GA-based Method for Performance Improvement of Distribution Systems Using DG Sources M. Abdel-Salam, M. Th. El-Mohandes, Ali M. Yousef, Alaa E. Abdel-Hakim and R. Ramadan* Department of Electrical Engineering Assiut University Assiut, Egypt
[email protected] with their determined locations in the first stage. The proposed methodology was tested on IEEE-33 bus system. The methodology was based on two unjustified assumptions. The authors assumed that the loss was based on the active components of the branch currents. However, the reactive components contribute also to the power loss in the distribution system. The authors assumed also that currents of all branches connected to a bus having a DG unit are changed by the same value of DG current. The same assumptions were adopted [9] for optimal placement of capacitor using GA for electric transmission systems. The objective function was multi objective including the minimization of (i) system loss, (ii) cost of capacitor and (iii) voltage deviation from nominal value at system buses. The proposed algorithm was tested on IEEE 6-bus system. The multi-objective function was formulated [10]-[12] for GA- based optimal location of DG units in radial distribution systems. The objective function was formulated [10] to minimize the power loss and to improve the tail-end node voltage. On the other hand, the objective function was formulated [11] to minimize the loss due to both the active and reactive components of the branch currents as well as to minimize the cumulative voltage deviations from the nominal value at system buses. The objective function was formulated [12] to minimize both the power loss and the fuel cost. The proposed algorithms were tested on IEEE 33-bus system [10], [11] and IEEE 5-bus system [12]. The multi-objective function was formulated [13] for GAbased optimal placement of static-var-compensator for minimization of both the installation cost and voltage deviation from nominal value at distribution-system buses. The proposed algorithm was tested on IEEE 30-bus system. A single objective function was formulated [14] for GAbased placement of DG units to reduce losses in distribution system. The B-matrix loss formula was used for power loss evaluation. The proposed algorithm was tested on IEEE 30bus system. The optimal placement of DG and capacitor units for minimizing power loss using GA was proposed before [15], [16]. The GA defines the location and size of capacitor units for minimum loss. At the same locations, the DG units were installed and their sizes were determined. The proposed algorithm was tested on IEEE -33bus system. It is worthy to mention the DG units inject active power [7]-[8], [11], [14]-[16] against active and reactive power [10]. It was not stated whether DG units inject active or
Abstract --This paper presents a Genetic Algorithm (GA)based method to determine the location and size of DG sources in distribution systems using single DG placement algorithm for determining the locations at first. Then, the GA is utilized to determine the global sizes of DG sources which minimize single- or multi-objective function related to these systems. The influence of active- and reactive-power injection on the sizing and placement of DG sources is investigated. The predictions of the proposed method as regards the sizing and placement of DG sources are compared with those obtained before using particle swarm optimization. Index Terms—DG placement, Genetic Algorithm, single DG placement algorithm, single objective function, multi objective function, IEEE 33-bus system.
I.
INTRODUCTION
As distribution generation (DG) accommodates green technology, its installation in distribution systems is continuously increasing. Distribution systems are characterized by low voltage level and high R/X ratio with a subsequent high power loss. Several techniques were attempted to reduce distribution losses such as capacitor installation [1], system reconfiguration [2], and DG installation [3]. Installing capacitor banks in distribution networks tends to reduce active and reactive power losses, increases feeder utilization and allows for the installation of more loads on existing distribution systems, thus increasing utility savings. Insertion of DG in distribution systems to minimize system losses depends [4] on mode of DG placement (single or multiple) and type of DG (DG injects P only or Q only or P and Q). Allocation of distribution generation at optimal places leads to decreased power loss and improving bus voltage profile [5], [6]. A two-stage methodology was proposed [7], [8] for placement and sizing of DG units to minimize loss in radial distribution systems. In the first stage, a single DG placement algorithm was used to find the optimal location of DG units. The optimal size and location of DG units in the system are defined to achieve maximum loss saving. For multi DG placement, the process is repeated by modifying the distribution system through insertion of the defined DG unit into the system one– by- one. In the second stage, a GA-based algorithm was developed to determine the optimal sizes of DG
1
reactive power [12]. This paper is aimed at presenting a GA-based method for performance improvement of distribution systems using DG sources. The paper is structured as follows: section II describes problem formulation, section III explains GA procedure and solution methodology for single and multi DG placement to determine the global optimum sizes of DG sources. Simulation results and discussions are reported in section IV. Finally, conclusions are reported in section V.
