Power consumption control of multi-pump systems of the main water drainage in underground mines based on the Mamdani fuzzy inference system

The article considers synthesis of an expert system for controlling electric power consumption by pumps of main water drainage facilities of an underground mine on the basis of the Mamdani fuzzy inference algorithm. The proposed system has a MISO-structure (multiple-input, single-output) with two input variables, such as water inflow and power cost as well as one output coordinate – power of pumping units. Two bases of fuzzy rules such as conjunction (AND) and disjunction (OR) are formed. By simulation modelling, a comparative analysis of fuzzy control systems for power consumption by water drainage facilities is carried out, as well as a system without control, when the pump performance is stabilized, during week and month periods. It is established that OR-rule based systems can reduce power costs by 1.89% during a week and by 2.28% during a month, and AND-rule based systems by 4.13%, as well as by 5.43% during week and month, respectively. At the same time, we note that the economic effect is achieved not through a decrease in power consumption, but by adjusting the operation mode of the water drainage facility, which involves ensuring maximum efficiency of groundwater drainage when the power cost is high, and minimum efficiency when it is low.


Introduction
Creation of the power market in Ukraine and widespread introduction of distributed generation facilities has resulted in a radical change in principles of mutual financial settlements between distribution operators and consumers due to rapid improvement of power production technologies using renewable sources.Dynamic pricing in determining power prices has provided ample opportunities to develop new algorithms for controlling power supply and consumption in power systems of various hierarchical levels.Given that the most energy-intensive objects are industrial enterprises, there are great prospects for improving energy efficiency specifically for them.
Simultaneously, the constant change in power costs requires a significant revision of principles of managing technological operations, which have traditionally remained unchanged for many years.In particular, this concerns main water drainage facilities of underground mines designated to pump groundwater from internal working spaces of enterprises engaged in underground mineral mining.Their operation is critical for creating safe working conditions for personnel, so water drainage is controlled through ensuring maximum efficiency of pumps.At the same time, energy efficiency is improved by optimizing performance characteristics of technological units using an automated electric drive.Design features of mine water drainage, namely reservoir for accumulating mine water, make it possible to implement a different approach to controlling the system.It will involve limiting the performance of pumps and, as a result, power consumption, in certain periods of time when the power cost is high and its significant use is economically inefficient.In this case, the main limitation will involve preventing overflow of reservoirs in case of an intensive water inflow that can cause flooding of the underground mine.
The power system, regardless of its architecture and operation algorithm, aims to reduce the cost of purchasing power from an external distribution operator.Given that for enterprises power cost can vary widely during the day, it would be logical to ensure maximum power consumption during the period of the minimum power cost.However, this is not always possible to implement for consumers, because their operation is related to ensuring safe working conditions for personnel of a certain production facility, in particular, mine water drainage.If during the enterprise operation there is a significant or abnormal water inflow into the underground mine, it is required to pump water with maximum efficiency, despite high or average power costs.Therefore, the power control system of main water drainage facilities of underground mines should have two input actions: water inflow and power cost (or the cost of power generation in case of availability of sources of distributed generation).The initial coordinate is the power of electromechanical complexes of pumps that are simultaneously in operation, i.e. their total power.

