Optimal Integration of Distributed Renewable Generation in Distribution Network for Reliability Enhancement

The electrical power system comprises three key parts: generation, transmission and distribution systems [1]. The failure of vertical approach system that is of transmitting power from generation through the transmission to the load centre has inherent technical losses leading to increase in interruption frequency and interruption duration of power supply resulting in poor reliability of power supply to the consumers with severe economic impact. The poor reliability of power supply to consumers particularly at the distribution level raised many concerns on economic impact on both the utility provider and consumers. One of the solutions to vertical approach system is to extend the existing power system to cater for the increase in power demand but unfortunately large-scale facilities construction faces significant obstacle [2]. It is also established that 90% of power losses and frequent interruptions can be traced to the distribution network thereby making distribution network vulnerable to frequent interruption [3]. The increase in the demand for electrical power has made the expansion of the existing distribution networks inevitable. However, this increase faces significant obstacles when building large-scale facilities (power plants and transmission networks). Therefore, researchers and utility companies are looking for feasible, time-saving and economical techniques to cope with the demand and subsequently improve poor power system reliability. The solution proposed by most researchers revolves around Distributed Renewable Generations (DRGs) [4]. Increased interest in renewable energy resources comes from the desire to have clean, cheap and reliable electric power in line with the Sustainable Development Goals (SDGs) which project affordable and Clean Energy, Sustainable Cities and Communities and Responsible Consumption and Production termed SDG 7, SDG 11 and SDG 12 respectively. These discentralized and modular distributed renewable generation can be installed quickly by utilities or end users without the need for large scale utility projects with their insistence bottlenecks. However, how to properly and carefully site, locate and integrate these decentralized and modular distributed generation in the distribution network and with what method is a source of concern. This necessitated this research work with the development of an improved cuckoo search algorithm for optimal DRGs sizing and positioning in a large and real distribution network.

3.1 System description

The WAEC 88-Bus radial distribution system in Ikorodu distribution unit was used as test system. The line, load and reliability parameters were collected from Ikorodu business unit and Ikeja distribution company in Nigeria as presented in Appendixes A and B. The sub-station base voltage and MVA values are 11 kV and 15 MVA respectively. The total system active load is 11,654 kW while the total active power loss before DRG integration is 2120 kW with a minimum voltage of 0.9368 p. u at Bus 85. The single line diagram of a simple radial distribution system is presented in Figure 1 while the Single line diagram of 88-Bus WAEC 11 kV radial distribution network with 3-integrated DGs shown in Figure 2. Figure 3 presents the modified cuckoo search optimization computational implementation procedure.

tu_pian_17.png

Figure 1. Single line diagram of simple radial distribution system

tu_pian_18.png

Figure 2. Single line diagram of 88-Bus WAEC 11 kV radial distribution network with 3-integrted DG

tu_pian_19.png

Figure 3. Improved cuckoo search optimization computational implementation procedure

3.2 Problem formulation

In this work, the optimal sizing and location of distributed generation in WAEC-88 Bus radial distribution network is formulated as an objective problem. The main objective function of this research is to minimize the real power loss and improve reliability and voltage profile with DRG integration. Therefore, evaluation of power loss was conducted using BIBC-BCBV matrix method.

In implementation of BFSM Kirchhoff’s current and voltage laws are used. The real and reactive power flowing from Bus ‘i’ to Bus ‘j’ are calculated using Backward direction rule, that is from receiving node to sending node.

The real power flowing is given as

$P_{\mathrm{ij}}=\left(P_{\mathrm{j}}+P_{\mathrm{lj}}\right)+R_{\mathrm{ij}} \frac{\left(P_{\mathrm{j}}+P_{\mathrm{lj}}\right)^2+\left(Q_{\mathrm{j}}+Q_{\mathrm{lj}}\right)^2}{V_{\mathrm{i}}^2}$     (1)

Also, the reactive power flowing is given as

$P_{\mathrm{ij}}=\left(P_{\mathrm{j}}+P_{\mathrm{lj}}\right)+R_{\mathrm{ij}} \frac{\left(P_{\mathrm{j}}+P_{\mathrm{lj}}\right)^2+\left(Q_{\mathrm{j}}+Q_{\mathrm{lj}}\right)^2}{V_{\mathrm{i}}^2}$     (2)

where, $P_{\mathrm{lj}}$ and $Q_{\mathrm{lj}}$ are connected loads at Bus ‘j’.

