A hybrid fuzzy-stochastic technique for planning peak electricity management under multiple uncertainties

doi:10.1016/j.engappai.2017.04.014

Engineering Applications of Artificial Intelligence

Volume 62, June 2017, Pages 252-264

https://doi.org/10.1016/j.engappai.2017.04.014 Get rights and content

Highlights

•
Interval-fuzzy chance-constrained method (IFCCP) is developed for planning EPS.
•
It can address uncertainties as probability distributions and fuzzy sets.
•
IFCCP can satisfy peak-electricity demand and optimize energy allocation.
•
Solutions under various α-cut levels and fuzzy dominance indices are analyzed.
•
Results create tradeoff among system cost and peak-electricity demand violation risk.

Abstract

In this study, an interval-fuzzy chance-constrained programming (IFCCP) method is developed for reflecting multiple uncertainties expressed as interval-fuzzy-random (integration of interval values, fuzzy sets, and probability distributions). IFCCP has advantages in uncertainty reflection and policy analysis as well as avoiding complicated intermediate models with high computational efficiency. The developed IFCCP method is applied for planning a regional-scale electric power system (EPS) with consideration of peak-electricity demand issue. Results reveal that different peak demands in different seasons lead to changed electricity-generation pattern, pollutant emission and system cost. IFCCP is more reliable for the risk-aversive planners in handling high-variability conditions by considering peak-electricity demand. Results also disclose that fossil-fuels consumption should be cut down in future (i.e. the energy-supply structure would tend to the transition from fossil-dominated into renewable-energy dominated) in order to meet the increased power demand and mitigate the pollutant emissions. Results can help decision makers improve energy supply patterns, facilitate dynamic analysis for capacity expansion, as well as coordinate conflict interactions among system cost, pollutant mitigation and energy-supply security.

Introduction

As the foundation for sustaining social and economic development, electricity plays an important role in a variety of human activities throughout the world. Over the past decades, electricity demand and supply have been steadily increasing in response to life standard improvement, economic development and population growth (Han et al., 2015, Kato et al., 2016). The rapid increase of electricity demand and the integration of renewable energy have imposed great stress on the power grid, especially in maintaining grid power balance (IEA, 2014). The power supply and demand of a grid must always balance and such real time balance is a critical system requirement. Any power imbalance/mismatch will affect the reliability and quality of power supply (e.g. power outages, voltage fluctuations), which will cause severe consequences such as widespread blackouts and increased electricity expenses for end-users (OECD, 2005). Therefore, how to solve the power balance issues becomes an utmost attention for decision makers of EPS planning.

Lots of efforts were adopted for planning EPS in response to power balance issues such as power reserve, electricity-generation expansion, renewable energy integration, electricity purchase, electricity prices, load shedding and load shifting control as well as electricity transmission infrastructure upgradation (Chen and Li, 2011, Yoon et al., 2014, Rejc and Čepin, 2014, Gao and Sun, 2016). For example, Fernandez et al. (2013) proposed a novel “Just-for-Peak” buffer inventory methodology to reduce the electricity consumption without compromising system throughput during peak periods, in which 20.1% power demand reduction during peak periods could be achieved. Werminski et al. (2017) used the decentralized active demand response automation for reducing the peak power in the Polish EPS, where about 4% of typically peak power value was reduced. Generally, the above measures were mainly based on demand response controls and they were merely focused on maximizing the benefits of power grid in terms of load profile alterations. The load profiles of end-users sectors were changed into an uncoordinated way and leading to an aggregated load profile, which would greatly impact the normal operation of each sector. Through such uncoordinated control, the overall peak demand of the aggregated load profile could not be effectively and efficiently reduced in a desired way of a grid. Renewable energy integration and electricity purchase are useful tools for satisfying peak electricity demand with an environment-friendly way, which can effectively reduce the pollutant emissions and can improve the reliability of power demand-supply (Yu et al., 2016).

Section snippets

Related work

Over the past decades, many studies were effective for planning EPS by considering peak electricity demand with an environment-friendly way in terms of linear programming (LP), integer programming (IP), dynamic programming (DP) and artificial intelligence (Silva et al., 2012, Moazzami et al., 2013, Cocaña-Fernández et al., 2016, Loganthurai et al., 2016, Dababneh et al., 2016, Pham et al., 2016). For instance, Dudhani et al. (2006) used a linear programming algorithm for peak load demand

Interval chance-constrained programming

Chance-constrained programming (CCP) is effective for handling decision problems whose coefficients (input data) are not certainly known but could be represented as chances or probabilities (Simic, 2016). A general stochastic linear programming problem can be formulated as follows: $Min f = C (t) X$

