Load Flow Analysis – Power System Analysis (Matlab Programming)

Load Flow analysis in power system

Load flow is a simulation of an electrical power system that analyzes power distribution networks from the given line and bus data. It is the process of calculating the amount of power that will be drawn from a network. The basic principle behind load flow is that if we know the current demand on a particular bus, we can calculate how much power is being drawn from the system. This power is then distributed to all other buses in the network. Distribution power flow analysis includes voltage, current, power factor, real and reactive power losses, harmonics, etc.

In some applications, particularly in power system planning, distribution automation, and practical studies, it is crucial to solve the load flow problem efficiently so that the load flow solution can be repeatedly calculated for different situations.

power flow analysis is done to determine if there are any equipment problems or if the network is overloaded. If a problem is found, the analysis helps determine where the problem exists and how to fix it to enhance the quality of power supply to customers.

Electrical Power Systems Design and Analysis

In a power system, steady state stability refers to maintaining the system’s initial condition after a slight disturbance. In other words, the system tends to restore itself to the initial conditions quickly. Power systems are very complex, and many variables need to be taken into account when solving for the steady state operation of the power system.

In a distributed load flow analysis for the power grid, four quantities are classified as Real and Reactive Power, Voltage Magnitude and Phase Angle. In the distribution system or electrical power transmission, power flow analysis buses, and quantities are associated with each other. The buses are entitled Load bus, Generator bus, and reference slack bus.

clc;
clear all;
format short;
tic
m=load('loaddata33bus.m');
l=load('linedata33bus.m');

% m=load('loaddata69bus.m');
% l=load('linedata69bus.m');

br=length(l);
no=length(m);
f=0;
d=0;
MVAb=100;
KVb=12.66;
Zb=(KVb^2)/MVAb;
% Per unit Values
for i=1:br
    R(i,1)=(l(i,4))/Zb;
    X(i,1)=(l(i,5))/Zb;
end
for i=1:no
    P(i,1)=((m(i,2))/(1000*MVAb));
    Q(i,1)=((m(i,3))/(1000*MVAb));
end
R;
X;
P;
Q;
C=zeros(br,no);
for i=1:br
    a=l(i,2);
    b=l(i,3);
    for j=1:no
        if a==j
            C(i,j)=-1;
        end
        if b==j
            C(i,j)=1;
        end
    end
end
C;
e=1;
for i=1:no
    d=0;
    for j=1:br
        if C(j,i)==-1
            d=1;
        end
    end
    if d==0
        endnode(e,1)=i;
        e=e+1;
    end
end
endnode;
h=length(endnode);
for j=1:h
    e=2;
    
    f=endnode(j,1);
   % while (f~=1)
   for s=1:no
     if (f~=1)
       k=1;  
       for i=1:br
           if ((C(i,f)==1)&&(k==1))
                f=i;
                k=2;
           end
       end
       k=1;
       for i=1:no
           if ((C(f,i)==-1)&&(k==1));
                f=i;
                g(j,e)=i;
                e=e+1;
                k=3;
           end            
       end
     end
   end
end
for i=1:h
    g(i,1)=endnode(i,1);
end
g;
w=length(g(1,:));
for i=1:h
    j=1;
    for k=1:no 
        for t=1:w
            if g(i,t)==k
                g(i,t)=g(i,j);
                g(i,j)=k;
                j=j+1;
             end
         end
    end
end
g;
for k=1:br
    e=1;
    for i=1:h
        for j=1:w-1
            if (g(i,j)==k) 
                if g(i,j+1)~=0
                    adjb(k,e)=g(i,j+1);            
                    e=e+1;
                else
                    adjb(k,1)=0;
                end
             end
        end
    end
end
adjb;
for i=1:br-1
    for j=h:-1:1
        for k=j:-1:2
            if adjb(i,j)==adjb(i,k-1)
                adjb(i,j)=0;
            end
        end
    end
end
adjb;
x=length(adjb(:,1));
ab=length(adjb(1,:));
for i=1:x
    for j=1:ab
        if adjb(i,j)==0 && j~=ab
            if adjb(i,j+1)~=0
                adjb(i,j)=adjb(i,j+1);
                adjb(i,j+1)=0;
            end
        end
        if adjb(i,j)~=0
            adjb(i,j)=adjb(i,j)-1;
        end
    end
end
adjb;
for i=1:x-1
    for j=1:ab
        adjcb(i,j)=adjb(i+1,j);
    end
end
b=length(adjcb);

