Overview of Methodology

8/2/2019 Overview of Methodology

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I. Overview of methodologyTo realise this project, an interconnection of the Southern Interconnected Grid (SIG) and

Northern Interconnected Grid (NIG) of Cameroon is realised with a HVDC connection with the

aim of minimising the active power transmission losses in the AC networks, while studying the

voltage stability of the HVDC link in terms of voltage values between nodes.

I.1 Active Power minimizationIn this section, the basic concept applied for the minimization of active power transmission

losses is explained. The following steps are then followed in order to attain the objective of (see

flow chart below);


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Apply the particle swarm Optimization method to the OPFControl variables

Reactive power generated bycapacitor banks

Position of OLTC trans formers

Voltages at the generator buses

Output variables

Optimal position of control variables forminimum trans mission loss es

Formulation of the Optimal Power Flow Problem (OPF)

Objective function Network constraints

Solution of the Power Flow Problem by the Newton Raphson methodInput variables

Bus admittance matrix

Active and reactive power generatedand consumed at the different nodes

Output variables

Voltage and phas e at the differentnodes

Active and reactive power generated

Formulate the Power Flow Problem

Formulate the bus admittance matrix Power Flow Equation

Impedance model of the different network elements

Impedance model of transmissionlines

Impedance model of transformers

Adaptation of the SIG and NIG mode

Hypothesis for themodeling of the SIG

Determine the numberof nodes

One line diagram of theSIG model


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I.2 Model of the SIGGeneral Hypothesis for SIG and NIG

The following assumptions were made in modelling the SIG:

The base apparent power is

and the base

corresponds to the nominal

voltage at a particular node;

For two transmission lines in parallel, the equivalent resistance and reactance are

calculated. This implies for two nodes connected by two lines in parallel, only one

equivalent transmission line is considered;

In all power plants (except Song Loulou and Lagdo) with two or more generators, the

latter are considered as one and the power generated is the sum of the power

generated by these different generators. This signifies the power generated by

individual generators is not specified;

The power consumed at a node varies as a function of the voltage across the node. In

this model, the loads were considered constant irrespective of the voltage across them

Generally, the reactive power injected by a capacitor bank varies as a function of its

capacitance and the voltage across it. This was not taken into account in this model. The

reactive power injected by a capacitor bank was considered constant regardless of the

voltage across it.

All the HV substations with capacitor banks have two capacitor banks each. Only one

capacitor bank is indicated with a capacity equal to the sum of the reactive power

injected by the two capacitor banks.

Diagram of the SIG model

The figure below is a diagram showing the different bus bars, generators and transformers of

the SIG model considered. A total of 46 buses and 50 branches (branches are transmission lines

or transformers). Table below indicates the generator nodes together with their corresponding

node indices and Table shows the different transformers as well as their departure and arrival

nodes;


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Ta b le 1: Generators in the m odel and their corresponding node indicesLocation of Power

plant

Number of generators

considered

Name used in model Node index as

represented in the model

Song Loulou 4 SLL1 1

SLL2 2SLL3 3

SLL4 4

Oyomabang 2 Oyo HFO 11

Oyo LFO 12

Edea 1 Edea PP 23

Dibamba 1 Dibamba PP 27

Logbaba 2 Logbaba HFO 29

Logbaba LFO 30

Bassa 2 Bassa2 34

Bassa3 35Limbe 1 Limbe HFO 41

Bafoussam 1 Bafoussam PP 44

Ta b le 2: Transformers and the ir corresponding arrival and departure node indices

Location of transformerDeparture node Arrival node

Song Loulou 1 5

2 5

3 5

4 5

Oyomabang Substation 9 10

9 18

Oyomabang HFO 10 11

Oyomabang LFO 10 12

Mangombe Substation 8 25

Logbaba Substation 7 28

Logbaba HFO 28 29

Logbaba LFO 28 30

Bekoko Substation 6 39

Bassa2 33 34

Bassa3 33 35

Edea Power plant 22 23

Dibamba 26 27

Limbe 41 42

Bafoussam 44 45


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Some of the transmission lines are of particular interest because the amount of power that

flows through them is very high, and others by virtue of the fact that they are very long and

thus have very high resistances. These two factor affect considerably the active power

transmission losses in these lines. The length of the 225kV and some 90kV transmission lines

are indicated in the figure below.

