned to the grid during the second quarter cycle, so no real power is consumed.Instantaneous and average power calculated from AC voltage and current with a lagging power factor (=45, cos=0.71). The blue line shows some of the power is returned to the grid during the part of t
9、he cycle labelled .In a purely resistive AC circuit, voltage and current waveforms are in step (or in phase), changing polarity at the same instant in each cycle. All the power entering the loads is consumed. Where reactive loads are present, such as with capacitors or inductors, energy storage in t
10、he loads result in a time difference between the current and voltage waveforms. During each cycle of the AC voltage, extra energy, in addition to any energy consumed in the load, is temporarily stored in the load in electric or magnetic fields, and then returned to the power grid a fraction of a sec
11、ond later in the cycle. The “ebb and flow“ of this nonproductive power increases the current in the line. Thus, a circuit with a low power factor will use higher currents to transfer a given quantity of real power than a circuit with a high power factor. A linear load does not change the shape of th
12、e waveform of the current, but may change the relative timing (phase) between voltage and current. Circuits containing purely resistive heating elements (filament lamps, strip heaters, cooking stoves, etc.) have a power factor of 1.0. Circuits containing inductive or capacitive elements (electric mo
13、tors, solenoid valves, lamp ballasts, and others ) often have a power factor below 1.0.Definition and calculation AC power flow has the three components: real power (also known as active power) (P), measured in watts (W); apparent power (S), measured in volt-amperes (VA); and reactive power (Q), mea
14、sured in reactive volt-amperes (var).The power factor is defined asIn the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle such that: If is the phase angle between the current and voltage, then the power factor is equal to the cosine of the
15、angle, , and: Since the units are consistent, the power factor is by definition a dimensionless number between 0 and 1. When power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns to the source on each cycle. When the power factor is 1, all the energy
16、 supplied by the source is consumed by the load. Power factors are usually stated as “leading“ or “lagging“ to show the sign of the phase angle. If a purely resistive load is connected to a power supply, current and voltage will change polarity in step, the power factor will be unity (1), and the el
17、ectrical energy flows in a single direction across the network in each cycle. Inductive loads such as transformers and motors (any type of wound coil) consume reactive power with current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cable generate reactive power wi
18、th current phase leading the voltage. Both types of loads will absorb energy during part of the AC cycle, which is stored in the devices magnetic or electric field, only to return this energy back to the source during the rest of the cycle. For example, to get 1 kW of real power, if the power factor
19、 is unity, 1 kVA of apparent power needs to be transferred (1 kW 1 = 1 kVA). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor, 5 kVA of apparent power needs to be transferred (1 kW 0.2 = 5 kVA). This
20、apparent power must be produced and transmitted to the load in the conventional fashion, and is subject to the usual distributed losses in the production and transmission processes. Electrical loads consuming alternating current power consume both real power and reactive power. The vector sum of rea
21、l and reactive power is the apparent power. The presence of reactive power causes the real power to be less than the apparent power, and so, the electric load has a power factor of less than 1.Power factor correction of linear loadsIt is often desirable to adjust the power factor of a system to near
22、 1.0. This power factor correction (PFC) is achieved by switching in or out banks of inductors or capacitors. For example the inductive effect of motor loads may be offset by locally connected capacitors. When reactive elements supply or absorb reactive power near the load, the apparent power is red
