Probabilistic optimal power flow in islanded microgrids with load, wind and solar uncertainties including intermittent generation spatial correlation

doi:10.1016/j.energy.2021.119847

Energy

Volume 222, 1 May 2021, 119847

https://doi.org/10.1016/j.energy.2021.119847 Get rights and content

Abstract

Increased investiture towards Distribution Generation (DG) in recent past had prompted for transmutation of existing networks to form microgrids that can operate autonomously or in conjunction with main-grid. In particular, the augmenting zeal for renewable DGs is thriving at recent times; but non-dispatchability and uncertain nature pose specific challenges, which is the primary concern in this work. This paper employs Point Estimate Method (PEM) for handling uncertainties to solve the probabilistic-optimal power flow problem (POPF) with multiple objectives formulated in an islanded microgrid with droop coordinated DGs including uncertainties involved in load, wind and solar PV with suitable probability distributions. The devised POPF problem is proposed to solve for optimal droop parameters by multi-objective ant-lion optimization algorithm; tested and verified on modified 33-bus system. Furthermore, in actuality, spatial correlations among renewables play vital role in devising operational schedule for energy management strategies. This paper deals with PEM compounded with Nataf Transformation for POPF to handle spatial correlations in renewable generations. The dominance of wind correlation over solar PV correlations in POPF problem is highlighted. The robustness of proposed approach is verified with benchmark Monte Carlo Simulation (MCS) to affirm about its accuracy for suitable replacement of proposed approach to MCS.

Section snippets

Credit author statement

Jithendranath J: Conceptualization, Methodology, Software, Data curation, Software, Writing – original draft preparation. Debapriya Das: Visualization, Investigation, Validation, Writing- Reviewing and Editing. Josep. M. Guerrero: Supervision, Writing- Reviewing and Editing.

Probabilistic multi-objective optimization by PEM without correlation

In this section, the mathematical formulations of proposed multi-objective POPF problem in IMG is established; and later the modeling of uncertain variables suitable for implementation of uncorrelated PEM are stated.

Multi-objective Ant Lion Optimization (MALO) algorithm for POPF problems

In this section, the application of MALO algorithm to the formulated multi-objective POPF problem in droop regulated IMG is discussed. The MALO algorithm [37] is the multi-objective version of ALO [38] that involves with the animated version of exclusive hunting behaviour of the doodlebugs (ant-lions) to catch its food; the prey ants [37]. To hunt the ants, the ant-lions dig a cone-shaped pit in the sand so that if ant falls into the pit, it will be caught by ant-lions and pulled into the sand

PEM with Nataf Transformation for correlated variables

The PEM described earlier in Section 2, does not take the effect of correlation of random variables in the formulated POPF problem. In consideration with correlation, Rosenblatt transformation based PEM [31,32,50], later Orthogonal Transformation (OT) was proposed which deals by transforming random variables from correlated space to independent space [[16], [17], [18]]. The method of OT is simple to use, but the transformation is independent of the nature of the correlated probabilistic

Simulation results

In this section, the simulation results for the proposed probabilistic optimization problem with multiple objectives in droop coordinated autonomous microgrids with renewable generations are presented; followed to it the effect of renewable site correlations on objective functions were investigated in detail.

Test system and required data

The modified single line diagram of 33-bus distribution test system is shown in Fig. 4; which is considered as an islanded microgrid operating off the main grid

Conclusion

This paper proposes a new POPF formulation in islanded microgrids with droop coordinated DGs considering uncertainties in load and intermittent renewable generations. The POPF problem is formulated with net generation cost, emissions and voltage variations that influence together both the active and reactive power droop coefficients is considered and solved for optimal droop parameters of individual dispatchable droop coordinated DG. The uncertainty nature was handled using suitable PDFs that

