Distribution System Reconfiguration Considering ...

Journal of Science & Technology 101 (2014) 012-019

Distribution System Reconfiguration Considering Distributed Generation for Loss Reduction Using Gravitational Search Algorithm Nguyen Thanh Thuan1, Truong Viet Anh2,* 1

2

Dong An Polytechnic University of Technical Education Ho Chi Minh City, No.1, Vo Van Ngan, Thu Duc District, Ho Chi Minh City Received: March 04, 2014; accepted: April 22, 2014 Abstract This paper presents a method for determining radial configuration of distribution network which is used in reconfiguration problem and an effective method based on Gravitational Search Algorithm(GSA) to identify the tie switchs in distribution network with Distributed Generation (DG). The main objective is to reduce the real power losses in the system while satisfying all the distribution constraints. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on 8 buses, 16 buses, 33 buses, 69 buses systems and the results are presented and compare with the TOPO/PSS-Adept software and PSO Algorithm.The simulation results have showed that the method of determining the radial configuration enables the optimization algorithms do not lose results and GSA algorithms are powerful optimization algorithm with a fast convergence and can be applied in reconfiguration distribution network problems having large searching space. Keywords: Reconfiguration, Gravitational Search Algorithm, Loss Reduction.

This paper uses GSA to reconfigure the electric distribution network with DG connection to reduce power loss. The major contribution of this research is to present a method of determining the optimal operating structure for the network and a simple method of determining the radial structure to achieve the minium power loss.

1. Introduction *

The distribution network transfers the electric energy directly from the intermediate transformer substations to consumers. The transmistion networks are often operated with loop or radial structures, the distribution networks are always operated radially. By operating radial configuration, it significantly reduces the short-circuit current. The restoration of the network from fauls is implemented through the closing/cutting manipulations of electrical switch pairs located on the loops, consequently, hence, there are many switches on the distribution network. Network reconfiguration is the process of altering the topological structures of distribution feeders by changing the open/close status of the sectionalizers and tie switches, while respecting system constraints to satisfy the operator's objectives. This is a non-linear optimization problem, the objective function is always interrupted so it is difficult to solve the problem by the traditional mathematical techniques. In recent years several optimization methods have been proposed for solving the reconfiguration problem such as GA, PSO, ACS, ABC [1-4], which is contributed to improve the convergence and calculation speed and the newest technique which is developed based on Newton’s laws is the Gravitational Search Algorithm (GSA). This algorithm has showed many advantages in solving optimization problems [5-7]

2. Mathematical model The distribution network often uses loop structure but operates radially through open switches in the electrical systems.The power loss on the system is equal to the total loss on the branches [1,3,4]. 𝑁

𝑁

𝑃𝑙𝑜𝑠𝑠 = ∑ 𝑘𝑖 ∆𝑃𝑖 = ∑ 𝑘𝑖 . 𝑅𝑖 . |𝐼𝑖 |2 𝑖=1 𝑁

= ∑ 𝑘𝑖 𝑖=1

𝑃𝑖2

+ 𝑉𝑖2

𝑖=1 𝑄𝑖2

(1)

Where, ΔPi : active power loss on the ith branch N : total number of branches Pi, Qi : active power and reactive power on the ith branch Vi, Ii : connection bus voltage of the branch and current on the ith branch Ploss : active power loss of system ki : state of switches, if ki = 0, the ith switch opens and vice versa.

*

Corresponding Author: Tel: (+84) 913117659 Email: [email protected]

12


To reduce power loss of the electric distribution network, the objective function is: F(x) = min (Ploss)

(2)

And the network constraints must be satisfied are voltage and current that maintained within their permissible ranges to maintain power quality. 𝑉𝑖,𝑚𝑖𝑛 ≤ |𝑉𝑖 | ≤ 𝑉𝑖,𝑚𝑎𝑥 |𝐼𝑖 | ≤ 𝐼𝑖,𝑚𝑎𝑥

(3) (4)

To solve the problem, power flow problem should be solved many times for network reconfiguration and the Radial network structure must be retained in all cases.

Fig. 1. Objects interact with each other

3. Gravitational search algorithm

-

GSA is one of the optimal algorithms which are recently developed by Rashedi in 2009 [5, 6, 7]. The algorithm is based on Newton’s rules on gravity load and mass. In GSA, each element is considered as one object (Fig.1) and its characteristics are measured by their masses. Each object represents one solution or part of solution to solve the problem. All candidate solutions (objects) attracted each other by gravity force and this force of attraction is produced due to the movement of all objects to the direction of objects having heavier mass. Due to heavier objects having better objective function value, they describe better the solution to handle the problem and they move slowly than lighter ones representing worse solutions. GSA is described in details as follows: -

𝑑 𝐹0𝑑 (t) = ∑𝑁 (8) 𝑗=1,𝑗≠𝑖 𝑟𝑎𝑛𝑑𝑗 𝐹ị𝑗 (t) where randj is a random number in the interval [0,1].

