Control mechanism of electricity consumption in a transport company

. To reduce electricity consumption in hierarchical management of fabrication, it is necessary to take into account the activity of managers associated with the presence of their own targets. A three-level model of managing electricity consumption in production is considered. At its top level is the superior who evaluates the executive who is at the middle level. At the bottom of the system is the director of fabrication. The superior must to manage the consumption of the executive in such a way as to save electricity. But the executive knows own electricity-saving opportunities better than the superior. In turn, the director knows his own electricity-saving capabilities better than the executive. So, both the executive and the director can manipulate their electricity consumption to gain more incentives. To avoid this, a control system for electricity consumption management in fabrication is proposed. This system includes procedure for machine learning of the superior and procedure for grading of the executive. Sufficient conditions of the optimality of this system are found, in which random opportunities of decreasing electricity consumption are used. With such a system, the executive is interested in minimizing electricity consumption. The Theorem is proved that for this it is sufficient to use linear procedures of adaptive standardization and stimulation of the director. The proposed approach to control of electricity consumption is illustrated by the example of railcars repairing in the Russian Railways company.


Introduction
The use of Artificial Intelligence methods can reduce energy consumption in transport systems.For example, smart meters are able to measure energy consumption [1] and use the capabilities of household energy storage units [2].Machine learning (ML) is used to control energy consumption in a large company [3].
In addition, to reduce electricity consumption, it is necessary to take into account the human factor.To achieve their own goals, people can manipulate the consumption of electricity in order to influence the results of ML and the decisions of stakeholders in their favor.Accordingly, an important area of energy saving is associated with the disclosure of internal reserves and resources through the activation of employees.To solve such problems, the mathematical theory of organizational management is used [4].This made it possible to obtain mechanisms for reducing energy consumption in a transport company through training [5].Supervised energy cost management was studied in [6].
This paper is devoted to the study, using rigorous mathematical reasoning and evidence, a three-level energy saving management model with two-level ML.This model includes the top manager (the superior), the subordinated manager (the executive), and the director of fabrication.The superior does not know the random minimum possible consumption of electricity by the executive and the director.For this reason, the superior must learn.The executive knows about this consumption better than the superior.Thus, the executive can manipulate the consumption of electricity in order to influence the results of superior's learning and management in his favor.But the executive himself does not know the random minimum consumption of electricity in fabrication.This can be used by the director to achieve his own goal.So, the executive also needs to learn how to manage electricity consumption in fabrication.Due to the complexity of the model under consideration, the Model Based Systems Engineering approach [7] is used.

Grading of Electricity Consumption
Let denote t the period of time, t E -electricity consumption, for which the executive is responsible in the period t, t=0,1,...There t E is equal to the sum of fabrication electricity consumption t F and the own executive electricity consumption Thus, the minimum electricity consumption for which the executive is responsible is equal to: The superior does not know the minimum possible electricity consumption by the executive (and, moreover, of the director).But the superior can monitor deviations of actual consumption from some rate.Based on this, the superior can conclude whether the executive is using the electricity effectively.In the framework of grading concept, this means that the superior assigns the executive one of two grades -1 (effective use of electricity) and 0 (ineffective use of electricity).Such grading is often used in fabrication [3,5,6].
The grade in period t is determined based on the executive consumption


The optimal value of this parameter *) b ( can be determined by solving the task of average damages minimization [5]: Usually, the superior does not know d(c).So, it is impossible to solve task (2).Consider solution of task (2) in case when damage functions are linear: where kicoefficients, Then the condition of minimum average risk (2) is: where Me is the expectation operator.Using (4), one can use stochastic approximation to obtain a sequence of evaluations bt, t=0,1,..., of an unknown parameter .* b Namely, substituting (3) into (4), we obtain learning algorithm to obtain evaluations bt, t=0,1,..., which solve (4), in the form: Using ( 5), the superior determines the executive's grade: where is the learning procedure of the superior, where is the grading procedure.Denote ).g ( t 1

=
It is assumed that the reward of the executive grows with the increase in the grade of electricity saving [3,5,6].

Electricity Consumption Management with Grading
A set of procedures of learning (8) and grading (9) constitute the grading control of electricity consumption denoted

Target of the Executive
Let us now consider the target of the executive in case of control where ] [ H • is a monotonically increasing function of its arguments, T is the executive foresight.To make a decision about t E on the conditions of uncertainty, the executive focuses on a guaranteed value of target function (10): Then the set of the executive possible decisions is the set of is not known to the executive.This is the example of asymmetric awareness of the parties [9].Consequently, the executive must take into account the activities of the director: to achieve own target, the director can manipulate electricity consumption in fabrication.This is typical for repairing [5].Thus, the executive must motivate the director to minimize electricity consumption: , = t t x f t=0,1,… For this the executive needs special control to minimize fabrication electricity consumption.

