DG Placement in Loop Distribution Network with New Voltage Stability Index and Loss Minimization Condition Based Planning Approach under Load Growth
Abstract
:1. Introduction
- (1)
- DG allocation in LDN with a new VSI based approach.
- (2)
- Derivation of formulations for LM; based on equivalent electrical models of LDN.
- (3)
- Evaluation of loss minimization condition (LMC) in LDN with single and two DGs under various power factors (PF); such as unity PF (PF1) and lagging PF (PFL), respectively.
- (4)
- Demonstration of planning approach (comprised of two variants) on 69-bus test DN.
- (5)
- Demonstration of DG allocation in LDN as first variant of planning approach for LM and VM.
- (6)
- Demonstration of three cases (variant 2) with various scenarios for one and two DG placement.
- (7)
- Evaluations of DGP under load growth scenarios.
- (8)
- Detail comparison of single and two DG placement on various performance indicators.
- (9)
- Overall comparison of results with other methods available in the literature.
2. Background Concepts
2.1. Voltage Assesment Method for Loop Distribution Network
2.2. Loss Minimization Formulations in Loop Distribution Network
2.2.1. Loss Minimization Case without Distributed Generation Units in Loop Distribution Network
2.2.2. Loss Minimization Case with One Distributed Generation Unit in Loop Distribution Network
2.2.3. Loss Minimization Case with Two Distributed Generation Units in Loop Distribution Network
2.2.4. Impact of Distributed Generation Units Operating at Various Power Factors on Loss Minimization
2.3. Distributed Generation Penetration by Percentage in Loop Distribution Network
2.4. Cost of Energy Losses in Loop Distribution Network
2.5. Annual (Annualized) Investment Cost of Distributed Generation Units
3. Proposed Planning Approach
3.1. Variant 1: Potential Locations for Distributed Generation Units in Loop Distribution Network
- (1)
- Find potential locations for DG allocation in test LDN.
- (2)
- Considers DGP at PF1 and PFL equal to PF of test LDN, respectively.
- (3)
- The impacts of DGP have shown in terms of proposed VSI values and associated voltage profile; respectively.
- Step 1
- Read system data and select the potential tie-switch (TS) for the loop case, as in [36].
- Step 2
- Run the power flow for test LDN without DG at normal load level (CP-SLL).
- Step 3
- Calculate proposed VSI and receiving end node voltage (VR) value, for real case at each node in the loop in accordance with Equations (1) and (2), respectively, as derived in [36].
- Step 4
- Select the node with minimum VSI value, since this node is potential candidate for first DG (DG1) placement.
- Step 5
- Run power flow for test LDN with DG1 at normal load level. Increase capacity of DG1 at lagging power factor ± 2% (or unity power factor), which is equal to the power factor of DN load (0.82 ± 2%). The PFL is taken 0.82 ± 2% as a reference to cater small load variations.
- Step 6
- Calculate proposed VSI for real case at DG node in LDN according to Equation (1) i.e., resulting voltage at node with DG as in Equation (2); approaches a numerical value close to 1.0 pu, that is nearly equal or little less than substation reference voltage; respectively.
- Step 7
- Select the node with minimum VSI value after DG1 installation, since this new node is the potential candidate for second DG (DG2) placement.
- Step 8
- Repeat step 5 i.e., the power flow across the TL and ITL must be ideally zero, such that the VSI and VR values of end nodes across TL (including TS) have a minimum difference of numerical values, according to Equations (1) and (2), respectively.
- Step 9
- Furthermore, increase and decrease the capacities of DG2 and DG1 (at PF1 or PFL = 0.82 ± 2%) in steps; and find out the LMC according to Equations (11a) and (11b), respectively.
- Step 10
- When the end-nodes across the TL (including TS) have the lowest difference of the numerical values according to Equations (1), (2), (11a) and (11b); the condition for VM and LMC has met, i.e., respective DG capacities and their power factors (PF) are optimal choices.
3.1.1. Discussion on Results with Type-II Distributed Generation Units in Loop Distribution Network
3.1.2. Discussion on Results with Type-I Distributed Generation Units in Loop Distribution Network
3.2. Variant 2: Impact of Distributed Generation Units under Normal and Increased Load
3.2.1. Case 1: Distributed Generation Unit Placement in Loop Distribution Network at Normal Load
- Scenario 1
- LM with one DG operating at PF1.