Literature review
A number of works are devoted to controlling multi-pumping systems.
Thus, [1][2][3][4][5][6][7] consider various aspects of functioning of pumping systems with several pumps using both group and individual electric drives.At the same time, some works specify parameters of pumps and the hydraulic system.In particular, Arun Shankar et al [7] looks into cavitation and water hammer, and Vodovozov et al [4] -pressure.Papers [1][2][3]5] are devoted to control with the optimal operating point of the system determined by pump efficiency.Additionally, practical implementation of control using industrial logic controllers is proposed.Beshta et al. [6] is worth highlighting as it directly considers the process of controlling pumps of main water drainage facilities of the underground mine.At the same time, we note that the authors focus on improving efficiency of the pumping system in terms of its performance, but the control over power consumption depending on power costs is not sufficiently considered.
Gong and Zhu [8] optimizes operation of a group of pumping stations operating in parallel, according to the criterion of minimizing losses for power consumption by the entire technological complex.Efficiency of water drainage and flows between individual units of each pumping station are considered as limitations.A multifactor optimization criterion is proposed, which takes into account power costs in a certain period of time.The authors consider a three-tariff system with differentiation by time periods.The optimization procedure includes determining the best conditions for the functioning of each individual station according to the developed criterion using a genetic algorithm, followed by their aggregation.As a result, power costs decrease for all stations.Meanwhile, on one of them, the savings amount to almost 20%.Besides, power consumption is regulated by frequent starting/stopping of individual pumps, which, as the authors themselves note, significantly affects their reliability.
Wang et al [9] deals with development of an algorithm for controlling a multi-level system for pumping water in an urban environment during heavy rains or floods using the Particle Swarm Optimization method.As optimization criteria, the number of starts/stops of pumps and duration of their operation are considered.The proposed algorithm has significantly reduced the number of pumps, so it can be used to improve the multifactor optimization system shown in [8].
Bordeas , u et al [10] explores the algorithm for controlling a multi-pump irrigation system powered by a distributed generation power system, which includes a centralized electrical grid and power production facilities using renewable energy sources, in particular, photovoltaic panels.The proposed system is multi-level.The top-level subsystem determines the procedure for starting/stopping individual pumps depending on the level of filling the tanks with water and the amount of power available for consumption.Lower-level subsystems implement a smooth start and frequency regulation of the rotation speed of the electric drive of each pump.One of the indicators of assessing efficiency of the system is the hourly level of power consumption.It is compared with the periods of different power costs.As in [8], the authors consider three-zone tariffs for different time periods.At the same time, when forming the control, the power cost is not directly used as a parameter for adjusting the algorithm, but is considered because of the power available for consumption.As a result, the system does not function in the peak tariff period.Thus, such a system is impractical to use for mine water drainage for safety reasons.
The papers [11][12][13][14] consider the control of industrial and household consumers power supply, taking into account fluctuations in the power tariff during the day.
To date, the most promising control methods include those based on fuzzy logic, artificial neural networks and machine learning, which are usually classified as smart.Moreover, in problems when an object has several input variables, it is advisable to apply a fuzzy logic inference due to simplified synthesis and control algorithms implemented.On its basis, there are developed irrigation control systems [15,16], pumping facilities powered from autonomous power plants using renewable energy sources [17][18][19][20][21][22], control systems of wind turbines electromechanical equipment [23], urban water supply [24], cascades of multi-pump systems [25], as well as the electric drive of a separate pumping unit [26].
As mentioned earlier, the power control system of main water drainage facilities of the underground mine can be represented by a MISO-structure (multiple-input, single-output) with two input (water inflow and power cost) and one output (the power of pumps) variables.Moreover, all three coordinates are subject to expert evaluation.As a result, it is advisable to develop a smart power control system for main water drainage facilities using the Mamdani fuzzy logic inference algorithm.
The research paper aims to synthesize a system for controlling power consumption levels by electromechanical equipment at main water drainage facilities based on the Mamdani fuzzy logic inference algorithm to reduce power costs of an industrial enterprise for the power supplied by an external distribution operator.
The developed fuzzy algorithm can be applied to controlling a peak pumped-storage power plant of main water drainage facilities of underground mines [27,28].

