EAI Endorsed Transactions on Energy Web and Information Article

Compositional fuzzy modeling of energy- and resource saving in socio-technical systems

A.V. Bobryakov1,*, V.V. Borisov2, A.I. Gavrilov3 and E.A. Tikhonova4

1National Research University “Moscow Power Institute”, [email protected] 2National Research University “Moscow Power Engineering Institute”, [email protected] 3The Branch of National Research University “Moscow Power Engineering Institute” in Smolensk, [email protected] 4National Research University “Moscow Power Engineering Institute”, [email protected]

Abstract

The paper poses the problem of increasing the efficiency of energy- and resource saving in socio-technical systems, which consist of resource-intensive subsystems (for example, subsystems of electricity, heat and water supply). A compositional fuzzy model for efficiency estimating of energy- and resource saving of socio-technical systems is proposed. This compositional fuzzy model consists of the following models: firstly, a set of fuzzy cognitive models for estimating the effects of actions on the subsystems’ indicators; secondly, a set of fuzzy rules-based models for efficiency estimating of energy- and resource saving of subsystems; thirdly, a generalized fuzzy model for efficiency estimating of energy- and resource saving of system as a whole. The procedure of compositional fuzzy modeling of energy- and resource saving in socio-technical systems is described.

Keywords: energy- and resource savings; socio-technical system; rules-based fuzzy model; fuzzy cognitive model.

Received on 30 May 2018, accepted on 14 October 2018, published on 25 October 2018

Copyright © 2018 A.V. Bobryakov et al., licensed to EAI. This is an open access article distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unlimited use, distribution and reproduction in any medium so long as the original work is properly cited.

doi: 10.4108/eai.12-9-2018.155863

*Corresponding author. E-mail: [email protected] these problems in the conditions of inaccuracy and incompleteness of the initial data. 1. Introduction According to this, modelling and management of energy- and resource saving in STSs should take into At present, the complexity of processes in socio-technical account the following features: firstly, a comprehensive systems (STS) is increasing. Therefore, the importance of approach of modelling, estimating and management of the problem of energy- and resource saving in these STS energy- and resource saving in STSs; secondly, the increases under the conditions of complex impact of system application of compositional models consisting of sets of and external parameters, as well as their . The models for implementation of separate stages of modelling, multi-factorial and nonlinear interactions between the evaluation and management of energy- and resource saving parameters of processes in STSs, the uncertainty how the processes; thirdly, the use of methods of fuzzy analysis and characteristics are interrelated and the complexity of the modelling of complex systems and processes, namely the formalization of the tasks to be solved determine the methods of fuzzy cognitive modeling and fuzzy logical urgency of developing modern analytical methods in this . area. The development and application of intellectual methods and technologies is a promising direction to solve

