Reasons of removing out of service power transformers.
Abstract
On the base of damage rate analysis of power transformers and methods of electrical energy system (EES) modes control the necessity of using the results of online diagnostics of LTC transformers not only for determinations of the expending of further operation or equipment repair but also for calculation of optimal transformation coefficients (with account of the suggested RRCT) for their application in the process of modes control has been proved. Improved method of determination of control action, realized by the LTC transformers by means of comparative analysis of the results calculation of EES modes with quasi resistances of the circuit branches. Such peculiarity of the suggested method of determination of control actions by LTC transformers, as the account of RRCT, in the process of EES mode control provides such advantages as reduction of the damage rate of the equipment, reduction of active power losses in EES. Due to the peculiarities of the method of determination of control actions by LTC transformers, with the account of their technical state, perspectives of the development and introduction in EES modern microprocessorbased systems of automatic control of transformers LTC open.
Keywords
 online diagnostics
 control
 normal modes
 active power losses
 similarity theory
 neurofuzzy modeling
 basic similarity criteria
 membership functions
 uncertainty
1. Introduction
Characteristic feature of present day situation are the attempts of utility companies to increase energy efficiency in conditions of continuing aging of high voltage equipment.
Practice of largescale introduction of the intelligent support of decision making of solution processes proves their efficiency. One of the directions of efficiency increase of electric energy transportation is improvement of methods and means of active power losses reduction on conditions of maintaining reliable operation of high voltage equipment, including outdated equipment.
The set of electric energy system (EES) states and the processes of transition from one state into another her is EES mode (furthermode), characterized by the parameters, for instance, electrical voltages an substations loads, currents in transmission lines transformation ratios of the transformers, etc., normal operation mode 07 of EES modes. Control by the system of online dispatching control (LDC). Modern LDS technologies, for instance, provided by smart grids concept, are aimed at improvement of its information support. This enables the optimal implement more efficiently energysaving technologies in electric systems, when out of date highvoltage equipment is using.
Means of similarity theory, in particular the criterion method (KM), can effectively solve and analyze optimization problems [1]. Criteriabased method can be defined as a set of techniques and principles, according to which the analysis, comparison and interpretation of baseline data to provide scientific and practical conclusions. The ultimate goal of studies using the criterial method is to reveal regularities, which under certain conditions can be represented as the law control [2]. The main purpose of KM is to find the variant of the process or the object. Most often, in the further analysis, the parameters are used as reference. According to his idea, KM is close to the geometrical programming [3]. This use of duality of optimization problems is the replacement of the direct problem for the corresponding dual. The main difference is that the basis for geometric programming is inequality between geometric and arithmetic averages, and the background of the KM—matrix properties of dimensions or indicators [4]. This is the meaning of dual variables. In geometric programming are weighting factors, in KM—similarity criteria. That is, the result of solving the tasks of the KM is values of criteria of similarity or, in other words, the optimum ratio of the individual parameters, and not they themselves. This specific feature characteristic only of KM, determines its scope.
2. Analysis of the literature data and problem set up
In [5] the technique of voltage drop decrease in separate parts of distribution electric grids is, suggested, but it does not take into account technical state of regulating devices [6]. In [7] on the example of Indian electric grids the statistics of the increase of power, transmitted in electric grid is considered.
It is stated that in order to improve the grid reliability and efficiency of energy transmission it is necessary to use power transformers, equipped with LTC and automatic or automated control systems for such LTC control. It enables to control power flows in EES by means of LTC so that the parameters of electric grids modes were within the limits of normal values of equipment (transmission lines, switching devices, transformers, etc.) parameter.
It is provided by usage of FACTS technologies. For instance, in [8], the possibilities of using phaseshift transformer for power flows change in electric energy system to reduce power losses in the process of energy transmission in transmission lines of Slovak Republic are considered. In [9] high price of FACTs technologies usage in energy branch for the reduction of electrical power is proved. In [10] three variants of power flows control in electric grid, using three FACTs devices are considered with Thyristor Controlled Series Capacitor (TCSC), Static Synchronous Series Compensator (SSSC) and phaseshift transformer (PST), but in [11] any attention is paid to the state of equipment, used for modes control. In [12] the conclusion is made that prolongation of power transformers operation term for 20–30 years is more profitable than their replacement by new ones, and the quantity of power transformers in the USA, that have been in operation for more than 25 years (certificate resource – 25 years) is approximately 65%.
In [13] attention is paid to the system of continuous monitoring of technical state of power transformers, the given system is used at the transformers of jointstock company “Magnitogorsk Metallurgical Complex”, HYDRAN analyzer, methods of localization and identification of faults, practical necessity of partial discharges control is underlined, but the results of diagnostics during modes control are not paid attention to.
In [14] it is noted that in local electric system in order to provide stable operation and indices of electric energy quality it is necessary to use modern control systems that take into consideration voltages in nodes and frequency and eliminate emergency deviations. At the same time, in [15] modeling of nonstationary critical operation modes of EES in the process of parameters change in wide limits by means of application of nonlinear mathematical models attention is paid to. This enables to study the consequences of such modes, promptly take measures, aimed at their prevention or elimination. In pages [16] technical state of the equipment of these systems is not taken into account, this can lead to the damage of the equipment and undersupply of energy to the consumers.
