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

In an N-bus power system with M synchronous machines, loads are modeled as constant admittances, and network nodal equations are formulated.
The admittance matrix is partitioned to include load admittances and inverted generator impedances.
With known machine voltages, the bus voltage equation is solved to find machine currents and electrical power.
Transient stability analysis requires solving swing equations for machines and power-flow equations for the network.
First, run a pre-fault power-flow program to determine initial bus voltages, machine currents, and electrical outputs.
Set mechanical power outputs equal to electrical outputs and initialize the frequency to the synchronous angular frequency.
Next, compute the load admittances, internal machine voltages, and the power-flow bus admittance matrix.
Adjust the admittance matrix for events like switching operations, load changes, or faults.
At each time step t plus delta t, calculate machine electrical power, power angles, and speeds.
Repeat this process until the desired time horizon is reached, ensuring the step size balances solution accuracy and computation time.

transiënte stabiliteit en systeemcontroles

Multimachine stabiliteitsanalyse is cruciaal voor het begrijpen van de dynamiek en stabiliteit van energiesystemen met meerdere synchrone machines. Het doel is om de swingvergelijkingen op te lossen voor een netwerk van M machines die zijn aangesloten op een N-bus energiesysteem.

Bij het analyseren van het systeem representeren de knooppuntvergelijkingen de relatie tussen busspanningen, machinespanningen en machinestromen. De knooppuntvergelijking wordt gegeven door:

<img alt="Equation1" src="/files/ftp_upload/16170/16170_PT_Equation_1.svg" style="height: 44px;">

V is de N-vector van busspanningen, E is de M-vector van machinespanningen, I is de M-vector van machinestromen. Y_11, Y_12, Y_21 en Y_22 zijn respectievelijk N×N, N×M, M×N en M×M admittantiematrices. De vergelijkingen kunnen als volgt worden ontkoppeld:

<img alt="Equation2" src="/files/ftp_upload/16170/16170_PT_Equation_2.svg" style="height: 28px;">

Ervan uitgaande dat E bekend is, kan de eerste vergelijking iteratief worden opgelost voor V met behulp van methoden zoals Gauss-eliminatie of Gauss-Seidel. Zodra V is berekend, kan I worden verkregen uit de tweede vergelijking.

Het werkelijke elektrische vermogen van de machine n is:

<img alt="Equation3" src="/files/ftp_upload/16170/16170_PT_Equation_3.svg" style="height: 16px;">

De procedure voor het berekenen van de transiënte stabiliteit omvat het iteratief oplossen van de swingvergelijkingen en de vermogensstroomvergelijkingen:

<ul style="list-style-type: disc; padding-left: 35px; margin: 0;">
 <li>Bepaal de initiële busspanningen V_k, de machinestromen I_n en de vermogensuitgangen pan.</li>
 <li>Bereken E_n.</li>
 <li>Wijzig Y_11 en bereken Y_22 en Y_12.</li>
 <li>Initialiseer t=0.</li>
 <li>Controleer of er schakelhandelingen of belastingveranderingen plaatsvinden.</li>
 <li>Bereken het elektrisch vermogen van de machine op tijdstip t.</li>
 <li>Gebruik initiële schattingen om de vermogenshoeken δ en de machinesnelheden ω op tijdstip t+Δt te berekenen.</li>
 <li>Verfijn de schattingen van elektrische vermogens op tijdstip t+Δt.</li>
 <li>Finaliseer de vermogenshoeken δ en de machinesnelheden ω op tijdstip t+Δt.</li>
 <li>Verhoog de tijd en herhaal de stappen tot het einde van de simulatie.</li>
</ul>

Een nauwkeurige selectie van tijdstappen is essentieel om instabiliteit bij numerieke integratie te voorkomen.

Door deze stappen te volgen en de gegeven vergelijkingen te gebruiken, kunnen ingenieurs de transiënte stabiliteit van energiesystemen met meerdere machines analyseren en een betrouwbare werking onder verschillende omstandigheden garanderen.

Transiënte stabiliteit en systeemcontroles

In an N-bus power system with M synchronous machines, loads are modeled as constant admittances, and network nodal equations are formulated.
The ...

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JoVE Core

Electrical Engineering

Elektrotechniek

Unit 1

Transient Stability and System Controls

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KEY TERMS AND CONCEPTS

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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

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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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electrical engineering

Power-System Stability in Multi-Machine Networks

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