Name: balanced three-phase power calculation
Uploaded: 2024-07-08T13:19:58.000Z
Duration: 1 min 15 s
Channel: JoVE

מפעל ייצור עם מספר מכונות כבדות דורש כוח משמעותי המסופק על ידי מערכת תלת פאזית מאוזנת.
כדי לקבוע את הכוח המיידי הנקלט על ידי עומס המפעל, הניתוח מתבצע על מעגל תחום זמן המחובר Y.
למתחי הפאזה יש הפרש פאזה של 120 מעלות והשורש הריבועי של שניים משמש להמרת מתחי שיא לערכי RMS לניתוח הספק מדויק.
כאשר מכונה פועלת, היא שואבת זרם מספק הכוח, מה שמוביל להשהיית פאזה בין זרמי הפאזה לבין מתחי הפאזה המתאימים להם.
ההספק המיידי הכולל הנמשך על ידי עומס המכונה מחושב על ידי סיכום ההספק המיידי בכל אחד משלושת השלבים.
הכוח המיידי הכולל המתקבל נשאר כמעט קבוע ואינו משתנה עם הזמן. זה מאפשר חישוב של כוח פעיל, תגובתי ונראה לעין לכל פאזה.
סך הכוח הפעיל הוא סכום הכוחות הפעילים בשלושה שלבים. באופן דומה, סך הכוח הריאקטיבי והמסתמן מחושב.
תוצאות אלה נכונות הן עבור עומסים המחוברים ל-Y והן לעומסים המחוברים לדלתא.

הספק במעגל תלת-פאזי

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למערכות תלת-פאזיות יש שתי תצורות: ה-wye (כוכב או Y) והדלתא (Δ או המשולש). תצורת כוכב יכולה להיות בעלת שלושה או ארבעה חוטים; בתצורת דלתא, הרכיבים מחוברים בלולאה סגורה. הספק רגעי מתייחס לערך ההספק ברגע נתון, ובמערכת תלת-פאזית מאוזנת, הוא קבוע. הסיבה לכך היא שסכום ההספקים הרגעיים בשלוש הפאזות נשאר יציב לאורך זמן, למרות תנודות בודדות, עקב הסימטריה ויחסי הפאזות. סך ההספק הרגעי במערכת תלת-פאזית מאוזנת הוא קבוע ואינו משתנה לאורך זמן.

הספק פעיל, ריאקטיבי ומרוכב:

ההספק הממוצע לפאזה הוא שליש מסך ההספק הממוצע במערכת תלת-פאזית מאוזנת. באופן דומה, ההספק הריאקטיבי לפאזה הוא שליש מסך ההספק הריאקטיבי במערכת. ההספק המרוכב, המשלב גם הספק פעיל וריאקטיבי לכל פאזה, הוא גם שליש מסך ההספק המרוכב.

שקילות בחישובי הספק:

לתצורות דלתא ו-Wye יש מתחים וזרמים בכל הפאזות והקווים. בתצורות אלה, העומסים מחוברים לכל פאזה בקצה העומס. ההספק הנצרך מהעומס והשוויון בין תצורות wye ודלתא משתרע לחישובי הספק. בין אם במערכת המחוברת ל-wye או במערכת המחוברת לדלתא, ההספק הכולל הוא סכום ההספק בכל אחד משלוש הפאזות. ניתן לחשב זאת באמצעות היחסים בין מתחי הקו והפאזה והזרמים. עבור מערכת המחוברת ב-wye ומערכת המחוברת בדלתא:

<img alt="Equation 1" src="/files/ftp_upload/15133/15133_Equation_1.svg" style="text-align: center; height: 16px;">

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מפעל ייצור עם מספר מכונות כבדות דורש כוח משמעותי המסופק על ידי מערכת תלת פאזית מאוזנת.
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Education

JoVE Core

Electrical Engineering

הנדסה חשמלית

Unit 1

יחידה 1

Three-Phase Circuits

מעגלי תלת-פאזה

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

Power in a Three-Phase Circuit

balanced three-phase power calculation

Balanced three-phase power calculation depends on the wye and delta connections used in the circuit. A wye, or star, configuration can use three wires or four wires. A delta configuration connects the components in a closed loop. These connection types change how voltages and currents are arranged, but both are used in three-phase systems.

In a balanced three-phase system, instantaneous power is the power at one exact moment. Even though the power in each phase changes over time, the total instantaneous power stays constant. The three phase powers add together in a steady way because the system is symmetric and the phases are shifted from one another.

The same one-third relationship applies to average power, reactive power, and complex power. The average power in each phase is one-third of the total average power. The reactive power per phase is also one-third of the total reactive power. Complex power, which combines active and reactive power for each phase, is likewise one-third of the total complex power.

These power rules apply to both wye-connected and delta-connected loads. In both configurations, the load is connected to each phase at the load end. The total power is the sum of the power in the three phases. It can be found by using the known relationships between line voltage, phase voltage, line current, and phase current in either a wye or delta system.