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

NOMENCLATURE

I: Sets and Indices
i,k: Bus number
j: Droop DG
L: Load demand
l: Line number
$N_{b u s}$: Set of bus in microgrid network
$N_{d r o o p}$: Set of droop CCHP DGs
$N_{l i n e s}$: Set of interconnecting lines
$d_{j}$: Set of droop parameters of DG

II. Parameters

$μ_{L}$: Mean value of Normal distributed load
$σ_{L}$: Standard deviation of Normal distributed load
k: Shape factor of Weibull distributed wind speed
c: Scale factor of Weibull distributed wind speed
$v_{i n}^{c r}$: Cut-in value of wind speed
$v_{o u t}^{c r}$: Cut-out value of wind speed
$v_{r a t e d}^{c r}$: Rated value of wind speed
$μ_{p v}$: Mean value of log-normal

References (58)

O. Palizban et al.
Microgrids in active network management –part i: hierarchical control, energy storage, virtual power plants, and market participation’
Renew Sustain Energy Rev
(2014)
M.H. Moradi et al.
A novel method for optimal DG units capacity and location in Microgrids
Int J Electr Power Energy Syst
(2016)
M. Abedini et al.
Optimal management of microgrids including renewable energy scources using GPSO-GM algorithm
Renew Energy
(2016)
M.H. Moradi et al.
Optimal operation of autonomous microgrid using HS-GA
Int J Electr Power Energy Syst
(2016)
A. Cagnano et al.
A cooperative control for the reserve management of isolated microgrids
Appl Energy
(2018)
M. Alves et al.
Increasing the penetration of renewable energy sources in isolated islands through the interconnection of their power systems. The case of Pico and Faial islands, Azores
Energy
(2019)
Y. Zhang et al.
Robust model predictive control for optimal energy management of island microgrids with uncertainties
Energy
(2018)
S.A. Alavi et al.
Optimal probabilistic energy management in a typical micro-grid based-on robust optimization and point estimate method
Energy Convers Manag
(2015)
M. Aien et al.
Probabilistic optimal power flow in correlated hybrid wind-PV power systems: a review and a new approach
Renew Sustain Energy Rev
(2015)
C. Chen et al.
Correlated probabilistic load flow using a point estimate method with Nataf transformation
Int J Electr Power Energy Syst
(2015)

S. Shargh et al.

Probabilistic multi-objective optimal power flow considering correlated wind power and load uncertainties

Renew Energy

(2016)

C. Delgado et al.

Point estimate method for probabilistic load flow of an unbalanced power distribution system with correlated wind and solar sources

Int J Electr Power Energy Syst

(2014)

P. Kayal et al.

Optimal mix of solar and wind distributed generations considering performance improvement of electrical distribution network

Renew Energy

(2015)

P.P. Biswas et al.

Multiobjective economic-environmental power dispatch with stochastic wind-solar-small hydro power

Energy

(2018)

S. Mirjalili

The antlion optimizer

Adv Eng Software

(2015)

H.M. Dubey et al.

Hydro-thermal-wind scheduling employing novel antlion optimization technique with composite ranking index

Renew Energy

(2016)

S. Mouassa et al.

Ant lion optimizer for solving optimal reactive power dispatch problem in power systems,” Engineering science and technology

Int J

(2017)

K. Roy et al.

Ant-Lion Optimizer algorithm and recurrent neural network for energy management of micro grid connected system

Energy

(2019)

E.S. Ali et al.

Ant lion optimization algorithm for renewable distributed generations

Energy

(2016)

M.J. Hadidian-Moghaddam et al.

A multi-objective optimal sizing and siting of distributed generation using ant lion optimization technique

Ain shams engineering journal

(2018)

J. Wang et al.

An improved grey model optimized by multi-objective ant lion optimization algorithm for annual electricity consumption forecasting

Appl Soft Comput

(2018)

H.M. Dubey et al.

Ant lion optimization for short-term wind integrated hydrothermal power generation scheduling

Int J Electr Power Energy Syst

(2016)

H.A. Gabbar et al.

