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Markov Chains || Step-By-Step || ~xRay Pixy

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Learn Markov Chains step-by-step using real-life examples. Video Chapters: Markov Chains 00:00 Introduction 00:19 Topics Covered 01:49 Markov Chains Applications 02:04 Markov Property 03:18 Example 1 03:54 States, State Space, Transition Probabilities 06:17 Transition Matrix 08:17 Example 02 09:17 Example 03 10:26 Example 04 12:25 Example 05 14:16 Example 06 16:49 Example 07 18:11 Example 08 24:56 Conclusion
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Transmission Expansion Planning (TEP) |AC Optimal Power Flow|

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 Transmission Expansion Planning (TEP)

Transmission Systems are Large and Interconnected. Transmission Systems carry large quantities of electricity (from utility-scale to low voltage lines – distributed system).  Transmission Expansion Planning (TEP) is process of identifying needed investment and expansion in transmission. Transmission Expansion Planning (TEP) is a complex decision-making process. 

TEP Process include different analysis :

  • System Cost.
  • Reliability and Modeling.
  • Compute Risk and burden.
  • Number of Generators required.
  • The number of Equipment required.
  • How a transmission system should develop over time? 
  • Determine the Number of Electric Power Transmission facilities required in the future power grid.

Transmission Expansion Planning (TEP): A list of types of equipment can be inserted on the grid:

  • Cables
  • Transformers
  • Transmission Lines

Transmission Expansion Planning (TEP) Problem: Objective Functions

  • Investment Function
  • Operational Cost Function
  • Power Loss Function 

Approaches in Transmission Expansion Planning Problems

Static Approach: System Information (i.e., load, types of equipment) is only considered at the planning horizon in one shot.

Dynamic Approach: System Information (i.e., load, types of equipment) is handled over sub-periods of the planning horizon

What is the Role of Metaheuristic Algorithms in TEP?

Bio-inspired Meta-heuristic algorithms are widely used to solve Transmission Expansion Problems. Metaheuristic algorithms provide the best solutions to TEP problems as compared to other traditional methods.  Metaheuristic algorithms are problem independent [not dependent on particular information about the problem].  

Transmission Expansion Planning |Evolutionary Particle Swarm Optimization (EPSO)|

Optimal Power Flow (OPF) Models

  • AC - Optimal Power Flow  

  • DC – Optimal Power Flow

Define General formulation of TEP Problem

Minimize / Maximize of                                (2.1)

  Subject to:

 Physical Constraints                                       (2.2)

Financial Constraints                                        (2.3)

Quality of Service Constraints                          (2.4)

Evolutionary Particle Swarm Optimization (EPSO) Algorithm

Evolutionary Particle Swarm Optimization is a powerful tool to solve complex TEP problems. Evolutionary Particle Swarm Optimization provides the best solutions.  Evolutionary Particle Swarm Optimization combines the best features of the Genetic Algorithm (GA) and Particle Swarm Optimization Algorithm (PSO).


Evolutionary Particle Swarm Optimization Step-by-Step

Different TEP Formulations are Handled by Metaheuristic Algorithms.

Artificial Neural Network

Bee Colony Algorithm

Ant Colony Algorithm

Bat Algorithm

Firefly Algorithm

Particle Swarm Optimization Algorithm

Evolutionary Particle Swarm Optimization Algorithm  

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