Optimal Siting and Sizing of Distributed Generation Through Power Losses and Voltage Deviation Roger Samuel Zulpo, Roberto Chouhy Leborgne, Arturo Suman Bretas Department of Electrical Engineering Federal University of Rio Grande do Sul - UFRGS Porto Alegre, Brazil
[email protected],
[email protected],
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Abstract—This work aims at the optimal siting and sizing of distributed generation (DG) in distribution feeders. It is used an objective function which computes a penalty for voltage deviation in each bus coupled with the active power losses of the system. In this way, it is considered the equality and inequality constraints concerning the power flow, total apparent power of DG, number of installed DGs, fixed or variable power factor and voltage limits. To this end, it is implemented a nonlinear programming model with discontinuous derivatives, which employs binary variables to define the location of the generation through a classical optimization approach. Index Terms-- distributed power generation, energy efficiency, power quality, power systems, voltage control.
I.
INTRODUCTION
The distributed generation is a new way to meet some of the load of the electrical system that is gaining momentum due to several aspects. Among these, may be mentioned the reduction of losses in transmission and distribution lines, delaying investments in infrastructure, voltage control by reactive power injection and increased energy efficiency with the use of heat supplied during the generation. However, there are some points that need to be considered, such as lower revenues from utility costs, incentives to producers of clean energy, logistics related to the supply of fuel and equipment costs and maintenance [1].
algorithms, particle swarm or sensitivity analysis. The results, in general, shows that integrating DG with the power system, using the adequate power injection, can improve both the power losses and the voltage profile. It also can be seen that if the DG is installed at not appropriate locations without careful power dispatch study, the losses can increase and the voltage can achieve undesired values [2]-[7]. II.
OPTIMIZATION MODEL
A. Objective Function The optimization model proposed is aimed at the minimization of an objective function (1) which is composed of active power losses (2), directly related to economical concerns, and a penalty for voltage deviation (3) that is one of the most important power quality parameters [8]-[9]. The losses are calculated by means of the difference between the injected and the load active power. The voltage deviation is evaluated through its absolute value variation, being one pu the reference.
Legally, in Brazil, distributed generation is defined by the 5163 decree of 2004 which states, at article 14, that it is considered DG the electricity produced from utility, permissionaires or authorized agents connected directly to the electrical distribution system of the buyer. It is excluded from this context the hydropower with installed capacity greater than 30 MW, and thermal power plants with less than 75% energy generation efficiency. However, thermoelectric plants which use biomass or process waste as fuel need not to meet this percentage to be considered DG. In regards of the optimization problem, there are some published studies that consider power losses or voltage deviation through optimization techniques such as genetic This research is supported by CAPES and CNPq.
978-1-4673-6487-4/14/$31.00 ©2014 IEEE
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(1)
μ
(2)
|
1|
Where: µ: proportionality coefficient (kW/pu). P1: utility active power injection (kW). n: total number of buses. Pkdg: active power injection by the DG (kW). Pkl: load active power (kW). Vk: voltage absolute value (pu).
(3)
B. Line Model The line representation of the power syystem is shown in Fig. 1, where the shunt admittance (jbkmsh) is observed. The lines are considered to be balanced andd the buses are connected through an ykm admittance.
Furthermore, several limits can be included in the definition of the optimization probleem. The aim is to limit the search space, so the problem resollution time can decrease. Thus, there is the possibility of usiing limits for the voltage module, power injected into the sysstem and power factor, as shown in Table I. It is importantt to note that DG never demands active power of the system m, and the reactive power has a negative sign for an inductive characteristic and a positive sign for a capacitive one. TABLE I.
Figure 1. Line model.