23、uced.Power factor correction may be applied by an electrical power transmission utility to improve the stability and efficiency of the transmission network. Correction equipment may be installed by individual electrical customers to reduce the costs charged to them by their electricity supplier. A h
24、igh power factor is generally desirable in a transmission system to reduce transmission losses and improve voltage regulation at the load.Power factor correction brings the power factor of an AC power circuit closer to 1 by supplying reactive power of opposite sign, adding capacitors or inductors wh
25、ich act to cancel the inductive or capacitive effects of the load, respectively. For example, the inductive effect of motor loads may be offset by locally connected capacitors. If a load had a capacitive value, inductors (also known as reactors in this context) are connected to correct the power fac
26、tor. In the electricity industry, inductors are said to consume reactive power and capacitors are said to supply it, even though the reactive power is actually just moving back and forth on each AC cycle.The reactive elements can create voltage fluctuations and harmonic noise when switched on or off
27、. They will supply or sink reactive power regardless of whether there is a corresponding load operating nearby, increasing the systems no-load losses. In a worst case, reactive elements can interact with the system and with each other to create resonant conditions, resulting in system instability an
28、d severe overvoltage fluctuations. As such, reactive elements cannot simply be applied at will, and power factor correction is normally subject to engineering analysis.An automatic power factor correction unit is used to improve power factor. A power factor correction unit usually consists of a numb
29、er of capacitors that are switched by means of contactors. These contactors are controlled by a regulator that measures power factor in an electrical network. To be able to measure power factor, the regulator uses a current transformer to measure the current in one phase.Depending on the load and po
30、wer factor of the network, the power factor controller will switch the necessary blocks of capacitors in steps to make sure the power factor stays above a selected value (usually demanded by the energy supplier), say 0.9. Instead of using a set of switched capacitors, an unloaded synchronous motor c
31、an supply reactive power. The reactive power drawn by the synchronous motor is a function of its field excitation. This is referred to as a synchronous condenser. It is started and connected to the electrical network. It operates at a leading power factor and puts vars onto the network as required t
32、o support a systems voltage or to maintain the system power factor at a specified level. The condensers installation and operation are identical to large electric motors. Its principal advantage is the ease with which the amount of correction can be adjusted; it behaves like an electrically variable
33、 capacitor. Unlike capacitors, the amount of reactive power supplied is proportional to voltage, not the square of voltage; this improves voltage stability on large networks. Synchronous condensors are often used in connection with high voltage direct current transmission projects or in large indust
34、rial plants such as steel mills.Non-sinusoidal components Non-linear loads change the shape of the current waveform from a sine wave to some other form. Non-linear loads create harmonic currents in addition to the original (fundamental frequency) AC current. Filters consisting of linear capacitors a
35、nd inductors can prevent harmonic currents from entering the supplying system.In linear circuits having only sinusoidal currents and voltages of one frequency, the power factor arises only from the difference in phase between the current and voltage. This is “displacement power factor“. The concept
36、can be generalized to a total, distortion, or true power factor where the apparent power includes all harmonic components. This is of importance in practical power systems which contain non-linear loads such as rectifiers, some forms of electric lighting, electric arc furnaces, welding equipment, sw