- Scenario 2
- LM with one DG operating at PFL equal to PF of DN (0.82 ± 2%).
- Scenario 3
- VM with one DG operating at PF1.
- Scenario 4
- VM with one DG operating at PFL equal to PF of DN (0.82 ± 2%).
- Scenario 5
- Simultaneous LM and VM with two DGs operating at PF1.
- Scenario 6
- Simultaneous LM and VM with two DGs operating at PFL equal to the PF of test DN (0.82 ± 2%).
- Step 1
- Repeat Steps 1–4, same as in variant 1 (case 0) and place DG at the weakest node.
- Step 2
- Run the power flow for test LDN at normal load, increase the capacity of DG (at PF1 or PFL = 0.82 ± 2%) in steps and calculate proposed VSI and VR for real case at each node in loop according to Equations (1) and (2) i.e., resulting voltage at node with DG according to Equation (2) approaches close to 1.0 pu (nearly substation reference voltage); respectively. This step gives two scenarios for VM with single DG operating at PF1 and PFL (C1/S3 and C1/S4), respectively.
- Step 3
- Decrease the capacity of DG (at PF1 or PFL equal to 0.82 ± 2%) in steps and find out the LM according to Equations (9a) and (9b), respectively.
- Step 4
- When LMC with one DG has achieved according to Equations (9a) and (9b), i.e., the end-nodes across the TL (including TS) have the lowest difference of the numerical values VSI and VR; according to Equations (1) and (2), respectively. The respective DG capacities and their operating power factors are the optimal choices. This step gives two scenarios (C1/S1 and C1/S2) for LM for single DG operating at PF1 and PFL, respectively.
- Step 5
- Repeat step 2 and place second DG in test LDN. Increase the capacity of DG at PF1 or PFL = 0.82 ± 2% in steps and calculate proposed VSI and VR according to Equations (1) and (2), respectively.
- Step 6
- Decrease the capacity of DG1 and increase the capacity of DG2 in steps at PF1 or PFL equal to 0.82 ± 2%. Then find out the LM according to Equations (11a) and (11b), respectively.
- Step 7
- When LMC has achieved according to Equations (11a) and (11b), i.e., the end-nodes across the TL (including TS) have the lowest difference of the numerical values according to Equations (1) and (2), the condition has met the respective DG capacities and their power factors are the optimal choice. This step gives two scenarios (C1/S5 and C1/S6) for LM and VM with two DGs, each operating at PF1 and PFL, respectively.
3.2.2. Case 2: Impact of Same Distributed Generation Unit Capacity as Case 1 under Load Growth
3.2.3. Case 3: Impact of Modified Distributed Generation Unit Capacity under Load Growth
4. Evaluation of Results and Discussion
4.1. Evaluation of Results for Case 1
4.2. Evaluation of Results for Case 2
4.3. Evaluation of Results for Case 3
5. Performance Analysis and Comparison of Results
5.1. Performance Analysis of the Proposed Planning Approach
- DG capacities (DGC) in each case: The DG capacities, numbers, locations, operating power factors, and applications; utilized in the performance analysis of all cases (1–3) and their relevant scenarios (1–6); have summarized in Table 2.
- Active and reactive loss minimizations: It has found that scenario 6 in all cases (1–3) outperforms their relative counterparts from the perspective of LM. It is worth-mentioning that single DG for LM follows Equation (9). Whereas, two DGs for LM, requires to obey Equation (11).
- DG Penetration (DG%) in loop distribution network: It has been observed that scenario 5 in all cases (1–3) outperforms their relative counterparts from the perspective of DG penetration, in particular, type-I DG operating at PF1 and represents the application of renewable energy generation (REG) such as photovoltaic power based DG [34].
- Capacity Release from sub-station in loop distribution network: It has been observed that scenario 6 in all cases (1–3) outperforms their relative counterparts from the perspective of capacity release in distribution network due to the reduction of power flows from the substation with two DGs at optimal location and size, respectively.
- Annual investment cost (AIC) of distributed generation units: The annual investment cost (AIC) for DGs operating at respective PF (by type) in each case is shown in million USD ($). It has found that scenario 2 perform better among the two scenarios for LM with single DG. Similarly, scenario 4 in all cases performs better among the two scenarios for VM with single DG. However, high AIC values for scenario 6 in comparison with other scenarios seems justified due to the application of simultaneous VM and LM, with two DGs placed at the optimal location and relative capacity, respectively.
