**Part 1 – CW – Transmission and Distribution Power System Performance**

The performance of a 275-kV transmission line (TL) is to be studied with regard to power flow analysis. The line may be assumed to be fed from an ‘infinite’ generator (the Grid) and terminated with a lumped load with fixed real and reactive power. The following system data applies: –

**System Bases**

2000 MVA, 50 Hz, 275 kV

**Infinite Generator (Grid)**

275 kV, 50 Hz, 3-ph, 100,000 MVA Fault level 3-ph & 1-ph, X/R ratio =10, Voltage set at 1.0 p.u.

**Busbars**

275 kV, 50 Hz, 100,000 MVA Fault level, voltage limit is 1 p.u. +8%, -15%

**Transmission Line**

275 kV, 3-ph, 50-Hz, R = 0.0081 Ohms/km, L = 0.51 mH/km, C = 0.0078 μF/km, with the maximum current Summer/Winter/Spring/Autumn = 850 A.

I. Calculate, the receiving end current, the sending end (voltage, current and power) using the line models discussed in the lecture notes. The load parameters are as follows;

**325 MVA, 0.91 pf lagging, 50 Hz, 275 kV**for the following transmission line lengths;

a. (20 + the first digit of your student id#) km (short line) [10%]

b. (350 + the second digit of your student id#) km (long line)

Then, create and run load flow model of the above system in ERACS (pay extra attention to parameters to be considered in each model). Outline any assumptions made in representing the system.**c. Compare your calculation with the simulation results. [10%]**

[please add a neat hand-written calculation as appendix to the report].

II. For only the simulation study conducted in Part (I), ** calculate **the transmission system performance indicators, i.e. voltage regulation and line efficiency, for both line lengths, pay attention to the used formulas.

III. For the system described above (Grid, Long Transmission Line), calculate the surge impedance loading (SIL), verify by running appropriate simulation, the power system performance under SIL condition, consult your lecture notes.

[10%]

## Solution

**Transmission and Distribution Power System Performance**

**Introduction:**

The power system network consists of 275kV transmission line fed from an infinite generator (the grid) and terminated with a lumped load with fixed apparent power.

Details of the major components of the power system network are given in the input table.

**Objectives:**

- To calculate the receiving end current, the sending end (voltage, current, power) for short and long transmission line models, and compare calculations with simulation results.
- To calculate the voltage regulation and line efficiency for both short and long transmission line models.
- To calculate the surge-impedance loading for the power system network consists of grid and long transmission line and verify with simulation results.
- For the power system network consists of grid, long transmission line followed by step down transformer
- a)To investigate the maximum unity power factor load that can be connected at the secondary side of transformer without violating the system constraints, showing the evidence for constraint violations.
- To investigate the maximum lagging power factor load that can be connected at the secondary side of transformer without violating the system constraints, showing the evidence for constraint violations.
- For the maximum power factor load as discussed in (b), to design a capacitive shunt compensation that restrict overall load power factor to 0.95 and evaluate the impacts of the compensation.

**Input data:**

Sr. No. | Components of the power system network | Description |

1. | Infinite Generator (Grid) | 275kV, 100000MVA, 50Hz, X/R=10, V=1∟0° |

2. | Busbar | 275kV, 50Hz, 100000MVA, V=1∟0°, Voltage limits +8%, -15% |

3. | Transmission line | 275kV, 850A, 50Hz, R=0.0081 Ω/km, L=0.51 mH/km, C=0.0078µF/km |

4. | Load | 275kV, 50Hz, 325MVA, 0.91 pf lag |

5. | Transformer | 275kV/33kV, 110MVA |

**Assumptions:**

- The line capacitance in case of short line is assumed to be zero.
- The parameters for the transformer are assumed from the typical transformer data of 275/33kV 120MVA available in ERACS reference library and converted to the new base of 110MVA using p.u. conversion.
- For part IV, it is assumed that the 33kV load bus has the same voltage limits as of 275kV, given in the input data table.
- For part IV, the overall load side power factor correction is considered at 33kV side.

**Simulation Results:**

**Short Line – 27km**

The load flow simulation results for a short line of length 27km is shown in the figure below:

It can be observed that the difference between voltage drop and sending end power in both the hand calculation and the ERACS simulation (without considering line capacitance) is negligible.

In the hand calculation, the capacitance of the line is not considered as the line is classified as a short line. From Fig.1, it is to be noted that the reactive power loss in the line is around 6.15MVAr when the line capacitance is not considered. The active power loss is around 0.31MW.

