Sergey Pelykh and Maksim Maksimov

Odessa National Polytechnic University, Odessa

Ukraine

1. Introduction

The problem of fuel life control at nuclear power plants (NPP) with WWER-type light-water reactors (PWR) will be discussed for design (normal) loading conditions only. That is, emergency nuclear reactor (NR) operation leading to cladding material plastic deformation is not studied here, therefore the hot plasticity (stress softening) arising at the expense of yield stress decrease under emergency cladding temperature rise, will not be considered here.

Analysing the current Ukrainian energetics status it is necessary to state that on-peak regulating powers constitute 8 % of the total consolidated power system (CPS), while a stable CPS must have 15 % of on-peak regulating powers at least. More than 95 % of all thermal plants have passed their design life and the Ukrainian thermal power engineering averaged remaining life equals to about 5 years. As known, the nuclear energetics part in Ukraine is near 50 %. Hence, operation of nuclear power units of Ukraine in the variable part of electric loading schedule (variable loading mode) has become actual recently, that means there are repeated cyclic NR capacity changes during NR normal operation.

Control of fuel resource at WWER nuclear units is a complex problem consisting of a few subproblems. First of all, a physically based fuel cladding failure model, fit for all possible regimes of normal NR operation including variable loading and burnups above 50 MW-d/kg, must be worked out. This model must use a certified code developed for fuel element (FE) behaviour analysis, which was verified on available experimental data on cladding destruction.

The next condition for implementation of nuclear fuel resource control is availability of a verified code estimating distribution of power flux in the active core for any reactor normal operation mode including variable loading.

It should be noticed that calculation of nuclear fuel remaining life requires estimating change of the state of a fuel assembly (FA) rack. For instance, the state of a rack can change considerably at core disassembling (after a design accident) or at spent fuel handling. Generally speaking, the total fuel handling time period must be considered including the duration of dry/wet storage. Before designing a nuclear fuel resource control system, using

probability theory and physically based FA failure criteria, the failure probability for all FA must be estimated. Having satisfied the listed conditions, a computer-based system for control of nuclear fuel remaining life can be worked out.

The FEMAXI code has been used to calculate the cladding stress/strain development for such its quality as simultaneous solution of the FE heat conduction and mechanical deformation equations using the finite element method (FEM) allowing consideration of variable loading (Suzuki, 2000). Sintered uranium dioxide was assumed to be the material of pellets while stress relieved Zircaloy-4 was assumed to be the material of cladding (Suzuki, 2010). Cladding material properties in the FEMAXI code are designated in compliance with (MATPRO-09, 1976). But the manufacturing process and the zircaloy alloy used are not specified here.

FE behaviour for UTVS (the serial FA of WWER-1000, V-320 project), TVS-А (the serial FA of WWER-1000 produced by OKBM named after I. I. Aphrikantov) and TVS-W (the serial FA produced by WESTINGHOUSE) has been analysed.

The full list of input parameters used when analyzing the PWR fuel cladding durability can be seen in (Suzuki, 2000). The NR regime and FA constructional parameters were set in compliance with Shmelev’s method (Shmelev et al., 2004). The main input parameters of FE and FA used when analyzing the WWER-1000 fuel cladding durability are listed in Table 1.

		TVS
Parameter	UTVS	TVS-А	TVS-W
Cladding outer diameter, cm	0.910	0.910	0.914
Cladding inner diameter, cm	0.773	0.773	0.800
Cladding thickness, cm	0.069	0.069	0.057
Pellet diameter, cm	0.757	0.757	0.784
Pellet centre hole diameter, cm	0.24	0.14	—
Pellet dish	—	—	each side
Equivalent coolant hydraulic diameter, cm	1.06	1.06	1.05
Total fuel weight for a FE, kg	1.385	1.487	1.554

Table 1. Different parameters of UTVS, TVS-А and TVS-W.