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2. Problem formulation jth subsystem; q( a()s j ) – an indicator which determines the 3 k j Let's assume that the efficiency of energy- and resource cost of implementing the action. saving of the STS S is estimated by a generalized indicator It is required to choose a set of actions CS() (from ES() . groups of events{AAA,, } ) to maximize the efficiency of s1 s 2 s 3 The system S consists of subsystems: energy- and resource saving all system, with restrictions on = = S{ sj }, j 1, ..., J . the financial costs and the time TCS( ()) of implementation For the problem being solved: of the set of actions: = →CS() S{,,} s1 s 2 s 3 , ES( ) max, ()s where s,, s s – energy- and resource-intensive ∑ q() aj ≤ p( s ), j = 1, ..., J , 1 2 3 3 kj 3 j ∈ subsystems of power supply, heat supply and water supply, kj K J ()()≤ respectively. TCSTCS()().max Efficiency of energy- and resource saving of STS is determined by the energy- and resource efficiency of its subsystems and expressed by the following dependence: 3. Compositional fuzzy model for the = ( ) E() S F e (),...,( s1 e sJ ) . efficiency estimation of energy- and = resource saving in STS where e( sj ), j 1, ..., J – an indicators of energy- and resource efficiency of subsystems s, j= 1, ..., J . j 3.1. Structure of the composite model ∈ Each subsystem sj S is characterized by a set of indicators: Figure 1 shows the structure of the compositional fuzzy model for the efficiency estimation of energy- and resource P( s )={ p ( s ),} l = 1,..., L . j l j saving in STS, based on the proposed problem formulation. For the problem being solved: The compositional fuzzy model consists of the sets of the following models: ∀sPs:() = { pspspsps (), (), (), ()} , j j 1j 2j 3 j 4 j • fuzzy cognitive models for estimating the effects of where p() s – an indicator which characterizes the state of actions on the subsystems’ indicators (power supply, 1 j heat and water supply); jth subsystem; p2 () s j – an indicator of energy- and • -based models for efficiency estimating of resource saving potential of the jth subsystem; p3 () s j – energy- and resource saving of subsystems: power share in total cost allocated for energy- and resource saving supply, heat and water supply; • of the jth subsystem; p() s – tariffs for energy- and generalized fuzzy rule-based model for efficiency 4 j estimating of energy- and resource saving of system resource savings of the jth subsystem. as a whole. For each subsystem s, j= 1, ..., J , its own group A of j sj The fuzzy cognitive models are affected by events from actions has been formed, aimed at increasing its energy- and =()s j = groups of measures As{ a k}, k j 1, ..., K j , resource efficiency: j j ∀ ∈ corresponding to subsystems sj S . As a result, the A={ a()s j }, k = 1, ..., K . sj k j j j values of the output variables p1 () s j and p2 () s j of these The actions a()s j ∈ A, k = 1, ..., K are characterized by models, which (together with indicators p() s and p() s , kj s j j j 3 j 4 j the following set of indicators: do not depend on the impact of the events) are fed to the inputs of fuzzy rule-based models for efficiency estimating Q( a()s j ) = { q( a()s j )}, m= 1, ..., M . = k j m k j e( sj ), j 1, ..., J of energy- and resource saving of For the problem being solved: subsystems. Then, these estimates are aggregated into a generalized indicator ES() of energy and resource ∀e()()s j : Q( as j ) = { q( a()s j ),,, q( a()s j ) q( a()s j )} k j k j 1 k j 2 k j 3 k j efficiency of the entire system S using generalized fuzzy rule-based model. where q( a()s j ) – an indicator which characterizes impact of 1 k j Sections 3.2–3.5 of this article present more details on how to construct and how to use these models for assessing the action a()s j on jth subsystem condition; q( a()s j ) – k j 2 k j the effectiveness of energy and resource saving in STSs. indicator which characterizes the impact of the action a()s j k j on changing the energy- and resource saving potential of the

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ES()

Model of the generalized assessment of the effectiveness of energy and resource saving system S

e() s1 e() s2 e() s3

Model of the energy and Model of the energy and Model of the energy and resource efficiency resource efficiency resource efficiency evaluation of subsystem evaluation of subsystem evaluation of subsystem s1 of power supply s2 of heat supply s3 of water supply () () () () () () () () () () () () 2 1 3 1 1 1 4 1 2 3 4 3 3 3 1 3 3 2 4 2 1 2 2 2 p s p s p s p s p s p s p s p s p s p s p s p s

Fuzzy cognitive model Fuzzy cognitive model Fuzzy cognitive model for estimating the for estimating the for estimating the effects of actions on the effects of actions on the effects of actions on the indicators p1(s1) and indicators p1(s2) and indicators p1(s3) and p2(s1) indicators of the p2(s2) of the heat supply p2(s3) of water supply electricity subsystem s1 subsystem s3 subsystem s2

A= { a()s1 } A= { a()s2 } A= { a()s3 } s1 k j s2 k j s3 k j

Figure 1. Structure of the compositional fuzzy model

C8 Infrastructure capacity

C1 C7 Population The state of the electricity p1() s 1 living subsystem standards } 1 j s C2 () 0.4 C6 Potential { 0.8 Industrial -0.6 for energy p2() s 1 = 1

s k consumption -0.8 and resource

A a saving Measures to improve electrical efficiency electrical improve to Measures

C5 C3 Households 1.0 Rate of city consumption development

C4 Ecosystem quality

Figure 2. Fuzzy cognitive model for estimating the impact of actions a()s1 ∈ A kj s1

