Name: power flow analysis in electric networks
Uploaded: 2024-11-21T14:54:26.000Z
Duration: 1 min 26 s
Channel: JoVE

전력 흐름 문제는 균형 잡힌 3상 정상 상태 전력 시스템에서 전압 크기, 위상 각도, 실제 및 무효 전력 흐름을 계산합니다. 세 개의 입력 데이터를 제공하는 단일 선 다이어그램을 고려하십시오. 각 버스에는 4개의 변수가 있는데, 2개는 입력 데이터이고 2개는 계산된 데이터입니다.
버스에 공급되는 전력은 발전기 및 부하 조건으로 분할됩니다. 버스는 세 가지 유형으로 나뉩니다. 각 유형에 대해 특정 변수는 입력으로 제공되고 다른 변수는 전력 흐름 프로그램에 의해 계산됩니다.
전송 라인은 등가 파이 회로로 표시됩니다. 입력 데이터에는 직렬 임피던스, 션트 어드미턴스, 커넥티드 버스 및 최대 메가볼트-암페어 정격이 포함됩니다.
이 데이터는 버스 어드미턴스 매트릭스를 구성하여 네트워크에 대한 노드 방정식을 구성하고 각 버스에 전달되는 복잡한 전력을 결정할 수 있도록 합니다.
Gauss-Seidel 전력 흐름 솔루션은 이러한 노드 방정식을 사용하여 제공되는 복잡한 전력을 계산합니다. 파생된 방정식의 실수 부분과 허수 부분을 취하여 각 버스에 대한 전력 균형 방정식이 형성됩니다.
Newton-Raphson 전력 흐름 솔루션은 이러한 비선형 전력 흐름 방정식을 사용하여 더 높은 정확도와 더 빠른 수렴을 제공합니다.

전력 흐름 문제와 해결책

전력 흐름 문제 분석은 송전선, 변압기, 부하와 같은 네트워크 구성 요소에서 실제 및 무효 전력 흐름을 결정하는 데 기본이 됩니다. 전력 시스템의 단선 다이어그램은 버스, 송전선, 변압기에 대한 데이터를 제공합니다. 시스템의 각 버스 k는 전압 크기 V_k​, 위상 각도 δ_k​, 실제 전력 P_k, 무효 전력 Q_k​의 네 가지 주요 변수로 특징지어집니다. 이 네 가지 변수 중 두 가지는 입력이고 전력 흐름 프로그램은 나머지를 계산합니다. 버스 k에 전달되는 전력은 발전기 및 부하 구성 요소로 표현할 수 있습니다.

<img alt="Equation1" src="/files/ftp_upload/16149/16149_PT_equation_1.svg" style="height: 14px;">
<img alt="Equation2" src="/files/ftp_upload/16149/16149_PT_equation_2.svg" style="height: 14px;">

전력 시스템 내의 버스는 운영 특성에 따라 스윙 버스, 부하(PQ) 버스, 전압 제어 버스의 세 가지 유형으로 분류됩니다. 스윙 버스는 단위당 1.0에 가까운 전압 크기와 0도의 위상각을 갖습니다. 부하(PQ) 버스에서는 유효 전력과 무효 전력이 지정되지만 전압 크기와 위상각은 알 수 없습니다. 전압 제어 버스의 경우 유효 전력과 전압 크기가 제공됩니다.

네트워크에 대한 현재 방정식은 어드미턴스 행렬을 기준으로 표현됩니다.

<img alt="Equation3" src="/files/ftp_upload/16149/16149_PT_equation_3.svg" style="height: 13px;">

여기서 I는 주입된 소스 전류의 벡터이고, V는 버스 전압의 벡터입니다. 각 버스 k에 대해 전류와 복소 전력은 다음과 같습니다.

<img alt="Equation4" src="/files/ftp_upload/16149/16149_PT_equation_4.svg" style="height: 28px;">
<img alt="Equation5" src="/files/ftp_upload/16149/16149_PT_equation_5.svg" style="height: 16px;">

전력 흐름 문제를 해결하는 두 가지 주요 반복적 방법은 Gauss-Seidel과 Newton-Raphson입니다. Gauss-Seidel 방법은 노드 방정식을 반복적으로 풀고, 알려진 전력 값을 사용하여 부하 버스의 전류를 재계산하고, 전압 제어 버스의 무효 전력을 수렴할 때까지 조정합니다. Newton-Raphson 방법은 전력 흐름 방정식을 선형화하고 전압 보정을 위해 Jacobian 행렬을 사용하여 일반적으로 더 빠르고 대규모 시스템에 더 적합하게 수렴합니다. 이러한 반복적 방법은 전력 시스템이 지정된 매개변수 내에서 작동하고 네트워크 전체에서 안정성과 효율성을 유지하는 데 기본이 됩니다.