- Active power loss reduction by percentage (P_LR): It has been observed that scenario 6 in all cases (1–3) outperforms their relative counterparts from the perspective of active power loss reduction in LDN by percentage. The reason is a reduction of power flows from the substation and active and reactive powers are fed directly to the loads with two DGs at the optimal location, size, and PFL; respectively.
- The cost of Active Power losses (CPL): The cost of active power losses (CPL) have presented in million USD ($), with DG operating at relevant PFs in each case, respectively. It has been observed that scenario 6 in all cases (1–3) outperforms their relative counterparts from the perspective of CPL aiming at the application of LM, with two DGs in LDN.
- Analysis of VSI values and Voltage Profile: It has been observed that during normal loading scenarios in case 1 and load growth scenarios in case 3; scenario 6 outperforms the other respective scenarios from the perspective of better VSI values and voltage profile. Thus, satisfying both the LMC (Equations (11a) and (11b)) and VM conditions (Equations (1) and (2)), as aforementioned in the variant 2 of proposed planning approach (Section 4), respectively.
5.2. Comparison of the Results
5.2.1. Active (System) Losses Reduction vs. Distributed Generation Capacity
5.2.2. Annual Investment Cost (AIC) vs. Distributed Generation Capacity (DGC)
5.2.3. Comparison of the Results with the Existing Research Works
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
ADN | Active distribution network |
AF | Annualized factor |
AIC | Annual (annualized) investment cost |
C (no.) | Case for planning with case number ranging from 1 to 3 |
C (no.)/S (no.) | Case (number) and Scenario (number) for planning |
CEL | Cost of energy losses |
CP-SLL | Constant power (Load) and Single Load Level |
CUk | Cost for Distributed generation unit in USD/KVA |
DG | Distributed generation |
DG% | Distributed generation penetration (in distribution network) by percentage |
DGC | Distributed generation units capacities (MVA/MW) |
DGCmax | Maximum distributed generation units capacities in MVA/MW |
DGP | Distributed generation units placement |
DN | Distribution network |
IC | Investment cost |
IR% | Interest rate by percentage |
LDN/RDN/MDN | Loop/Radial/Mesh distribution network |
LM/LMC | Loss minimization/Loss minimization condition |
Loc. | Location of potential node in distribution network for DG placement |
MV/LV | Medium voltage/Low voltage |
ODGP | Optimal distributed generation units placement |
PF/PF1/PFL | Power factor/Unity power factor value equal to 1/Lagging power factor |
P_LR | Active power loss reduction in distribution network by percentage |
PU or pu | Per unit system values |
S (no.) | Scenario for planning in each case with scenario number ranging from 1 to 6 |
SS | Substation |
SCC | Short circuit current (level in a distribution network) |
SDN/SG | Smart distribution network/Smart grid |
T | Type of DGs on the basis of power factors varying from I-II |
TG/SG | Traditional grid |
TL | Tie-line/Tie-switch (normally open switch) |
TPL/TQL | Total active power losses/Total reactive power losses |
VM/VSI/VSM | Voltage maximization/Voltage stability index/Voltage stability margin |
VSI-LMC | VSI (New) and LMC (New) based planning approach |
Appendix A
- LDN is balanced and can be represented by the equivalent single line diagram.
- The thermal limits of all lines/branches are considered 5 MVA.
- Line shunt capacitance is negligible and shunt capacitor banks are considered as loads.
- The protection system is considered to be upgraded.
- The maximum number of allowable DGs is two and maximum allowable DG% is equal to 100%.
- It is assumed that a LMC exists, where two receiving ends (RE) nodes (m2 and m4) are ideally at the same voltage i.e., V(m2) = V(m4) or simply VRE2 = VRE4. Hence no current (ITL) flows through TL.
- The DG units can be placed at load buses only (not at the slack bus).
- DGP has not allowed at the same time, i.e., initially, DG1 is placed and later DG2, respectively.
- DN Loading conditions considered normal (heavy) load i.e., a single load level & constant power. The variation in load of DN has considered up to ±2%.
- The variation in the optimal power factor of PFL based DGs has considered up to ±2%.
- The considered conditions include normal/heavy load (single load level/constant power).
