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Three-Phase Circuits 三相电路
中文部分三相电源三相电路单相交流电动势的产生三相电源
三相电路的基本概念三相电路对称三相电路相的概念相线电压电流
对称三相电路的线相关系星形联接(Y联接)线相电流关系(相同)线相电压关系(线=√3 超前30°)
三角形连接线相电压关系(相同)线相电流关系(线=√3 滞后30°)
对称Y-Y三相电路的计算非Y -Y对称三相电路的计算三相电路应用举例:简单照明系统及其故障分析三相电路的功率一般三相电路的功率对称三相电路的功率
三相电路的功率测量三表法(对称,非对称)
一表法(对称)二表法(对称,不对称)
12.1Introduction12.2 Balanced Three-Phase VoltagesThe generator connectionsThe three-phase load and connectionsThe relationship between line voltages and phase voltagesThe relationship between line currents and phase currents
12.3 Balanced Wye-Wye Connection12.4 Balanced Wye-Delta Connection12.5 Balanced Delta-Delta Connection12.6 Balanced Delta-Wye Connection12.7 Power in a Balanced SystemThe instantaneous power(瞬时功率)The average power(平均功率)The reactive power(无功功率)The apparent power(视在功率) and The complex power(复功率)Three-wattmeter method(三表法)Two-wattmeter method(两表法,与连接方式无关,)
12.8 Unbalanced Three-Phase Systems相序的判断
中文部分
三相电源
三相电路
由三相电源、三相负载和三相传输线路组成的电路 是一类特殊的正弦稳态电路 应用:发电、输电、配电,以及大功率用电设备等电力系统 目前电力系统采用的主要供电方式 三相电路的优点: 1) 发电:比单相电源可提高功率50% 2) 输电:比单相输电节省钢材25% 3) 配电:三相变压器比单相变压器经济且便于接入负载 4) 用电设备:具有结构简单、成本低、运行可靠、维护方便等优点 单相交流电动势的产生
![]() ![]() ![]() ![]() ![]() 对称三相电源和三相负载联接起来组成的系统 当电源和负载都对称时,称对称三相电路 三个绕组均产生电动势,对应三电源 相电压:每相电源(负载)的电压 线电压:端线与端线之间的电压
我国供电系统提供三相对称电源采用三相四线制,相电压为220V,线电压为380V,负载接入原则: 1) 电源提供的电压=负载的额定电压 2) 单相负载尽量均衡地分配到三相电源上 三相电动机绕组:可以星形,也可以三角形 照明负载:一般都是星形(具有中性线) 三相负载的联接原则 每相负载上的电压=其额定电压 负载的额定电压 = 电源的线电压 Δ联结 负载的额定电压 = 1 3 \frac{1}{\sqrt {3}} 3 1电源线电压 Y 联结
用单相等效电路求解: 1)对三角形连接的对称三相电源: 按线相电压关系进行等效:设三相电 源用Y接电源替代,保证其线电压不变 2)对三角形连接的对称三相负载 Z Y = 1 3 Z Δ Z_Y=\frac{1}{3}Z_Δ ZY=31ZΔ 对电源:将电源用Y接电源替代,保证线电压不变 对称三相电源线电压为U,负载和线路阻抗分别为Z和 Zl![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 一般对称三相电路的计算 1) 将三相电源、负载都等效看成Y联接; 2) 画出单相等效电路,求出一相的电压、电流; 3) 求解单相等效电路,根据线(相)电压及线(相)电流的关系,求出原电路的电流、电压;(要回到原电路) 4) 由对称性,写出其它两相的电压、电流。 三相电路应用举例:简单照明系统及其故障分析
简
单
照
明
系
统
的
线
电
压
为
380
V
,
若
灯
泡
R
A
=
R
B
=
R
C
=
5
Ω
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1
)
求
线
电
流
及
中
性
线
电
流
I
N
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2
)
R
A
=
5
Ω
,
R
B
=
10
Ω
,
R
C
=
20
Ω
,
求
线
电
流
及
I
N
(
3
)
A
相
短
路
,
中
性
线
断
开
(
未
断
)
时
,
求
负
载
相
电
压
(
4
)
A
相
断
路
,
中
性
线
断
开
(
未
断
)
时
,
求
负
载
相
电
压
简单照明系统的线电压为380V,若灯泡R_A=R_B= R_C = 5Ω\\ (1)求线电流及中性线电流I_N\\ (2)R_A=5Ω,R_B=10Ω,RC=20Ω,求线电流及I_N\\ (3)A相短路,中性线断开(未断)时,求负载相电压\\ (4)A相断路,中性线断开(未断)时,求负载相电压
简单照明系统的线电压为380V,若灯泡RA=RB=RC=5Ω(1)求线电流及中性线电流IN(2)RA=5Ω,RB=10Ω,RC=20Ω,求线电流及IN(3)A相短路,中性线断开(未断)时,求负载相电压(4)A相断路,中性线断开(未断)时,求负载相电压 结论 1)若负载不对称且没有中线,负载的相电压就不对称当超过用电设备的额定电压时,可能烧损或减少使用寿命;而当达不到其额定电压不能正常工作 2)中线的作用:保证Y形不对称负载的相电压对称 为保证这种对称性,中线绝对不允许断开。因此,三相电源的中线内不接入熔断器或闸刀开关 三相电路的功率 一般三相电路的功率三相瞬时功率=各相瞬时功率之和 p = p A + p B + p C p=p_A+p_B+p_C p=pA+pB+pC 三相平均功率=各相平均功率之和 P = P A + P B + P C P=P_A+P_B+P_C P=PA+PB+PC 三相无功功率=各相无功功率之和 Q = Q A + Q B + Q C Q=Q_A+Q_B+Q_C Q=QA+QB+QC 三相视在(表观)功率 S = P ² + Q ² S=\sqrt {P²+Q²} S=P²+Q² 对称三相电路的功率三相瞬时功率=各相瞬时功率之和 p = p A + p B + p C = 3 p A p=p_A+p_B+p_C=3p_A p=pA+pB+pC=3pA 三相平均功率=各相平均功率之和 P = P A + P B + P C = 3 P A P=P_A+P_B+P_C=3P_A P=PA+PB+PC=3PA 三相无功功率=各相无功功率之和 Q = Q A + Q B + Q C = 3 Q A Q=Q_A+Q_B+Q_C=3Q_A Q=QA+QB+QC=3QA 三相视在(表观)功率 S = P ² + Q ² = 3 S A S=\sqrt {P²+Q²}=3S_A S=P²+Q² =3SA 1) 对称三相电路瞬时功率的特点
