The application of Monte Carlo simulation (MCS) is a corner-stone in the sensitivity and quantitative probabilistic analysis. Among many of its great virtues is its powerful ability to accurately evaluate the reliability of the electrical grid, which allowed several studies to emerge in this arena. The deterministic approach in assessing the reliability of the power systems is criticized for not being sensitive to the stochastic nature of the grid as well as to customer demands and components failures, which may lead to either an overinvestment or catastrophic consequences. Therefore, the need for probabilistic evaluation of the electrical system behavior has been emphasized in the most recent decade. MCS, as a process of simulation, is strictly random and can be divided into two main types; sequential and non-sequential (random) Monte Carlo methods. The sequential MCS simulates the system operation as an up-and-down, where a system operating cycle is obtained by combining all the cycles of the system components in chronological order. This usually requires more computational efforts than the other approach, the non-sequential MCS, which simulates the system with a higher efficiency by choosing intervals randomly, yet cannot simulate the chronological aspect of the system behavior. The MCS process is central in the stochastic simulation using random variables, where it can simulate the electrical components considering the grid’s behavior with the goal of evaluating its expected reliability parameters [1] [2] . It also provides distribution information for the load point indices, system indices, and the energy not served costs [3] [4] .

The goal of this work is to apply the Monte Carlo technique on the IEEE 34-node test system, shown in Figure 1, to evaluate the reliability of the distribution network using the applications of the smart grid concept considering different case scenarios. Specifically, we consider the impact of the automatic reclosers (ARs) as well as the distributed generators on the system with the optimal placement of the ARs on the feeder, as MCS helps in building an artificial history for each component operation for a simulation time, which was set in this work to be 2000 years. The work aims to compare the results obtained using MCS with results obtained previously for the same test system using another approach [5] . The work also seeks to produce a sufficient MATLAB code that can be used to perform MCS analysis and provide the famous reliability indices SAIDI, SAIFI, CAIDI, EUE, and ASAI for any study-scale electrical test systems. The results should reflect the definition of the smart grid that identifies the ability of a sys- tem for a self-healing, self-interrupting of faults [6] . Reference [7] shows diffe-

rent emerging technologies of the auto-reclosers that are now available in the industry.

Monte Carlo technique is one of the most powerful, efficient methods to evaluate the reliability of the power distribution grids. In this work, we simulate the IEEE 34 node test system using the MSC technique, through a MATLAB code that was written by the authors of this paper and shown in Appendix A of this work. After modeled the IEEE feeder, shown in Figure 1, we made a comparison with a previous study done on the same system but with using another approach. Based on the results, we found that the MCS provided similar results with those obtained using analytical technique [5] and DISREL, an intelligent based program that builds on the brute force concept. The study using the developed MCS MATLAB code shows the impact of the smart grid technologies in improving the reliability indices of the test feeder.

The study shows different scenarios of applying the auto reclosers and the DG units in various parts of the feeder. Furthermore, the automatic reclosers, once installed optimally in the grid as proposed by the software, significantly improve the reliability of the power distribution network by isolating the healthy parts of the system automatically, which maintain the service to a substantial number of customers and reduce the repair time. The distributed generators, although dated back to the late 1970’s, are now considered to be one of the applications that define the smart grid concept. The results of integrating them in the distribution feeder show the advantages of using reliable, assumed dispatchable, DG units near load center. Along with the installation of the automatic recloser, the DGs provide the opportunity of operating the distribution grid as a microgrid, allowing service to continue to parts in the network, something will be greatly admired especially during major outages and blackouts. Also, the study provided in this work shows the amount of energy (in kW) that is saved for the utility in this real life test feeder, through the EUE index which measures the reduction in the energy-not-served for each case option. Also, the comparison of these results with that one obtained previously on the same test feeder using the same real-life inputs shows the MCS MATLAB code we developed is effective, and serves as a tool that can be used in evaluating the reliability of distribution feeders when applying small modifications only. That reflects the difference from the test system used in this study.

Aljohani, T.M. and Beshir, M.J. (2017) Matlab Code to Assess the Reliability of the Smart Power Distribution System Using Monte Carlo Simulation. Journal of Power and Energy Engineering, 5, 30-44. https://doi.org/10.4236/jpee.2017.58003

clear;

N = 33; % number of components

lambda = [0.3979; 0.8209; 0.7666; 0.1206; 0.8577; ...

0.2586; 0.7049; 0.2429; 0.3521; 0.8118; ...