C. Constraints Besides the objective function, binary ddecision variables (4) are considered. These define the alllocation or nonallocation of the DG in a particular system buus. 1, 0,
(4)
There are also equality and inequality cconstraints which evaluates the power flow (5) and (6), lim mit the maximum apparent power (7), guarantee the potenciees relationship (8) and adjust the power factor of each unit (9)), if wanted. Thus covering a multitude of configuration possibilities and analysis. 0
(5)
0
(6)
LIMITS FOR EACH VARIABLE
Variable
Minimum
Maximum
Vk
0.85
1.05
Pkdg
0
Sdg
Qkdg
-Sdg
Sdg
Skdg
0
Sdg
FPk
0
1
D. Problem Resolution m injection of active and In order to obtain the optimum reactive power in the network by th he DG, it is necessary to gather data on the system, such as lines, loads and the characteristics of the studied feed der. This information is inserted in MATLAB algorithm which w creates the nodal admittance matrix and all the variab bles used in the problem. Then the nonlinear constrained optim mization model is written in a text document in general alg gebraic modeling system (GAMS) format. Once this is done, the model can be sent to "NEOS Server for Optimization" where the results are obtained through KNITRO solver [10 0]. III.
CASE STUDY T
The system used is the IEEE 33 bus b shown in Fig. 2. It is a electricity distribution feeder of balaanced lines and loads. The substation is symbolized by bus 1 and has a nominal line voltage of 12.66 kV. It is also obseerved that there is a main section from 1 to 18 as well as threee side sections, from 2 to 22, from 3 to 25 and from 6 to 33.
(7) (8) (9) Where: ΔPk and ΔQk: active (kW) and reactivee (kVAR), power flow estimation error. Pkdg and Qkdg: active (kW) and reactiive (kVAR), DG injected power. Pkl and Qkl: active (kW) and reactivve (kVAR), load consumed power. Pkcalc and Qkcalc: active (kW) and reactivve (kVAR), power injection calculated. Skdg and Sdg: DG apparent power ((kVA) and total apparent power (kVA). FPk: DG power factor.
Figure 2. IEEE 33 bus sysstem topology.
In relation to the voltage level off the feeder, it can be seen that the minor voltage modules are given g in the furthest buses from the substation, as shown in Fiig. 3. The lowest value is 0.904 at bus 18, which is at the end of the main section of the feeder. It is also noticed that the high h level voltage in bus 19 is
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due to the system topology, since this point is connected near the substation. In this way, the vertical lines were added in Fig.3 to avoid any misunderstood regarding topology.
distributed generation, resulting in an OF value of 218.35, a reduction of 80.39 percent when compared to the base case. The result at bus 1 (square) shows the OF value when there is no DG in the system, thus all others buses can improve the system performance when injecting the proper amount of power.
Figure 3. IEEE 33 bus voltage profile.
As for the power flow, it can be seen briefly in Fig. 4. Each value presented is the injection of apparent power (kVA), into the section, by the first bus upstream the arrow. Thus, the apparent power injected by bus 6 in the section 6-33 is 951+j974 kVA. Note that positive values of reactive power are related to capacitive power factors.
Figure 4. IEEE 33 bus apparent power (kVA) injection.
IV.
RESULTS AND DISCUSSIONS
In order to verify if the model sent to KNITRO estimates the system correctly, this result is compared with power system analysis toolbox (PSAT), which is taken as reference, in Table II. What can be seen is that the values are the same for the system active power losses and the system total voltage deviation, considering three places after the decimal point. Note that, for this entire section, the objective function value is calculated using a proportionality coefficient of 500 kW/pu and the substation voltage is kept at 1 pu. TABLE II.
Figure 5. Optimal OF value for optimal power injection at each bus.
Also, what can be said is that for the section 1-18, the OF decreases till the best value then increases in each step. For section 19-22, it seems to be almost no variation in the function value, this may be explained because of the light load and high voltage profile of this stretch when there is no DG. For section 23-25, the best bus is the one closer to the main section, but this behavior does not occur in the 26-33 stretch where the best possible bus is the second one from the main feeder, which may be partially explained by the heavy spot load placed at bus 30. Fig. 6 shows the optimal active and reactive power injection when allocating one DG at a time. All buses show capacitive power factors, this can be explained due to the substation voltage combined with the penalty for voltage deviation. In this scenario, bus 7 optimal injection is approximate 4 MVA with a power factor of 0.815. The buses 20 to 22, which posses the worst OF values, are also the ones that inject the lowest values of active and reactive power, which seems to be connected with the light load of the branch. Note that bus 1 is disregarded since no distributed generation is installed at this point. It is also important to notice that with higher voltage levels on the substation, the optimal reactive power injection tends to decrease towards an inductive power, since the OF forces this behavior once it tries to minimize voltage deviation. The same operation occurs when the bus 1 voltage is decrease but in the opposite direction.