p
=
p
A
+
p
B
+
p
C
=
3
U
I
c
o
s
φ
p=p_A+p_B+p_C=3UIcosφ
p=pA+pB+pC=3UIcosφ 2) 对称三相电路平均功率的特点
P
=
3
P
A
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3
U
p
I
p
c
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s
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P =3P_A = 3U_p I_pcosφ
P=3PA=3UpIpcosφ 工程应用2 电机星三降压启动 电机启动时定子绕组接成Y:降低启动电压,限制启动电流 启动后接成三角形,使电机全压运行 接成Y,加载绕组上的启动电压为三角形直接启动的 1 3 \frac{1}{\sqrt {3}} 3 1 启动电流为三角形直接启动的1/3,转矩也是直接启动的1/3 三相电路的功率测量 三表法(对称,非对称)
A single-phase ac power system consists of a generator connected through a pair of wires(a transmission line)to a load. What is more common in practice is a single-phase three-wire system.It contains two identical sources(equal magnitude(量级) and the same phase)that are connected to two loads by two outer wires and the neutral. The normal household system is a single-phase three-wire system because the terminal voltages have the same magnitude and the same phase. Circuits or systems in which the ac sources operate at the same frequency but different phases areknown as polyphase(多相的). The three-phase system is by far the most prevalent and most economical polyphase system. ➢Nearly all electric power is generated anddistributed in three-phase. ➢The instantaneous power in a three-phase system can be constant(not pulsating). ➢For the same amount of power,the three-phasesystem is more economical than the single-phase. 12.2 Balanced Three-Phase VoltagesA typical three-phase system consists of three voltage sources connected to loads by three or four wires(or transmission lines). Three-phase voltages are often produced with a three-phase ac generator(or alternator). A three-phase generator
A balanced load is one in which the phase impedances are equal in magnitude and in phase. A three-phase load is said to beunbalanced if the phase impedances are not equal in magnitude or phase. The three-phase load and connections
A typical three-phase system consists of three-phase voltage sources connected to three-phase loads by transmission lines. Fourpossible connections: ➢Y-Y(Y-connected source with a Y-connected load). ➢Y-Δ. ➢Δ-Y. ➢Δ-Δ. Balancedthree-phase system:Sources and loads are both balanced.
A balanced Δ-Δ system is one in which boththe balanced source and balanced load are Δ-connected. Convert both the source and the load to their Y equivalents. 12.6 Balanced Delta-Wye ConnectionA balanced Δ-Y system consists of a balanced Δ-connected source feeding a balanced Y-connected load.Replace the delta-connected source with its equivalent wye-connected source.
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P=P_1+P_2=U_{AC}I_Acosφ_1+U_{BC}I_Bcosφ_2=P_A+P_B+P_C
P=P1+P2=UACIAcosφ1+UBCIBcosφ2=PA+PB+PC
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