0.1850; 0.5135; 0.3920; 0.7194; 0.6776; ...

0.2065; 0.3197; 0.3226; 0.8566; 0.3348; ...

0.8950; 0.8833; 0.6400; 0.0412; 0.0518; ...

0.9458; 0.2257; 0.7303; 0.2191; 0.0101; ...

0.7205; 0.1289; 0.1327];

MTTR = [0.3546; 0.6970; 0.8490; 0.8724; 0.0411; ...

0.2098; 0.7382; 0.7379; 0.1978; 0.4534; ...

0.2299; 0.0704; 0.3979; 0.8555; 0.6809; ...

0.2954; 0.8536; 0.7195; 0.3405; 0.0495; ...

0.0174; 0.7846; 0.2554; 0.6597; 0.8496; ...

0.2965; 0.2238; 0.0066; 0.0684; 0.4306; ...

0.7953; 0.7759; 0.9673];

power = [0 55 0 16 0 0 0 5 34 0 0 4 40 7 45 15 146 82 ...

0 67 9 405 45 83 0 0 4 0 32 0 28 2 0 450];

users = ceil(power/2)-1;

%% failure history

duration = 1000; % years

interuption = 0;

outage_time = 0;

maxT = 0;

for i = 1:N

[downT{i},upT{i}] = failure_history2(lambda(i),MTTR(i),duration);

cur = max(upT{i}(1:end));

if (maxT < cur)

maxT = cur;

end

interuption = interruption + length(downT{i})-1;

outage_time = outage_time + sum(upT{i}-downT{i});

% figure;

line(1:length(downT{i}),downT{i});

line(1:length(downT{i}),upT{i},’color’,’r’,’Marker’,’.’);

end

% INDEXES calculation

average_interuption = interuption/duration;

average_outage_time = outage_time/duration;

customers_num = sum(users);

total_power = sum(power);

SAIFI = average_interuption*customers_num/customers_num;

SAIDI = average_outage_time*customers_num/customers_num;

CAIDI = SAIDI/SAIFI;

ASAI = (customers_num*8760 - average_outage_time*customers_num)/ (customers_num*8760);

EUE = average_outage_time*total_power; % kW*hour

disp(‘-------------------------------’);

disp(‘Step 1’);

disp([‘SAIFI ‘ num2str(SAIFI)]);

disp([‘SAIDI ‘ num2str(SAIDI)]);

disp([‘CAIDI ‘ num2str(CAIDI)]);

disp([‘ASAI ‘ num2str(ASAI)]);

disp([‘EUE ‘ num2str(EUE)]);

%% Step2 switches

switch_834_lines = [20 21 22 31 32];

switch_832_lines = [17 18 19 30 23 24 25 switch_834_lines];

switch_834_elements = [19 20 21 30 31];

switch_832_elements = [switch_834_elements 18 22 23 24 25 29 32];

interaptionXcustomer_number = 0;

interaptionXcustomer_duration = 0;

unservedEnergy = 0;

cur_t = 0;

while cur_t < maxT

% find next failure time

min_t = (duration + 1)*24*365;

fail_line_number = 0;

for i = 1:N

clear indx;

indx = find(downT{i} > cur_t);

if (~isempty(indx))

indx = indx(1);

if (downT{i}(indx) < min_t)

min_t = downT{i}(indx);

fail_line_number = i;

n = indx;

cur_outage_time = upT{i}(indx) − downT{i}(indx);

end

end

end

cur_t = upT{fail_line_number}(n);

in_switch_834 = ~isempty(find(switch_834_lines == fail_line_number));

customer_834 = sum(users(switch_834_elements));

power_834 = sum(power(switch_834_elements));

in_switch_832 = ~isempty(find(switch_832_elements == fail_line_number));

customer_832 = sum(users(switch_832_elements));

power_832 = sum(power(switch_832_elements));

% interaption calculation

if (~in_switch_832)

interaptionXcustomer_number = interaptionXcustomer_number + customers_num;

interaptionXcustomer_duration = interaptionXcustomer_duration + customers_num*cur_outage_time;

unservedEnergy = unservedEnergy + total_power*cur_outage_time;

else

if (in_switch_834)

interaptionXcustomer_number = interaptionXcustomer_number + customer_834;

interaptionXcustomer_duration = interaptionXcustomer_duration + customer_834*cur_outage_time;

unservedEnergy = unservedEnergy + power_834*cur_outage_time;

else

interaptionXcustomer_number = interaptionXcustomer_number + customer_832;

interaptionXcustomer_duration = interaptionXcustomer_duration + customer_832*cur_outage_time;

unservedEnergy = unservedEnergy + power_832*cur_outage_time;

end

end

end

% INDEXES calculation

SAIFI = interaptionXcustomer_number/customers_num/duration;