The forward direction rule was used to calculate the angle and voltage magnitude at each node as follows:

We assume that a voltage $V_{\mathrm{i}}<\emptyset_{\mathrm{i}}$ at Bus ‘i’ and $V_{\mathrm{j}}<\emptyset_{\mathrm{j}}$ at Bus ‘j’ resulted into current ‘í’ and ‘j’ flowing through line ‘N’ with an impedance of $Z_{\mathrm{ij}}=R_{\mathrm{ij}}+X_{\mathrm{ij}}$. Backward forward sweep method was chosen because of its simple computational procedure, fast, high convergence rate and requires less memory compared to the conventional methods. Therefore, the current flowing is calculated thus:

$I_{\mathrm{ij}}=\frac{V_{\mathrm{i}}<\emptyset_{\mathrm{i}}-V_{\mathrm{j}}<\emptyset_{\mathrm{j}}}{R_{\mathrm{ij}}+j X_{\mathrm{ij}}}$     (3)

and

$I_{\mathrm{ij}}=\frac{P_{\mathrm{i}}-Q_{\mathrm{j}}}{V_{\mathrm{i}}<-\emptyset_{\mathrm{i}}}$     (4)

Evaluating Eqs. (3) and (4) above gave the voltage at Bus ‘j’.

$\begin{gathered}V_{\mathrm{j}}=\left[V_{\mathrm{i}}^2-2 \times\left(P_{\mathrm{i}} R_{\mathrm{ij}}+j Q_{\mathrm{i}} X_{\mathrm{ij}}\right)+\left(R_{\mathrm{ij}}^2+X_{\mathrm{ij}}^2\right) \times\right. \\ \left.\left(\frac{P_{\mathrm{i}}^2+Q_{\mathrm{i}}^2}{V_{\mathrm{i}}^2}\right)\right]\end{gathered}$     (5)

Therefore, the power losses per branch between nodes ‘i’ and ‘j’ through ‘N’ line is given as

$P_{\text {loss(ij) }}=R_{\mathrm{ij}} \frac{\left(P_{\mathrm{ij}}^2+Q^2{ }_{\mathrm{ij}}\right)}{V_{\mathrm{j}}^2}$     (6)

$Q_{\text {loss }(\mathrm{ij})}=X_{\mathrm{ij}} \frac{\left(P_{\mathrm{ij}}{ }^2+Q^2{ }_{\mathrm{ij}}\right)}{V_{\mathrm{j}}{ }^2}$     (7)

This implies that the total real and reactive power losses in the distribution network with ‘M’ number of branches can be written as:

$P_{\text {loss }(\mathrm{ij})}=\sum_{j=1}^M P_{\text {loss }(\mathrm{ij})}$      (8)

$Q_{\text {loss(ij) }}=\sum_{j=1}^M Q_{\text {loss(ij) }}$      (9)

The fitness function to minimize the total real power loss is expressed as:

$F=\min \left(P _{\mathrm{L}}=\sum_{i=1}^N I_{\mathrm{i}}^2 R_{\mathrm{i}}\right)$     (10)

where, N is the total number of branches, I is the line current in branch i and R is the resistance of the branches.

The constraints to be satisfied when minimizing the objective function are:

A. Power balance constraint

$\sum P_{\mathrm{DG}}+P_{\text {grid }}=\sum P_{\text {loss }}+P d$     (11)

where, $P_{\text {loss}}$ is the total active power loss in the network, $Pd$ is the active power demand, Pgrid is the active power from utility and $P_{\mathrm{DG}}$ is the active real power generation.

B. Bus constraint

The Bus voltage magnitude must satisfy legal requirement and design limitation restriction limits. Therefore, the voltage magnitude limits are expressed as:

$0.95 \leq V_{\mathrm{i}} \leq 1.0$      (12)

where, 0.95 and 1.0 are the lower and upper voltage Vᵢ at Bus ‘i’.