FE cladding rupture life control for a power-cycling nuclear unit having the WWER-1000 NR is a key task in terms of rod design and reliability. Operation of a FE is characterized by
long influence of high-level temperature-power stressing leading to uncontrollable cladding material creep processes causing, after a while, its destruction, and fission products enter the circuit in the quantities exceeding both operational limits and limits of safe operation. In this connection, estimation of cladding integrity time for a NR variable loading mode, taking into account some appointed criteria, becomes one of key problems of FE designing and active core operational reliability analysis.

In accordance with the experience, there are following main characteristic cladding destruction mechanisms for the WWER-1000 varying loading mode (Suzuki, 2010): pellet­cladding mechanical interaction (PCMI), especially at low burnups and stress corrosion cracking (SCC); corrosion at high burnups (>50 MWd/kg-U); cladding failure caused by multiple cyclic and long-term static loads.

It is supposed that influence of low-burnup PCMI is eliminated by implementation of the WWER-1000 maximum linear heat rate (LHR) regulation conditions. Non-admission of cladding mechanical damage caused by SCC is ensured by control of linear heat power permissible values and jumps also. The high-burnup corrosion influence is eliminated by optimization of the alloy fabrication technique.

As all power history affects fuel cladding, it is incorrect to transfer experimental stationary and emergency operation cladding material creep data onto the FE cladding working at variable loading. Emergency NR operation leading to cladding material plastic deformation is not studied here, therefore hot plasticity (stress softening) arising at the expense of yield stress decrease under emergency cladding temperature rise, is not considered.

To solve this problem, we are to define main operating conditions affecting FE cladding durability and to study this influence mechanism. The normative safety factor Knorm for cladding strength criteria is defined as

where Rmax is the limit value of a parameter; R is the estimated value of a parameter.

The groupe of WWER-1000 cladding strength criteria includes the criteria SC1…SC5 — see Table 2 (Novikov et al., 2005). According to SC4, the WWER-1000 FE cladding total damage parameter is usually estimated by the relative service life of cladding, when steady-state operation and varying duty are considered separately:

, . NC: T dt „

o(t) = V—— — + I—— < 1

i NCi 0 t

where (Or) is the cladding material damage parameter; NCi and NCtmax are the number of i-type power-cycles and the allowable number of i-type power-cycles, respectively; t is time; tmax is the creep-rupture life under steady-state operation conditions.

The cladding material damage parameter can be considered as a structure parameter describing the material state ((O = 0, for the intact material and (O = 1, for the damaged
material). The second possible approach is considering o(t) as a characteristic of discontinuity flaw. That is when O =0, there are no submicrocracks in the cladding material. But if O =1, it is supposed that the submicrocracks have integrated into a macrocrack situated in some cross-section of the cladding

Criterion		Definition	к ^norm
SCI	_max a	< 250 MPa, where arx Is maximum circumferential stress.	1.2
SC2	< a (Т, ф), where is maximum equivalent stress, Pa; O0 is yield stress, Pa; Т is temperature, К; ф is neutron fluence, cm-2 •s-1.	—
SC3	VI	Pcmax , where Pc is coolant pressure, Pa.	1.5
SC4		, , ^ NCi л dt o(t) = > — — + < 1 . 4 ‘ Tyrpmax J «max і NCi 0 t	10
SC5	„max ^в, pi	< 0.5 % , where is cladding limit circumferential plastic strain	—

Table 2. Cladding strength criteria.

An experimental study of Zircaloy-4 cladding deformation behavior under cyclic pressurization (at 350 °С) was carried out in (Kim et al., 2007). The investigated cladding had an outer diameter and thickness of 9.5 mm and 0.57 mm, respectively. The microstructure of Zircaloy-4 was a stress-relieved state. A sawtooth pressure waveform was applied at different rates of pressurization and depressurization, where the maximum hoop stress was varied from 310 MPa to 470 MPa, while the minimum hoop stress was held constant at 78 MPa. Using the cladding stress-life diagram and analyzing the metal structure and fatigue striation appearance, it was found that when loading frequency v < 1 Hz, creep was the main mechanism of thin cladding deformation, while the fatigue component of strain was negligibly small.