Optimal scheduling of interconnected micro energy grids with multiple fuel options

Sustainable Energy Grids and Networks

(2016)

Global energy transformation: a roadmap to 2050

(2018)

J.M. Guerrero et al.

‘Hierarchical control of droopcontrolled AC and DC microgrids –a general approach toward standardization’

IEEE Trans Ind Electron

(2011)

H. Zhang et al.

‘Probabilistic analysis for optimal power flow under uncertainty’, IET Generation

Transm Distrib

(2010)

F. Xinli et al.

Coordinated dispatch in multiple cooperative autonomous islanded microgrids

Appl Energy

(2016)

M.N. Fonseca et al.

Multi-objective optimization applied for designing hybrid power generation systems in isolated networks

Sol Energy

(2018)

M.S. Borujeni et al.

Accurate modeling of uncertainties based on their dynamics analysis in microgrid planning

Sol Energy

(2017)

Cited by (40)

Bayesian deep neural networks for spatio-temporal probabilistic optimal power flow with multi-source renewable energy
2024, Applied Energy
Probabilistic optimal power flow (POPF) plays a crucial role in ensuring the economic and secure operation of power systems with multiple fluctuating loads and renewable energy power generations. However, the practical application of POPF faces challenges because of the lack of accurate input scenarios and the heavy computational burden. With the increasing power system uncertainties and frequent changes in topologies, the existing POPF analysis methods struggle to achieve both high precision and efficient training. To address these issues, firstly, this work decomposes the POPF into three stages: 1) the generation of source-load random scenarios; 2) the non-linear mapping derived from the Karush-Kuhn-Tucker conditions; and 3) the non-linear mapping derived from the power flow equations. Secondly, this work proposes two Bayesian deep neural networks to separately solve each stage of the POPF. Multi-collinearity reduction conditional variational autoencoder can generate source-load random scenarios while consistency condition guided Bayesian deep neural network can predict POPF calculation results. The work further conducts numerical simulations on four IEEE benchmark power systems with multiple renewable energy sources, using uncertainty data collected from the Belgian wind power generation, photovoltaic power generation and load dataset. The simulation results demonstrate that: 1) the precision in generating source-load random scenarios has been enhanced, leading to a reduction of up to 128% in the distribution statistical quantities of the accuracy measures; and 2) the mean absolute error of active power injections, and voltage angles as well as the mean absolute percentage error of the voltage amplitudes in the benchmark systems are reduced by at least 0.7% compared to deterministic neural networks.
Cleaner production of energy and fuels from a renewable energy-based self-sufficient system with energy storage options
2023, Journal of Energy Storage
The present study investigates a newly developed solar and wind-driven integrated energy system to achieve self-sufficiency for communities in a sustainable fashion. In order to overcome the fluctuating nature of solar and wind sources, energy storage options are considered through reliable meteorological data and capacities. The non-thermal electricity, heat, and cooling demands of a community with 65,000 people are met by using a 340 MW wind farm and 1500 MWp linear Fresnel concentrated solar system coupled with thermal energy storage. The integrated system consists of a wind farm with 170 wind turbines, linear Fresnel concentrated solar plant, molten salt energy storage tanks, steam Rankine cycle, lithium-bromide absorption refrigeration cycle, anion exchange membrane electrolysis unit, multi-effect distillation desalination unit, district heating system. Both steady-state analysis for different operating conditions and time-dependent analysis with changing source and load data are carried out from energy and exergy aspects of thermodynamics. The proposed system was able to meet 100 % of 363,344.7 MWh of electricity, 544,468.2 MWh of heat, and 192,112.7 MWh of cooling loads in a year; moreover, it generated 24,142 kt of fresh water and 38,843 t of hydrogen in a year, in order to exploit the excess and waste energy. For the overall integrated system, the average energy and exergy efficiencies are found to be 37.69 % and 28.27 %, respectively. In order to benefit from the full potential of wind and solar-based systems in a combined, the current study provides a unique solution with energy storage option and generates multiple useful outputs for the targeted communities in a sustainable manner.
Probabilistic optimal power allocation of dispatchable DGs and energy storage units in a reconfigurable grid-connected CCHP microgrid considering demand response
2023, Journal of Energy Storage
This paper proposes a hierarchical two-stage coordinated stochastic energy management strategy (SEMS) for a multi-energy carrier grid-tied AC microgrid in presence of combined cooling-heat-power (CCHP) based dispatchable distributed generators, renewable generators, distribution static synchronous compensator, energy storage units, auxiliary boiler, chiller and loads. The first-stage of the optimization strategy deals with a mixed-integer non-linear programming framework aiming at maximizing estimated day-ahead operation profit. In this stage, a mixed demand response program as part of demand side management measures is implemented for responsive electric loads to achieve both supply-side and demand-side benefits. The second stage of the power management strategy is driven by the objective of reducing expected hour-ahead operation cost including pollutant emission conversion cost and the associated optimization problem is solved using a meta-heuristic optimizer called hybrid particle swarm and