Abstract
This paper introduces a new hybrid approach for efficiently optimizing the placement and sizing of DG units in the radial distribution power network (RDPN) by combining the loss sensitivity index (LSI) and voltage sensitivity index (VSI) with a novel heuristic algorithm known as the hippopotamus optimization algorithm (HOA). The hybrid approach pre-locates the optimal buses using the LSI and VSI and then optimizes the DG sizes using the food-searching intelligence and communication strategy of hippos. The effectiveness and adoptability of the suggested hybrid optimization approach are demonstrated for single and multiple units of Type I and Type III DG allocation to minimize the active power losses (APL) in the IEEE 33-bus benchmark RDPN. For the 33-bus test system with normal load, a single Type I and Type III DG optimization minimizes the total APL from 210.98 kW (Without DG) to 65.24 kW and 58.75 kW, respectively. Conversely, higher power loss reductions are obtained for multiple units of Type I and Type III DG placements, viz., 81.58% and 91.68%. Similarly, single and multiple DG integrations in the same test system with power demand growth provide a maximum APL reduction of 66.12% and 89.80%, respectively. With LSI and VSI pre-selection and the diverse search capability of HOA, the proposed hybrid approach yields a superior percentage of APL reduction compared to the literature works. Furthermore, the simulation study is extended to a large RDPN (136-bus RDPN) to demonstrate the scalability of the proposed approach.
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The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Abbreviations
- Γ:
-
Gamma function
- α:
-
Small random parameter
- β:
-
Random number controlling movement of hippopotamus
- w, and υ:
-
Random values
- C1, C2 and C3 :
-
Candidate bus location for DG placement
- D:
-
Dominant hippopotamus
- d, f and g:
-
Random numbers
- \({F}_{i}^{FB}\) :
-
Fitness of immature hippopotamus
- F i :
-
Fitness value of objective function
- \({F}_{i}^{HR}\) :
-
Fitness score of hippopotamus facing the predator
- \({F}_{i}^{HE}\) :
-
Fitness score of hippopotamus in safe place
- G:
-
Actual solar insolation at the optimal site
- Gr :
-
Rated solar insolation of the Earth’s surface
- h:
-
Stochastic parameter
- h1 and h2 :
-
Random vectors
- Ik :
-
Current through branch
- k:
-
Distribution line or branch
- Lb:
-
Lower boundary for decision variable
- m:
-
Number of decision variables
- MGi :
-
Mean position of a random group
- nbus :
-
Number of buses in a distribution power network
- nbranch :
-
Number of branches in a distribution power network
- NDG :
-
Number of DG units
- Npop :
-
Population size
- Pj :
-
The position of the predator
- PDG :
-
Active power output of a DG unit
- PL,i+1 :
-
Active power demand at bus i + 1
- Pi+1 :
-
Active power flow at bus i + 1
- \({\text{P}}_{\text{pvr}}\) :
-
Rated active power output of a PV system
- PS :
-
Substation’s active power capacity
- Pr :
-
Rated active power output of wind turbine system
- Vcin :
-
Cut-in wind velocity
- Vr :
-
Rated wind velocity
- Vcout :
-
Cut-out wind velocity
- Vmin :
-
Minimum allowable voltage level
- Vmax :
-
Maximum allowable voltage level
- x:
-
Time in years
- \({x}_{i,j}^{FB}\) :
-
Immature hippopotamus position
- PDG,Total min :
-
Maximum allowable real power capacity of DGs
- \({P}_{L}(i)\) :
-
Active power demand at bus ‘i’
- \({P}_{DGT}\) :
-
Total real power capacity of the DG units
- \({Q}_{DG}\) :
-
Reactive power output of a DG unit
- \({Q}_{L, i+1}\) :
-
Reactive power demand at bus i + 1
- \({Q}_{i+1}\) :
-
Reactive power flow at bus i + 1
- \({Q}_{1}and{Q}_{2}\) :
-
Integer random numbers
- \({Q}_{S}\) :
-
Substation’s reactive power capacity
- \({Q}_{L}(i)\) :
-
Reactive power demand at bus ‘i’
- \({Q}_{DGT}\) :
-
Total reactive power capacity of the DG units
- \({Q}_{DG,Total}max\) :
-
Maximum allowable reactive power capacity of DGs