on indicators p1() s 1 and p2() s 1 of the subsystem s1

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To simulate a change in concept values, the following equation is used (separately for positive and negative values, 3.2. Fuzzy cognitive models for the estimating w followed by combining the results obtained): the effects of actions on the subsystems ij  n  + = + indicators Cj( t 1) f C j ( t )∑ w ij C i ( t ) ,  i=1  The input factors of these models are actions Where, as a function f - a non-linear is a()s j ∈ A, k = 1, ..., K for the corresponding subsystem used, designed to prevent the concept values out of range [0, kj s j j j 1] or [–1, 1]. = sj , j 1, ..., J . The output variables of these models are: the Let's give an example of the proposed fuzzy cognitive model for the estimating the impact of actions on the indicator p1 () s j characterizing the state of this subsystem; indicators of the of electricity subsystem [6]. the indicator p() s of the energy- and resource saving 2 j Figure 2 shows the structure of fuzzy cognitive model potential of the j-th subsystem. which can be used for estimating the impact of actions Nonlinear and indirect dependencies between the factors a()s1 ∈ A on the indicators p() s and p() s , which using of the models make it possible to justify the using of fuzzy kj s1 1 1 2 1 cognitive models (maps) as such models [1], [2], [3], [4], [5]. for characterizing the state of the subsystem s1 and energy- The advantages of using fuzzy cognitive models are as and resource saving potential, respectively. follows: ()s1 ∈ Modeling of the impact of actions ak A s on the • formalized assignment of system factors of STS, j 1 indicators p() s and p() s of subsystem s is carried out and direct, indirect and aggregated influence of 1 1 2 1 1 these factors on each other as well; in accordance with the following stages: • consideration of the nature and degree of the direct • firstly, setting the initial values of the concepts of and indirect influence of various factors of the fuzzy cognitive model; model on each other; • secondly, the starting the simulation in accordance • flexible analytical tool for various types of STS with the expression to change the values of the with a constant model structure (a set of system concepts; factors and the interactions between them); • thirdly, changing the values of the model concepts

• modeling of various events to assess and identify (including changing its output indicators p1() s 1 and the factors and interactions of mutual influence p2() s 1 ) under the influence of the events from As ; provoking instability of STS; 1 • fourthly, the completion of the simulation either at the • modelling the dynamics of changes in subsystems set time, or when the model goes to a stable state, or and the system as a whole, with an assessment of when the criterial values of any concepts are reached. the impact of various systemic factors, as well as Similarly, the designing and using of fuzzy cognitive various actions on these changes. models for estimating the impact of actions on the indicators Fuzzy cognitive model is fuzzy-cause-and-effect- of heat- and water supply subsystems are performed. networks (FCE-Nets): GCW= ,, where CCC= { ,..., } – many concepts, 3.3. Fuzzy rule-based models for efficiency 1 N estimating of energy- and resource saving of W={ w| i , j = 1, ..., N} – many influence relationships in ij subsystems: power supply, heat and water ∈ − the form of directed arcs with weights wij [ 1, 1]. supply = − Indicator wij 1 means the maximum negative impact of We will use a fuzzy approach to design models for , = the concept wij 1 – maximum positive impact of the estimating of energy- and resource efficiency for different = subsystems. This approach makes it possible to take into concept Ci on the concept C j , and indicator wij 0 account the uncertainty in the estimating the impact of determines the absence of any direct influence C on C . i j various factors on energy- and resource efficiency [7], [8], wij [9], [10], [11]. → With a positive effect CCi j and an increase in the The procedures for the designing and using the proposed models will be considered using the example of the energy- value Ci the value C j increases, and with a decrease, it and resource efficiency of the power supply subsystem s1 . decreases. With a negative value wij an increase in the value Step 1. The designing of model's structure. Input variables Ci causes a decrease in the value C j and vice versa. In of the model: p() s – the state of the subsystem s ; p() s – addition, it is possible the simultaneous direct influence of a 1 1 1 2 1 potential of energy- and resource saving subsystem s ; p() s – pair of concepts on each other with a mismatch wij and w ji . 1 3 1

