Name: power-system stability in multi-machine networks
Uploaded: 2024-11-21T14:54:38.000Z
Duration: 1 min 25 s
Channel: JoVE

Em um sistema de energia N-bus com máquinas síncronas M, as cargas são modeladas como admitâncias constantes e as equações nodais da rede são formuladas.
A matriz de admitância é particionada para incluir admitâncias de carga e impedâncias de gerador invertidas.
Com tensões de máquina conhecidas, a equação de tensão do barramento é resolvida para encontrar as correntes da máquina e a energia elétrica.
A análise de estabilidade transitória requer a resolução de equações de oscilação para máquinas e equações de fluxo de potência para a rede.
Primeiro, execute um programa de fluxo de energia pré-falta para determinar as tensões iniciais do barramento, as correntes da máquina e as saídas elétricas.
Defina as saídas de energia mecânica iguais às saídas elétricas e inicialize a frequência para a frequência angular síncrona.
Em seguida, calcule as admitâncias de carga, as tensões internas da máquina e a matriz de admitância do barramento de fluxo de potência.
Ajuste a matriz de admitância para eventos como operações de comutação, alterações de carga ou falhas.
Em cada passo t mais delta t, calcule a potência elétrica da máquina, os ângulos de potência e as velocidades.
Repita esse processo até que o horizonte de tempo desejado seja alcançado, garantindo que o tamanho da etapa equilibre a precisão da solução e o tempo de computação.

estabilidade transitória e controles do sistema

A análise de estabilidade multimáquina é crucial para entender a dinâmica e a estabilidade de sistemas de energia com várias máquinas síncronas. O objetivo é resolver as equações de oscilação para uma rede de máquinas M conectadas a um sistema de energia de barramento N.

Ao analisar o sistema, as equações nodais representam a relação entre tensões de barramento, tensões de máquina e correntes de máquina. A equação nodal é dada por:

<img alt="Equation1" src="/files/ftp_upload/16170/16170_PT_Equation_1.svg" style="height: 44px;">

V é o vetor N de tensões de barramento, E é o vetor M de tensões de máquina, I é o vetor M de correntes de máquina. Y_11, Y_12, Y_21 e Y_22 são matrizes de admitância N×N, N×M, M×N e M×M, respectivamente. As equações podem ser desacopladas como:

<img alt="Equation2" src="/files/ftp_upload/16170/16170_PT_Equation_2.svg" style="height: 28px;">

Assumindo que E é conhecido, a primeira equação pode ser resolvida iterativamente para V usando métodos como eliminação de Gauss ou Gauss-Seidel. Uma vez que V é calculado, I pode ser obtido a partir da segunda equação.

A potência elétrica real de saída da máquina n é:

<img alt="Equation3" src="/files/ftp_upload/16170/16170_PT_Equation_3.svg" style="height: 16px;">

O procedimento de cálculo da estabilidade transitória envolve a resolução iterativa das equações de oscilação e das equações de fluxo de potência:

<ul style="padding-left: 35px; list-style-type: disc;">
	<li>Determine as tensões iniciais do barramento V_k, as correntes da máquina I_n e as saídas de potência pan.</li>
	<li>Calcule E_n.</li>
	<li>Modifique Y_11 e calcule Y_22 e Y_12.</li>
	<li>Inicialize t=0.</li>
	<li>Determine se há alguma operação de comutação ou alterações de carga.</li>
	<li>Calcule as potências elétricas da máquina no tempo t.</li>
	<li>Use estimativas iniciais para calcular ângulos de potência δ e velocidades de máquina ω no tempo t+Δt.</li>
	<li>Refine as estimativas de potências elétricas no tempo t+Δt.</li>
	<li>Finalize ângulos de potência δ e velocidades de máquina ω no tempo t+Δt.</li>
	<li>Incremente o tempo e repita as etapas até o final da simulação.</li>
	<li>A seleção precisa do tempo é crucial para evitar instabilidades na integração numérica.</li>
</ul>

Seguindo essas etapas e usando as equações fornecidas, os engenheiros podem analisar a estabilidade transitória de sistemas de energia multimáquina e garantir uma operação confiável sob várias condições.

Estabilidade transitória e controles do sistema

Em um sistema de energia N-bus com máquinas síncronas M, as cargas são modeladas como admitâncias constantes e as equações nodais da rede são formuladas.
O...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Transient Stability and System Controls

Estabilidade Transitória e Controles do Sistema

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Multimachine Stability

power-system stability in multi-machine networks

Power-system stability in multi-machine networks focuses on how several synchronous machines behave as they stay connected to an N-bus power system. The analysis solves the swing equations for the machines and tracks how the network responds when conditions change. It is used to study transient stability, which is the system’s ability to stay in step after a disturbance.

The network is written with nodal equations that link bus voltages, machine voltages, and machine currents. In this model, V is the N-vector of bus voltages, E is the M-vector of machine voltages, and I is the M-vector of machine currents. The admittance matrices Y11, Y12, Y21, and Y22 describe the connections between buses and machines.

These equations can be separated into two parts. If E is known, the first equation can be solved iteratively for V using Gauss elimination or Gauss-Seidel methods. After V is found, I can be calculated from the second equation. The real electrical power output of machine n is then determined from these values.

Transient stability is computed by stepping through time and solving the swing equations together with the power flow equations. The procedure starts with initial bus voltages Vk, machine currents In, and power outputs pan. Next, En is computed, Y11 is modified, and Y22 and Y12 are calculated. Time begins at t = 0, and the model checks for switching operations or load changes.

At each time step, the machine electrical powers are calculated at time t. Initial estimates are then used to find the power angles δ and machine speeds ω at time t + Δt. The electrical powers are refined at t + Δt, and the final values of δ and ω are obtained. The process repeats until the simulation ends.

Choosing a proper time step is important because it helps prevent numerical instability in the integration. With these equations and steps, engineers can analyze transient stability in multimachine power systems and judge how reliably the network will operate under changing conditions.

Power-System Stability in Multi-Machine Networks

power-system-stability-in-multi-machine-networks

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multimachine stability

Power-system stability in multi-machine networks focuses on how several synchronous machines behave as they stay connected to an N-bus power system. The analysis solves the swing equations for the machines and tracks how the network responds when conditions change. It is used to study transient stability, which is the system’s ability to stay in step after a disturbance. The network is written with nodal equations that link bus voltages, machine voltages, and machine currents. In this model, V...

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key terms and concepts

Learn how multi-machine power systems use nodal equations, swing equations, and time-step simulation to test transient stability after switching or load changes.

Power-System Stability in Multi-Machine 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-System Stability in Multi-Machine Networks

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