The inequality constraint limits the bus voltage tween a maximum limit and a minimum one, expressed by (7) .
be, as (7)
III. GA –BASED DETERMINATION OF OPTIMUM SIZES AT OPTIMUM LOCATION OF DG SOURCES This section illustrates how GA is used to size single and multi-DG sources and to determine the locations of DG sources using single DG placement algorithm. Two solution methodologies have been developed in this section.one for simple single DG placement and other for multiple DG placements.
II. PROBLEM FORMULATION A. The Objective Functions 1) Single Objective Problem Formulation: The main objective of the considered problems is to minimize the active power loss. Therefore, the problem can be formulated as a single objective optimization problem (SOP) where the power loss is the only objective to be optimized for a given distribution system. The objective function is expressed as follows to minimize the total active power loss PL [17]: ∑ ∑ (1) where N is number buses of distribution system and is the active power loss in a branch extending between and buses. 2) Multi Objective Problem Formulation: On minimizing the active power losses and improving the voltage profile for a given system, the problem is to be considered as a Multi-objective Optimization problem (MOP). Through MOP both objectives are to be optimized simultaneously. The MOP is formulated to combine two objective functions, i.e. active power losses minimization and voltage profile improvement. The goal is to combine these two objective functions into a single fitness function using weighting coefficients. The Multi-objective function is expressed as follows [18]: (2) where weighting coefficients for active power losses PL and voltage profile VP, respectively. (3) where . The objective function for power loss PL is expressed by (1). The objective function is formulated for voltage profile optimization as: ∑ (4) where is voltage set at 1 pu and is the pu voltage at the bus.
A. GA Procedure GA searches for the best DG size. For each location of DG, a power flow is made in order to assess the objective function which is requested to evaluate the DG size using GA as shown in Fig.1.
Input GA parameters
Start Create a set of possible solutions to the optimal DG-sizing problem
Run power flow and compute the objective function for each solution
Based –on the objective values, select next generation
Convergence (Stop criteria)
YES
NO Make reproduction using crossover and mutation Replace the old solution with new ones
B. Problem Equality and Inequality constraints Equality constraints lie in the balance of active and reactive powers [17]. The balance between the active power injected , the active power demand , and the active power loss at any bus i as expressed by (5). The same balance applies for the reactive power , , and as expressed by (6). (5) (6)
Stop and print result Optimal DG-sizing
New Generation Fig.1. Flow chart of GA-based DG –Sizing
B. Solution Methodology for Simple Single DG Placemen The optimal size of DG sources installed at given bus is determined by using GA. The procedure is repeated for all buses. The optimal location of DG is selected at the bus corresponding to the lowest value of objective function as shown in Fig.2.
2
5.
Set Bus No i=2
6.
Use GA to calculate optimized DG by inserting DG at bus i
7. 8. 9.
i=i+1
Record objective function at bus i
Remove DG inserted at bus i
YES
𝑖
Repeat step3 and 4for all combinations of GA population. Give objective function values as fitness values to the GA. Check GA convergence criteria if satisfied go to step9. Generate a new generation and go to step3. Print result for candidate buses. IV.
SIMULATION RESULTS AND DICUSSION
The proposed method has been tested on IEEE 33-bus radial distribution system [19]-with total load of 3.715 MW and 2.3MVAR as shown in Fig.3. The system has 32 lines connecting the 33buses. The system power losses PL is 0.203 MW for the base case (without DG sources) at a base voltage of 12.66 kV and a base MVA of 100 MVA. The minimum and maximum allowed bus voltages are set at 0.9 and 1 per unit [18], respectively. GA is used to optimize the sizing of DG sources installed in the system. Newton-Raphson algorithm based load flow is used to solve the load flow problem for the distribution system. The used GA parameters are population size of 30, maximum number of iteration of 51, number of DG units, crossover probability of 0.8, and maximum number of generations of 100. In multi objective function, the weighting coefficients for active power losses and voltage profile are = 0.9 and = 0.1, respectively [18].