Thus, the problem of development of the methods of diagnostics results account during control of EES modes is not solved.
It is known that operation control (RTOC) in Ukraine is carried by a man. Overloading of this person with a great volume of diagnostic parameters data, especially in conditions of limited time for decisionmaking, leads to their actions. In the process of modes online control, especially postoccident modes. It is expedient to assess the state of equipment by generalized indices, for instance, by residual resources coefficient of the transformers (RRCT). The development of the method of online diagnostics of the transformers and the account of RRCT in the process of ESS modes control for minimization of total losses of active power are not considered in literature sources and is the subject of authors study.
3. Objectives and tasks of the research
The objective of the research is the development of the method of diagnostics of the transformers with LTC and account of PRCT values in the process of EES modes control for minimization of active power losses. To realize this objective the following problems are to be solved:
substantiate the expediency of applying the results of diagnostics of LTC transformers in the process of optimal control of EES modes;
develop neurofuzzy model of residual resource coefficient of the transformers (RRCT);
develop the method of RRCT values and power transformers with LTC state account in the process of EES modes control.
4. Materials and methods of transformers diagnostic study
Automation of the process of power flow control may be provided by means of centralized remotely controlled alternative usage of switching devices (LTC) of the transformers. Under such conditions, there appears the possibility of the analysis of control actions of separate LTC on mode parameters of EES by means of the feedback. This approach improves the operation quality of adaptive control automatic systems of the LTC position control. For this purpose, at considerable changes of load schedule it is necessary to perform ranking of the transformers with LTC by the quality of their impact on maintaining parameters of the modes.
Realization of measures, aimed at reduction of power losses is limited by the possibilities of the equipment involved in the provision of mode; namely, by its technical state. It is known, that the damage of high voltage equipment during mode control (for instance, power transformers) leads to losses, which considerably exceed the cost of electric energy, saved as a result of losses decrease. Failure rate of the outdated high voltage equipment (power transformers, shunting reactors, instrument current and voltage transformers, switches, etc.) increases, when such equipment has been in operation for more than 25 years [17]. Taking into consideration the fact that the control of EES modes is accompanied by the operation of switching devices, regulation devices of transformers, emergence of switching surges, ferroresonances, currents increase in power and instrument transformers, transmission lines, etc., then the control of modes must be realized, taking into consideration their technical state [18] and possible expenses for their replacement or repair.
Thus, it is necessary to know current state of high voltage electric equipment of EES, which is in operation during modes control.
5. Determination of current technical state of power transformers
We will consider the method of determination of power transformers current state and RRCT values in the process of EES modes control on the example of power high voltage transformers, which have onloadtap changing device.
We suggest to evaluate technical state of power transformer by means of the analysis of the value of its residual resource coefficient. Power transformer residual resource coefficient has the dimensionality in relative units and can change in the process of operation in the range from one (the best technical state) to zero (the worst technical state, when the transformer must be removed out of service for inspection, repair, replacement, etc.).
Then, we will consider the example of residual resource coefficient determination of the transformer АТDCTN 125000–330/110. First we will study the statistics of failure rate of such transformers. Table 1 contains the example of possible reasons and amount of transformers removal out of service, that is close to data, published in studies [19].
Transformer element  Designation  Parameter name  Units  % 

Windings  Z_{k}  Winding deformation  8  1.6 
t^{0}  Deterioration of contact joints state  10  2  
P_{i.p}  Idle power that characterizes of the magnetic quality  15  3  
Insulation  R_{in}R  Contamination of isolation  65  13.4 
W  Humidification of the isolation  48  10  
Bushings  k_{bush}  Defects of bushings  74  15.2 
Oil  CADG_{c}  Content of dissolved gases  71  14.6 
PCA  High moisture content and deviations of other parameters of the oil  43  9  
CADG_{d}  Discharges in oil  64  13.2  
LTC  k_{def.LTC}  LTC defects  45  9.3 
Cooling system  I_{motor} or I_{mt}  The current of oil pump drive motor  14  2.9 

Coolers temperature  16  3.3  
Tank  k_{tank}  Tank leakage  12  2.5 
Total  485  100 
In Table 1 such symbols are used: Z_{k} is the resistance of the transformer windings (during measurements in short – circuit mode); t° is the temperature of contact points (for instance, bushing of the bus duct or with winding lead); P_{i.p.} idle mode power, that characterizes the quality of magnetic circuit; R_{in} is the resistance of the insulation for revealing the contamination and aging of solid and liquid insulation (also it is necessary to determine the capacity and dielectric loss tangent, also it is desirable to determine the degree of polymerization); W humidification of the isolation; k_{resid.res.bush} or k_{bush} is the residual resource coefficient of the bushings; CADG_{C} is residual resource coefficient of the transformer by the results of chromatographic analysis of dissolved gas in the transformer oil of the tank and LTC (ethylene, ethane, methane) of the transformer, that characterizes oil contamination by the gases, dissolved in it and among them acetylene and hydrogen (for revealing of discharges); PCA residual resource coefficient of the transformer by the results of physical–chemical analyses of transformer oil from transformer tank, contactor and LTC tap changer; CADG_{d} is residual resource coefficient of the transformer by the results of chromatographic analysis of the dissolved hydrogen and acetylene in the transformer oil of the tank and LTC of the transformer tap changer in order to reveal the discharge; k_{def.LTC} or k_{LTC} coefficient of the transformer LTC residual resource; I_{m} is the current of electric motors oil pumps and fans of cooling system; t°_{cool} is coolers temperature; k _{tank} is the residual resource coefficient of the transformer tank, determined by the availability (takes the value “0”) or absent of oil leakage (takes the value 1).