Similarly, it can be observed from the simulation result (Fig.2, with line capacitance) that the reactive power loss in the line is around 1.15MVAr and the active power loss is not effected.

**Long Line – 355km**

The load flow simulation result for a short line of length 355km is shown in the figure below:

It can be observed that there is a significance difference in the voltage drop and sending end power in both the calculations.

It can also be observed from the simulation result that the reactive power loss in the line is around 43.33MVAr and the active power loss is around 5.06MW during the given loading condition.

**Surge Impedance Loading**

The calculated SIL for the long line is 295.75MVA.

To investigate the SIL of the long line in the simulation, the load at the receiving end is modelled as purely resistive, i.e., at upf. The load value obtained in the hand calculation is considered initially and the line flows are observed for varying load P, refer to the below:

MW multiplier | Load in MW | Sending end Voltage, p.u. | Receiving end Voltage, p.u. | Reactive power at sending end, MVAr |

1 | 295 | 1 | 0.988 | 2.077 |

0.995 | 293.53 | 1 | 0.988 | 1.346 |

0.991 | 292.35 | 1 | 0.988 | 0.765 |

0.989 | 291.76 | 1 | 0.989 | 0.475 |

0.986 | 290.87 | 1 | 0.989 | 0.042 |

0.9855 | 290.72 | 1 | 0.989 | -0.03 |

0.9857 | 290.782 | 1 | 0.989 | -0.001 |

0.98571 | 290.784 | 1 | 0.989 | 0.000 |

From the table, it can be noted that the sending end Q in the line is 0 MVAr for a load value of 290.784MW. During this load condition, the sending end P is 294.07 MW and sending end Q is 0 MVAr which implies that the inductive and capacitive Q are balanced, and the Q flow through the line 0 MVAr. There is a difference of 0.011 p.u. between the sending end and the receiving end voltage which is due to the line resistive loss.

The line current during the SIL is also found to be constant and the line loading is around 72.64%, which is evident from the simulation result.

Fig.3 shows the simulation result for long line under SIL.

IV . **Long line connected to a step-down transformer**

A step-down transformer of 110MVA, 275/33kV is included in the model at the receiving end bus.

**Max upf load at the secondary of the transformer**

The simulation has been carried out with the load equivalent to the MVA rating of the transformer secondary. The transformer is assumed to be at the neutral tap position. Please refer to the table below, which shows the system constraints against the varying load at 33kV.

Load at 33kV, MW | Sending end voltage, p.u. | Receiving end voltage, p.u. | Line loading, % | Transformer loading in % | 33kV Voltage, p.u. |

110 | 1 | 0.992 | 28.73 | 104.91 | 0.946 |

107.5 | 1 | 0.994 | 27.95 | 102.26 | 0.95 |

105 | 1 | 0.995 | 27.19 | 99.63 | 0.954 |

105.35 | 1 | 0.995 | 27.29 | 99.99 | 0.953 |

From the table, it can be observed that the system parameters are within acceptable limits for upf load of 105.35MW at the transformer secondary side.

**Capacitive shunt compensation to restrict the overall pf to 0.95 at 33kV side**

Considering the case where the system is within acceptable limits in (b), for P=75MW and Q=34.5MVAr, the power factor at the 33kV side is 0.908 lag and Q is 34.496MVAr (see Fig.7). The power factor is to be corrected to 0.95 lag by using a shunt compensation.

It is known that the reactive power required to achieve a power factor of cos(phi2) at active power P is given by,

Q_{2} = P*(tan(φ_{1})-tan(φ_{2}))

Where P=75MW

cos φ_{1 }= 0.908 (pf before compensation), φ_{1 }= 24.769

cos φ_{2 }= 0.95 (required pf), φ_{2 }= 18.195

therefore, Q_{2} = P*(tan(φ_{1})-tan(φ_{2})) = 75*(tan(24.769)-tan(18.195))

Q_{2} = 9.95MVAr

The simulation result is shown in Fig.9. It is to be noted that the shunt compensation is modelled as a fixed PQ load with a negative value of 9.95MVAr and 0MW.

It can be observed that with a shunt compensation of 9.95MVAr at 33kV receiving end bus, the power factor is corrected to 0.95. It can also be observed that the 275kV receiving end bus voltage is improved to 0.987p.u. from 0.976p.u. (see Fig.8), 33kV bus voltage is improved to 0.896p.u. from 0.85 (see Fig.8) and the Q flow through the transformer is reduced to 43.29MVAr from 57.28MVAr (see Fig.8) which improved the transformer loading by 7.1%.