Appendix B
Appendix C
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Description | Simulation Parameters | |
---|---|---|
DG Technology | Photovoltaic (PV) | Gas-Turbine |
DG Type (T) by PF | PF = 1/Type-I (T-I) | Lag/Type-II (T-II) |
DGCmax (MVA)/(MW) | 0.001 to 4 | 0.001 to 4 |
CUk (USD/KVA) | 5250 | 1800 |
Life Span (Years) | 20 | 10 |
Interest Rate (IR%) | 7% | 7% |
Case (No.)/Scenario (No.) | DG Size (KW/KVA) | Loc./PF. (Node/PF Value) | LM (KW + jKVAR) | DG% Penetration | Capacity Release (SS) (KW + jKVAR) | AIC (Million USD$) | P_LR (%) | CPL in (Million USD$) | Minimum VSI (Node) | Min. Voltage (Node) | No. of Application |
---|---|---|---|---|---|---|---|---|---|---|---|
C1/S1 | 1726.102 KW | 61/PF1 | 83.275 + j41.27 | 45.39% | 2159.773 + j2733.875 | 0.45648 | 68.06% | 0.04377 | 0.8812/@27 | 0.9687/@65 | 1 LM |
C1/S2 | 2020.2 KVA | 61/0.82L | 25.686 + j15.9 | 43.36% | 2170.523 + j1552.488 | 0.3650345 | 90.15% | 0.0135 | 0.8971/@27 | 0.9731/@27 | 1 LM |
C1/S3 | 2309.25 KW | 61/PF1 | 151.98 + j76.94 | 60.73% | 1805.542 + j2769.637 | 0.6107 | 41.712% | 0.07988 | 0.9224/@22 | 0.9799/@22 | 1 VM |
C1/S4 | 2529.1 KVA | 61/0.828L | 86.722 + j58.46 | 54.28% | 1793.524 + j1335.584 | 0.457 | 66.74% | 0.0456 | 0.9314/@22 | 0.9822/@22 | 1 VM |
C1/S5 | 1970.228 KW 385.985 KW | 61/PF1 22/PF1 | 80.998 + j46.05 | 61.96% | 1527.389 + j2738.723 | 0.62312 | 68.935% | 0.0426 | 0.9394/@65 | 0.9839/@65 | 2 VM & LM |
C1/S6 | 2328 KVA 400 KVA | 61/0.825L 22/0.824L | 25.367 + j17.26 | 58.55% | 4043.9579 + j4037.864 | 0.493 | 90.27% | 0.013333 | 0.9620/@27 0.9632/@65 | 0.9903/@27 0.9903/@65 | 2 VM & LM |
C2/S1 | 1726.102 KW | 61/PF1 | 310.94 + j172.1 | 31.62% | 3915.746 + j2779.878 | 0.45648 | 45.66% | 0.163428 | 0.7349/@64 | 0.9261/@64 | - |
C2/S2 | 2020.2 KVA | 61/0.82L | 113.21 + j70.6 | 30.20% | 3350.0276 + j3969.307 | 0.3650345 | 80.21% | 0.05950 | 0.7581/@64 | 0.9334/@64 | - |
C2/S3 | 2309.25 KW | 61/PF1 | 200.38 + j103.5 | 42.30% | 3440.5956 + j2503.21 | 0.6107 | 64.98% | 0.10532 | 0.7936/@64 | 0.9439/@64 | - |
C2/S4 | 2529.1 KVA | 61/0.828L | 77.5186 + j53.7 | 37.81% | 3299.2665 + j3970.469 | 0.457 | 86.4526% | 0.040744 | 0.8111/@65 | 0.9484/@65 | 1 LM |
C2/S5 | 1970.228 KW 385.985 KW | 61/PF1 22/PF1 | 196.08 + j103.9 | 43.16% | 3286.201 + j2372.905 | 0.62312 | 65.732% | 0.10306 | 0.7851/@64 | 0.9414/@64 | - |
C2/S6 | 2328 KVA 400 KVA | 61/0.825L 22/0.824L | 76.76 + j49.846 | 40.80% | 4043.9579 + j4037.865 | 0.493 | 86.58% | 0.040345 | 0.8143/@64 | 0.9502/@65 | 2 VM & LM |
C3/S1 | 2498.05 KW | 61/PF1 | 176.86 + j102.1 | 45.76% | 3137.9363 + j3967.85 | 0.66063 | 69.1% | 0.09296 | 0.8138/@65 | 0.9491/@65 | 1 LM |