From Table 1 shows that the transformers are often displayed in repairs due to moisture and oil contamination, insulation and highvoltage inputs defects.
The task of creating a mathematical model complicated with incomplete initial data as part of the parameters known at the time of payment, such as the reasons for the need for additional studies. To establish reciprocal links diagnostic parameters very constructive simulation technology is unclear. This simulation allows to obtain more reliable results compared to the results of existing diagnostic systems.
In Table 1 under the term the controlled diagnostic parameter we mean the parameter deviation of which from the norm helped to remove the transformer out of service or was taken into account in the process of its removal out of service. In Table 1 the following diagnostic parameters are given: parameters, that characterize the state of the windings, insulation, bushings, oil, LTС, cooling systems, tank.
Having analyzed the data of Table 1 the scheme was created that shows whether dependent or independent is the impact of diagnostic parameters on the coefficient of total residual resource of the transformer (Figure 1).
Figure 1 does not show mutual impact of one controlled diagnostic parameter on the other one; it is shown either in dependent or independent manner how these parameters influence the coefficient of total residual resource of power transformer (PT).
In Figure 1 over the parameter the percentage amount of revealed faulty transformers by the given parameter is shown, that is given in percent from the total amount of faulty transformers.
The blocks with parameters whose deviations from the norm substantiate the necessity of the output of the transformers for repair, are shown sequentially and are shown k_{res} – residual resource coefficient of the transformer (RRCT). In parallel, blocks with parameters are also depicted. A large change in these parameters proves the necessity of outputting a power transformer (PT) for repair. PT is repaired in case of deviation from the norms of these parameters. This is due to the requirements for the reliability of the transformers. In each of the given blocks parallel can be allocated but it are not shown to simplify the calculation (for instance, currents of electric motors of oil pumps and fans).
In order to obtain the generalized parameter of the residual resource of the transformer, it is proposed from the known values of diagnostic parameters to pass to the corresponding values of residual resources coefficients (in relative units) by each diagnostic parameter. This will allow you to take into account the value of all diagnostic parameters and the impact of each of them.
These coefficients are defined in relative units by (1) and that is why they characterize total output of the transformers from the moment of their technical state control to transition to boundary state that is residual technical resource (12). Residual resource coefficient
where
We perform the reduction of the circuit by the following expressions. For serial part of the circuit (Figure 1) the coefficient of total residual resource is found by the expression:
where k_{τ} is the coefficient of residual resource of PT by τ^{th} diagnostic parameter; τ is τ^{th} diagnostic parameter; ν is the amount of blocks in the serial part of the circuit of Figure 1, p_{τ} probability of control parameters deviator from maximum permissible normalized value of this parameter is found by means of the expression (3):
where y_{τ} is a number of controlled parameter deviations from admissible limiting normalized value of this parameter, which were revealed by means of τth diagnostic parameter control (τ for serial part of the circuit) from the total number of the revealed deviations of controlled parameters from admissible limiting normalized value; m_{2} is total quantity of the revealed deviations of controlled diagnostic parameter from their admissible limiting normalized values.
For parallel part of the circuit the coefficient of total residual resource is found by the expression (4)
where k_{res,j} is the coefficient of residual resource of РТ by jth diagnostic parameter; j is number of jth diagnostic parameter; m_{1} is a quantity of blocks(parameters) in parallel part of the circuit that is reduced.
The coefficient of total residual resource of РТ is determined by the expression (5):
where k_{wind}, k_{in}, k_{bush}, k_{oil}, k_{LIC}, k_{cool}, k_{tank} are known at the moment of calculation values of the coefficient of residual resource: of the windings, of the insulation, of bushings, of the oil, of LTC, of system of the cooling, of tank of the transformer, by the elements of the transformer, correspondingly.
For the creation of mathematical model of residual resource coefficient of the transformer parameters were used, by each of these parameters the conclusion regarding the state of the transformer can be made. But none of these parameters completely characterizes technical state of the transformer, it only shows certain changes of technical state of power transformer.
Mathematical model of residual resource coefficient of the transformer was created by means of MatLab. Using this model, it is possible to edit the already created (5) probabilistic sample of teaching data. These data help to obtain analytical dependence of residual resource coefficient of the transformer on diagnostic parameters in the form of the polynomial. For seven input parameters of the model, that randomly changed from 0 to 1, the coefficient of total residual resource of the transformer (5) was determined, where input parameters of the model were reduced to relative units of their deviation from the norm.
By means of Anfis Editor using hybrid teaching algorithm and applying Sugeno algorithm of neurofuzzy conclusion neurofuzzy model of residual resource coefficient of the transformer (using subclusterization method) was obtained.
Figure 2 contains the copy of screen saver in Matlab environment where the structure of the obtained neural network is shown.
For each input variable of neuromodel four linguistic terms with Gaussian membership functions were used:
where
These are such terms as: “normal” values of diagnostic parameter, “minor deviations” of diagnostic parameter value, “prefault” values of diagnostic parameter, “emergency” value of diagnostic parameter.