General characteristics of main water drainage facilities of the underground mine as a fuzzy control object
The synthesis of a fuzzy control system for power consumption by main water drainage facilities as part of a mining enterprise can be clearly demonstrated on the example of the Kryvorizka underground mine (Kryvyi Rih).Main water drainage facilities are placed on appropriate levels and include several pumps, usually of the same type and power.On the same levels, there are additional water reservoirs, the size of which allows accumulating required volumes of mine water entering a specific level from others (deeper ones).
A 500 m water drainage level is adopted as a control object (figure 1).Given that this level is the final stage before pumping water to the surface, where water from the entire internal space of the underground mine enters, it is equipped with the largest water reservoir and consequently the most powerful pumps.As a result, it is one of the most energy-intensive consumers of water drainage and the entire underground mine as a whole.The water drainage section of the 500m level contains seven pumps of the CNS-300x600 type with a nominal power of 800 kW each.Due to the reduced production volumes, compared to the design ones observed in recent years, there is a decrease in water inflow to the underground mine (table 1).This caused the need to simultaneously use only three pumps at the maximum water inflow into the working spaces and one or two under normal conditions.After taking into account the above features during fuzzification of the fuzzy system for controlling power consumption by electrical equipment of the 500 m level, let us consider this procedure in more detail.
4. Development of a smart expert system for controlling power consumption by main water drainage facilities of the underground mine 4.1.Fuzzification of linguistic variables of a fuzzy control system Each coordinate of the fuzzy logic inference MISO-structure, namely "water inflow", "power tariff" and "pump power" are represented by corresponding linguistic variables.
A finite set Q, used to form the membership functions of the linguistic variable "water inflow", is defined on the interval {q i ∈ R | q min ≤ q i ≤ q max }, where q min and q max are the minimum and maximum levels of groundwater inflow into the underground mine.We assume that the linguistic variable includes three fuzzy sets: "low inflow" (Q L ), "medium inflow" (Q M ), and "high inflow" (Q H ). Membership functions to the above-mentioned fuzzy sets are formed by piecewise linear functions.This reduces computational complexity while implementing a fuzzy logic inference algorithm.The membership function for the fuzzy set "medium water inflow" is defined as triangular, for the set "high water inflow" as S-shaped, and for the set "low water inflow" as Z-shaped.
When parametrizing membership functions, the average value of water inflow over 6 years (table 1) is taken as the mean value, which is q m = 484.85m 3 /h.We assume that the high water inflow exceeds 2.5 times the medium one, while the low water inflow is twice smaller, and make q l = 1212.13m 3 /h and q h = 242.43m 3 /h respectively.At the same time, we set the minimum value at the level of q min = 0 m 3 /h, and the maximum value of q max = 1500 m 3 /h.
The membership function to the fuzzy set Q M is defined by the following expression: Here is an expression for determining the membership function to the fuzzy set Q L : µ Q L (q) = f (q; q min − 1, q min , q l , q m ) = = max min q − (q min − 1) q min − (q min − 1) , 1, while: Here is the expression for determining the membership function to a fuzzy set Q H : Given the membership functions to the fuzzy sets Q L and Q H , both the upper and lower reference values go beyond the limits of the finite set Q, that is, they increase and decrease by one respectively.This is done to avoid dividing by zero cases.
A diagram representation of membership functions to the fuzzy sets of the linguistic variable "water inflow" is shown in figure 2.
The fuzzification of the linguistic variable "power tariff" is performed on the basis of the following considerations.In compliance with the Law of Ukraine On the Electric Power Market [29] as of January 07, 2019, a new power cost system for industrial enterprises and distributors was established.This system involves the introduction of an hourly tariff mode, where power cost changes every hour depending on the market condition.What is more, one day in advance, an enterprise orders from a distributor the amount of power that is expected to be consumed during each hour of the following day.This approach is fundamentally different from payments according to tariffs differentiated by time periods, which were in effect before, when the power cost was fixed.At the same time, the analysis of the hourly payment structure allows us to state that it is appropriate to distinguish three zones based on power cost, when its level is high, medium or low.Moreover, the day periods when the specified zones are virtually active coincide with peak, half-peak and night periods.This is explained by the nature of the power load schedule, namely, a high level of power consumption in morning and evening hours, a low level at night and a medium level during daylight hours.Thus, in order to formalize the fuzzy control algorithm, we differentiate the power cost in the "peak", "half-peak" and "night" zones.