-

𝑀𝑎𝑗 (t)+ 𝑀𝑝𝑖 (t) 𝑅𝑖𝑗 +𝜀

(9)

+ 1) = 𝑟𝑎𝑛𝑑𝑖 . 𝑉𝑖𝑑 (t) + 𝑎𝑖𝑑 (t) (10) 𝑑 𝑑 𝑑 𝑋𝑖 (t + 1) = 𝑋𝑖 (t) + 𝑉𝑗𝑖 (t + 1) (11) where randi is a random number in the interval [0,1]. -

(5)

-

(𝑋𝑗𝑑 (t) − 𝑋𝑖1 (t)) (6)

where Maj is the active gravitational mass related to agent j, Mpi is the passive gravitational mass related to agent i, G(t) is gravitational constant at time t, ε is a small constant, and Rij(t) is the Euclidian distance between two agents i and j: 𝑅𝑖𝑗 (t) = ||𝑋𝑖 (t), 𝑋𝑗 (t)||2

𝑀𝑖𝑖

where 𝑀𝑖𝑖 is the inertial mass of ith agent.

Initially, the agents of the solution are defined randomly and according to Newton gravitation theory, a gravitational force from mass j acts mass i at the time t is specified as follows:

𝐹𝑖𝑗𝑑 (t) = G(t)

𝐹𝑖𝑑 (t)

𝑉𝑖𝑑 (t

where: 𝑋𝑖𝑑 presents the position of ith agent in the dth dimension -

The acceleration (adi (t)) and velocity (Vid (t + 1)) of the ith agent at t time and t+1 time in dth dimension are calculated through law of gravity and law of motion as follows: 𝑎𝑖𝑑 (t) =

At the beginning of the algorithm the position of a system are described with N (dimension of the search space) masses:

𝑋𝑖 = (𝑋𝑖1 , . . . , 𝑋𝑖𝑑 , . . . , 𝑋𝑖𝑛 ) with i = 1,2,...,N.

The total force acting on the ith agent is calculated as follows:

The gravitational constant, G is a function of the initial value (G0) and time (t): G(t) = G(𝐺0 , t) (12) Gravitational and inertia masses are calculated by the fitness evaluation. A heavier mass means a more efficient agent. This means that better agents have higher attractions and move more slowly. Assuming the equality of the gravitational and inertia mass, the values of masses are calculated using the fitness function. The gravitational and inertial masses are updated by the following equations:

𝑀𝑎𝑖 = 𝑀𝑝𝑖 = 𝑀𝑖𝑖 = 𝑀𝑖 , i = 1,2, … , N. 𝑚𝑖 (t) =

(7)

𝑀𝑖 (t) =

𝑓𝑖𝑡𝑖 (t)+𝑤𝑜𝑟𝑠𝑡(t) 𝑏𝑒𝑠𝑡(𝑡)−𝑤𝑜𝑟𝑠𝑡(t) 𝑚𝑖 (t) ∑𝑁 𝑗=1 𝑚𝑗(t)

(13) (14) (15)

where fiti(t) represent the fitness value of the agent i at time t. 13


𝑏𝑒𝑠𝑡(t) = min 𝑓𝑖𝑡𝑗 (t); j ∈ (1, … 𝑁) 𝑤𝑜𝑟𝑠𝑡(t) = max 𝑓𝑖𝑡𝑗 (t) , 𝑗 ∈ (1, … 𝑁)

Where, switchi and switchj are the collection of switches belonged only to the independent i loop and the independent j loop respectivily; switchij is the collection of switches belonged to two independent loops i and j.