For determining the value of total residual coefficient neurofuzzy nonlinear autoregressive model of the total residual resource coefficient of the transformer is used. This model establishes neurofuzzy nonlinear transformation between the values of residual resource coefficients by diagnostic parameters and total residual resource coefficient of the transformer (7):
where F is neurofuzzy functional transformation.
For determination of the value of total residual resource coefficient of the transformer, we use TakagiSugeno model of logic conclusion.
Mathematical model of total residual resource coefficient is the system of logic equations (8).
Output of the model total k_{tot.resid.res.} is found as weighted sum of conclusions (8) of rules base written in the form the system of logic equations:
where
ANFIS is the simplest network of direct propagation that contains adaptive nodes, using the teaching rules the parameters of these nodes are arranged to minimize the error between the real output of the model k_{tot.resid.mod.} and real total residual resource coefficient k_{tot.resid.res} of the transformer
where N is number of rows in teaching sample; k_{3} is the number of the row in teaching sample, starting from the row with consecutive number “0”.
Taking into account the iterative computation experiments carried out the vector of membership functions parameters is determined in Table 2.
Parameters  Input parameters of the model  Name of the term  Number of the rule  Parameters of membership function  

σ  С  
Winding state  K_{wind.}  Normal  1  0.3825  0.7944 
Minor deviation  2  0.479  0.5197  
Prefault  3  0.4903  0.5668  
Emergency  4  0.4  0.1697  
Insulation state  k_{іn.}  Normal  1  0.3653  0.8698 
Minor deviation  2  0.4642  0.6104  
Prefault  3  0.5102  0.5267  
Emergency  4  0.3949  0.1742  
State of BB  k_{bush.}  Normal  1  0.3202  0.9221 
Minor deviation  2  0.3419  0.7649  
Prefault  3  0.4914  0.5376  
Emergency  4  0.4032  0.1925  
State of oil  K_{oil}  Normal  1  0.4369  0.9273 
Minor deviation  2  0.3404  0.9674  
Prefault  3  0.412  0.599  
Emergency  4  0.4031  0.2057  
State LTC  K_{LTC}  Normal  1  0.3984  0.973 
Minor deviation  2  0.3316  0.963  
Prefault  3  0.4468  0.5881  
Emergency  4  0.4428  0.2349  
State of cooling system  k_{соol.}  Normal  1  0.3439  1153 
Minor deviation  2  0.3507  0.9706  
Prefault  3  0.437  0.597  
Emergency  4  0.4263  0.2397  
State of tank  K_{tank}  Normal  1  0.3454  0.9506 
Minor deviation  2  0.3801  1017  
Prefault  3  0.4582  0.6273  
Emergency  2  0.5451  0.564 
It is seen from Figure 2 that in the process of formation of the structure of neuro fuzzy model of the transformer seven inputs and one output of this model were set. Each of seven inputs has four terms. That is, each set of possible values of input parameters of the model is conventionally divided into four subsets: “normal” values of input parameter, “miner deviations” of the values of input parameter, and “prefault” values of input parameter, “emergency” values of input parameter. Membership degree of each value of input parameter to corresponding set of values is determined by Gaussian membership function. The model is intended for determining the numerical value of total residual resource coefficient of the transformer, that is why it has one output. This numerical value is found by means of solution of linear equation, that describes the dependence of the coefficient of total residual resource of the transformer on input parameters.
The obtained neurofuzzy model allows to determine the value of total residual resource coefficient of the transformer depending on the values of input parameters residual resources coefficients by each of controlled diagnostic parameters. The error of PPCT mathematical model changes from +0,004 relative units, if PPCT equals 0, to −0,032, when PPCT equals 1.
Taking into account the data of the Table 1 and Table 2 and (9) we obtain mathematical model of the coefficient of total residual resource in the form:
The obtained neurofuzzy model allows to determine the value of total residual resource coefficient of the transformer depending on the values of input parameters residual resources coefficients by each of controlled diagnostic parameters. The error of PPCT mathematical model changes from +0.004 relative units, if PPCT equals 0, to −0.032, when PPCT equals 1.
Despite the complexity of dependences, mathematical model of residual resource coefficient of the transformer (11) may be used for programming neurofuzzy controller in order to create the device for online determination of transformer state by means of analysis of residual resource coefficient of the transformer value.
6. Account of the forecast current value of residual resource of the transformers in the process of control of EES modes
It is known that in the process of operation, energy enterprise plans to remove out of service the equipment in the overhaul, cost of is forecast. Removal of the transformer into overhaul in a planned number of years (T_{WF}) of troublefree operation (12 years) provides certain list of works and their expected cost B_{oh pl.} For instance, for 330/110 kV transformers of 125–250 MVA power the cost (B) of such repair is 770–11,550 $. We propose to assume that removal out of service the transformers into current repair requires unscheduled cost.