Subject to: $A (t) X \leq B (t)$ $x_{j} \geq 0, x_{j} \in X, j = 1, 2, \dots, n$ where $X$ is a vector of decision variables, and $A (t)$ , $B (t)$ , and $C (t)$ are sets with random element defined on a probability space $T$ , $t \in T$ . To solve model (1), an

Overview of the study system

Peak demands in the summer for air-conditioning and in the winter for heating are rapidly growing. For a regional EPS, the peak demands of summer and winter are expected to increase to 1930 MW and 1880 MW, respectively. In summer refrigeration and air-conditioning are the main contributors to the seasonal peak, whereas in winter, space heating is the main contributor to the seasonal peak. Especially, in China, the cooling load of electric chiller accounts for 1/4 of the total load demand in

Peak electricity demand

In this study, a set of probabilistic constraints on maximum allowable peak load demands were considered, which were used for examining the risk of peak-electricity demands violation and generate desired regional EPS planning under uncertainty. Monte Carlo simulation was used for generating the peak-load probability distribution information. The normal distribution was the best fit for the logarithm of allowable peak-load through one thousand time's Monte Carlo runs. Fig. 2 presents an

Comparison with the conventional EPS model

Peak-electricity demand has risen significantly and been one of the major concerns for the planning EPS, causing widespread blackouts and increasing the cost of electricity for all consumers. Due to different uncertainties existing in EPS, different peak-electricity demands would correspond to different attitudes towards system-violation risk, power supply security and economic objective. If peak-electricity demand was not considered in EPS, the study problem can be treated as a

Conclusions

In this study, an interval-fuzzy chance-constrained programming (IFCCP) method has been developed for planning peak-electricity demand management problems in a regional-scale EPS. Solutions of different seasons under various α-cut levels and fuzzy dominance indices have been generated by solving a series of deterministic submodels, which can help determine optimized peak electricity components that could hedge appropriately against peak load levels. Several findings can be revealed as follows:

Acknowledgements

This research was supported by Beijing Natural Science Foundation of China (L160011), the National Key Research Development Program of China (2016YFC0502803), the National Natural Science Foundation of China (51225904) and the 111 Project (B14008). The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

References (51)

K.B. Burke
The reliability of distributed solar in critical peak demand: a capital value assessment
Renew. Energy
(2014)
A. Charnes et al.
Chance Constrained Programming: An Extension of Statistical Method
(1971)
Y.H. Chen et al.
Comparison of security constrained economic dispatch formulations to incorporate reliability standards on demand response resources into Midwest ISO co-optimized energy and ancillary service market
Electr. Power Syst. Res.
(2011)
M. Coatalem et al.
Optimizing industries' power generation assets on the electricity markets
Appl. Energy
(2017)
A. Cocaña-Fernández et al.
Leveraging a predictive model of the workload for intelligent slot allocation schemes in energy-efficient HPC clusters
Eng. Appl. Artif. Intell.
(2016)
F. Dababneh et al.
Peak power demand reduction for combined manufacturing and HVAC system considering heat transfer characteristics
Int. J. Prod. Econ.
(2016)
D. Dubois et al.
Ranking fuzzy numbers in the setting of possibility theory
Inf. Sci.
(1983)
S. Dudhani et al.
Renewable energy sources for peak load demand management in India
Int. J. Electr. Power Energy Syst.
(2006)
A. Elyasi et al.
Stochastic scheduling with minimizing the number of tardy jobs using chance constrained programming
Math. Comput. Model.
(2013)
M. Fernandez et al.
“Just-for-Peak” buffer inventory for peak electricity demand reduction of manufacturing systems
Int. J. Prod. Econ.
(2013)

Cited by (14)