SAIDI = interaptionXcustomer_duration/customers_num/duration;

CAIDI = SAIDI/SAIFI;

ASAI = (customers_num*8760 − interaptionXcustomer_duration/duration)/ (customers_num*8760);

EUE = unservedEnergy/duration; % kW*hour

disp(‘-------------------------------’);

disp(‘Step 2’);

disp([‘SAIFI ‘ num2str(SAIFI)]);

disp([‘SAIDI ‘ num2str(SAIDI)]);

disp([‘CAIDI ‘ num2str(CAIDI)]);

disp([‘ASAI ‘ num2str(ASAI)]);

disp([‘EUE ‘ num2str(EUE)]);

%% Step 3 switches from Step 2 and DGs

switch_834_lines = [20 21 22 31 32];

switch_832_lines = [17 18 19 30 23 24 25 switch_834_lines];

switch_834_elements = [19 20 21 30 31];

switch_832_elements = [switch_834_elements 18 22 23 24 25 29 32];

interaptionXcustomer_number = 0;

interaptionXcustomer_duration = 0;

unservedEnergy = 0;

cur_t = 0;

while cur_t < maxT

% find next failure time

min_t = (duration + 1)*24*365;

fail_line_number = 0;

for i = 1:N

clearindx;

indx = find(downT{i} > cur_t);

if (~isempty(indx))

indx = indx(1);

if (downT{i}(indx) < min_t)

min_t = downT{i}(indx);

fail_line_number = i;

n = indx;

cur_outage_time = upT{i}(indx) − downT{i}(indx);

end

end

end

cur_t = upT{fail_line_number}(n);

in_switch_834 = ~isempty(find(switch_834_lines == fail_line_number));

customer_834 = sum(users(switch_834_elements));

power_834 = sum(power(switch_834_elements));

in_switch_832 = ~isempty(find(switch_832_elements == fail_line_number));

customer_832 = sum(users(switch_832_elements));

power_832 = sum(power(switch_832_elements));

customer_800 = customers_num-customer_832;

power_800 = total_power-power_832;

% interaption calculation

if (~in_switch_832)

interaptionXcustomer_number = interaptionXcustomer_number + customer_800;

interaptionXcustomer_duration = interaptionXcustomer_duration + customer_800*cur_outage_time;

unservedEnergy = unservedEnergy + power_832*cur_outage_time;

else

if (in_switch_834)

interaptionXcustomer_number = interaptionXcustomer_number + customer_834;

interaptionXcustomer_duration = interaptionXcustomer_duration + customer_834*cur_outage_time;

unservedEnergy = unservedEnergy + power_834*cur_outage_time;

else

interaptionXcustomer_number = interaptionXcustomer_number + customer_832;

interaptionXcustomer_duration = interaptionXcustomer_duration + customer_832*cur_outage_time;

unservedEnergy = unservedEnergy + power_832*cur_outage_time;

end

end

end

% INDEXES calculation

SAIFI = interaptionXcustomer_number/customers_num/duration;

SAIDI = interaptionXcustomer_duration/customers_num/duration;

CAIDI = SAIDI/SAIFI;

ASAI = (customers_num*8760 − interaptionXcustomer_duration/duration)/ (customers_num*8760);

EUE = unservedEnergy/duration; % kW*hour

disp(‘-------------------------------’);

disp(‘Step 3’);

disp([‘SAIFI ‘ num2str(SAIFI)]);

disp([‘SAIDI ‘ num2str(SAIDI)]);

disp([‘CAIDI ‘ num2str(CAIDI)]);

disp([‘ASAI ‘ num2str(ASAI)]);

disp([‘EUE ‘ num2str(EUE)]);

IEEE: Institute of Electrical and Electronics Engineering.

AR: Automatic Recloser.

SAIDI: System Average Interruption Duration Index.

DG: Distributed Generation.

CAIDI: Customer Average Interruption Duration Index.

U: Annual Unavailability Time.

EUE: Expected Un-served Energy.

R: Annual Outage Time.

λ: Failure Rate of an Electrical Component.

TTR: Mean Time to Repair.

TTF: Mean Time to Fail.

MCS: Monte Carlo Simulation.