(16) (17)

4. GSA application in distribution network reconfiguration 4.1. Definition and controlled variables

1 sw1

In the reconfiguration problem of power network, switches are considered as controlled variables. These switches have two states “0” for tie switches and “1” for the closed ones. But when the power network is larger, the switch number is more numerous, the searching space of every open switch is greater. In [1], the algorithm for checking the system radial topology is proposed. However when performing this algorithm, the problem becomes complicated, the searching space is larger since the feasible searching space is not limited. Some researches in [2,4] proposed the method of determining the tie switches and the searching space by independent loops. However as each switch is placed only in one unique independent loop at specific times, the best solutions will be lost. For instance, considering the power network in Fig. 2 there are two independent loops. Assuming the best system structure has two tie switches being sw7 and sw9. However, If independent loops are defined as follows:

sw2

7

2

sw3

3

sw8

8

sw7

sw4

sw9 sw6

6

sw5

4

5

Fig. 2. 8-bus network

Begin Input data of network, Determine the search pace of every switches in independent loops Generate initial population (Each agent presents for one network configuration) Evaluate fitness for each agent (Solving power flow for every network configuration). Evaluate the operating constrains (Vmin, Radial topology)

Loop_1 includes switches: sw2, sw8, sw9, sw6, sw7

Update G, minimum power loss (best) and maximum power loss (worst) of agents in population

Loop_2 includes switches: sw3, sw4, sw5 This definition will not give the best solution since the problem shall have two open switches and the searching space of the first switch will be in Loop_1, the second open switch will be in Loop_2. While the best solution is placed in space of Loop_1.

Calculate acceleration and velocity for each agent using (9),(10) Update the position of agents. The configurations are changed depent on the value of velocity and acceleration

To solve this matter, the paper recommends the method for determining the number of open switch and the radial configuration of power network as follows:

YES

Meeting end of criterion? NO Return best solution (network configuration has minimum power loss)

The number of open switch equals to the number of independent loop and is determined by the expression: 𝑁𝑠𝑤𝑖𝑡𝑐ℎ = 𝑁𝑙𝑜𝑜𝑝 = 𝑁𝑏𝑟𝑎𝑛𝑐ℎ − 𝑁𝑏𝑢𝑠 + 1

End

(18)

Fig. 3. DeltaP reduction flowchart for GSA algorithm

Loopj = [switchj]

If the open switch i belong to independent Loopi then the searching space of secondary open switch j will be Loopj + Loopij and inverse if open switch i belong to Loopij then the searching space of the secondary open switch j will be Loopj.

Loopij = [switchij]

4.2. The distribution network reconfiguration

1 ≤ i, j ≤ Nloop

GSA algorithm in the problem is described as follows:

The element number of each independent loop is defined: Loopi = [switchi]

14


Step 1: Determine the searching space include the number of tie switches, searching space of each tie switch.

number; the result is compared to PSO and TOPO/PSS/Adept algorithms respectively. Case 1:

Step 2: Create the randomly parameters ( position of open switches via Eqs.5). Each collection of tie switches is considered as an agent and the tie switches of collection are considered the position of the agent.

Loop_1=[s2, s4, s7, s8, s5] and Loop_2 = [s3, s6, s9] The proposed algorithm gives the smallest power loss of 71.87 kW with two tie switches are selected at s8, s9

Step 3: Calculate the value of objective function for each agent (power loss to each agent) via Eqs.1 is implemented by solving power flow problem. Step 4: Update the value of G(t), minimum power loss best(t), maximum power loss worst(t) and Mi(t) with i = 1, 2, …N via Eqs.12, 15, 16 and Eqs.17. Mi(t) presents relationship between power loss of current configuration with configurations have minimum power loss and maximum power loss and others in current iteration. Step 5: Calculate the total force in different directions via Eqs.8. Value of total force presents the interaction between two network configurations (two agents) Step 6: Calculate acceleration and velocity via Eqs.9 and via Eqs.10. Velocity values present the change of switches’s position in each configuration.

Fig. 4. Convergence characteristics of 8-bus network power loss in case 1

Step 7: Update the position of agents (position of tie switches via Eqs.11) Step 8: Return to step 3 until stopping criteria has been achieved Step 9: Result output, which returns the configuration has the minimum power loss. Step 10: Finish Fig. 3 presents the proposed flowchart to perform network reconfiguration for power loss reduction using GSA algorithm. 4.3. Numerical Results The distribution network reconfiguration based on GSA is tested in Matlab software, its result is compared to that performed in TOPO/ PSS/ADEPT and PSO algorithm respectively.

