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

El problema de flujo de potencia calcula la magnitud del voltaje, el ángulo de fase y los flujos de potencia real y reactiva en un sistema de energía trifásico equilibrado de estado estacionario. Considere su diagrama unifilar que proporciona tres datos de entrada. Cada bus tiene cuatro variables: dos son datos de entrada y dos se calculan.
La energía entregada al bus se divide en términos de generador y carga. Los autobuses se dividen en tres tipos. Para cada tipo, ciertas variables se dan como entrada, mientras que otras se calculan mediante un programa de flujo de energía.
Las líneas de transmisión están representadas por circuitos pi equivalentes. Los datos de entrada incluyen la impedancia en serie, la admitancia de derivación, los buses conectados y la clasificación máxima de megavoltios-amperios.
Estos datos construyen la matriz de admitancia del bus, lo que conduce a la construcción de ecuaciones nodales para la red y la determinación de la potencia compleja entregada a cada bus.
Las soluciones de flujo de potencia de Gauss-Seidel utilizan estas ecuaciones nodales para calcular la potencia compleja entregada. Al tomar partes reales e imaginarias de la ecuación derivada, se forman ecuaciones de equilibrio de potencia para cada bus.
Las soluciones de flujo de potencia de Newton-Raphson utilizan estas ecuaciones de flujo de potencia no lineales, lo que ofrece más precisión y una convergencia más rápida.

el problema del flujo de potencia y su solución

El análisis de problemas de flujo de potencia es fundamental para determinar los flujos de potencia real y reactiva en los componentes de la red, como líneas de transmisión, transformadores y cargas. El diagrama unifilar del sistema de potencia proporciona datos sobre el bus, la línea de transmisión y el transformador. Cada bus k del sistema se caracteriza por cuatro variables clave: magnitud de tensión V_k, ángulo de fase δ_k, potencia real P_k y potencia reactiva Q_k. Dos de estas cuatro variables son entradas, mientras que el programa de flujo de potencia calcula las restantes. La potencia entregada al bus k se puede expresar en términos de componentes de generador y carga:

<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;">

En función de sus características operativas, los buses dentro del sistema de potencia se clasifican en tres tipos: bus oscilante, bus de carga (PQ) y bus controlado por tensión. El bus oscilante tiene una magnitud de tensión cercana a 1,0 por unidad y un ángulo de fase de cero grados. En el bus de carga (PQ), se especifican la potencia real y reactiva, mientras que la magnitud de la tensión y el ángulo de fase son desconocidos. Para un bus controlado por tensión, se dan la potencia real y la magnitud del voltaje.

Las ecuaciones actuales para una red se expresan en términos de matrices de admitancia:

<img alt="Equation3" src="/files/ftp_upload/16149/16149_PT_equation_3.svg" style="height: 13px;">

Donde I es el vector de corrientes de fuente inyectadas y V es el vector de tensión del bus. Para cada bus k, la corriente y la potencia compleja son:

<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;">

Los dos métodos iterativos principales para resolver el problema del flujo de potencia son Gauss-Seidel y Newton-Raphson. El método Gauss-Seidel resuelve iterativamente las ecuaciones nodales, recalculando la corriente para los buses de carga utilizando valores de potencia conocidos y ajustando la potencia reactiva para los buses controlados por tensión hasta la convergencia. El método Newton-Raphson linealiza las ecuaciones de flujo de potencia y utiliza la matriz jacobiana para las correcciones de tensión, generalmente convergiendo más rápido y siendo más adecuado para sistemas grandes. Estos métodos iterativos son fundamentales para garantizar que el sistema de potencia funcione dentro de sus parámetros especificados, manteniendo la estabilidad y la eficiencia en toda la red.

El problema del flujo de potencia y su solución

El problema de flujo de potencia calcula la magnitud de voltaje, el ángulo de fase y los flujos de potencia real y reactiva en un flujo de potencia trifásico ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Steady-State Transmission Lines and Power Flows

Líneas de transmisión en estado estacionario y flujos de potencia

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

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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