𝑁𝑏𝑢𝑠
NO
Optimal location of DG = Bus number corresponding lowest value of objective function
END Fig. 2. Flowchart for finding optimal size and location of DG in distribution system using GA
C. Solution Methodology for Multi DG Placement The solution methodology for multi DG placement takes place in two steps. First step is to identify the optimal location of DG as determined by using single DG placement algorithm. Then, the optimal size of DG is selected at the optimal location using GA. 1) Optimal Locations of DG Sources : The above process is repeated for multiple DGs locations. The base system is modified by fixing the optimal size of DG at optimal location in distribution system at first one, i.e. inserting a DG unit into the system one-by-one. The obtained DG is placed in system forming a new base case and the steps of single DG placement are repeated. The optimal choice of sizes of DG sources may not be the optimal global ones. It is quite clear that the selected DG (size and location) is optimum at each DG source addition, but not for system a whole. However, the optimal global DG sizes are determined by using GA provided that the locations of DG sources. which are determined by single DG placement algorithm. 2) Global Optimal Sizes of DG Sources using GA: The following describes the procedure in steps by which the optimal size of multiple DG placements is obtained: 1. Input candidate buses, which are the optimal locations of DG sources, are determined by single DG placement and apply GA again. 2. Randomly select the initial GA population. 3. Apply power flow for the distribution system with the inserted DG at the optimal location. 4. Evaluate the objective function using power flow with DGs inserted from the GA search.
Fig.3. IEEE 33-bus test distribution system
A. The Optimal Size and Location of DG Sources Using Single Objective Function
Power losses after DGi (MW)
1) DG sources supplying Active power: a) Optimal locations of DG sources : In single DG placement, the optimum size of DG is calculated at each bus for base -case, Fig.4 shows the active power loss corresponding to installation of the optimum DG sources. As shown in Fig.4, the best location is at bus 6. Installation of a DG source with of 2.578MW capacity at bus 6 brings down the power loss to 0.104162MW. It is considered as the base –case of the second DG placement. 0.3
Case1
0.2 0.1 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Bus No
Fig.4. Power losses with DG placement at each bus of the base case at injecting active power using single objective function
The procedure is repeated to install of 0.438 MW at bus 15 to bring the loss down to 0.0927, as shown in Fig.5. Now the candidate location is bus 15 with 0.438 MW size and total power loss of 0.0927MW.
3
Case 2
Fig.5. Power losses with DG placement at each bus of the base case with added DG source at bus 6 at injecting active power using single objective function
I II
Installation of in addition to to the base-case forming the base-case of the third DG placement. The procedure is repeated to install of 0.66 MW at bus25 to drop the loss value to 0.0855 as shown in Fig.6. Table I reports the optimum sizes, locations and corresponding loss values for the three successive DG placements.
Voltage Magnitude (p.u)
Power losses after PDGi (MW)
0.1
III
Case 3
0.05
0 1
7 10 13 16 19 22 25 28 31 Bus No Fig.6. Power losses with DG placement at each bus of the base case with added DG sources at buses 6 and 15at injecting active power using single objective function
Loss reduction %
0.203 0.10416 0.0927 0.0855
-----48.76 55.66 57.88
2.57 1.96 0.565 1.78 0.568 0.773
2.577 1.97 0.575 1.75 0.575 0.7826
2.577 0.104
48.76
2.525 2.5464 0.089
2.57
56.157
3.121
3.0884 0.079
61.1
1.02 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86
Fig.7. comparison of voltage magnitude with and without of DG using GA (with globally optimized three DG placement) at injecting active power using single objective function
active power using single Power Losses (MW)
6 6 15 6 15 25
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Bus No Base case(no DG sources) Case I( one DG source inject P at bus 6 ) Case II (two DG sources inject P at buses 6 and 15) Case III (three DG sources inject P at buses 6,15 and 25)
4
Table I- Placement of single DG source injecting objective function Bus DG size No. (MW) Present Previous Present Previous [20] [20] ----0 0 6 6 2.57 2.4886 15 15 0.438 0.4406 25 25 0.66 0.6473
6 6 15 6 15 25
Loss Reduction %
1 3 5 7 9 111315171921232527293133 Bus No
Power losses (MW)
0
Previous [20]
0.02
Present
0.04
Previous [20]
0.06
present
0.08
previous [20]
Table II- Global optimum sizes of DG sources injecting active power for candidate buses by GA using single objective function Total DG Bus DG Size Size No. (MW) (MW)
present
0.1
Case
Power losses after PDGi (MW)
0.12
2) DG Sources Supplying Reactive Power: a) Optimal locations of DG Sources: In single DG placement algorithm, the optimum size of DG is calculated at each bus for base -case, Fig.8 shows the active power loss corresponding to installation of the optimum DG sources. As shown in Fig.8, the best location is at bus 30. Installation of a DG source with of 1.251 MVAR capacity at bus 30 brings down the power loss to 0.143879MW. It is considered as the base –case of the second DG placement. This process is repeated following same procedure with DG sources supplying active power but the reactive replaces the active power.