C. Distributed generation size constraint

Generally, the active power limits of the generator are restricted within a given maximum and minimum limits. Therefore, the DG unit total power limit is expressed as:

$P_{D G}^{\min } \leq P_{\mathrm{DG}} \leq P_{D G}^{\max }$     (13)

where, $P_{\mathrm{DG}}$ is the total power generation of DG units, $P_{DG~}^{min}$ and $P_{DG~}^{max}$ are the lower and upper limits of DG.

D. Reliability indices techniques

The first category is called load point indices or global indices or primary indices, which comprise of average failure rate, λₐ, average outage time, rₐ, and average annual outage time, Uₐ and are expressed mathematically as:

$\lambda_{\mathrm{a}}=\sum_{\mathrm{i}} \lambda_{\mathrm{i}}$    (14)

$U_{\mathrm{a}}=\sum_{\mathrm{i}} \lambda_{\mathrm{i}} r_{\mathrm{i}}$     (15)

$r_{\mathrm{a}}=\frac{\sum_i \lambda i . r_{\mathrm{i}}}{\sum_i \lambda i}$     (16)

The second category is called system indices which are averages that measure every customer’s in the same way. They are generally accepted as reliability measures of worth and often used as reliability benchmarks and for target improvement. These are System Average Interruption Frequency Index (SAIFI), System Average Interruption Duration Index (SAIDI), Customer Average Interruption Duration Index (CAIDI) and Average Service Availability (Unavailability) Index (ASAI) (ASUI). These are expressed mathematically as follows:

$\begin{gathered}S A I F I=\frac{\text { total number of sustained outages per customer }}{\text { total number of served customers }} \\ =\frac{\sum_{\mathrm{i}}\left(\lambda_{\mathrm{i}} \times N_{\mathrm{i}}\right)}{\sum_{\mathrm{i}} N_{\mathrm{i}}}(\text { out } / \text { cust. } \text { yr })\end{gathered}$    (17)

where, λᵢ and Nᵢ are failure rate and number of customers at load point i, respectively. This is used to measure the number of outages an average customer encounter over a period of a year.

$\begin{gathered}S A I D I=\frac{\text { Sum of sustained outages length by a customer }}{\text { total number of served customer }} \\ =\frac{\sum_{\mathrm{i}}\left(U_{\mathrm{i}} x N_{\mathrm{i}}\right)}{\sum_{\mathrm{i}} N_{\mathrm{i}}}(h r / \text { cust. } y r)\end{gathered}$    (18)

where, Uᵢ is annual average time at load point i and Nᵢ stands for number of customers at load point i. This is utilized to evaluate the unavailability of power supply in a year per customer.

$\begin{gathered}C A I D I=\frac{\text { Sum of sustained outages lenght by acustomer }}{\text { total number of customer outages }} \\ =\frac{\sum_{\mathrm{i}}\left(U_{\mathrm{i}} x N_{\mathrm{i}}\right)}{\sum_{\mathrm{i}} \lambda_{\mathrm{i}} .N_{\mathrm{i}}}(h r / c u s t . i n t)\end{gathered}$   (19)

where, Uᵢ, λᵢ and Nᵢ are annual average time, failure rate and number of customers at load point i respectively. This is utilized to ascertain the time taken by the utility during contingencies.

$\begin{gathered}A S A I=\frac{\text { Service available hours to customer }}{\text { customer hours demanded }} \\ =\frac{\sum_{\mathrm{i}} N_{\mathrm{i}} .8760-\sum_{\mathrm{i}} U_{\mathrm{i}} . N_{\mathrm{i}}}{\sum_{\mathrm{i}} N_{\mathrm{i}} .8760}\end{gathered}$    (20)

$\begin{gathered}A S U I=\frac{\text { Service unavailable hours to customer }}{\text { customer hours demanded }} \\ =\frac{\sum_{\mathrm{i}} U_{\mathrm{i}}.N_{\mathrm{i}}}{\sum_{\mathrm{i}} N_{\mathrm{i}} . 8760}\end{gathered}$   (21)

ASAI and ASUI are indices used to calculate power received and not received per customer. When the ASAI value is high, the ASUI value is less and vice visa.