전력 흐름 문제는 전압 크기, 위상 각도, 실제 및 무효 전력 흐름을 균형 잡힌 3상 정상 상태 전력 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Steady-State Transmission Lines and Power Flows

정상 상태 송전선로 및 전력 조류

steady-state-transmission-lines-and-power-flows

KEY TERMS AND CONCEPTS

주요 용어 및 개념

The Power Flow Problem and Solution

power flow analysis in electric networks

Power flow analysis helps determine how real and reactive power move through an electric network. It uses the system’s single-line diagram, which shows the buses, transmission lines, transformers, and loads. The analysis focuses on balanced three-phase steady-state operation.

Each bus in the system has four key variables: voltage magnitude V k, phase angle δ k, real power P k, and reactive power Q k. Two of these four variables are treated as inputs. The power flow program solves for the remaining values.

Buses are grouped by operating role. A swing bus usually has a voltage magnitude close to 1.0 per unit and a phase angle of zero degrees. A load or PQ bus has specified real and reactive power, while its voltage magnitude and phase angle are unknown. A voltage-controlled bus has given real power and voltage magnitude.

The network equations are written with an admittance matrix, where I is the vector of injected source currents and V is the vector of bus voltages. For each bus k, current and complex power are related through these equations. The power flow problem is then solved with iterative methods.

Two main methods are used: Gauss-Seidel and Newton-Raphson. Gauss-Seidel repeatedly solves the nodal equations, updates current for load buses from known power values, and adjusts reactive power for voltage-controlled buses until the results converge. Newton-Raphson linearizes the power flow equations and uses the Jacobian matrix to correct voltages, so it usually converges faster and is better for large systems. These methods help keep the power system within its specified limits and support stable, efficient network operation.

Power Flow Analysis in Electric Networks

transmission-line differential equations

Modeling Voltage and Current on Transmission Lines

Transmission lines carry electric power, and their resistance, inductance, and capacitance are spread out along the line. Because these properties are distributed per unit length, voltage and current change as they move from one end of the line to the other. Differential equations are used to describe that variation. A line-section model helps show how this works. In the model, a small length, Δx, is used to represent the line. Voltage V(x) and current i(x) are measured from the receiving end.

lossless lines

Lossless Lines and Voltage Behavior

Lossless transmission lines in electrical engineering are described by a purely imaginary propagation constant and a resistive characteristic impedance. Their ABCD parameters show an equivalent pi circuit with an imaginary series impedance and a shunt admittance. When the product of beta and line length is less than pi, the line has inductive series impedance and capacitive shunt admittance, which keeps it lossless. Wavelength is the physical length over which voltage or current phase changes...

maximum power flow and line loadability

Transmission Line Power Limits and Loadability

Transmission line power limits and loadability depend on voltage, angle, and line impedance. For lossy transmission lines, ABCD parameters in phasor form are used to relate sending-end and receiving-end voltages and currents. This matrix relation makes it possible to find the receiving-end current and then calculate the complex power delivered to the load. From the complex power, the real and reactive power components can be determined. For a lossless line, the equations become simpler, and...

the power flow problem and solution

Power flow analysis helps determine how real and reactive power move through an electric network. It uses the system’s single-line diagram, which shows the buses, transmission lines, transformers, and loads. The analysis focuses on balanced three-phase steady-state operation. Each bus in the system has four key variables: voltage magnitude V k, phase angle δ k, real power P k, and reactive power Q k. Two of these four variables are treated as inputs. The power flow program solves for the...

control of power flow

Voltage and Reactive Power Control

Voltage and reactive power control help keep a power system stable and efficient. In this topic, generator settings, switched equipment, and transformer taps work together to guide how power moves through the network. A generator can be modeled with a Thevenin equivalent circuit under balanced steady-state conditions. The main terms are terminal voltage Vt, excitation voltage Eg, power angle δ, and positive-sequence synchronous reactance Xg. From this model, the generator current and the...

fast decoupled and dc powerflow

Power Flow Shortcuts for Grid Contingencies

Fast decoupled power flow and DC power flow give engineers faster ways to study a power system during contingencies such as generator outages or transmission line failures. These methods help operators get quick power flow solutions, which is important for real-time system adjustments. Fast decoupled power flow simplifies the Jacobian matrix, the set of equations used in power flow calculations, by neglecting some elements. The method drops J2 and J3 and assumes voltage magnitudes stay close...

key terms and concepts

Learn how power flow analysis tracks voltage, real power, and reactive power in electric networks using bus types, admittance matrices, and iterative methods.

Power Flow Analysis in Electric Networks | 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

Power Flow Analysis in Electric Networks

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