As reference values for assigning membership functions for the linguistic variable "power tariff", we will use the tariff values set by the power distributor DTEK Dniprovski Elektromerezhi [30].Also, we use the data for the case of centralized power supply and for the case of the installed distributed generation facilities.In the latter case, this variable is equivalent to the cost of power production.
For the consumers of the first voltage type, namely from 35 kV and higher, at the limit of balance distribution, which includes the Kryvorizka mine, the tariff of c HP = 0.13788 UAH/kWh has been effective since January 01, 2022.This value will determine the power cost in the "half-peak" zone.Accordingly, the "peak" tariff is 1.5 times higher than the "half-peak" one, and the "night" tariff is 0.4 times lower.They are c P K = 0.20682 UAH/kWh and c N T = 0.055152 UAH/kWh respectively.These three values are used as references when forming membership functions and their further parameterizing.
The linguistic variable "power cost" is defined by a finite set on the interval {c ∈ R | c min ≤ cq ≤ c max }, and c min = 0 UAH/kWh, c max = 0.3 UAH/kWh.Let us represent the variable as three fuzzy sets -"night zone", "half-peak zone" and "peak zone".
The membership function to the fuzzy set "night zone" is defined as Z-shaped: where: 13788 UAH/kWh.The membership function to the fuzzy set "half-peak zone" is triangular and has the following characteristics: while: 151668 UAH/kWh.The membership function to the fuzzy set "peak zone" is S-shaped and has the following characteristics: while: core 16212 UAH/kWh.A diagram representation of membership functions to the fuzzy sets of the variable "power tariff" is in figure 3.
The output coordinate of the fuzzy power consumption control system is the total output power consumed by the drainage pumps.Moreover, it is advisable to focus on the value of this electrical parameter, and not on the number of units that are operated at a time as modern electric drives of pumps are equipped with semiconductor frequency inverters making it possible to adjust the output power of flow-generation mechanisms over a wide range.According to the static characteristics P = f (Q) of the CNS-300x600 pump, its operating performance for the nominal angular rotation frequency of 1485 rpm is within efficiency limits of 220 − 360 m 3 /h with a power change range of 625 − 825 kW.Taking into account the fact that one to three pumps are used for water drainage, the final set for the linguistic variable "pump power" should be determined on the interval {p ∈ R | p min ≤ p ≤ p max }, where p min = 625 kW is a lower level of drainage power consumption, which corresponds to the minimum power of one CNS (centrifugal) pump p max = 2475 kW, i.e. when all three pumps work with the highest performance and at maximum power.
During fuzzification, we represent the linguistic variable "pump power" as three fuzzy sets corresponding to the total power consumed by one, two or three pumps.All three membership functions to the fuzzy sets are defined as triangles and the fuzzification procedure is performed.
The membership function to the fuzzy set "power of one pump" is defined by the following expression: while: core (P ON ) = {p nom } = 800 kW; supp (P ON ) = {p ∈ R | p min ≤ p ≤ p max + p min } = 825 kW.The peculiarity of this function is that the upper reference value is taken in such a way that one pump is supposed to work at maximum power, while the second one additionally drains water with the minimum permissible power consumption, i.e. p max + p min = 1425 kW.
The following membership function to the fuzzy set "power of two pumps" is formulated from the following considerations.The reference value of the lower limit is taken considering the fact that both pumps will work simultaneously at the minimum of their operating characteristics, so their power will be 2p min = 1250 kW.The reference value of the upper limit is set assuming that two pumps will work simultaneously at the maximum working section of the static characteristics, and the third is put into operation at the minimum, i.e. 2p max +p min = 2275 kW.As a result, the membership function is as follows: while: Similarly, the membership function to the fuzzy set "power of three pumps" is given.At the same time, it is assumed that the reference value for the lower limit involves the operation of three pumps with the minimum power consumption of 3p min = 3 • 625 = 1875 kW, and for the upper limit -three pumps with the maximum power 3p max = 3 • 825 = 2475 kW: while:  For the first two membership functions, the upper limit includes an extra pump operation with a minimum power consumption, when intervals that do not belong to any fuzzy set defined for the linguistic variable emerge in the system of fuzzy logic inference in the domain of the finite set.For example, the upper reference value for the membership function to the fuzzy set "power of one pump" should be given at p max = 825 kW.However, the lower limit of the function to the fuzzy set "power of two pumps" is 2p min = 1250 kW.As a result, the power range from 825 kW to 1250 kW does not belong to any fuzzy set, which greatly reduces control flexibility.

