Power flow actually it, Summaries of Low Power Electronic Systems

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Power Flow/Load Flow

Pratyasa Bhui Power and Energy Group, Dept. of Electrical Engg., IIT Dharwad March, 2021

• Admittance matrix (Ybus)
• Newton Raphson Power Flow
• Gauss Seidel Power Flow EE223, Jan, 2021

Contents

Chapter Outline

• Calculates the steady state operating point for a given load and generation data.
• Steady state operating point data is required for time domain simulation.
• Steady state operating point is required for planning studies, also security studies.
• Impact of adding any new equipment can be analysed with power flow.
• To plan any reactive power compensation, voltages must be known.

Importance

• Relates node current injections with bus voltage terms. 𝐼 = 𝑌 𝑏𝑢𝑠

𝑏𝑢𝑠 is symmetric and sparse, can be calculated very easily.

Admittance Matrix

• Transformer is modelled with a series inductance 𝑥 𝑙

𝑙 = 𝑥 in pu.

𝑞

1 𝑗𝑥

1 −𝑗𝑥 − 1 −𝑗𝑥 1 𝑗𝑥

𝑞

Admittance Matrix- Transformer

• Suppose a transformer is rated 400kV/66kV, 500 MVA.
• In per unit, voltage at both side of the transformer will be same. .. hence 1:1. Can be included in 𝑌 𝑏𝑢𝑠 as shown in previous slide.
• Now suppose tap has been changed to change the number of turns in primary to make it 440kV/66kV. Hence, turns ratio in pu is 440 400

66 66

Admittance Matrix- Tap Changing

Transformer

Example 9.4, Bergen & Vittal

Admittance Matrix

𝑏𝑢𝑠

• If we know the current injections at the buses, and 𝑌 𝑏𝑢𝑠 matrix, we can calculate the voltage. This is a set of complex linear equations, can be solved very easily with Gauss Elimination Method.
• However, generally current injections are not known. Generator 𝑃&𝑉 are generally specified, load bus 𝑃&𝑄 are also specified. Equations become nonlinear and can be solved iteratively using Gauss Siedel method or Newton Raphson method.

Network Solution

• Complex power generated at 𝑖 𝑡ℎ 𝑏𝑢𝑠: 𝑃 𝐺𝑖

𝐺𝑖

• Complex power drawn by loads 𝑖 𝑡ℎ 𝑏𝑢𝑠: 𝑃𝐷𝑖 + 𝑗𝑄𝐷𝑖
• Complex power injected into 𝑖 𝑡ℎ 𝑏𝑢𝑠
• 𝑆 𝑖

𝑖

𝑖

𝐺𝑖

𝐷𝑖

𝐺𝑖

𝐷𝑖

Power Flow Problem

• Each bus is characterized with 4 variables, 𝛿, 𝑉, 𝑃&𝑄.
• For 𝑛 bus system, 2𝑛 variables known, 2𝑛 variables are unknown.
• 𝑃𝑄 𝐵𝑢𝑠: 𝑃𝑖&𝑄𝑖 are known, 𝛿𝑖, 𝑉𝑖 are unknown. Load buses are always PQ Bus.
• 𝑃𝑉 𝐵𝑢𝑠: 𝑃𝑖&𝑉𝑖 are known, 𝛿𝑖, 𝑄𝑖 are unknown. These are either generator bus or voltage controlled bus.
• Slack Bus/Swing Bus: 𝑉 𝑖 &𝛿 𝑖 are known. Only one slack bus in the system generally. Transmission line loss is not known initially, hence slack bus is required to supply the line loss and any difference in generation and load.

Power Flow problem

• Reactive Power of the generator is calculated from power flow. Generator has certain reactive power limits. If the 𝑄 𝑖 obtained from power flow is out of the range, the bus will no longer be a PV bus or voltage controlled bus. It will be treated as a PQ bus.

Power Flow Problem-Limits

• For PV Bus, we know only magnitude, but not angle. Hence, after calculating voltage phasor, only angle is updated.
• For PV bus, if reactive power is out of limit, it is treated as PQ bus.

Gauss Seidel Method

𝑖 𝑟+ 1 = 𝑉 𝑖 𝑟

• 𝛼 𝑉 𝑖 𝑟+ 1 − 𝑉 𝑖 𝑟

• 𝛼 = 1. 6 − 1. 8

Acceleration of Convergence