Management of Fabrication Electricity Consumption
Suppose that the executive has sufficient statistics on minimum electricity consumption , he can use big data analytics for time series of electricity consumption [1].If such statistics is insufficient, the adaptive methods for short-term electricity load in real time can be used [10].
Consider model of real-time management of electricity consumption in fabrication.Formally, assume t x becomes known the director prior to period t.After that, the director makes a decision about electricity consumption , f and adaptive models can be used for real-time management of electricity consumption in fabrication with forecasting and standardization [11].Namely, suppose the executive calculates the standard 1 + t s of plant electricity consumption in period t+1 by adaptive Brown's model [12]: We will call ) , ( t t f s S standardization procedure, and ε its elasticity.The introduction of such a procedure is typical for data standardization in intelligent electricity management [11].
Consider the practical aspects of the director motivation to save electricity consumption in fabrication.Usually, in the practice of adaptive management in fabrication, both impetuses and standards for the future grow with saving of electricity consumption, compared to the current standard [5].Then the future adaptive standards for electricity consumption will be the lower, the smaller their consumption today.In fact, this standardization is carried out "from the achieved level" [6].Usually, such adaptive standards will be decreased by a certain percentage, compared to the current standard.But the lower future standards for electricity consumption, the more difficult it is to get the impetus in the future.As a result, subordinated employee may not be interested in saving electricity.For example, such undesirable activity is typical for the operation of energy storage units [2].To avoid this, the executive can assign to the director's impetus: where ) • ( I is linear impetus procedure.

Example: Control System of Electricity Consumption During Railcar Repairing
Let us illustrate the results obtained on the example of control system of electricity consumption during the repairing of railcars in Carriage Repair Company which is the part of the Russian Railways company [13].The model of electricity consumption management in this company includes top manager (as the superior), regional manager (as the executive), and the director of depot (as the director of fabrication).The superior must learn and grade the executive to minimize electricity consumption in company.
According to Statement 2, to save electricity, for the executive it is enough to use adaptive control   1a) is recalculated with the aid of (8).
Using , t a the superior determines monthly grade t g of the executive responsible for electricity consumption (9).For his part, the executive monitors average monthly electricity consumption t f for one railcar, .12 , 1 = t This example illustrates the simplicity and transparency of developed control system of electricity consumption of fabrication in a company, and the applicability of proved Theorem.

Statement 2
defines an easily interpretable control method of motivation the director in saving electricity.Namely, Statement 2 means that in order to motivate the director in saving electricity, the executive can use adaptive control System of Electricity Consumption in Fabrication Combining Statements 1 and 2, we obtain Theorem.To minimize the electricity consumption of fabrication, the superior sufficient to use the grading control )In this case, the sequence of appraisals at, t=0,1,..., converges to unknown parameter * b .In this case, the sequence of appraisals at, t=0,1,..., converges to unknown parameter b*.According to Statement 2, to guarantee this, the executive is sufficient to choose both adaptive control the period t, Q.E.D.The Theorem defines an easily interpretable control method to minimize the electricity consumption of fabrication: combining the executive control obtain control system of electricity consumption in fabrication.

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13) and impetuses (14) of the director.According to theorem, in order to motivate the executive to minimize electricity consumption, the superior only needs to use the grading control )., ( = G A C Thus, control system of electricity consumption during the repairing of railcars includes grading control The results of this control system functioning are illustrated in Figure1.There t E (black line in Figure1a) is average electricity consumption during the repairing of one railcar, in thousands of kilowatt-hours in

Fig. 1 .
Fig. 1. a) average electricity consumption during the repairing of one railcar Et (black line) and its appraisal at (red line), in thousands of kilowatt-hours in month t; b) grade of the executive gt in month t.
grade, the superior is based on observation t E and the appraisal t a .In general, the sequence of appraisals at, t=0,1,..., does not converge to unknown parameter * b .Replacing in (7) unknown t e with the observed t E and evaluation t b with appraisal t a , we get executive's grade:

Fabrication Electricity Consumption 4.1 Decision Making of the Executive
[6]the other hand, in the practice of fabrication, the future appraisal of electricity consumption often decreases with the decrease of actual consumption.This problem is similar to the problem of rationing carried out «from the achieved level»[6].So it is necessary to develop an effective control system that motivates the executive to save electricity in every period: t E decreases to .e t This should make the executive interested in lowering .E t t t Consider the dependence of the future grade t f t O and .t F t x Suppose the director seeks to increase the own target function -discounted sum of impetuses (14) in the current and N future periods: E3S Web of Conferences 376, 01077 (2023) https://doi.org/10.1051/e3sconf/202337601077ERSME-2023 a (red line in Figure