Synthesis of the rule base for the fuzzy inference system
On completing the fuzzification phase, it is necessary to form the rule base of the Mamdani fuzzy inference system.This procedure is carried out taking into account technological requirements for operating modes of mine water drainage.The key requirement is to ensure the efficient groundwater pumping, depending on intensity of its inflow into the underground mine.This is done to avoid flooding a shaft and mine levels, as it creates a danger to human life and makes it impossible to carry out technological operations of rock mass mining.Therefore, the highest level of significance is given to those comprising the fuzzy set "high inflow".
Since the system has two inputs, the conditional part of the base rules uses fuzzy AND conjunction operators to establish a logical relationship between the input variables of the fuzzy inference system.
Let us formalize the rules.In all cases, if there is a high water inflow into the underground mine, all three pumps must be put into operation, regardless of the current power tariff.Moreover, the significance of this block of rules is 1, which determines the highest importance of these rules.As a result, they have the following form: R1: Given a medium water inflow, the output power consumption of pumps depends on the current tariff.It is expedient to pump out water with maximum efficiency at the "night" tariff with all three pumps of a level, at the "half-peak" tariff with two, and at the "peak" tariff with only one.The significance of this block of rules is 0.75.As a result, the rules have the following form: R4: Regardless of power costs, it is advisable to drain water with only one pump at low water inflow, so the following set of rules looks like this: R7: The significance of this block of rules is 0.75 as well.Table 2 summarizes the fuzzy rules.
Table 2. AND-type rule base of the fuzzy system controlling power consumption by water drainage facilities.