AENS = average energy not supplied

$\begin{gathered}A E N S=\frac{\text { total energy not supplied }}{\text { total number of customer served }} \\ =\frac{\sum_{\mathrm{i} E E N_{\mathrm{i}}}}{\sum_{\mathrm{i}} N_{\mathrm{i}}}(k W h r / c u s t . y r)\end{gathered}$    (22)

3.3 Improved cuckoo search method

3.3.1 Cuckoo search technique

Cuckoo search technique (CST) is a simulation of random walk processes of cuckoo species searching for suitable host next to lay their eggs. This is proposed by Yang and Deb [28]. It is a population-based algorithm with simple procedure and less control parameters. There are specified principles to be followed when using cuckoo search algorithm in solving optimization problems. These principles are:

1. A cuckoo lays only one egg at a time. This egg will be dumped in a randomly chosen nest from a fixed number of host nests that are available at that time.
2. The nests that contain high quality eggs are termed better solution and are considered as next solution.
3. The number of host nests is assumed to be fixed and the probability that host bird will detect an alien egg is given as Pa = [0,1]. In detecting a strange egg, the host bird will throw away the strange egg or erect a new nest entirely.

Levy flights random walk and selective random walk are used by cuckoo in laying their eggs in host nests. Levy flight is a random walk used to generate new solution and can be expressed mathematically as:

$S_{\mathrm{i}}^{\mathrm{t}+1}=S_{\mathrm{i}}^{\mathrm{t}}+\alpha \otimes \operatorname{Lev} y(\beta)$      (23)

where, $\alpha ~$denotes change of position and is expressed as:

$\alpha=\alpha^0 \times c \times\left(S_{\mathrm{i}}^{\mathrm{t}}-S_{\mathrm{best}}\right)$     (24)

where, ${{\alpha }^{0}}$ is the scaling factor with an assigned value of 0.1.$S_{\mathrm{b}_{\mathrm{est}}}$ represents the global best solution so far obtained and c represents a random step size generated with the help of Levy distribution and is expressed as:

$c=\frac{\mathrm{U}}{|v|^{1 / \beta}}$    (25)

Therefore, substituting Eqs. (24) and (25) in Eq. (23) we have

$S_{\mathrm{i}}^{\mathrm{t}+1}=S_{\mathrm{i}}^{\mathrm{t}}+\alpha^0\left(\frac{\mathrm{u}}{|v|^{\frac{1}{\beta}}}\right)\left(S_{\mathrm{i}}^{\mathrm{t}}-S_{\mathrm{b}_{\mathrm{est}}}\right)$     (26)

$u=randn~\left( size~\left( s \right) \right)*\sigma $    (27)

$v=randn~\left( size~\left( s \right) \right)$     (28)

where, the sigma function$~\sigma $ is expressed as

$\sigma_{\mathrm{u}}=\left(\frac{\left(\Gamma(1+\beta) \times \sin \left(\pi \times \frac{\beta}{2}\right)\right.}{\Gamma\left(\frac{1+\beta}{2}\right) \times \beta \times 2^{(\beta-2) / 2}}\right)^{1 / \beta}$  (29)

β is a constant and usually set to a value of 1.5. Г represents a gamma distribution and u and v are random numbers from normal distribution. In implementing cuckoo search algorithm these have values attached as shown in Eqs. (20) and (21).

Probability based random walk

This is usually used to detect the new global best. Here, current best is considered as a base vector with two different solutions which are randomly selected then the new global solution is determined through probability formulations. That is

If r < Pa then

$S_{i, m}^{t+1}=S_{i, m}^t+\operatorname{rand}\left(S_{p, m}^t-S_{q, m}^t\right)$      (30)

If not, we have

  $S_{i, m}^{t+1}=S_{i, m}^t$     (31)

where, p and q are random integer numbers and m represents m^th dimension of solution while rand is random number in the range of (0,1) and Pa is fractional probability.