PSAT AND KNITRO COMPARISON
Variables Losses (kW) Deviation (pu) Objective Function
PSAT 210.988 1.805 1113.488
KNITRO 210.988 1.805 1113.488
Δ (%) 0.00 0.00 0.00
In this sense, Fig. 5 presents the optimal value of the objective function for a DG in each bus at a time, what can be observed is that the bus 7 offers the best possible location when combined with the optimal power injection by
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Figure 6. Optimal power injection at each bus.
In Fig. 7 it is shown the system active power losses due to optimal power injection at each bus a time, where the square symbol presents the losses for the system without DG, which is 211 kW. It is noticeable that even the bus 7, with proper power dispatch, being the optimal point of operation, it does not guarantee the lowest level of power losses, which occurs at bus 28 at 79 kW, a reduction of 62.52 percent. It is also interesting to observe that for some locations, as bus 2, 3 and 19, the optimal power injection increases the losses, which, of course, decreases the voltage deviation in order to minimize the objective function. That is, for some buses, it is interesting to sacrifice the energy efficiency of the feeder for the purpose of achieve a better voltage regulation.
Following this context, Fig. 9 presents a comparison between the voltage profiles of the base case (open circles), without DG; and the optimal injection on bus 7, which is the optimal bus for this objective function. The comparison shows that for each single bus, the deviation is minimized and the lowest voltage level of base case, which is 0.904 pu at buses 17 and 18, turns to 0.987 pu with the installed DG. Besides that, this injection reduces the active power losses from 211 to 86 kW, minus 59.41 percent.
Figure 7. System power losses for optimal power injection at each bus.
Figure 9. Comparison between the base case and optimal bus with the optimal power injection.
The idea is easier to understand when Fig. 8 is analyzed with the last two. This figure shows the system total voltage deviation when the optimal power is generated each bus at a time e. g. for bus 33 (last one), the optimal power injection is 1851+j1287 kVA (Fig. 6), this state reduces the active power losses from 211 to 106 kW (Fig. 7) and the total voltage deviation from 1.805 to 0.771 pu (Fig. 8) with this single DG installed and running at a optimal point for this bus. Still on Fig. 8, one can visualize that for all exposed cases, the total voltage deviation is smaller than the base case value, and the minimum occur on bus 7 at 0.265 pu, a reduction of 85.32 percent, and the worst value is presented on bus 22 at 1.774, a reduction of only 1.72 percent. Observing the Fig. 5 to 8 is simple to perceive that there are some buses much well suited to receive the DG and there some buses at which, even with an optimal power injection, the benefits to the system will be minimum.
V.
CONCLUSION
This work proposed a novel optimization model based on siting and sizing of DG, resulting in power losses and voltage deviation minimization through a classical optimization approach. In this sense, the model needs almost no tuning to work properly and it is extremely easy to implement. The studied case shows that the proper location and power injection of the distributed generation can significantly improve the system losses and voltage profile. It also exposes that the optimal point of operation is dependent on the system topology and load location, where some buses seems to be more adequate to receive the DG. As for other systems and cases, there are many possibilities of studies to be evaluated with this optimization model. The proportionality coefficient can be adjusted to a lower value in order to obtain better results with power losses, or it can be increased so that the voltage profile is the privileged characteristic. VI. TABLE III. Branch Sending Receiving number end end
Figure 8. Total voltage deviation for optimal power injection at each bus.
874
ANNEX
IEEE 33 BUS SYSTEM DATA R (ohms)
X (ohms)
Pa (kW)
Qa (kVAR)
1
1
2
0.0922
0.0477
100
60
2
2
3
0.4930
0.2511
90
40
3
3
4
0.3660
0.1864
120
80
4
4
5
0.3811
0.1941
60
30
TABLE III.