C3/S2 | 2772.66 KVA | 61/0.823L | 50.88 + j31.952 | 41.45% | 3227.4756 + j2350.61 | 0.501 | 91.1% | 0.026745 | 0.8311/@27 | 0.9547/@65 | 1 LM |
C3/S3 | 3322.561 KW | 61/PF1 | 214.31 + j105.5 | 60.8625% | 2350.8721 + j3971.26 | 0.87868 | 62.546% | 0.11264 | 0.8735/@22 | 0.9666/@22 | 1 VM |
C3/S4 | 3645.5 KVA | 61/0.825L | 106.92 + j66.73 | 54.50% | 2558.5169 + j1872.237 | 0.65872 | 81.31% | 0.0592 | 0.8880/@22 | 0.9706/@22 | 1 VM |
C3/S5 | 2881.596 KW 526.027 KW | 61/PF1 22/PF1 | 170.98 + j96.2 | 62.42% | 2222.4844 + j3962 | 0.901172 | 70.12% | 0.08987 | 0.9003/@65 | 0.9732/@65 | 2 VM & LM |
C3/S6 | 3347.56 KVA 497.06 KVA | 61/0.829L 22/0.825L | 47.86 + j29.252 | 57.475% | 2320.8792 + j1743.294 | 0.6947 | 91.64% | 0.025155 | 0.9212/@27 0.9216/@65 | 0.9794/@65 0.9796/@27 | 2 VM & LM |
Performance Indicators | [29] | [23] | [32] | C1/S1 | C1/S5 |
---|---|---|---|---|---|
DG Location | 61 | 61 | 61 | 61 | 61, 22 |
DG Size (KW) | 1863.1 | 1832.45 | 1870 | 1726.102 | 1970.228, 385.985 |
DG quantity | 1 | 1 | 1 | 1 | 2 |
P-loss (KW) | 83.142 | 83.195 | 83.13942 | 83.275 | 80.998 |
Q-loss (KVAR) | 40.512 | 40.58 | 40.50 | 41.268 | 46.051 |
V-Min (bus) | 0.968@26 | 0.968@26 | 0.968@26 | 0.9687@65 | 0.9839@65 |
VSI-Min (bus) | 0.86555@57 | 0.8642@57 | 0.86585@57 | 0.8812@27 | 0.9394@65 |
CEL ($) | 43700 | 43727 | 43698.1 | 43769.34 | 42572.55 |
CEL savings ($) | 74491 | 74464 | 74493 | 74469.64 | 75634.89 |
DG capacity (MW) | 1863.1 | 1832.45 | 1870 | 1726.102 | 2356.213 |
DG Penetration (%) | 49 | 48.19 | 49.18 | 45.39 | 61.96 |
Indicators | [32] PF1 | [34] PF1 | [34] PFL | C1/S5 PF1 | C1/S6 PFL |
---|---|---|---|---|---|
DG Location | 61 | 61, 22 | 61, 22 | 61, 22 | 61, 22 |
DG Size (KW/KVA) | 1870 | 1757; 491 | 2147; 590 | 1970.23; 386 | 2328; 400 |
DG quantity | 1 | 2 | 2 | 2 | 2 |
P-loss (KW) | 83.13942 | 99.9 | 23.4 | 80.998 | 25.367 |
Q-loss (KVAR) | 40.50 | - | - | 46.051 | 17.2607 |
V-Min (bus) | 0.968@26 | - | - | 0.9839@65 | 0.9903@65 |
VSI-Min (bus) | 0.866@57 | - | - | 0.9394@65 | 0.9620@27 |
CEL ($) | 43,698.1 | 52,507.44 | 12,299.04 | 42,572.55 | 13,332.9 |
CEL savings ($) | 74,493 | 65,700 | 105,908.4 | 75,634.89 | 104,874.55 |
Loss Reduction (%) | 63.03 | 61.70 | 91.03 | 68.935 | 90.27 |
AIC (Million USD) | 0.4945 | 0.5946 | 0.4945 | 0.62312 | 0.493 |
DG capacity (MW) | 1870 | 2248 | 2737 | 2356.213 | 2728 |
DG Penetration (%) | 49.18 | 59.12 | 58.74 | 61.96 | 58.55 |
Indicators | [32] | C1/S2 | C1/S4 | C1/S6 |
---|---|---|---|---|
DG Location | 61 | 61 | 61 | 61, 22 |
DG Size (KW) | 2240 | 2020.2 | 2529.075 | 2328, 400 |
DG quantity | 1 | 1 | 1 | 2 |