The cost of repair may increase by the value ΔВ_{1}, replacement of damaged blocks of the transformer and additional work, connected with the replacement. These costs are not provided in case of “typical” planned overhaul
where B_{i} is the cost of replacement of
Repair cost may increase by the cost of ΔB_{2} (as compared with expected) in case of enlarged current (instead of planned overhaul) repair of the transformer, that did not operate for planned number of years:
where j is a number of the transformer, T_{j} is time, the
It should be noted that removal the transformer out of service takes place not only as a result of relay protection, emergencies control automation operation but also by a person responsible for safety operation by the results of control of diagnostic parameter, values of which sometimes only approaches to limiting values.
Within the context of creation of modern Smart Grids and to provide safe, reliable, quality and economic efficient operation of EES it is necessary to perform the control over active power overflow to realize by means of the transformer, performing reliable and information archons on the mode. That is why, we suggest to take into account the coefficient of regulating transformer limitation:
where B_{cq} is the coefficient of repair cost value growth of the jth transformer.
As the example, we will consider 23 nodes 230/138 kV test circuit (Figure 3). In branches 11–9, 12–14, 12–9, 11–4, and 3–7 transformers АТDCTN63000/230/138, АТDCTN100000/230/138 and АТDCTN125000/230/138 are installed. Initial node loads, complex transformation ratios and corresponding transformers LTC positions (number of taps) are given in Tables 3 and 4.
Branches  R (Ohm)  X (Ohm)  k_{active}  k_{reactive}  

№ of beginning  № of the end  
11  10  0.6  27  0.6487  0 
12  9  0.37  9.28  0.6498  0 
11  9  0.3  13  0.6479  0 
7  3  0.21  11.53  0.65  0 
1  2  0.4951  26.471  1  0 
1  3  10.398  40.221  1  0 
1  5  41.516  16.092  1  0 
2  4  62.464  24.129  1  0 
2  6  94.649  36.565  1  0 
3  9  9.882  20.962  1  0 
4  9  51.038  19.749  1  0 
5  10  4.342  16.816  1  0 
8  9  8.82  15.124  1  0 
8  10  2.067  2.145  1  0 
11  23  5.207  22.793  1  0 
11  14  28.566  22.112  1  0 
12  23  5.207  25.18  1  0 
12  13  65.596  51.101  1  0 
23  13  58.719  45.759  1  0 
14  16  2.645  20.578  1  0 
15  16  2.338  8.404  1  0 
16  17  17.457  13.701  1  0 
16  19  3117  11.206  1  0 
17  18  0.9522  76.176  1  0 
17  22  71.415  55.704  1  0 
21  22  46.023  35.866  1  0 
7  15  5.68  24.865  1  0 
21  18  0.873  6.851  1  0 
21  15  1.666  12.96  1  0 
19  20  1.349  10.474  1  0 
20  13  0.741  5.713  1  0 
12  10  0.31  14  0.6524  0 
10  6  26.471  11.522  1  0 
№ of the node  U (kV)  Phase (grad)  P_{load} (MW)  Q_{load} (MVAr)  P_{gen} (MW)  Q_{gen} (MW) 

1  136.34  −5.73  108  22  182  30 
2  135.54  −6.27  187.15  76  172.9  30 
3  141.22  −0.94  176.4  36.26  0  0 
4  136  −8.2  74  15  0  0 
5  137  −8.11  68.16  13.44  0  0 
6  136.36  −10.3  129.2  25.27  0  0 
7  218.84  2.99  19.4  1.94  0  0 
8  142.57  −7.72  169.29  34.65  131.55  131.75 
9  141.55  −5.6  275  66  0  0 
10  141.64  −7.29  191.1  49  0  0 
11  222.36  −3.12  40  10  0  0 
12  219.92  −4.12  54.88  17.64  0  0 
13  236.15  7.89  0  0  495  150 
14  228.34  1.56  184.3  37.05  0  101.39 
15  233.22  11.21  304.32  61.44  235.2  51.32 
16  233.45  10  100  20  185  80 
17  237.79  15.28  35.64  13.86  0  0 
18  241.5  16.92  323.01  65.96  417.1  176.19 
19  231.47  7.6  177.38  36.26  0  0 
20  233.81  7.31  128  26  0  0 
21  241.5  17.83  0  0  425.7  146 
22  241.5  25.95  0  0  420  −3.69 
23  234.6  0  265  54  417.85  281.37 
Knowing the circuit and normal node parameters we define transformation ratios.
where N_{k.bal.b} is the second matrix of branches connection in contour balanced transformation ratios; Z diagonal matrix of complex branches resistances; C_{e} is the matrix of currents distribution coefficients for economic mode of electric network (corresponds to minimal losses of electric energy); J vectorcolumn of currents in nodes; U_{b} is the voltage of basic node; E*_{bal.a} and E*_{bal.r} are balancing is electric moving in relative units (EMF) in relative units (active and reactive components).
Taking in the consideration the discrete character of LTC switching’s, errors of instrument transforms, errors of data transmission channels and recommendations [20] we assume that nonsensitivity zone of active power losses may be considered as regulating actions on LTC of the transformer—to be 3% [21].
As initial conditions we assume that in accordance with load graph LTC of transformers 9–11, 9–12, 11–10, 12–10 have transformation ratios 0.6413 (14 tap), 0.6347 (14 tap), 0.6397 (14 tap), 06446 (14 tap).
It should be noted that further changes of operation mode were realized at admissible voltage deviations ±5%, from nominal voltage U_{nom}.
Regulation of the transformer 7–3 is inexpedient on conditions of the usage of the given technique of determination of transformation ratios.