Taking into account the experimental results (Kim et al., 2007), it can be concluded that estimation of o(t) by separate consideration of NR steady-state operation and varying duty (2) has the following disadvantages: the physical mechanism (creep) of cladding damage accumulation and real stress history are not taken into account; uncertainty of the cladding durability estimate forces us into unreasonably assumption Knorm = 10; there is no public data on Ntmax and fmax for all possible loading conditions.

Now the WWER-1000 fuel cladding safety and durability requirements have not been clearly defined (Semishkin et al., 2009). As strength of fuel elements under multiple cyclic power changes is of great importance when performing validation of a NR project, a tendency to in­depth studies of this problem is observed. The well-known cladding fatigue failure criterion based on the relationship between the maximum circumferential stress amplitude O^^ and the allowable number of power-cycles NCmax is most popular at present (Kim et al., 2007). Nevertheless, in case of satisfactory fit between the experimental and calculated data
describing the maximum number of cycles prior to the cladding failure, still there stays the problem of disagreement between experimental conditions and real operating environment (e. g. fluence; neutron spectrum; rod internal pressure; coolant temperature conditions; cladding water-side corrosion rate; radiation growth; cladding defect distribution; algorithm of fuel pick-and-place operations; reactor control system regulating unit movement amplitude and end effects; loading cycle parameters, etc.). In connection with this problem, to ensure a satisfactory accuracy of the cladding state estimation at variable loading conditions, it is necessary to develop physically based FE cladding durability analysis methods, on the basis of verified codes available through an international data bank.

As is known, when repair time is not considered, reactor capacity factor CF is obtained as

where At — NR operating time at the capacity of Pi ; T — total NR operating time; P — maximum NR capacity (100 %).

Using (3), the number of daily cycles Ne,0 that the cladding can withstand prior to the beginning of the rapid creep stage, expressed in effective days, is defined from the following equation:

Ne, o = No ■ CF,

where No — the number of calendar daily cycles prior to the beginning of the rapid creep

stage.

It should be stressed that CF is a summary number taking into account only the real NR

loading history. For instance, the following NR loading modes can be considered:

1. Stationary operation at 100 % NR capacity level, CF = 1.

2. The NR works at 100 % capacity level within 5 days, then the reactor is transferred to 50 % capacity level within 1 hour. Further the NR works at the capacity level of 50 % within 46 hours, then comes back to 100 % capacity level within 1 hour. Such NR operating mode will be designated as the (5 d — 100 %, 46 h — 50 %) weekly load cycle, CF = 0.860.

3. The NR works at 100 % capacity level within 16 hours, then the reactor is transferred to 75 % capacity level within 1 hour. Further the NR works at 75 % capacity level within 6 hours, then comes back to 100 % capacity level within 1 hour. Such NR operating mode will be designated as the (16 h — 100 %, 6 h — 75 %) daily load cycle, CF = 0.927.

4. The NR works at 100 % capacity level within 16 hours, then the reactor is transferred to 75 % capacity level within 1 hour. Further the NR works at 75 % capacity level within 6 hours, then comes back to 100 % capacity level within 1 hour. But the NR capacity decreases to 50 % level within last hour of every fifth day of a week. Further the reactor works during 47 hours at 50 % capacity level and, at last, within last hour of every seventh day the NR capacity rises to the level of 100 %. Such NR operating mode will be designated as the (5 d — 100 % + 75 %, 2 d — 50 %) combined load cycle, CF = 0.805.