IEEE 33 BUS SYSTEM DATA (CONTINUATION)
Branch Sending Receiving number end end
R (ohms)
X (ohms)
Pa (kW)
Qa (kVAR)
5
5
6
0.8190
0.7070
60
20
6
6
7
0.1872
0.6188
200
100
7
7
8
1.7114
1.2351
200
100
8
8
9
1.0300
0.7400
60
20
9
9
10
1.0400
0.7400
60
20
10
10
11
0.1966
0.0650
45
30
11
11
12
0.3744
0.1238
60
35
12
12
13
1.4680
1.1550
60
35
13
13
14
0.5416
0.7129
120
80
14
14
15
0.5910
0.5260
60
10
15
15
16
0.7463
0.5450
60
20
16
16
17
1.2890
1.7210
60
20
17
17
18
0.7320
0.5740
90
40
18
2
19
0.1640
0.1565
90
40
19
19
20
1.5042
1.3554
90
40
20
20
21
0.4095
0.4784
90
40
21
21
22
0.7089
0.9373
90
40
22
3
23
0.4512
0.3083
90
50
23
23
24
0.8980
0.7091
420
200
24
24
25
0.8960
0.7011
420
200
25
6
26
0.2030
0.1034
60
25
26
26
27
0.2842
0.1447
60
25
27
27
28
1.0590
0.9337
60
20
28
28
29
0.8042
0.7006
120
70
29
29
30
0.5075
0.2585
200
600
30
30
31
0.9744
0.9630
150
70
31
31
32
0.3105
0.3619
210
100
32
32
33
0.3410
0.5302
60
40
Generation,” IEEE Transactions on Power Systems, vol. 21, nº 2, pp. 533-540, May 2006. [6] M. A. Kashem, A. D. T. Le, M. Negnevitsky, and G. Ledwich, “Distributed Generation for Minimization of Power Losses in Distribution Systems” in Power Engineering Society General Meeting IEEE, Montreal, Que., 2006, pp. 1-8. [7] C.Tautiva, A.Cadena. “Optimal Placement of Distributed Generationon Distribution Networks” in Universities Power Engineering Conference (UPEC), Proceedings of the 44th International, Glasgow, 2009, pp. 1-5. [8] R. A. Barr, P. Wong and A. Baitch, “New Concepts for Steady State Voltage Standards” in 15th International Conference on Harmonics and Quality of Power (ICHQP), Hong Kong, 2012, pp. 678-681. [9] C. Masetti, “Revision of European Standard EN 50160 on Power Quality: Reasons and Solutions” in 14th International Conference on Harmonics and Quality of Power (ICHQP), Bergamo, 2010, pp. 1-7. [10] R. H. Byrd, J. Nocedal and R. A. Waltz, “Knitro: An Integrated Package for Nonlinear Optimization,” unpublished. 6 Feb. 2006. Available: users.eecs.northwestern.edu/~rwaltz/articles/knitro paper.pdf
a. Load placed at receiving end.
VII. REFERENCES [1] [2]
[3]
[4] [5]
M. Rawson, “Distributed Generation Costs and Benefits Issue Paper,” California Energy Commission, California, CA, Rep. 500-04-048, July 2004. C. Bulac, F. Ionescu and M. Roscia, “Differential Evolutionary Algorithms in Optimal Distributed Generation Location” in 14th International Conference on Harmonics and Quality of Power (ICHQP), Bergamo, 2010, pp. 1-5. G. Celli, E. Ghiani, M. Loddo and F. Pilo, “Voltage Profile Optimization with Distributed Generation” in Power Tech IEEE, St. Petersburg, 2005, pp. 1-7. P. Chiradeja, “Benefit of Distributed Generation: A Line Loss Reduction Analysis” in Transmission and Distribution Conference and Exhibition IEEE/PES, Dalian, 2005, pp. 1-5. V. H. M. Quezada, J. R. Abbad, and T. G. S. Román, “Assessment of Energy Distribution Losses for Increasing Penetration of Distributed
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