37、itched-mode power supplies and other devices.A typical multimeter will give incorrect results when attempting to measure the AC current drawn by a non-sinusoidal load; the instruments sense the average value of a rectified waveform. The average response is then calibrated to the effective, RMS value
38、. An RMS sensing multimeter must be used to measure the actual RMS currents and voltages (and therefore apparent power). To measure the real power or reactive power, a wattmeter designed to work properly with non-sinusoidal currents must be used.Measuring power factorPower factor in a single-phase c
39、ircuit (or balanced three-phase circuit) can be measured with the wattmeter-ammeter-voltmeter method, where the power in watts is divided by the product of measured voltage and current. The power factor of a balanced polyphase circuit is the same as that of any phase. The power factor of an unbalanc
40、ed polyphase circuit is not uniquely defined. A direct reading power factor meter can be made with a moving coil meter of the electrodynamic type, carrying two perpendicular coils on the moving part of the instrument. The field of the instrument is energized by the circuit current flow. The two movi
41、ng coils, A and B, are connected in parallel with the circuit load. One coil, A, will be connected through a resistor and the second coil, B, through an inductor, so that the current in coil B is delayed with respect to current in A. At unity power factor, the current in A is in phase with the circu
42、it current, and coil A provides maximum torque, driving the instrument pointer toward the 1.0 mark on the scale. At zero power factor, the current in coil B is in phase with circuit current, and coil B provides torque to drive the pointer towards 0. At intermediate values of power factor, the torque
43、s provided by the two coils add and the pointer takes up intermediate positions.Another electromechanical instrument is the polarized-vane type. In this instrument a stationary field coil produces a rotating magnetic field, just like a polyphase motor. The field coils are connected either directly t
44、o polyphase voltage sources or to a phase-shifting reactor if a single-phase application. A second stationary field coil, perpendicular to the voltage coils, carries a current proportional to current in one phase of the circuit. The moving system of the instrument consists of two vanes which are mag
45、netized by the current coil. In operation the moving vanes take up a physical angle equivalent to the electrical angle between the voltage source and the current source. This type of instrument can be made to register for currents in both directions, giving a 4-quadrant display of power factor or ph
46、ase angle. Digital instruments can be made that either directly measure the time lag between voltage and current waveforms and so calculate the power factor, or by measuring both true and apparent power in the circuit and calculating the quotient. The first method is only accurate if voltage and cur
47、rent are sinusoidal; loads such as rectifiers distort the waveforms from the sinusoidal shape.功率因数流到负载的实际功率与电路中视在功率的比率被定义为交流电力系统的功率因数，并且经常表示为（0 和 1 之间的一个比例，例如 0.5 PF =50PF） 。有功功率是指在一个特定的时间内电路能够进行工作的能力。视在功率是电路中电流和电压的比值。由于它存储在负载中，并返回到电源，或由于它是从电源汲取的电流的波形失真的一个非线性负载的能量，因而会有更大的视在功率比的实际功率存在。在电力系统中，具有低功率因数负
48、载的电路与具有高功率因数的负载相同量的电路相比，有用功率会转移更多的电流。越大的电流增加的分布系统中的能量损失越大，并需要更大的导线和其它设备以达到要求。由于较大的设备和过多的能源会更加浪费成本，因此电力公司通常会收取较高的费用为工业或商业客户提供一个低功率因数。低功率因数（如感应电机）的线性负载可以被电容器或电感器的无源网络校正。非线性负载，如整流器，整流从系统中所汲取的电流。在这种情况下，主动或被动的，也可以使用功率因数校正抵消失真，以提高功率因数。设备的功率因数校正可在中央变电所，在一个分布系统，内置的功率消耗设备中校正。线性电路的功率因数线性电路的功率因数的瞬时和平均功率与单位功率因数
49、（= 0，因素cos= 1）是从交流电压和电流计算而来的。由于蓝线是上述的轴，所有的电源是真实的负载所消耗的功率。计算出的瞬时和平均的功率是从交流电压和电流具有零功率因数（= 90，因素 cos= 0）中得出的。蓝线显示了所有的电能暂时存储在第一季度的负载周期，并返回到电网在第二季度的周期，所以没有真正的功率消耗。对于计算瞬时功率和平均功率交流电压和电流的滞后功率因数（= 45，COS = 0.71） 。蓝线表示出了一些电源期间返回到电网标记 的周期的一部分，在纯电阻性的交流电路中，在步骤（或相位）的电压和电流波形的每个周期中的同一时刻改变极性。所有进入负载的功率被消耗。在电抗性负载中，如电容器或电感器，是能量存储在负载中的电流和电压波形之间的时间差的结果。在交流电压的每个周期期间，除了在负载消耗的任何能量，额外的能量被暂时存储在电场或磁场的载荷，然后返回到电力网循环中的一小部分的第二延缓。 “潮起潮落”并不在生产性功率增加的行列中。因此，将使用一个低功率因数的电路具有更高的电流传输比一个高功率因数的电路具有一个给定的数量的实际功率更有意义。线性负载不改变的电流的波形的形状，但有可能改变电压和电流之间的相对定时。纯电阻加热元件（白炽灯，热水器，厨灶，等）的电路的功率因数为 1.0。含有电感性或电容元件的电路（电动