NT HP PK L ON ON ON M TR TW ON H TR TR TR
The output surface of the Mamdani fuzzy inference system with nine AND rules is shown in figure 5.
For comparison, let us synthesize the rule base using the fuzzy disjunction operator OR.Water drainage facilities will consume the maximum power either at high water inflow or during the "night" tariff, and the minimum power either at low water inflow or at the "peak" tariff.Similarly, we formulate the rule for medium water inflow and the "half-peak" tariff.The resulting rule base is as follows: R1: The first rule R1 has the significance of 1 and the other two -0.75.It should be noted that this approach does not cover all possible combinations of value pairs of input variables.
The output surface of the Mamdani fuzzy inference system with three OR-type rules is shown in figure 6.

Modelling the expert system for controlling power consumption by main water drainage facilities of the underground mine
Let us analyze the efficiency of the fuzzy power consumption control system of the 500 m level.To do this, we will implement the system in MATLAB/FuzzyLogicToolbox and simulate its operation.
As a test signal for the input coordinate "water inflow", we use a stochastic process of a random variable.The law of probability distribution is assumed to be normal with mathematical expectation E [Q] = 500m 3 /h and variance σ 2 = D [Q] = 200m 3 /h The state of the pseudorandom number generator is recorded by the software to ensure representativeness when comparing several control systems.Therefore, the stochastic process implementation will be conditionally constant for all experiments.The test signal for the input variable "power tariff" is generated by distributing tariff zones during the day.That is, the "night" zone is effective for 8 hours from 23.00 to 7.00, the "halfpeak" zone -11 hours from 7.00 to 8.00, from 11.00 to 20.00 and from 22.00 to 23.00, the "peak" zone -5 hours from 8.00 to 11.00, from 20.00 to 22.00.To simplify, we assume that the underground mine is supplied with electric power in a centralized way by an external distributor, so the test signal has a stable periodic nature.
A comparative analysis will be performed for fuzzy logic inference systems with AND-and OR-type rule bases, as well as with a system without power consumption control, in which two   The obtained results of the water drainage modelling over a week (table 3) demonstrate that when using fuzzy power consumption control systems, power costs decrease, compared to the system without such control.
The controlled system that uses the fuzzy inference algorithm with the OR-type rule base  This trend persists if we consider a longer period, for example, a month (table 4).Moreover, the level of savings on power costs is only increasing.Thus, the fuzzy system with the OR rule base allows reducing power costs by 2.28% (by UAH 3379.66), the system with the AND-type rule base -by 5.43% (by UAH 8058.36).That is, the percentage ratio increases for both systems by 0.39% and by 1.3% compared to the week's operation.The cumulative nature of the economic effect is observed.At the same time, the AND-type rule base system provides 3.23% (or UAH Two characteristic features of fuzzy control systems of water drainage power consumption at underground mines should be noted.The average power of the facilities at the mine level almost does not deviate from 1600 kW during the considered periods of operation.What is more, the power consumption level of uncontrolled systems is lower.This is due to the fact that in fuzzy control systems, power is consumed unevenly and there are long periods when the water inflow is high and three pumps are running at the same time, which leads to an increased level of power consumption.However, the fuzzy control algorithm allows increasing economic efficiency of the system due to the transfer of the high power consumption period to the "night" tariff time, thereby reducing the total cost of produced power.

Conclusions
The proposed expert control system of power consumption by main water drainage facilities of the underground mine based on the Mamdani fuzzy logic algorithm demonstrates its expected economic efficiency.Correspondingly, it is to be recommended for implementation at the relevant facility of iron ore underground mines.
The higher quality of control is demonstrated by the system with a conjunction-type fuzzy rule base.The level of power consumption in the uncontrolled system is lower due to uniformity of output power distribution by electromechanical drainage facilities during the day.
Further improvement of fuzzy control systems consists in increasing energy efficiency, i.e. reducing power consumption by main water drainage facilities of underground mines, which can be achieved by introducing an additional limitation for the power level of pumps running simultaneously during fuzzification of the corresponding linguistic variable.

Figure 1 .
Figure 1.Water drainage facilities of the 500 meters horizon of the Kryvorizka underground mine.

Table 1 .
Annual groundwater inflow into the Kryvorizka underground mine for 2016-2021.No Year Water inflow, m 3

Figure 2 .
Figure 2. Membership functions to the fuzzy set "water inflow".

Figure 3 .
Figure 3. Membership functions to the fuzzy set "power tariff".

Figure 4 .
Figure 4. Membership functions to the fuzzy set "pump power".

Figure 6 .
Figure 6.Output surface of fuzzy inference system.

Figure 7 .
Figure 7. Results of modelling the operation of the water drainage power consumption control system based on the Mamdani fuzzy inference algorithm with the AND-type rule base over 7 days.

Figure 8 .
Figure 8. Results of modelling the operation of the water drainage power consumption control system based on the Mamdani fuzzy inference algorithm with the OR-type rule base over 7 days.

Figure 9 .
Figure 9. Results of modelling the water drainage power consumption control system based on the Mamdani fuzzy inference algorithm with the OR-type rule base over 31 days.

Figure 10 .
Figure 10.Results of modelling the water drainage power consumption control system based on the Mamdani fuzzy inference algorithm with the AND-type rule base over 31 days.

Table 3 .
Modelling results of power consumption fuzzy control by the water drainage facilities of the level over 7 days.

Table 4 .
Modelling results of power consumption fuzzy control by the water drainage facilities of the level over 31 days.