PSR-FCCLP model based total maximum allocated loads optimization of TN and TP in Bohai Bay
2022, Marine Pollution Bulletin
Eutrophication is a global problem for coastal ecosystems, one that Bohai Bay, China, has been severely afflicted due to rapid economic and social development in the past decades. It was urgent to manage the total maximum allocated loads (TMALs) of the total nitrogen (TN) and total phosphorus (TP) on land-based, which was closely related to coastal eutrophication. In this study, from the perspective of economy-resources-environment (ERE) system, we presented the fuzzy credibility constrained linear programming based on pressure-state-response (PSR-FCCLP) model, which calculated the TMALs of TN and TP at three credibility levels (λ = 0.55, 0.75, and 0.95) in Bohai Bay. The results showed that when the credibility level increased from 0.55 to 0.95, the TMALs of TN and TP would decrease from 13,573.38 t/a to 12,820.00 t/a and from 2665.58 t/a to 2514.90 t/a, respectively. This study will provide support for environmental management in coastal regions.
Achieving the tradeoffs between pollutant discharge and economic benefit of the Henan section of the South-to-North Water Diversion Project through water resources-environment system management under uncertainty
2021, Journal of Cleaner Production
Citation Excerpt :
Interval-parameter programming (IPP) is an effective approach for resolving the above uncertain information by using interval numbers instead of deterministic values (Li et al., 2006; Dai et al., 2012), but unknown membership distribution functions. Fuzzy-credibility constrained programming (FCP) can effectively resolve the challenge posed by inaccurate parameters through the use of fuzzy sets (Figueroa-García et al., 2012; Yu et al., 2017). FCP is a category of fuzzy programming which defines the average value of the necessary and possible degrees of the development of systems as credibility to reflect the relationship between satisfaction and the risk of system violation.
Environmental water quality problems resulting from pollutant discharges have received extensive attention with the increasingly severe challenges facing global resources and the environment. A consideration of hierarchy within water resources-environment system (WRES) management under uncertainty can effectively improve the accuracy and applicability of management decisions. This study developed an interval fuzzy-credibility constrained two-level programming (IFCTP) model for WRES planning which considers uncertain information through the use of interval values and fuzzy sets and can also resolve conflicting goals among decision-makers in different departments. The IFCTP-WRES model was then formulated and applied for planning of the middle route of South-to-North Water Diversion Project (SNWDP) in Henan Province, China. Multiple water allocation, pollution control, and economic benefit solutions encompassing three departments and thirteen water-receiving cities involving dual uncertainties and varied credibility levels were examined. The results showed that: (1) the proportion of water resources allocated to ecological flows should increase from [14.12, 14.15]% to [17.97, 17.99]% over the entire planning period; (2) the proportion of water resources allocated to small cities (e.g., Huaxian County) should show a constant increase; (3) municipal wastewater can contribute more than half of the total pollutant load; (4) as compared to the economic benefit that can be obtained through solutions identified by two single-objective models, the interval fuzzy-credibility constrained programming environmental management system (IFCP-EMS) model and interval fuzzy-credibility constrained programming water resources management system (IFCP-WMS) model, that by the IFCTP-WRES model has higher by 5.0% and lower by 4.5%, respectively. These findings can provide abundant alternatives for achieving sustainable development and can help decision-makers to effectively plan WRES management under uncertainty.
Optimization of uncertain agricultural management considering the framework of water, energy and food
2021, Agricultural Water Management
Synergetic development of water, energy and food is prerequisite for coping with issues of increment of global population, deterioration of ecological environment and aggravation of climate change. This study aims to develop a scenario-based type-2 fuzzy interval programming (STFIP) approach for planning agricultural water, energy and food (WEF) as well as crop area management. Uncertainties presented as interval numbers, scenarios and fuzzy sets as well as the dual uncertainties (i.e. interval-scenario and type-2 fuzzy interval) can be effectively tackled by the STFIP method. Then, a STFIP-WEFN model is developed and applied to maximize net agricultural profit with integrated management of productive resources for Henan Province, China. Solutions of different water resources, diverse energy resources and multiple agricultural crops in association with various water supply structures between current situation and future policy orientation are examined. Results disclose that: over the entire planning horizon, a) the total planting area of crops can increase from [129.3, 133.6] × 10³ km² to [132.0, 135.6] × 10³ km² by optimizing resources allocation; b) uncertainties existing in the WEFN system can lead to a change rate of the system benefit by 16.93%; c) the total planting area can increase by [4.00, 6.05] % when the groundwater ratio changes from 40% to 55%. These findings can help effectively optimize the existing planting structure and coordinate the development of Henan Province among water, energy, food, economy, society and environment.
Robust master planning of a socially responsible supply chain under fuzzy-stochastic uncertainty (A case study of clothing industry)
2020, Engineering Applications of Artificial Intelligence