% voltage current program

for i=1:no
    vb(i,1)=0.99;
end
for s=1:10
for i=1:no
    nlc(i,1)=conj(complex(P(i,1),Q(i,1)))/(vb(i,1));
end
nlc;
for i=1:br
    Ibr(i,1)=nlc(i+1,1);
end
Ibr;
xy=length(adjcb(1,:));
for i=br-1:-1:1
    for k=1:xy
        if adjcb(i,k)~=0
            u=adjcb(i,k);
            %Ibr(i,1)=nlc(i+1,1)+Ibr(k,1);
            Ibr(i,1)=Ibr(i,1)+Ibr(u,1);
        end
    end      
end
Ibr;
for i=2:no
      g=0;
      for a=1:b 
          if xy>1
            if adjcb(a,2)==i-1 
                u=adjcb(a,1);
                vb(i,1)=((vb(u,1))-((Ibr(i-1,1))*(complex((R(i-1,1)),X(i-1,1)))));
                g=1;
            end
            if adjcb(a,3)==i-1 
                u=adjcb(a,1);
                vb(i,1)=((vb(u,1))-((Ibr(i-1,1))*(complex((R(i-1,1)),X(i-1,1)))));
                g=1;
            end
          end
        end
        if g==0
            vb(i,1)=((vb(i-1,1))-((Ibr(i-1,1))*(complex((R(i-1,1)),X(i-1,1)))));
        end
end
s=s+1;
end
nlc;
Ibr;
vb;
vbp=[abs(vb) angle(vb)*180/pi];


for i=1:no
vbp(i,1)=abs(vb(i));
vbp(i,2)=angle(vb(i))*(180/pi)
end


toc;
for i=1:no
    va(i,2:3)=vbp(i,1:2);
end
for i=1:no
    va(i,1)=i;
end
va;


Ibrp=[abs(Ibr) angle(Ibr)*180/pi];
PL(1,1)=0;
QL(1,1)=0;

% losses
for f=1:br
    Pl(f,1)=(Ibrp(f,1)^2)*R(f,1);
    Ql(f,1)=X(f,1)*(Ibrp(f,1)^2);
    PL(1,1)=PL(1,1)+Pl(f,1);
    QL(1,1)=QL(1,1)+Ql(f,1);
end

Plosskw=(Pl)*100000;
Qlosskw=(Ql)*100000;
PL=(PL)*100000;
QL=(QL)*100000;


voltage = vbp(:,1);
angle = vbp(:,2)*(pi/180);
plot(m(:,1),abs(voltage));
% hold on

% Plosskw
sum(Plosskw );
sum(Qlosskw);

%
Plosskw(33,1)=PL;
Qlosskw(33,1)=QL;

sprintf('Power-Loss=%d KW, Power-Loss=%d KVAr' ,PL,QL')     
Sr=(1:33)';

plot(voltage)

    %% EXCEL FOR DG
T =table(Sr,Plosskw,Qlosskw,angle,voltage);        
T(:,1:5);
excel_file = 'NO_DG_IEEE33.xlsx';
writetable(T,excel_file,'Sheet',1,'Range','H1');

Bus Bar in Power System

When we look at our power grid system, we see it as one extensive bus network. The power grid uses buses that connect multiple lines, components like generators, and loads. Four parameters are associated with different types of buses in power flow studies like

Voltage magnitude

Voltage phase angle

Reactive power

Active power

Buses in the load flow study of the distribution system or other networks are classified as generation buses, load buses, or slack buses.

Power Distribution Terminal Bus Bar

1) A generation bus (P-V bus) is a name for the generator station in a power grid. If you have solar panels on your roof, you could run a photovoltaic bus, the generator station in the network. The generator bus is known to have unknown variables. They are the phase angle θ of the voltage and the reactive power Q. The bus voltage is always defined with the other buses that share this bus.