Balanced Three-Phase Power Calculation

three-phase circuits

How Three-Phase Power Delivers Electricity

Three-phase power is a major part of AC power distribution, especially where steady and efficient electricity delivery is needed. AC systems are grouped into single-phase, two-phase, and three-phase systems. These categories help describe how power moves from the source to the load. Single-phase circuits are common in homes. They usually use a two-wire system that connects one AC source to loads. These circuits can supply everyday appliances such as lamps, televisions, and microwaves at 120 V...

generation of three-phase voltage

Three-Phase AC Generator Windings

A three-phase AC generator uses rotating magnet windings and a stationary stator to make three-phase voltage. The rotor carries a magnet that spins inside the stator. The stator holds the three-phase winding, and mutual induction creates the voltage. The stator windings are spread evenly around the inside of the stator. They are placed 120 electrical degrees apart. These windings consist of three separate coils, or groups of coils, called phases. The phases can be connected in a Y, or star,...

three-phase voltages

Three-Phase Power Connections

Three-phase power connections use balanced voltages that are equal in magnitude and separated by 120 degrees. A three-phase generator produces these voltages, and the balance helps reduce power loss while keeping energy delivery steady to connected loads. Three-phase sources can be arranged in either wye or delta form. The loads connected to the system can also use wye or delta. This flexibility gives control over how the system is designed and managed. In a wye connection, one end of each...

the y-to-y circuit

Balanced Wye-to-Wye Neutral Current

A balanced wye-to-wye circuit uses three wye-connected sinusoidal voltage sources and three wye-connected loads. A neutral wire links the neutral node of the source to the neutral node of the load. The load impedance is connected across each phase of the load. The source and load can be connected in either a four-wire or a three-wire arrangement. A three-phase system is balanced when each phase has the same load. In that case, the current flow and phase angle are uniform across the system. If...

the y-to-delta circuit

Wye Source and Delta Load Currents

A balanced wye source and delta load form a common three-phase circuit with no neutral line connection. The source is Y-connected, and the load is delta-connected. To analyze the circuit, the first step is to assume a positive phase sequence. These phase voltages are then used to find the line voltages that appear across the delta load impedances. In the wye source, the phase voltages are V an, V bn, and V cn. In the delta load, the line voltages are V ab, V bc, and V ca. These line voltages...

the delta-to-delta circuit

Balanced Delta-Delta Power Circuit

A balanced delta-delta power circuit uses a delta-connected source and a delta-connected load. The two deltas form a closed loop that creates three separate phases. In this setup, the phase voltages are the same as the line voltages. If the source is in positive sequence, the phase voltages can be written directly, and no neutral wire is needed. The delta-connected load current is found by dividing the phase voltage by the impedance of each phase. For line current, Kirchhoff’s Current Law...

the delta-to-y circuit

Delta-Wye Source and Load Connections

A balanced delta-wye circuit connects a delta-connected source to a wye-connected load. In this setup, the phase voltage of the delta source equals the line voltage of the wye load. The source also sets the line currents that flow into the load. For a balanced system, the phase difference between currents makes it possible to find one line current from the other by using the positive sequence of phases. In the wye-connected load, each phase current equals the line current from the delta source.

power in a three-phase circuit

Balanced three-phase power calculation depends on the wye and delta connections used in the circuit. A wye, or star, configuration can use three wires or four wires. A delta configuration connects the components in a closed loop. These connection types change how voltages and currents are arranged, but both are used in three-phase systems. In a balanced three-phase system, instantaneous power is the power at one exact moment. Even though the power in each phase changes over time, the total...

power distribution in three-phase and single phase circuits

power-distribution-in-three-phase-and-single-phase-circuits

Single-Phase vs. Three-Phase Power Loss

Single-phase and three-phase circuits distribute electrical power in different ways. Single-phase power is common in homes, while balanced three-phase power is widely used in industrial settings with heavy machinery. Both systems deliver energy, but their current flow and wire needs are not the same. A single-phase circuit usually uses a two-wire system. The current depends on the power absorbed by the load and the line voltage. Because wire loss from resistance follows the square of the...

line loss

Reducing Power Loss in Three-Phase Lines

Three-phase power lines can lose energy as electricity travels from the source to the load. This line loss affects how efficiently power reaches the load. In balanced three-phase circuits, the symmetry makes the analysis easier because one phase can represent the whole system. The source-load connection can use wye, also called star, or delta configurations. These setups change the relationship between line voltage, phase voltage, line current, and phase current. A per-phase equivalent circuit...

reducing line loss

Cutting Heat Loss in Three-Phase Lines

Three-phase power systems can lose energy as heat in transmission lines because the wires have resistance. This line loss becomes important when electricity travels over a distance. A common solution is to use transformers to change the voltage and current in the system. The setup uses two three-phase transformers. A step-up transformer is placed at the source, and a step-down transformer is placed at the load. Raising the voltage at the source lowers the current in the transmission lines, and...

key terms and concepts

Learn how balanced three-phase systems handle instantaneous, active, reactive, and complex power in wye and delta connections for high school physics.

Balanced Three-Phase Power Calculation | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Balanced Three-Phase Power Calculation

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