- \({R}_{k}\) :
-
Resistance of branch k
- \(\overrightarrow{R}_L\) :
-
Random vector
- \(\overrightarrow{r}_1, \overrightarrow{r}_2, \overrightarrow{r}_3, \overrightarrow{r}_4\) :
-
Random vectors
- r5, r6, and r7 :
-
Random numbers
- \(\overrightarrow{r}_8,\overrightarrow{r}_9\) :
-
Random vectors
- r10, r11, r12 and r13 :
-
Random number
- r:
-
Rate of power demand growth per year
- rand:
-
Random number
- \({S}_{1}\) :
-
Random number encouraging localized search
- \({S}_{DG}\) :
-
DG unit size
- \({S}_{DG,Min}\) :
-
Minimum DG size
- \({S}_{DG,Max}\) :
-
Maximum DG size
- \({S}_{DG,Best}\) :
-
Best DG size
- t:
-
Iteration counter
- \({T}_{max}\) :
-
Maximum iteration of optimization run
- T:
-
Time-varying control parameter
- \({U}_{b}\) :
-
Upper boundary for decision variable
- \(\left|{V}_{i}\right|\) :
-
Voltage magnitude at bus i
- \({V}_{i+1}\) :
-
Voltage magnitude at bus i + 1
- V:
-
Actual wind velocity
- \({x}_{i,j}^{M}\) :
-
Male hippopotamus position
- \({X}_{k}\) :
-
Resistance of branch k
- \({x}_{i,j}^{HR}\) :
-
Position of hippopotamus facing the predator
- \({x}_{i,j}^{HE}\) :
-
Safe location for hippopotamus
- \(y\)y1 :
-
Random number
- \({Z}_{1}and{ Z}_{2}\) :
-
Integers
- AP:
-
Active power
- AQiEA:
-
Adaptive quantum inspired evolutionary algorithm
- AHA:
-
Artificial hummingbird algorithm
- ALO:
-
Ant lion optimization
- APL:
-
Active power losses
- APD:
-
Active power demand
- ABC:
-
Artificial bee colony
- AGTO:
-
Artificial gorilla troops optimizer
- BA:
-
Bat algorithm
- BSA:
-
Backtracking search algorithm
- BSOA:
-
Backtracking search optimization algorithm
- CS:
-
Cuckoo search
- DA:
-
Dragonfly algorithm
- DG:
-
Distributed Generation
- EDO:
-
Exponential distribution optimizer
- FWA:
-
Fireworks algorithm
- GA:
-
Genetic algorithm
- GWO:
-
Grey wolf optimizer
- GTO:
-
Gorilla troops optimization
- HOA:
-
Hippopotamus optimization algorithm
- HSA:
-
Harmony search algorithm
- LSI:
-
Loss sensitivity Index
- MFO:
-
Moth-flame optimization
- OOA:
-
Osprey optimization algorithm
- PL:
-
Power losses
- PSO:
-
Particle swarm optimization
- PV:
-
Photovoltaic
- PO:
-
Puma optimizer
- QOFBI:
-
Quasi-oppositional forensic-based investigation
- RPFO:
-
Red fox pathfinder algorithm
- ROA:
-
Rider optimization algorithm
- RP:
-
Reactive power
- RPL:
-
Reactive power losses
- RPD:
-
Reactive power demand
- RDPN:
-
Radial distribution power network
- SA:
-
Simulated annealing
- SOA:
-
Seagull optimization algorithm
- SCA:
-
Sine cosine algorithm
- SSA:
-
Salp swarm algorithm
- TLBO:
-
Teaching learning based optimization
- VD:
-
Voltage deviation
- VP:
-
Voltage profile
- VSI:
-
Voltage sensitivity Index
- WOA:
-
Whale optimization algorithm
- WHO:
-
Wild horse optimization
- WSO:
-
White shark optimization
- WT:
-
Wind turbine
- ZOA:
-
Zebra optimization algorithm
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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. As the corresponding author is based in Malawi, a low-income country, we request a waiver of the article processing charge.
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Rajakumar P: Writing – Original Draft, Methodology, Conceptualization. Ashokaraju D: Formal analysis, Software, Visualization. Senthil Kumar M: Investigation, Formal Analysis, Validation. Chandramohan J: Methodology, Software. Thangaraj D: Visualization, Formal Analysis and Conceptualization. Sabarish P: Validation, Visualization, Conceptualization. Eric Sylvester Mwanandiye: Writing – Review & Editing, Supervision, Investigation.
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Rajakumar, P., Ashokaraju, D., Kumar, M.S. et al. Minimizing power loss in radial power distribution networks via optimal DG allocation using sensitivity indices aided hippopotamus optimization algorithm. Sci Rep (2026). https://doi.org/10.1038/s41598-026-47563-x
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DOI: https://doi.org/10.1038/s41598-026-47563-x