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the share of energy- and resource saving costs of subsystem s1 ; Step 3. Activation of conclusions for each rule. For example, for the Ry: p4() s 1 – tariffs for energy- and resource saving subsystem s1 . µ () = α µ () M ′ e( s1 ) min( y , M e ( s1 )) . The output is the indicator of energy- and resource e() s1 e() s1 efficiency e() s1 of the power supply subsystem s1 . Step 4. Accumulation of activated conclusions according to all the rules: Step 2. The designing of linguistic scales for input and  µ ()  output fuzzy variables. For this, typical L–R functions L′ e(s1 ) , ...,  e() s1  (Gaussian, triangular) can be used [7]. We set the same terms µ() =  µ ()  e′′( s )e() s 1 maxM e (),...,.s1 for the describing all the variables {L – small, M – medium, H 1  e() s1  – large}:  µ ()  H ′ e() s1  e() s1  • for p() s – {,,}LMH ; 1 1 p1()()() s 1 p1 s 1 p1 s 1 Step 4. Getting clear output variable values: • for p() s – {,,}LMH ; N 2 1 p2()()() s 1 p2 s 1 p2 s 1 ⋅µ ∑e()() s′ () e s • 1 (n ) e ( s1 ) 1 ( n ) for p() s – {,,}LMH ; n=1 3 1 p3()()() s 1 p3 s 1 p3 s 1 e′() s = , 1 µ () • for p() s – {,,}LMH ; e′( s )e() s 1 ( n ) 4 1 p4()()() s 1 p4 s 1 p4 s 1 1 • where K – the number of elements in the sampled base set for e() s1 – {,,}LMHe()()() s e s e s . 1 1 1 output variable e() s . Figure 3 shows an example of a linguistic scale for a 1 fuzzy input variable p1() s 1 . Similarly, the designing and using of fuzzy rules-based µ models for efficiency estimating of energy- and resource

Lp() s M p() s H p() s saving of heat- and water supply subsystems are performed. 1 1 1 1 1 1 1

0,5 3.4. Generalized fuzzy rules-based model for efficiency estimating of energy- and resource 0 saving of system as a whole p1() s 1 Figure 3. An example of a linguistic scale for The process of designing a generalized fuzzy rules-based model for assessing the effectiveness of energy- and resource input fuzzy variable p() s 1 1 saving of system is similar to designing a model for a separate subsystem. Step 3. Generation of the fuzzy rules: The input fuzzy variables of this model are fuzzy

R : If p() s is L AND p() s is L AND p() s is indicators e( s1 ), e ( s 2 ), e ( s 3 ) of energy- and resource 1 1 1 p1() s 1 2 1 p2() s 1 3 1 L And p() s is L , Then e() s is L ; efficiency of electrical, heat and water subsystems, p3() s 1 4 1 p4() s 1 1 e() s1 respectively. The output fuzzy variable is a generalized fuzzy … indicator ES() of energy- and resource efficiency of the Ry: If p() s is M AND p() s is M AND p() s 1 1 p1() s 1 2 1 p2() s 1 3 1 system S. The fragment of fuzzy rules base of this model is is M AND p() s is M , Then e() s is M ; p3() s 1 4 1 p4() s 1 1 e() s1 presented in Table 1. … Table 1. The fragment of fuzzy rules base of this RY: If p() s is H AND p() s is H AND p() s 1 1 p1() s 1 2 1 p2() s 1 3 1 generalized model is H AND p() s is H , Then e() s is H . p3() s 1 4 1 p4() s 1 1 e() s1 Input variables Output No variable, The energy- and resource efficiency of the power supply e() s e() s e() s subsystem is evaluated based on fuzzy logic inference [7]. 1 2 3 ES() This procedure consists of the following steps. L L L L R1 e() s1 e() s2 e() s3 ES() Step 1. Determination of the degrees of membership of R2 Le() s Le() s M e() s LES() the values of input variables for all fuzzy statements in the 1 2 3 … … … … … premises of all rules. Rg M e() s M e() s M e() s M ES() For example, for the Ry: 1 2 3 µ ( ′ ) µ ( ′ ) µ ( ′ ) µ ( ′ ) … … … … … M p1(),(),(),(). s 1 M p2 s 1 M p3 s 1 M p4 s 1 p1() s 1 p2() s 1 p3() s 1 p4() s 1 H H M H RQ–1 e() s1 e() s2 e() s3 ES() Step 2. Aggregation of degrees of fuzzy statements R He() s He() s He() s H of prerequisites for each rule. Q 1 2 3 ES() For example, for the Ry: The algorithm of the generalized evaluation of the  µ ( p′(),(), s ) µ ( p′ s )  M p() s 1 1 M p() s 2 1 energy- and resource efficiency of the system is implemented α = min  1 1 2 1 . y  µ ()()′ µ ′  M p3(),() s 1 M p4s 1  p3() s 1 p4() s 1 