Fig. 5. Convergence characteristics of 8-bus network power loss in case 2 Table 1. Comparison of two cases performing algorithm with performance result from PSS/AdeptTopo

4.3.1. 8-bus distribution network Considering the simple distribution network includes one generating unit of 12.6 kV connected to bus 1, 7 load buses and 9 switches. The system parameters are shown in appendix 1. Single line diagram is shown in Fig. 2. The initial system has two tie switches of s5 and s7 with the real power loss of 86.06 kW. Using GSA algorithm with searching dimension of d = 2, the number of agent N = 3 and Iteration = 10, calculating the best configuration of two cases determining the different independent loop

Method Initial configuration TOPO/ PSS/ADEPT Case 1 (PSO) Case 1 (GSA) Case 2 (PSO) Case 2 (GSA) 15

Loss (kW) 86.06 68.50

Open Iterations switch s5, s7 s7, s8 -

71.87 71.87 68.53 68.53

s8, s9 s8, s9 s8, s7 s8, s7

4 3 8 4


Case 2: Loop_1=[s2, s5, s8], Loop_2 = [s3, s6, s9] and Loop_12 = [s4, s7] The proposed algorithm gives the smallest power loss of 68.53 kW with two tie switches of s8, s7 The two results collected in these 2 cases have shown: - GSA has fast convergence degree. With the agent number of N=3 and the same initial conditions, in case 1, GSA algorithm converges after 3 iterations while PSO converges after 4 iterations. In case 2, GSA converges after 4 iterations and PSO takes 8 iterations to find the best configuration of power network.

Fig. 7. Convergence characteristics of power loss of 16-bus test system without DG at bus 9

- The proposed technique for determining independent loops has found the solution which is better than the method in case 1 since the proposed solution do not miss good solutions. In case 1, both GSA and PSO algorithm have found the best configuration but this is not a global optimal configuration. At that time, with the definition of recommended independent loop, both the algorithms have found the best performance configuration of the power network with the smallest power loss. Fig. 8. Convergence characteristics of power loss of 16-bus test system with DG at bus 9

4.3.2. 16-bus test system 16-bus test system have parameters stated in [8], initial configuration having power loss of 511.4 kW corresponding to tie switches of s5, s11, s16 (Fig. 6). Assuming at bus 9, one DG having the output power of 16.38 + j8.943 MVA is used [9]

From the results shown in Table 2, the use of DG in the distribution network will supply the local energy and contribute to reduce of transmission power loss on the network and the use of GSA algorithm has found the best network configuration after 2-3 iterations while PSO algorithm takes 3-5 iterations when both algorithms have used the same initial searching space. This result is similar to that executed from TOPO and some recommended papers.

In this problem, the searching dimension of d = 3, the agent number of N = 10, Interaction = 25. After performing GSA, it found the best operating configuration with open switches of s9, s7, s16 and loss of 469.4 kW in case of without DG (Fig. 7). While in case of with DG is connected to the system, the open switches are s2, s14 and s16 with the power loss of 136.37 kW (Fig. 8).

1

s6 8

s1 DG

4 s9

s2 5 s5

s3 6

11

s4

IEEE 33-bus test system (Fig.9) have parameters shown in [8], using 4 DG [10, 11] with parameters are given in table 3. The initial configuration did not connect with DGs having power loss of 203.679 kW corresponding to open branches: 25-29, 18-33, 9-15, 12-22 and 8-2. As for the 33-bus power network, the author used the searching dimension of d = 5, the agent number of N = 20, interaction = 50. The proposed algorithm found the new configuration with the open branches of 7-8, 25-29, 9-10, 14-15, 32-33 and loss of 138.876 kW. But when applying GSA it takes only 5 iterations to find out the best configuration while PSO takes 23 iterations with the same initial searching space as shown in Fig.10.

3

2 s1

13

s8

s7 9

9

10

14

s16

s14

s11

s10

s13

12 7

4.3.3. IEEE 33-bus distribution network

16

s15

15

Fig. 6. 16-buses test system 16


Table 2. Comparison of GSA algorithm with performance result by PSS/Adept-Topo and PSO in 16-bus test system Method

Loss (kW) Open switch Iterations System without DG

Initial 511.4 s5, s11,s16 configuration Topo/ 469.4 s7, s9, s16 PSS/Adept PSO 469.4 s9, s7, s16 GSA 469.4 s9, s7, s16 [3, 8] s9, s7, s16 System connecting to DG atbus 9 Initial 279 s5, s11, s16 configuration Topo/ 136.37 s2, s14, s16 PSS/Adept PSO 136.37 s2, s14, s16 GSA 136.37 s2, s14, s16 [9] 137.46 s2, s14, s16

3 2 Fig. 11. Convergence characteristics of power loss of 33-bus network with DGs

-

Table 4. Comparison of GSA algorithm to result performed by PSS/Adept-Topo and PSO in 33-bus network