grey wolf optimizer. Several operational constraints are considered while solving the problem. In this stage, Hong's 2m+1 point estimate method coupled with Nataf transformation is employed to model the correlated uncertainties associated with random variables. Power outputs of dispatchable units, electricity market price, incentive rate, charging/discharging power schedule of energy storage units, and the power exchange between the main grid and microgrid are considered as the control parameters of optimization. Furthermore, a group of measures like remote-bus voltage-constrained power flow with different types of microgrid structures and network reconfiguration is incorporated within the energy management scheme to enhance the steady-state performance and reliability of the microgrid. The efficacy of the proposed framework is validated on a 33-node grid-tied AC microgrid test system.
DC Microgrid energy management with correlated uncertainties
2023, Sustainable Energy, Grids and Networks
A DC microgrid operator (DC $μ$ GO) economically balances the load demand and generation within a DC-Microgrid (DC $μ$ G) while satisfying different technical constraints. This paper deals with a multi-objective (MO) day-ahead energy management scheme (EMS) for a DC $μ$ G by leveraging different flexibilities available to the DC $μ$ GO. The objectives of the EMS are to minimize the operating cost (OC) and energy loss while meeting voltage and feeder current limits and other technical constraints associated with different DC $μ$ G components. Various flexibility resources like dispatchable and non-dispatchable distributed generation (DG), battery energy storage system (BESS), demand response (DR) participators, and DC soft open point (DCSOP) are considered in the developed model. Uncertainties of input random variables (RVs) are modelled using a probabilistic Point estimate method (PEM) approach. The correlation between the random variable (RV)s is incorporated using a Newton's Interpolation method embedded inverse Nataf Transformation (NT) technique. The MO optimization is solved using the epsilon-constraint method. Simulation studies on a ten-bus DC $μ$ G test network reveals that the proposed MO approach can reduce the expected OC in a day by $\sim$ 5.80% and the expected energy loss in a day by $\sim$ 1.01%.
Proposed frequency decoupling-based fuzzy logic control for power allocation and state-of-charge recovery of hybrid energy storage systems adopting multi-level energy management for multi-DC-microgrids
2023, Energy
This paper proposes a decentralized multiple-Direct-Current-Microgrid (multi-DCMG) system to supply affordable load demands while addressing challenges posed by Hybridized-Energy-Storage-Systems (H-ESS) limitations, consumption/generation complexities, and renewables volatility. The paper's contributions include a system feasibility assessment for isolated users and a demonstration of the effectiveness of the control strategies adopted. To improve system resiliency and reliability, the proposed system adopts a high-control level for energy/power balances, using a Mamdani 50 rule-based Fuzzy Logic energy management system (FL-EMS) to supervise State-of-Charge (SoC) recovery. The low-control level manages/supervises DC-DC power converters' powers adopting Proportional-Integral (PI), Hysteresis-Current-Controller (HCC), and Linear-Quadratic-Regulator (LQR) in closed-Control-loops, besides an advanced low-pass-filtering (A-LPF) for load frequency decoupling. The results show that the proposed H-ESS outperformed single-ESS systems in dynamic load changes and renewables' uncertainty, and supercapacitors improved load supply, voltage regulation, and current tracking. However, expensive costs and slow restoration of H-ESS banks from critical SoCs are major drawbacks. The global system assessment demonstrated promising results through proper FL-EMS setpoint computation, stable Bus voltage with 0.55–6.9% deviations due to robust controllers, accurate SoC recovery of HESS batteries at critical SoCs (<10% and >90%), fast and accurate convergence with 3.35–3.37% mismatch, and 99.3% supply efficiency at minor power losses of 0.7–1.55%.
Probabilistic optimal power dispatch in a droop controlled islanded microgrid in presence of renewable energy sources and PHEV load demand
2023, Renewable Energy Focus
This paper proposes a stochastic optimal power allocation strategy for a droop controlled islanded microgrid (DCIMG) with a medium X/R ratio in presence of combined heat and power-based distributed generators (DGs), renewable generators, switched capacitor banks, plug-in hybrid electric vehicle (PHEV) loads, voltage dependent electric loads and heat loads. Optimal values of stochastic power demand due to PHEV charging and discharging load are determined based on the goals of achieving target state-of-charge of PHEV batteries and effective peak shaving during peak load periods, respectively. Active power of dispatchable DGs is optimally allocated depending on the simultaneous fulfillment of an economic objective, an environmental objective along with three network related objectives. Hong's 2m+1 point estimate method (PEM) and Hong's 2m+1 PEM coupled with Nataf transformation (NT) are employed to handle the uncorrelated uncertainties accompanied with PHEV load demand and the correlated uncertainties associated with spatially correlated renewable generation and load demand. Active and reactive power static droop coefficients, and frequency and voltage reference settings of the dispatchable DG units are considered as the control variables for optimal dispatching of active power. A modified hybrid particle swarm and grey wolf optimizer embedded in fuzzy framework is used to solve the constrained multi-objective optimization problem. The efficacy of the proposed framework is validated on a 33-node droop controlled islanded microgrid test system.