EAI Endorsed Transactions on 5 Energy Web and Information Technologies 09 2018 - 01 2019 | Volume 6 | Issue 21 | e9 A. V. Bobryakov et al. in a manner analogous to the algorithm for estimating the modeling the development of the power system of Moscow. energy- and resource saving of a separate subsystem. According to the results of the simulation: first, the factors that have the most significant impact on the problem of energy and resource conservation have been identified; 3.5. Simulating for the selection of a set of secondly, measures are formed and justified to increase the actions to improve the efficiency of energy- efficiency of energy and resource saving of this system. and resource saving of system Acknowledgment The procedure for the selection of a set of actions CS() to improve the efficiency of energy- and resource saving of The work is conducted under the support of the Russian system consists in assigning various combinations of actions Science Foundation (project 16-19-10568). a()s j ∈ A, k = 1, ..., K for all resource-intensive kj s j j j References subsystems {,,}s1 s 2 s 3 (under the restrictions on the amount [1] Kosko B. Fuzzy cognitive maps. Int. Journal of Man-Machine of financial costs and the time of their implementation), and Studies, 1986, vol. 24, pp. 65-75. in determining such actions which provide the maximum [2] Borisov V.V., Fedulov A.S. Generalized Rule-Based Fuzzy value of the energy efficiency and resource saving of the Cognitive Maps: Structure and Dynamics Model. Lecture system (indicator ES() ). Notes in Computer Science, 2004, v. 3316, pp. 918-922. The given compositional fuzzy model is implemented as [3] Carvalho J.P., Tome J.A.B. Rule Based Fuzzy Cognitive software, and as a pilot project in 2018, it was used in Maps in Socio-Economic Systems. IFSA-EUSFLAT 2009, 2009, pp. 1821-1826. modeling the development of the power system of Moscow. [4] Papageorgiou E.I. Fuzzy Cognitive Maps for Applied According to the results of the simulation: Sciences and Engineering from Fundamentals to Extensions • the factors that have the most significant impact on and Learning Algorithms. Intelligent Systems Reference the problem of energy and resource conservation Library, 2014, vol. 54. have been identified; [5] Kang B., Mo H., Sadiq R., Deng Y. Generalized fuzzy • measures are formed and justified to increase the cognitive maps: a new extension of fuzzy cognitive maps. Int efficiency of energy and resource saving of this J Syst Assur Eng Manag. 2016. DOI 10.1007/s13198-016- system. 0444-0. [6] Borisov V., Stefantsov A., Gasho E., Postelnik M., Bobryakov A. Research into the Sustainable Development 4. Conclusion Problem of Urban Electric Power Systems on the Basis of Cognitive Modeling . International Journal of Applied Engineering Research. 2016, vol. 11, no 24, The formulation of the task of increasing the efficiency of pp. 11826-11831. energy and resource saving in STS. The choice of fuzzy [7] Babuška R. Fuzzy Modeling for Control. Boston, USA: cognitive modeling and fuzzy logical inference methods for Kluwer Academic Publishers, 1998, 240 p. evaluating the formation of a set of measures to improve the [8] Takagi T., Sugeno M. Fuzzy identification of systems and its efficiency of energy and resource conservation in STSs is application to modeling and control. IEEE Transactions on substantiated. Systems, Man and , 1985, v. 15, no 1, pp. 116-132. A compositional fuzzy model for efficiency estimating of [9] Mamdani E.H. Application of fuzzy logic to approximate energy- and resource saving of STSs is proposed. This reasoning using linguistic systems. Fuzzy Sets and Systems, 1977, v. 26, pp. 1182-1191. composite fuzzy model consists of the following models: [10] Jafari R., Yu W. Fuzzy Modeling for Uncertainty Nonlinear firstly, a set of fuzzy cognitive models for estimating the effects Systems with Fuzzy Equations. Mathematical Problems in of actions on the subsystems’ indicators; secondly, a set of Engineering, vol. 2017, article ID 8594738, fuzzy rules-based models for efficiency estimating of energy- https://doi.org/10.1155/2017/8594738. and resource saving of subsystems; thirdly, a generalized fuzzy [11] Jafari R., Razvarz S., Gegov A. A new computational method model for efficiency estimating of energy- and resource saving for solving fully fuzzy nonlinear systems. Lecture Notes in of system as a whole. The procedure of compositional fuzzy Computer Science (including subseries Lecture Notes in modeling of energy- and resource saving in STSs is described. and Lecture Notes in Bioinformatics), The given compositional fuzzy model is implemented as 2018, vol. 11055 LNAI, pp. 503–512. software, and as a pilot project in 2018, it was used in

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