10

LOGBABABEKOKO MANGOMBE

OYOMABANG

B

NSI

AHALANGOUSSO

KONDENGUI

NJOCK-

KONG

EDEA PP

ALUCAM

NGODI BAKOKO

KOUMASSI

DIBAMBA

MAKEPE

BASSA

DEIDO

BONABERI

LIMBE

NKONGSAMBA

BAFOUSSAM

BAMENDA

LIMBE HFO

1

SONGLOULOU

7

1

96 8

18

19

14

30

27

21

22

20

35

32

3334

38

40

37

41

46

45

2 3

5

11 12

24

23

26

25

28

31

29

36

39

43

42

44

4

15

DR NSIMALEN

Key

Hydo electric power gen

HFO thermal generato

LFO thermal generato

225kV____________

90kV_____________

HV capacitor banks

EDEA

(41.5km) (58km)

(65km)

(58km)(168.38km)

(94km)

(94k

m)

(70km)

Formulating the power flow problem

Formulation of the bus admittance matrix ()The first step in developing the mathematical model describing the power flow in the network is the

formulation of the bus admittance matrix. The bus admittance matrix is an matrix (where is thenumber of buses in the system) constructed from the admittances of the equivalent circuit elements of

the segments making up the power system. Most system segments are represented by a combination of

shunt elements (connected between a bus and the reference node) and series elements (connected


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between two system buses). Formulation of the bus admittance matrix follows two simple rules Error!

Reference source not found.:

Consider 2 nodes and , and be the corresponding admittance between and .If and k are linked by a transmission line or transformer

Else

For a node

Whereis the set of nodes connected to bus by a line or transformer and the reactance connectedto the node (shunt of reactance).In polar form, is expressed in the form || || Where are the real and imaginary parts of the admittance respectively.

Formulation of the power flow problem

The power flow problem is used to determine the values for all state variables (voltage magnitude and

angle) by solving an equal number of power flow equations based on the input data specifications. In

this section, the different input data known at each of the nodes are specified.The voltage at a bus of the system in polar coordinates is as follows: The voltage at another bus is simi larly written by changing the subscript from to .The net current injected into the network at bus in terms of the elements of the admittance matrixis given by

Let

and

denote the net real and reactive power injected at the bus

. The complex conjugate of

the power injected at bus is By substituting equations and in equation we obtain:

Expanding this equation into real and imaginary parts:


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Equations and constitute the polar form of the power-flow equations; they provide calculatedvalues for the net real power and the net reactive power injected at bus .Let denote the scheduled power generated at bus and denote the scheduled power demand.Then, is the net scheduled power being injected at bus . If the calculated value of isdenoted by , we can define the mismatch, as the scheduled value minus the calculatedvalue .i.e. Likewise, the reactive power mismatch at bus is:

Mismatches occur in the process of solving power flow problems when calculated values ofand do not coincide with the scheduled values and . If the calculated values and match the scheduled values and perfectly, then the mismatches and are zeroat the bus , i.e. If there is no scheduled value for bus , then the active power mismatch cannot be defined andthere is no requirement to satisfy equation in the course of solving the power flow problem.Similarly, if

is not specified at bus

, then equation

does not have to be satisfied.

Four unknown quantities associated with each bus are , voltage angle and the voltagemagnitude. For a system with N nodes, there are:N voltage amplitudes N voltage angles N active power at the node N reactive power at the node

4N unknowns can be identified. There are at most two equations available for each node, and so the

number of unknown quantities must be reduced to agree with the number of available equations before

beginning to solve the power flow problem. The general practice in power flow is to identify three types

of buses in the network. At each bus, two of the variables , andare specified and theremaining two are calculated.