We define the losses of active and reactive power in the branches of the circuit at current transformation ratios (Table 5).
Pters*  № of nodes  

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  
P_{load,} MW  19.44  37.43  38.8  17.02  13.63  24.55  3.49  27.08  60.5  38.22  8.4  10.43  0  29.49  39.6  20  8.55  80.75  35.47  26.88  0  0  53 
Q_{load,} MVAr  3.96  15.2  7.97  3.45  2.69  4.8  0.35  5.54  14.52  9.8  2.1  3.35  0  5.93  8  4  3.33  16.49  7.25  5.46  0  0  10.8 
ΔP_{Ʃ}, МW  4.49  
ΔQ_{Ʃ}, МVar  29.05  
11–10  —  —  —  —  —  —  —  —  —  0.6437  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  
12–10  —  —  —  —  —  —  —  —  —  0.6446  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  
9–11  —  —  —  —  —  —  —  —  0.6413  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  —  —  —  —  —  —  0.6397  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  13  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  0.65  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  — 
where
We define transformation ratios (16–17) and position of LTC on condition of minimal amount of switchings (in order to maintain switching resources of LTC) to provide minimal losses of active power in branches of the circuit of Table 6.
Pters  № of nodes  

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  
P_{load,} MW  19.44  37.43  38.8  17.02  13.63  24.55  3.49  27.08  60.5  38.22  8.4  10.43  0  29.49  39.6  20  8.55  80.75  35.47  26.88  0  0  53 
Q_{load,.} MVAr  3.96  15.2  7.97  3.45  2.69  4.8  0.35  5.54  14.52  9.8  2.1  3.35  0  5.93  8  4  3.33  16.49  7.25  5.46  0  0  10.8 
ΔP_{Ʃ,}. МW  4.42  
ΔQ_{Ʃ,}. МVar  28.69  
11–10  —  —  —  —  —  —  —  —  —  0.6513  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  
12–10  —  —  —  —  —  —  —  —  —  0.6542  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  15  —  —  —  —  —  —  —  —  —  —  —  
9–11  —  —  —  —  —  —  —  —  0.6507  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  —  —  —  —  —  —  0.6521  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  0.65  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  — 
As a result of realization of control actions, mode optimization power losses were reduced from ΔS_{1} = 4.49 + j29.05 (MVA) for mode (Table 5) to ΔS_{2} = 4.42 + j28.69 (MVA). Thus, the effect of realization of transformer LTC switchings is ΔS_{1}ΔS_{2} = 0.07 + j0.36 (MVA). The transition from the current to mode may be performed by switching the LTC of the transformer, installed in the branch 9–12 from 13 tap to 14 and carry out transformer regulation changing position of LTC from 14 tap to 15. We will consider the transition to another stage of daily load graph(load increase), its parameters are given in Table 7, and optimized transformation ratios and corresponding mode parameters  in Table 8.
Pters  № of nodes  

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  
P_{load,} MW  108  187.1  176.4  74  68.16  129.2  19.4  169.2  275  39.1  40  54.88  0  184.3  304.3  100  35.64  323.0  177.3  128  0  0  265 
Q_{load,} MVAr  22  76  36.26  15  13.44  25.27  1.94  34.65  66  10  10  17.64  0  37.05  61.44  20  13.86  65.96  36.26  26  0  0  54 
ΔP_{Ʃ}, МW  61.85  
ΔQ_{Ʃ}, МVar  412.73  
11–10  —  —  —  —  —  —  —  —  —  0.6513  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  
12–10  —  —  —  —  —  —  —  —  —  0.6542  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  15  —  —  —  —  —  —  —  —  —  —  —  
9–11  —  —  —  —  —  —  —  —  0.6507  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  —  —  —  —  —  —  0.6521  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  0.65  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  — 
Pters  № of nodes  

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  
P_{load,} MW  108  187.1  176.4  74  68.16  129.2  19.4  169.2  275  39.1  40  54.88  0  184.3  304.3  100  35.64  323.0  177.3  128  0  0  265 
Q_{load,} MVAr  22  76  36.26  15  13.44  25.27  1.94  34.65  66  10  10  17.64  0  37.05  61.44  20  13.86  65.96  36.26  26  0  0  54 
ΔP_{Ʃ}, МW  61.80  
ΔQ_{Ʃ}, МVar  412.68  
11–10  —  —  —  —  —  —  —  —  —  0,665  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  16  —  —  —  —  —  —  —  —  —  —  —  —  
12–10  —  —  —  —  —  —  —  —  —  0.651  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  
9–11  —  —  —  —  —  —  —  —  0.6753  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  17  —  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  —  —  —  —  —  —  0.659  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  15  —  —  —  —  —  —  —  —  —  —  —  
7–3  —  —  0.65  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  — 
As a result of performing control actions, mode optimization we succeeded in decreasing power losses from ΔS_{1} = 61.85 + j412.73 (MVA) for the mode (Table 7) to ΔS_{2} = 61.80 + j412.68 (MVA). Thus the effect of LTC transformer switchings is ΔS_{1}ΔS_{2} = 0.05 + j0.5 (MVA).