View all citing articles on Scopus

View full text

Probabilistic optimal power flow in islanded microgrids with load, wind and solar uncertainties including intermittent generation spatial correlation

Abstract

Section snippets

Credit author statement

Probabilistic multi-objective optimization by PEM without correlation

Multi-objective Ant Lion Optimization (MALO) algorithm for POPF problems

PEM with Nataf Transformation for correlated variables

Simulation results

Conclusion

Declaration of competing interest

NOMENCLATURE

II. Parameters

Renew Sustain Energy Rev

Int J Electr Power Energy Syst

Renew Energy

Int J Electr Power Energy Syst

Appl Energy

Energy

Energy

Energy Convers Manag

Renew Sustain Energy Rev

Int J Electr Power Energy Syst

Renew Energy

Int J Electr Power Energy Syst

Renew Energy

Energy

Adv Eng Software

Renew Energy

Int J

Energy

Energy

Ain shams engineering journal

Appl Soft Comput

Int J Electr Power Energy Syst

Sustainable Energy Grids and Networks

Global energy transformation: a roadmap to 2050

‘Hierarchical control of droopcontrolled AC and DC microgrids –a general approach toward standardization’

IEEE Trans Ind Electron

‘Probabilistic analysis for optimal power flow under uncertainty’, IET Generation

Transm Distrib

Coordinated dispatch in multiple cooperative autonomous islanded microgrids

Appl Energy

Multi-objective optimization applied for designing hybrid power generation systems in isolated networks

Sol Energy

Accurate modeling of uncertainties based on their dynamics analysis in microgrid planning

Sol Energy