This paper addresses an integrated physical supply channel, aggregate production, and transportation planning problem through the lens of social sustainability under uncertainty. The three-echelon supply chain network includes multiple suppliers, a manufacturer and multiple distribution centres. Social-related criteria such as workers’ job-security and health (i.e. working conditions) and social investment are contemplated in the supply chain under consideration. In doing so, a chance constraint mixed integer non-linear programming model is built to determine the centralized planning of procurement-production-transportation under fuzzy-stochastic uncertainty over the tactical planning horizon. Moreover, an efficient hybrid solution procedure is developed utilizing convexification and defuzzification strategies. Finally, a real-case study in clothing industry is presented to show the model applicability and the solution procedure efficiency.
Planning municipal-scale mixed energy system for stimulating renewable energy under multiple uncertainties - The City of Qingdao in Shandong Province, China
2019, Energy
Citation Excerpt :
Uncertainties related to peak-electricity demands can be projected into a matrix and vectors through Monte Carlo simulation, where each execution produces a sample output and the output samples can then be examined stochastically to determine the related cumulative probability distributions. The detailed procedures for Monte Carlo simulation can be referenced in the published work by Yu et al. [49]. Based on the Monte Carlo simulation, the fitting simulated peak-electricity demand under different violation probabilities would be used as the inputs of the IPSP to generate the desired MES planning results.
Rapidly increased coal consumption has caused dramatically pollutants and carbon dioxide (CO₂) emissions, such that utilizing renewable energy to substitute high pollutant and carbon fuels is crucial to fulfill sustainable development. In this study, an interval possibilistic-stochastic programming (IPSP) method that is capable of dealing with multiple uncertainties existed in the real-world mixed energy system (MES) is developed. Then, the IPSP method is applied to planning MES in the City of Qingdao (China) that aims to encourage developing renewable energies based on subsidy policy. Solutions under varied subsidies for stimulating renewable energies in association with different probabilities and α levels have been generated, which can help determine the optimized electricity generation and supply that could hedge appropriately against system violation risk. Compared to the results without subsidy, renewable energies with subsidy policy can increase by [2.4, 3.2] % and the share of renewable energies would raise to 17.5% at the end of planning horizon. The findings can provide useful information for the other municipal-scale MES planning issues to facilitate policy enactment of renewable energy, improvement of energy supply security, as well as accomplishment of planning environmental and sustainable MES.
Big-data clustering with interval type-2 fuzzy uncertainty modeling in gene expression datasets
2019, Engineering Applications of Artificial Intelligence
Citation Excerpt :
Therefore, the mathematical formulation, modeling,and implementation of uncertainty in the dataset can be very effective in the data analytics. There were few works where researchers integrated uncertainty in the dataset and used the data processing techniques to learn from data (Salaken et al., 2017; Yu et al., 2017). To handle these uncertainties in the data, fuzzy sets are used extensively over the years in various real-time applications.
The major bottleneck in microarray gene expression analysis is the lack of techniques required to cope up with the uncertain gene functionality and inherent complex gene interactions. More often the issues of unstructured, unorganized, noisy and incomplete data is confronted with the advent of uncertain gene expression big datasets. Moreover, big data is naturally associated with the uncertainties which are originated from multiple sources. In this paper, such uncertainties in the gene expression dataset are modeled using interval type-2 fuzzy sets (IT2 FSs). For this, the spread of footprint of uncertainty (FOU), which accounts for the all the possible noises in the gene expression dataset, is modeled both symmetrically and asymmetrically. The medical science big dataset of microarray gene expression data of the cancer patients are considered for the experimentations. Empirically, the effects of uncertainty modeling using IT2 FSs on the big data clustering is analyzed and observed. Fuzzy clustering approach allow the genes to belong to multiple clusters and thus allow the genes participation in cellular process, subcell variations, and cellular metabolism. The effect of the induced uncertainty on the big data clustering has been studied using various cluster validity measures. The clustering results, obtained based on the IT2 fuzzy uncertainty modeling, are compared with same obtained with type-1 fuzzy sets based uncertainty modeling. It is demonstrated that our proposed IT2 FS based approach is more efficient in giving better clustering results for uncertain gene expression datasets and is scalable to the large gene expression datasets. Sensitivity analysis of the clustering results considering four different IT2 membership function shapes such as triangular, trapezoidal, semi-elliptic, and Gaussian are performed.

View all citing articles on Scopus

View full text

A hybrid fuzzy-stochastic technique for planning peak electricity management under multiple uncertainties

Highlights

Abstract

Introduction

Section snippets

Related work

Interval chance-constrained programming

Overview of the study system

Peak electricity demand

Comparison with the conventional EPS model

Conclusions

Acknowledgements

Renew. Energy

Electr. Power Syst. Res.

Appl. Energy

Eng. Appl. Artif. Intell.

Int. J. Prod. Econ.

Inf. Sci.

Int. J. Electr. Power Energy Syst.

Math. Comput. Model.

Int. J. Prod. Econ.

Energy Build.

Eng. Appl. Artif. Intell.

Struct. Saf.

Appl. Math. Lett.

Int. J. Electr. Power Energy Syst.

Electr. J.

Inf. Sci.

Energy Convers. Manag.

Adv. Water Resour.

Resour., Conserv. Recycl.

Energy

Eng. Appl. Artif. Intell.

Appl. Energy

Energy

Eng. Appl. Artif. Intell.