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

M 동기 기계가 있는 N-버스 전력 시스템에서 부하는 일정한 어드미턴스로 모델링되고 네트워크 노드 방정식이 공식화됩니다.
어드미턴스 매트릭스는 부하 어드미턴스와 반전된 발전기 임피던스를 포함하도록 분할됩니다.
알려진 기계 전압을 사용하여 버스 전압 방정식을 풀어 기계 전류와 전력을 찾습니다.
과도 안정성 해석을 위해서는 기계에 대한 스윙 방정식과 네트워크에 대한 전력 흐름 방정식을 풀어야 합니다.
먼저, 사전 결함 전력 흐름 프로그램을 실행하여 초기 버스 전압, 기계 전류 및 전기 출력을 확인합니다.
기계적 동력 출력을 전기 출력과 동일하게 설정하고 주파수를 동기 각 주파수로 초기화합니다.
다음으로, 부하 어드미턴스, 내부 기계 전압, 전력 흐름 버스 어드미턴스 행렬을 계산합니다.
스위칭 작동, 부하 변경 또는 오류와 같은 이벤트에 대한 어드미턴스 매트릭스를 조정합니다.
각 시간 단계 t에 델타 t를 더할 때마다 기계 전력, 동력 각도 및 속도를 계산합니다.
원하는 시간 지평에 도달할 때까지 이 프로세스를 반복하여 단계 크기가 솔루션 정확도와 계산 시간의 균형을 유지하도록 합니다.

과도 안정성 및 시스템 제어

다중 기계 안정성 분석은 여러 동기 기계가 있는 전력 시스템의 역학과 안정성을 이해하는 데 필수적입니다. 목표는 N-버스 전력 시스템에 연결된 M 기계 네트워크에 대한 스윙 방정식을 푸는 것입니다.

시스템을 분석할 때, 노드 방정식은 버스 전압, 기계 전압 및 기계 전류 간의 관계를 나타냅니다. 노드 방정식은 다음과 같습니다.

<img alt="Equation1" src="/files/ftp_upload/16170/16170_PT_Equation_1.svg" style="height: 44px;">

V는 버스 전압의 N-벡터이고, E는 기계 전압의 M-벡터이고, I는 기계 전류의 M-벡터입니다. Y_11, Y_12, Y_21, Y_22는 각각 N×N, N×M, M×N, M×M 어드미턴스 행렬입니다. 방정식은 다음과 같이 분리할 수 있습니다.

<img alt="Equation2" src="/files/ftp_upload/16170/16170_PT_Equation_2.svg" style="height: 28px;">

E가 알려져 있다고 가정하면, 첫 번째 방정식은 Gauss elimination 또는 Gauss-Seidel과 같은 방법을 사용하여 V에 대해 반복적으로 풀 수 있습니다. V가 계산되면 두 번째 방정식에서 I를 얻을 수 있습니다.

기계 n의 실제 전기 출력은 다음과 같습니다.

<img alt="Equation3" src="/files/ftp_upload/16170/16170_PT_Equation_3.svg" style="height: 16px;">

과도 안정성 계산 절차에는 스윙 방정식과 전력 흐름 방정식을 반복적으로 푸는 것이 포함됩니다.

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>초기 버스 전압 V_k, 기계 전류 I_n, 전력 출력 pan을 결정합니다.</li>
 <li>E_n을 계산합니다.</li>
 <li>Y_11을 수정하고 Y_22와 Y_12를 계산합니다.</li>
 <li>t=0으로 초기화합니다.</li>
 <li>스위칭 작업이나 부하 변경이 있는지 확인합니다.</li>
 <li>시간 t에서 기계의 전기 전력을 계산합니다.</li>
 <li>초기 추정치를 사용하여 시간 t+Δt에서 전력 각도 δ와 기계 속도 ω를 계산합니다.</li>
 <li>t+Δt 시점에서 전력 추정치를 세부화합니다.</li>
 <li>시간 t+Δt에서 전력 각도 δ와 기계 속도 ω를 확정합니다.</li>
 <li>시간을 증가시키고 시뮬레이션이 끝날 때까지 단계를 반복합니다.</li>
 <li>수치 적분의 불안정성을 피하기 위해서는 정확한 시간 단계 선택이 필수적입니다.</li>
</ul>

이러한 단계를 따르고 제공된 방정식을 사용하면 엔지니어는 다중기계 전력 시스템의 과도 안정성을 분석하고 다양한 조건에서 안정적인 작동을 보장할 수 있습니다.

M 동기 기계가 있는 N-버스 전력 시스템에서 부하는 일정한 어드미턴스로 모델링되고 네트워크 노드 방정식이 공식화됩니다.
그만큼 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Transient Stability and System Controls

과도 안정도 및 계통 제어

KEY TERMS AND CONCEPTS

핵심 용어 및 개념

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

the swing equation

Generator Rotor Motion and the Swing Equation

Generator rotor motion is described by the Swing Equation in power system dynamics. It is used to study generating units such as three-phase synchronous generators. The equation comes from Newton’s second law applied to the generator rotor. It links inertia, angular acceleration, and the balance between mechanical and electrical torques. In steady-state operation, the mechanical torque supplied to the generator is equal to the electrical torque produced by the generator. When these torques...

simplified synchronous machine model

Transient Stability in Synchronous Generators

The synchronous machine model helps students analyze transient stability in power systems. It represents a synchronous generator under balanced three-phase positive-sequence conditions. The model assumes constant excitation and ignores losses and saturation. These simplifications make it easier to study how a generator behaves during a disturbance. In this setup, the generator is connected to a network of transmission lines, transformers, loads, and other machines. That larger system is often...

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...

wind turbine machine models

Wind Turbine Types and Generator Control

Wind turbine machine models are used to study how wind turbines behave in transient stability analysis. In this setting, induction machines and synchronous machines are the main model types. Induction machines are common because they are simple and reliable. Induction machines work through the rotating magnetic field made by the stator and rotor. A key term is slip, which is the difference between synchronous speed and rotor speed relative to synchronous speed. Slip is zero at synchronous...

generator voltage control

Voltage Regulation in Generators and Wind Turbines

Generator voltage regulation helps keep synchronous generators and wind turbines working stably. Older systems use a DC generator driven by the rotor to supply DC power to the rotor field winding. That power is passed through slip rings and brushes. Newer systems use static exciters or brushless exciters. A static exciter rectifies AC power from the generator terminals and sends DC power directly to the rotor. A brushless exciter uses an inverted synchronous generator, takes AC power from...

turbine-governor control

How Turbine Governors Stabilize Power Output

Turbine-governor control helps keep generator frequency and rotor speed stable when electrical load changes. It does this by matching turbine mechanical power with the power demand on the system. In a power grid, that balance is important for steady operation. Turbine-generator units also store kinetic energy because their parts are rotating. When load increases, that stored energy is released to help meet the demand. At first, electrical torque rises while mechanical torque stays nearly...

load-frequency control

Load-frequency control in power grids

Load-frequency control keeps a power grid stable when electrical demand changes. It helps keep system frequency and power flow within acceptable limits. Turbine-governor control reduces rotor speed changes after a load shift, but a steady-state frequency error can still remain when the turbine-governor reference setting does not change. In an interconnected power system, each area agrees to export or import a scheduled amount of power through tie-lines, which are the transmission lines that...

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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