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Ta b le 3: Summary of power-flow problemBus type Number of

buses

Quantities

specified

Number of available

equations

Number of state

variables( ,)Slack (1)

Voltage controlled (2) Load (3) 2( ) 2( )Totals

The power flow formulation was applied to the SIG. As seen in Error! Reference source not

found., buses. The node types were defined as follows:All thermal generators, interconnection nodes and load nodes are PQ buses giving a

total of

buses. Nodes with thermal generators are PQ nodes because the amount of

power generated by these plants are considered fixed, in order to respect the cost

effective schedule made by QSOM ;

The generators in Edea and six generators of Song Loulou are PV buses giving a total of 4

PV buses;

Two generators in Song Loulou are connected to the slack bus.

Table gives a summary of the number of buses of each type and the number of corresponding

equations.

Ta b le 4: Node Configuration for the SIGBus type Number of buses Number of available

equations

Slack (1) Voltage controlled (2) Load (3) Totals

There are different computational techniques used by different programs to determine the state

variablesError! Reference source not found.. These are: the Gauss-Seidel Method, the Newton Raphson

Method and the Fast Decoupled method. In this work the Newton Raphson method will be applied

because the number of i terations required by the Newton Raphson method is independent of the

number of buses whi le the computation time using Gauss-Seidel increases almost directly with the

number of buses.


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Solution of Load flow using Newton Raphsons method

Taylor's series expansion for a function of two or more variables is the basis for the Newton-Raphson

method of solving the power flow problem Error! Reference source not found. . To apply the Newton-

Raphson method to the solution of the power-flow equations, we express bus voltages and line

admittances in polar form i.e.

These equations are differentiated with respect to the voltage angles and the magnitudes (state

variables). For active power we have

A similar mismatch equation can be written can written for the reactive power ,

Each non slack bus has two equations for . Collecting all the mismatch equations intovector-matrix form yields

(

[

] [

]

[

] [ ])

The partitioned form of the equation above emphasizes the four different types of partial

derivatives which enter into the Jacobian . The solution to this equation is found by iteration as follows:1. Estimate values for the state variables

and

(generally,

=0 and

;

2. Use the estimate to calculate from equations and and the mismatchesfrom equations and and the partial derivatives elements of the Jacobian;3. Solve equation below for initial corrections ;4. Add the solved corrections to the initial estimates to obtain


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5. Use the new values

as starting values for iteration 2.

Formulas for the update of state variables are as follows:

This process is repeated until the mismatch is less than a tolerance or when the number of iterations is greater than the maximum number of iterations (generally, the

tolerance is 0.005 and the maximum number of iterations is 12).

The NIG model


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Ta b le 5: Generators in the m odel and their corresponding node indicesLocation of Power

plant

Number of generators

considered

Name used in model Node index as

represented in the model

Lagdo 2 G1 1

G2 2Garoua 1 Gen 3 11

Ta b le 6: Transformers and the ir corresponding arrival and departure node indices

Location of transformerDeparture node Arrival node

Lagdo 1 Lagdo

2 Lagdo

Ngaoundere Substation Ngaoundere 6

6 7

Garoua substation Garoua1 8

Garoua substation 9 8



Guider 12 Guider

Maroua substation 12 Maroua

Maroua substation Maroua 15

Maroua substation 15 16

DC link modification on the N-R algorithm

The work to be realise is a study on the interconnected link using the HVDC, hence the AC-DC newton

Raphson load flow algorithm is given below

Where

Yac: the admittance matrix for the AC network

Ydc: the admittance matrix for the DC line

Jac: Jacobian matrix for AC network

Jac: Jacobian matrix for DC line

X: values obtained from iterations

: tolerance


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Overview of Methodology

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