The solution obtained above is a local optimum solution and not the global optimum solution. The optimum locations of DG sources are obtained from the single DG placement algorithm. With these locations, optimum sizes of DGs are determined by using GA. The results are shown in Table II. b) Global Optimal Sizes of DG Sources: The results tabulated in Table II clearly show that there is reduction in active power loss of system after adding DG sources. Total DG capacity installed in the system is smaller for multi DG placement in comparison with single DG placement. The percentage loss reduction assumed high values for global optimal sizes, Table II, in comparison with local optimal sizes, Table I. Fig.7 shows the voltage profile over the buses of the distribution system for the base –case, and the case with globally optimized three DG placement, respectively. The lowest voltage at bus 18 is improved from 0.913 to 0.974.
power losses after QDGi (MW)
0.3 Case 1
0.2 0.1 0
1 3 5 7 9 111315171921232527293133 Bus No
Fig.8. Power losses with DG placement at each bus of the base case at injecting reactive power using single objective function
As shown in Fig.9 the best location is at bus 13 of the second DG placement.
4
As shown in Fig.10 the best location is at bus 24 of the third DG placement. Table III reports the optimum sizes, loca tions and corresponding loss values for the three successive DG placements. power losses after QDGi (MW)
0.2
optimized three DG placement, respectively. The lowest voltage at bus 18 is improved from 0.913 to 0.937, but still below the minimum limit of bus voltage. The problem inequality constraints expressed by (7) was not achieved. It was impossible to adjust voltage at all system buses to line within the required ( = 0.95 and =1.05 p.u). With the increase of the reactive power, the losses decrease at a slow rate when compared with active power injection. Also, the voltage profile is improved at a slow rate with reactive power injection when compared with that due to active power injection.
Case 2
0.15 0.1
0.05 0
Voltage Magnitude in(p.u)
1 3 5 7 9 111315171921232527293133 Bus No
Fig.9. Power losses with DG placement at each bus of the base case with added DG source at bus 30 at injecting reactive power using single objective function
Case 3
power losses after QDGi (MW)
0.15 0.1
0.05 0 1 3 5 7 9 111315171921232527293133 Bus No
Fig.10. Power losses with DG placement at each bus of the base case with added DG sources at buses 30 and 13 at injecting reactive power using single objective function
1.251 0.359 0.488
0.1439 0.13695 0.133887
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Bus No Base Case (no DG sources) Case I(one DG source inject Q at bus 30) Case II (two DG sources inject Q at buses 30 and 13) Case III (three DG sources inject Q at buses 30,13 and 24)
Fig.11. comparison of voltage magnitude with and without of DG using GA (with globally optimized three DG placement)
B. The Optimal Size and Location of DG Sources Using Multi Objective Function
Table III- Placement of single DG source injecting reactive power using single objective function Bus DG size Power Loss No. (MVAR) losses reduction (MW) % ----- 0 0.203 ----30 13 24
1.02 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86
1) DG Sources Supplying Active power: a) Optimal locations of DG sources: As explained before, the same procedure of using single objective function expressed by (1) is applied using multi objective function expressed by (2). In single DG placement algorithm, the optimum size of DG is calculated at each bus for the base-case.