If as a result of determining the coefficient of regulating effect limitation for circuit transformers (Figure 3) the following values are obtained: k_{wind,9–11} = 0.85, k_{wind,12–9} = 0.4, k_{wind,11–10} = 0.3 а k_{wind,12–10} = 0,2, then expected quasidecrease of losses, taking into account these coefficient will be defined.
Control actions are performed by the transformer, installed in the branch 9–11, namely, we change position of LTC with 14 tap on 15, in this case, the expected losses of active power are ΔP_{9–11} = 61.82 (MW). We find the decrease of active power losses ΔР_{Σ}  ΔP_{9–11} = 61.85–61.82 = 0.03 (MW), however, having taken into account the coefficient of regulating effect limitation, losses decrease change δP_{quasi.9–11} = (ΔР_{Σ}  ΔP_{9–11})∙k_{wind,9–11} = 0.0255 (MW). New quasilosses ΔP_{quasi.9–11} = ΔP_{9–11 +} δP_{quasi.9–11} = 61.82 + 0.0255 = 61.8455 (MW). Results of the calculation of other transformers are given in Table 9.
Transf.  K_{tr.cur.}  K_{tr.opt.}  K_{wind.j}  ΔP_{tr.j} (MW)  ΔР_{Σ}  ΔP_{tr.j} (MW)  δP_{quasi.j} (MW)  ΔP_{quasi j.} (MW) 

N_{cur.}  N_{opt.}  
9–11  0.6507  0.659  0.85  0.03  0.0255  61.8455  
12–9  0.6521  0.6419  0.46  61.83  0.02  0.0092  
11–10  0.6513  0.665  0.34  61.835  0.015  0.0051  61.8401 
12–10  0.6542  0.651  0.25  61.84  0.01  0.0025  61.8425 
We define mode parameters for the circuit with quasiresistances from Table 11 and corrected transformation ratios from Table 12.
We find losses of active power in the branch, that contains the transformer, as function the element of vectorcolumn of complete power losses in the branches of the circuit by the expression
where ΔS_{α} = ΔU_{α}∙I_{α} is element of vectorcolumn of power losses in the branches, that contain transformers, ΔU_{α} is kth element of vectorcolumn of phase voltages drop in the branches, and I_{α} is the current of the branches with transformers couplings, α is the number of row, that correspond to the branch with transformer couplings in vectorcolumn ΔS_{br}.
The value of quasi resistance in kthbranch:
where
Applying this algorithm, according to (20), quasiresistances of the branches, containing transformers are found. The results of the calculations are given in Table 10. The aim of control is provider of minimum of all system active power losses that is determined by the expression
Parameters  Transformer 9–11  Transformer 12–9  Transformer 11–10  Transformer 12–10 

Branch resistance, Ohm  0.3 + j13  0.37 + j9.28  0.3 + j27  0.3 + j14 
Quasi resistance of the branch, Ohm  0.32 + j25.2  0.4 + j13.2  0.36 + j28.4  0.35 + j19.2 
Pters  № of nodes  

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  
P_{load,} MW  108  187.1  176.4  74  68.16  129.2  19.4  169.2  275  39.1  40  54.88  0  184.3  304.3  100  35.64  323.0  177.3  128  0  0  265 
Q_{load,} MVAr  22  76  36.26  15  13.44  25.27  1.94  34.65  66  10  10  17.64  0  37.05  61.44  20  13.86  65.96  36.26  26  0  0  54 
ΔP_{Ʃ}, МW  62.47  
ΔQ_{Ʃ}, МVar  422.16  
11–10  —  —  —  —  —  —  —  —  —  0.665  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  16  —  —  —  —  —  —  —  —  —  —  —  —  
12–10  —  —  —  —  —  —  —  —  —  0.651  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  
9–11  —  —  —  —  —  —  —  —  0.659  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  15  —  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  —  —  —  —  —  —  0.6419  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  13  —  —  —  —  —  —  —  —  —  —  —  
7–3  —  —  0.65  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  — 
Pters  № of nodes  

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  
P_{load,} MW  108  187.1  176.4  74  68.16  129.2  19.4  169.2  275  39.1  40  54.88  0  184.3  304.3  100  35.64  323.0  177.3  128  0  0  265 
Q_{load,} MVAr  22  76  36.26  15  13.44  25.27  1.94  34.65  66  10  10  17.64  0  37.05  61.44  20  13.86  65.96  36.26  26  0  0  54 
ΔP_{Ʃ}, МW  62.46  
ΔQ_{Ʃ}, МVar  422.28  
11–10  —  —  —  —  —  —  —  —  —  0.664  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  15  —  —  —  —  —  —  —  —  —  —  —  —  
12–10  —  —  —  —  —  —  —  —  —  0.641  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  —  13  —  —  —  —  —  —  —  —  —  —  —  
9–11  —  —  —  —  —  —  —  —  0.6753  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  17  —  —  —  —  —  —  —  —  —  —  —  —  
9–12  —  —  —  —  —  —  —  —  0.6492  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  —  —  —  —  —  —  14  —  —  —  —  —  —  —  —  —  —  —  
7–3  —  —  0.65  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
№ tap  —  —  14  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  — 
If
Thus, the transition from the current to the mode can be realized by switching the LTC of the transformer, installed in the branch 9–12 from 13 tap to 14tap and perform regulation of the transformer in branch 12–10, changing LTC position from tap 14 to 15 tap are shown in Figure 5.