5 3 25

Method

Loss (kW) Open switch System without DGs Initial 25-29, 18-33 203.679 configuration 9-15, 12-22, 8-21 Topo/ 7-8, 25-29, 9-10, 140.05 PSS/Adept 14-15, 32-33 7-8, 25-29, 8-9 PSO 138.876 14-15, 32-33 7-8, 25-29, 8-9 GSA 138.876 14-15, 32-33 21-8, 14-15, 8-9 [8] 139.5 28-29, 32-33 System with DGs Topo/ 7-8, 28-29, 9-10, 111.45 PSS/Adept 14-15, 32-33 7-8, 28-29, 8-9 PSO 111.45 14-15, 32-33 7-8, 28-29, 9-10 GSA 111.45 14-15, 32-33 7-8, 28-29, 9-10 [10, 11] 111.45 14-15, 32-33

Table 3. Parameters of DGs [4] No. 1 2 3 4 23

Bus 4 7 25 30

2

3 4

5

20 21

27 28

7 6

19

Q (kVar) 37.5 48.4 96.9 0

24 25

26

1

P (kW) 50 100 200 100

29 30 31

8

10 9

32 33

11 12 13 14

16 17 15

18

22

Fig. 9. IEEE 33-bus test system

Iterations 23 5 -

12 15 -

When putting 4 DGs into operation, the algorithm convergence characteristics are shown in Fig.11, with power loss of 111.145 kW after 12 iterations, while PSO algorithm converges after 15 iterations. The recommended algorithm result is fully similar to that performed by TOPO in PSS/Adept. 4.3.4. IEEE 69-bus test system IEEE 69-bus test system is proposed in [12] with initial configuration having power loss of 224.955 kW corresponding to open branches: 50-59, 27-65, 13-21, 11-43 and 15-46. In this case, the searching dimension of d = 5, the agent number of N = 25, interaction = 50 are used.

Fig. 10. Convergence characteristics of power loss of 33-bus network without DGs

17


GSA algorithm optimize the best tie switches in the distribution network with integrated DG based on the objective function of reducing the real power loss. The algorithm is simulated by Matlab 2008 and 8, 16, 33, 69 buses power networks are used for algorithm assessment.

28 29 30 31 32 33 34 35 47 48 49 50 53 54 55 56 57 58

60 61 62 63 64 65 59

66 67

1

2

5 3

6 7

10

8

4

9

68 36

14 15 16 17 18 19 20

12 11

The simulation results shown that the proposed method for determining the radial power network helps the optimal algorithms do not miss good solutions. Aplication of GSA algorithm in the distribution network reconfiguration problem has found the best configuration of power network quickly, efficiently from the power network of diffenrent power networks

22 23 24 25 26

13

21

27

69

37 38 39 40 41 42 43 44 45 46

Fig.12. 69-bus test system

Appendix 1: The data of 8-bus system From 1 2 2 2 3 4 5 6 7

Fig. 13. Convergence characteristics of power loss of 69-bus network Table 5. Comparison of GSA algorithm to result performed by PSO and PSS/Adept-Topo software in 69-bus network. Initial TOPO conf. 50-59 11-43 27-65 14-15 Open 13-21 13-21 branch 11-43 56-57 15-46 61-62 P 224.95 98.59 (kW) Loops -

GSA

PSO

[13,14]

11-43 14-15 13-21 57-58 61-62

11-43 14-15 13-21 55-56 62-63

11-43 61-62 58-59 13-14 12-13

98.57

99.75

98.90

12

5

It can be seen from the simulation results that the algorithm has found a new configuration with open branches of 11-43, 14-15, 13-21, 56-57, 61-62 and the power loss of 98.57 kW. While with the same initialed conditions, PSO algorithm has converged after 5 iterations and did not only find the global optimal configuration to the system but also dropping into the local optimization with power loss of 99.75 kW corresponding to open switches of 11-43 14-15 13-21, 55-56 and 62-63. (Fig. 13)

To 2 3 4 5 6 8 7 7 8

Line data R (p.u.) 1.091869255 1.091869255 1.091869255 2.18373851 1.091869255 1.091869255 2.18373851 2.18373851 1.091869255

Bus 1 2 3 4 5 6 7 8

Bus data Angle MW 0 0 0 0 0 0.3 0 0.05 0 0.5 0 0.5 0 0.1 0 0.1

X(p.u.) 1.902972131 1.902972131 1.902972131 3.805944261 1.902972131 1.902972131 3.805944261 3.805944261 1.902972131

MVar 0 0 0.15 0.03 0.4 0.3 0.05 0.05

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