2) The buses without generators are referred to as load bus or (P-Q bus) that integrates reactive and active power into the bus system. Here magnitude of the voltage V and phase angle θ is unknown. It would be best if you used the load flow equation to find both these quantities. The real and reactive power is known based on the line and load data. 

3) The significance of the slack bus in load flow analysis is that it does not carry any load and is known as a utility bus. The magnitude and phase of the voltage are fixed while real P and reactive power Q are unknown. The main advantage of a generator bus is that it provides active control, meaning that the bus can be used entirely by itself. Once the power loss is known, it is possible to create a distribution network to compensate for it.

“PV Bus” is the bus that supports the voltage and real power.

“PQ Bus” is the bus that needs real and reactive power.

“Reference Bus” is the bus that supports real and reactive power.

PV_Bus (Generation Bus).

PQ_Bus (Load Bus).

Slack_bus (Utility Bus).

Load Flow Analysis using Forward Backward Sweep Method

Three techniques are used to calculate load flow, with two being the most common. Gauss Seidel, Newton Raphson, and Fast Decoupled methods are used to solve linear systems.

Newton-Raphson & Gauss-Seidel are standard algorithms best for high voltage systems and complex non-linear problems. However, this method is more straightforward than the newton-raphson and gauss seidel method for power flow analysis having simpler implementation, good convergence speed, good accuracy, and low memory requirement. 

Unbalanced Load Flow Analysis

The need for optimizing power systems through efficient and reliable techniques has increased due to the increasing complexity of power distribution systems. Load flow studies should also be able to handle various system configurations accurately and quickly, so they are the most crucial power system analysis tool.

When using a radial system to supply power, you will often notice that the distribution systems are unbalanced due to single-phase, two-phase, or three-phase loads. So, in this case, you need to look at the load-flow solution and consider how they would be impacted if there were unbalanced.

The balanced load-flow approach cannot directly apply to an unbalanced network. Three-phase power flow analysis is an alternative to the single-phase method of analyzing unbalanced systems. However, it cannot develop by extending the single-phase balanced methods.

A three-phase load-flow method must be used to analyze power distribution problems. This will allow you to study the effects of fundamental connections like phase shifts and transformation ratios for each phase at different nodes and how they affect your power system. The balanced models are not useful anymore for un-transposed lines and cables.

Load Flow and Short Circuit Analysis

If a current-carrying conductor or a part of the circuit gets in contact with another wire, other parts of the circuit, or even the ground, it causes a short circuit. That is why short circuit study and analysis are important because the current flow in an excessive amount through the path of low resistance, then the system will become unstable, known as a power surge.

This may damage the power source by producing heat and fires, which is why fuses glow. So it is essential to check whether the power system is protected against short circuits, and what type of protective device should be used, as per its requirement, to counteract short circuit currents.

The extra heat effect weakens electrical wiring, insulation, and other components and can also damage. Overcurrent protection devices (OCPD) detect an overload current and then automatically disconnect the load in order to prevent damage to the load. Through the short circuit test, aka the short circuit analysis, you can find out the magnitude of the short circuit current to stop it.

What are the benefits of short circuit analysis?

Provides information on how to determine the level and type of protective equipment required for the specific use of each device and helps to avoid unplanned outages and downtime. It makes you comply with NEC and provides information required for NFPA.

Power system analysis of short circuit load flow and harmonics

With the Harmonic Load Flow Analysis, you can analyze harmonic current and voltage in your system, determine current characteristics and diagnose any faults affecting the objective function’s voltage and current constraints.

Electrical Load Flow Analysis Software:

ETAP

PowerWorld Simulator

DIgSILENT Power Factory

PSCAD

ETAP load flow analysis

The best load-flow software on the market is ETAP Load Flow Software. It is the industry-leading solution for performing voltage drop calculations and power flow analysis. It is user-friendly and a powerful calculation engine with efficient and reliable outcomes.

Power World Simulator

Load flow analysis using this software package designed to perform operations related to voltage power system on a time frame of up to several days. 

What is SKM used for?

SKM Power Tools is a simulation program used by power utilities to simulate real events that occur in power systems. It provides a graphical user interface that allows users to quickly and accurately visualize the behavior of large electric power networks.

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The End.