29.11 32.5 34.045
The solution obtained above is a local optimum solution and not the global optimum solution. The optimum locations of DG sources are obtained from the single DG placement algorithm. With these locations, global optimum sizes of DG sources installed in the system are determined by using GA. The results are shown in Table IV. b) Global Optimal sizes of DG Sources: The results tabulated in table IV clearly shows that there is reduction in active power loss of system after adding DG sources. The same as for active-power injection, the total DG capacity installed in the system is smaller for multi DG placement in comparison with single DG placement.
Table V- Placement of single objective function Bus DG No. Size (MW)
DG source injecting active power using multi multiobjective function
Power losses (MW)
Loss reduction %
----
0
0.3532
0.203
-----
6 16 25
3.72 0.52 0.488
0.156 0.136 0.1305
0.1217 0.1282 0.1251
40.89 36.85 38.37
The solution obtained above in Table V is a local optimum solution and not the global optimum solution. The optimum locations of DG sources are obtained from the single DG placement algorithm. With these locations, global optimum sizes of DG sources installed in the system are determined by using GA. The results are shown in Table VI. b) Global Optimal sizes of DG Sources: Voltage profile is improved and an active power loss is also reduced. The result of the global optimum sizes for candidate buses by GA as shown in Table VI. The result tabulated in Table VI clearly shows that there is reduction in active power loss of system after adding DG sources. Total DG capacity installed in the system is smaller for multi DG placement in comparison with single DG placement.
Table IV- Global optimum sizes of DG sources injecting reactive power for candidate buses by GA using single objective function Total Power Loss Case Bus DG size DG losses reduction No. No. (MW) size (MW) % (MW) Base ------------0.203 ------I 30 1.251 1.251 0.1439 29.11 30 1.117 II 1.489 0.13615 32.93 13 0.372 30 0.995 III 1.939 0.1325 34.729 13 0.375 24 0.569
Fig.11 shows the voltage profile over the buses of the distribution system for the base –case, and the case with globally
5
Fig.12 shows the voltage profile over the buses of the distribution system for the base –case, and the case with globally optimized three DG placement, respectively. The lowest voltage at bus 18 is improved from 0.913 to 0.9975.
VI. [1]
[2]
Voltage Magnitude in(p.u)
Loss reduction %
----3.72 2.819 0.778 2.693 0.713 0.88
Power losses (MW)
--6 14 26 6 15 32
Previous [18]
Previous [18]
Base --I 6 II 6 16 III 6 16 25
Present
Present
Case
Table VI- Global optimum sizes of DG sources injecting active power for candidate buses by GA using multi objective function Bus DG Total DG size No. size (MW) (MW)
0 3.72 3.597
0 3.6581 3.5292
0.203 0.121 0.1077
-----40.89 46.95
[5]
4.286
3.7197
0.097
52.22
[6]
[3]
[4]
[7]
1.02 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86
[8]
[9]
[10]
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Bus No Base Case (no DG sources) Case I(one DG source inject P at bus 6) Case II(two DG sources inject P at buses 6 and16 ) Case III (three DG sources inject P at buses 6 ,16 and 25 )
[11]
[12]
Fig.12. comparison of voltage magnitude with and without of DG using GA (with globally optimized three DG placement)
[13]
V. CONCLUSIONS 1) The predictions of the proposed method as regards the placement and sizing of DG sources (injecting active power) agreed with those obtained before using PSO for single objective function. 2) The predictions of the proposed method as regards sizing of DG sources only agreed with those obtained before using PSO for multi-objective function. However, the placement of the sources is different. 3) With the increase of active-power injection by DG sources in distribution systems, the losses decreased faster and the voltage profile is better improved when compared with reactive-power injection. 4) Global optimum sizing of DG sources recorded smaller sizes when compared with local optimum sizing. 5) Power losses assumed lower values on using global optimal sizing of DG sources in comparison with local optimal sizing. 6) Use of multi-objective function resulted in better improvement of voltage profile on the expense of increasing the system losses when compared with the use of single objective function.
[14]
[15]
[16]
[17]
[18]
[19]
[20]
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