3.3.2 Accuracy and convergence rate

Cuckoo search technique was improved to increase the efficiency, that is enhancing the accuracy and the converging rate of the system. Two modifications are made one on levy flight step size and the second on addition of information exchange between two groups of top eggs formulated. The value of step size in CS is one while in ICSA the step size value decreases as the number of generations increases resulting in increase in localized searching between the eggs or DRGs. Therefore, performing levy flight on nest or network Sᵢᵗ and generating new egg or DRG or solution Sᵢᵗ⁺¹ while distancing the worst nest or DRG from the best nest or DRG using the modified equation:

$\begin{gathered}S_{\mathrm{i}}^{\mathrm{t}+1}=\operatorname{round}\left(S_{\mathrm{i}}^{\mathrm{t}}+0.01 *\left(\frac{u}{|V|^{1^{\prime} \beta}}\right) *\left(S_{\mathrm{i}}^{\mathrm{t}}-\right.\right.  \left.\left.S_{\mathrm{i}}^{\mathrm{t}} \text { best }\right) * \operatorname{randn}\left(\operatorname{size}\left(S_{\mathrm{i}}^{\mathrm{t}}\right)\right)\right)+D / N I^2\end{gathered}$    (32)

where,

$u=randn(size\left( s \right)*\sigma $      (33)

$\text{v}=randn(size\left( s \right)$     (34)

$\sigma_{\mathrm{u}}=\left(\frac{\left(\Gamma(1+\beta) \times \sin \left(\pi \times \frac{\beta}{2}\right)\right.}{\Gamma\left(\frac{1+\beta}{2}\right) \times \beta \times 2^{(\beta-2) / 2}}\right)^{1 / \beta}$   (35)

We move a distance = $\left|S_{\mathrm{i}}^{\mathrm{t}}-S_{\mathrm{j}}^{\mathrm{t}}\right| / 0.1$ from worst nest to best nest to find the new solution expressed as

$S_{\mathrm{i}}{ }^{\mathrm{t}+1}=S_{\mathrm{i}}{ }^{\mathrm{t}}$ worst $+\frac{\left|S_{\mathrm{i}}^{\mathrm{t}}-S_{\mathrm{j}}^{\mathrm{t}}\right|}{0.1}$     (36)

In order to achieve the aim of this study, the outage data from WAEC distribution network in Ikorodu Business unit was collected using quantitative method. The reliability status of the network was determined to ascertain its healthiness through load flow analysis after data collected was processed and analysed using backward-forward sweep method for load flow analysis. The improved cuckoo search algorithm was employed for DRG integration at optimal location and size in the distribution network. Cuckoo search algorithm toolbox which was coded in MATLAB generated both optimal distributed renewable generation size and site as outputs. The size and site generated as outputs for 2DRG and 3DRG were integrated separately in the distribution network Figure 2 using Eq. (27) with computational procedure of Figure 3 in MATLAB software environment. The optimal 2-DRGs location and size are Bus 88 with 1000 kW and Bus 70 with 1000 kW. Also, the optimal 3-DGs location and size are Bus 88 with 1000 kW, Bus 76 with 1000 kW and Bus 53 with 1000 kW. Thereafter, the reliability indices values were calculated using Eqs. (10)-(15).

The following parameter are set prior to starting:

NBus_Min=2, NBus_Max=88,

DG_Size_Min=10, DG_Size_Max =1000,

Max_Iter=20, Initial Step_Size =2.

In conclusion, the viability of this design system was first tested on WAEC distribution network using Backward-Forward sweep method in MATLAB 2021 software environment for achieving the reliability enhancement. The ICSA provides both optimal location and sizing of DRGs as outputs. It is also demonstrated that the proposed method is capable of reducing power loss, reliability indices: SAIFI, SAIDI, CAIDI, EENS, AENS and ASAI coupled with improvement in ASUI and voltage profile by comparing the results before and after optimization in a real and large Nigeria distribution network. The study recommends further study on Impact of DRGs auxiliary components degradation, detailed reliability cost, economics studies, cost benefit analysis and worth analysis in distribution network.