P-loss (KW) | 23.124 | 25.686 | 86.722 | 25.367 |
Q-loss (KVAR) | 14.363 | 15.8985 | 58.4595 | 17.2607 |
V-Min (bus) | 0.954425@26 | 0.9731@27 | 0.9822@22 | 0.9903@65 |
VSI-Min (bus) | 0.8083@57 | 0.8971@65 | 0.9314@22 | 0.9620@27 |
CEL ($) | 12,154 | 13,500.56 | 45,581.1 | 13,332.9 |
CEL savings ($) | 106,053.5 | 10,4706.9 | 72,626.4 | 104,874.55 |
DG capacity (MW) | 2240 | 2020.2 | 2529.075 | 2728 |
DG Penetration (%) | 48.07 | 43.36 | 54.28 | 58.55 |
Indicators | [32] 5 Year | C3/S1 5 Year | C3/S3 5 Year | C3/S5 5 Year |
---|---|---|---|---|
DG Location | 61 | 61 | 61 | 61, 22 |
DG Size (KW) | 2720 | 2498.05 | 3322.561 | 2881.6, 526.03 |
DG quantity | 1 | 1 | 1 | 2 |
P-loss (KW) | 175.1943 | 176.8623 | 214.3091 | 170.9834 |
Q-loss (KVAR) | 85.12873 | 102.1297 | 105.5353 | 96.2307 |
V-Min (bus) | 0.954425@26 | 0.9491@65 | 0.9666@22 | 0.9732@65 |
VSI-Min (bus) | 0.8083@57 | 0.8138@65 | 0.8735@22 | 0.9003@65 |
CEL ($) | 92,082.12 | 92,958.82 | 112,640.863 | 89,868.875 |
CEL savings ($) | 173,830 | 173,267.36 | 153,585.26 | 176,357.25 |
DG capacity (MW) | 2720 | 2498.05 | 3322.561 | 3407.623 |
DG Penetration (%) | 49.84 | 45.76 | 60.86 | 62.42 |
Indicators | [32] 5 Year PFL | C3/S2 5 Year | C3/S4 5 Year | C3/S6 5 Year |
---|---|---|---|---|
DG Location | 61 | 61 | 61 | 61, 22 |
DG Size (KW) | 3230 | 2772.657 | 3645.50 | 3347.56; 497.1 |
DG quantity | 1 | 1 | 1 | 2 |
P-loss (KW) | 48.45194 | 50.8846 | 106.9169 | 47.85925 |
Q-loss (KVAR) | 29.92891 | 31.9527 | 66.7342 | 29.2522 |
V-Min (bus) | 0.960506@26 | 0.9547@65 | 0.9706@22 | 0.9794@65 |
VSI-Min (bus) | 0.85093@26 | 0.8311@27 | 0.888@22 | 0.9212@27 |
CEL ($) | 25,466.34 | 26,745 | 56,195.52 | 25,154.82 |
CEL savings ($) | 240,441.27 | 239,481.2 | 210,030.6 | 241,071.3 |
DG capacity (MW) | 3230 | 2772.657 | 3645.50 | 3844.62 |
DG Penetration (%) | 48.29 | 41.45 | 54.50 | 57.48 |
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Kazmi, S.A.A.; Shin, D.R. DG Placement in Loop Distribution Network with New Voltage Stability Index and Loss Minimization Condition Based Planning Approach under Load Growth. Energies 2017, 10, 1203. https://doi.org/10.3390/en10081203
Kazmi SAA, Shin DR. DG Placement in Loop Distribution Network with New Voltage Stability Index and Loss Minimization Condition Based Planning Approach under Load Growth. Energies. 2017; 10(8):1203. https://doi.org/10.3390/en10081203
Chicago/Turabian StyleKazmi, Syed Ali Abbas, and Dong Ryeol Shin. 2017. "DG Placement in Loop Distribution Network with New Voltage Stability Index and Loss Minimization Condition Based Planning Approach under Load Growth" Energies 10, no. 8: 1203. https://doi.org/10.3390/en10081203