As a result of realization of control actions the mode will be reached by transformer switching of the branch 11–10 from 14 to 16 tap of LTC, transformer of the branch 12–10 from 15 tap to 14 tap, transformer of the branch 9–11 transformer from 14 to 15 tap and transformer of the branch 9–12 from 14 to 13 tap of LTC, respectively, how are shown in Figure 6.
We see that due to consideration of technical state of transformers, their ranking occurred by the measure of impact on the reduction of active power losses. To reach mode now it is more expedient to use a transformer of 9–12 branch as it during one switching of LTC from 14 tap to 15 tap reduces most active power losses.
7. Discussion of the results of transformation ratios of EES transformers determination, taking into account the state of transformers
The analysis of the articles showed that neurofuzzy logic methods are used to solve various problems of operating electric power systems, such as improving power quality [18], classifying the faults of the electrical equipment based on sequence components [19], developing of the controller of the tariff, which based on neurofuzzy logic for the for distributing active power between a micro network and EPC for improving energy quality [20].
The error of RRCT determination by means of the developed mathematical neurofuzzy model, as compared with teaching sample and to the opinion of independent experts does not exceed the error of the devices, measuring diagnostic parameters. Such results are explained by complex usage of probability theory methods neurofuzzy modeling and modern software Matlab. These results also confirm the information provided in the article by Moudud Ahmed, Naruttam Kumar Roy. In their article [21], it is written that the use of automatic systems for adaptive control of electric power systems (EPS) based on neurofuzzy modeling and based on an inference system (ANFIS) is promising method. This improves EPS performance, for example, reduces power losses. Similar positive results of using neurofuzzy logic are described in the article by Priyanka Ray and A.K. Sinha [22]. This article says that the use of neurofuzzy logic has allowed the development of a hybrid control system that provides the maximum generated electrical power of hydro, wind and solar power plants even under incomplete data on current weather conditions and power consumption.
Also, in the works [23, 24, 25] of the authors H. Suna, R. M. Velasquez; J.W.M. Lara; Dong Ling; YaoYu Xu; Yu Liang; Yuan Li; Ning Liuand Quan and Jun Zhang were reviewed methods of intelligent diagnostics of transformers that use fuzzy logic and in the future can be applied to improve diagnostic systems and other power equipment.
Such feature of the suggested method for determining the control actions of LTCtransformers, as account of PPCT, in the process of ES modes control, provides such advantages as reduction of the equipment damage rate, decrease of active power losses in the EPS. Due to the of the peculiarities method of determination of control action of LTCtransformers, taking into account their technical state, perspectives of developments and introduction in EPS of modern microprocessor –based systems, automatic control of LTC of transformers become possible.
As compared with the known method of voltage drop control on the branches of EPS circuits, with the method of overloads decrease of transmission lines, at the expense of redistribution of power overflows in EPS, decrease of active power losses in the process of transportation by means of LTC transformers, the suggested method allows to select, by means of account the suggested RRCT, the transformer for EPS mode control, that would simultaneously provide the reduction of power losses and is more reliable.
Usage of quasiresistances of circuit branches, that unlike the transformers used, in the process of calculation of nominal resistances of the branches, take into account transformers state and possible losses of utility companies due to possible damages, allows to calculate EPS mode in rise of transformers transformation ratio change and by means comparison of calculated power losses select the most efficient transformer.
The suggested peculiarity of application the method of neurofuzzy modeling (usage in teaching sample the model of transformer resource instead of measured values of diagnostic parameters  calculated and partially corrected by independent experts of coefficients of residual resource) enables to take into account simultaneous impact on RRCT the results of both current and periodic control.
The drawback of the suggested mathematical neurofuzzy model of RRCT is necessity of large data base regarding coefficient of residual resource of diagnostic parameters CRRDP (Coefficient of residual resource of the diagnostic parameter) for specific transformers. Attempt to reduce database or use the model from other similar transformer results in the increase of model error. Limitation on the usage of RRCT model is the necessity of application only on one – investigated transformer. Therefore, we need models for each transformer. The method of determination of control actions by LTC transformers does not take into account voltage limitations in nodes and current limitations in the branches of the circuit.
Further development of the given research will be realized in the development of mathematical models of other types of high voltage equipment, involved in the process of EPS modes control, damage of which areas place (Figure 7).
Problems of the considered research development are caused by the necessity of long lasting experiments and observations over the processes of aging and development of high voltage equipment damage, processes of EPS modes parameters change not only on computer ad mathematical models of the equipment and EPS modes and on real equipment.
8. Conclusions
Analysis of damager ate of power transformers and methods of the EPS modes control allows to state that it is a necessary to use the results of online diagnostics of LTCtransformers not only to determine the expediency of further operation or repair of the equipment and for calculation transformation values (with the account of the suggested RRCT) for their usage in the process of modes control.
The model enables, by means of accounting, of both current and retrospective values of diagnostic parameters on RRCT and determine its current value. That is necessary for automatic and automated reliable and control of EPS modes.
Improved method of determination of control actions by LTC transformers, by means of comparative analysis of the results of EES modes with quasi resistances of circuit branches, enables to soled the transformer and calculate transformation ratio that provides minimal amount of LTC switching.
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