2. The CET-method of fuel cladding durability estimation at variable loading

The new cladding durability analysis method, which is based on the creep energy theory (CET) and permits us to integrate all known cladding strength criteria within a single calculation model, is fit for any normal WWER/PWR operating conditions (Pelykh et al.,

2008) . The CET-model of cladding behaviour makes it possible to work out cladding rupture life control methods for a power-cycling WWER-1000 nuclear unit. As the WWER-1000 Khmelnitskiy nuclear power plant (KhNPP) is a base station for study of varying duty cycles in the National Nuclear Energy Generating Company ENERGOATOM (Ukraine), the second power unit of KhNPP will be considered.

According to CET, to estimate FE cladding running time under multiple cyclic NR power changes, it is enough to calculate the energy A0 accumulated during the creep process, by the moment of cladding failure and spent for cladding material destruction (Sosnin and Gorev, 1986). The energy spent for FE cladding material destruction is called as specific dispersion energy (SDE) A(t). The proposed method of FE cladding running time analysis is based on the following assumptions of CET: creep and destruction processes proceed in common and influence against each other; at any moment т creep process intensity is estimated by specific dispersion power (SDP) W (t), while intensity of failure is estimated by A(t) accumulated during the creep process by the moment т

T

A(T) = J W(T) ■ dT, (4)

0

where SDP standing in (4) is defined by the following equation (Nemirovsky, 2001):

W T) = Oe ■ pe, (5)

where ae is equivalent stress, Pa; pe is rate of equivalent creep strain, s-1.

Equivalent stress <Je is expressed as

(6)

where ae and az are circumferential stress and axial stress, respectively.

The cladding material failure parameter о(т) is entered into the analysis:

aij) = A(T) / A0, (7)

where Ao is SDE at the moment of cladding material failure beginning, known for the given material either from experiment, or from calculation, J/ m3 (Sosnin and Gorev, 1986); о = 0 — for intact material, со = 1 — for damaged material.

The proposed method enables us to carry out quantitative assessment of accumulated о(т) for different NR loading modes, taking into account a real NR load history (Pelykh et al., 2008). The condition of cladding material failure is derived from (4), (5) and (7):

T /Т

га(г) = Ї e Ve ■ dr = 1 (8)

о A0

The CET-method of light-water reactor (LWR) FE cladding operation life estimation can be considered as advancement of the method developed for FE cladding failure moment estimation at loss-of-coolant severe accidents (LOCA) (Semishkin, 2007). The equations of creep and cladding damage accumulation for zirconium alloys are given in (Semishkin, 2007) as

Ve = f(ki, T, Oe, ю(г)), (9)

o{t) = °e Ve, (10)

A,

where ki are material parameters defined from experiments with micromodels cut out along the FE cladding orthotropy directions; T is absolute temperature, К.

According to (Semishkin, 2007), for LOCA-accidents only, using the failure condition (o(t) = 1, the SDE value A0 accumulated by the moment of cladding failure and supposed to be temperature-dependent only, is determined from the equations (9)-(10). At the same time, the assumption that the value of A0 at high-temperature creep and cladding failure analysis is loading history independent, is accepted for LOCA-accidents as an experimentally proved matter.

In contrast to the experimental technique for determining A0 developed in (Semishkin, 2007), the calculation method proposed in (Pelykh et al., 2008) means that A0 can be found by any of two ways:

1. As the SDE value at the moment t0 of cladding stability loss, which is determined by condition oemax (t ) = O^* (t ), when equivalent stress O^3* (г) becomes equal to yield stress o0"ax(r) for the point of the cladding having the maximum temperature (according to the calculation model, a fuel rod is divided into axial and radial segments).

2. As the SDE value at the rapid creep start moment for the cladding point having the maximum temperature. This way is the most conservative approach, and it is not obvious that such level of conservatism is really necessary when estimating A0 .

The equivalent stress ae and the rate of equivalent creep strain pe are calculated by the LWR fuel analysis code FEMAXI (Suzuki, 2000). Though cladding creep test data must have been used to develop and validate the constitutive models used in the finite element code FEMAXI to calculate the equivalent creep strains under cyclic loading, difficulty of this problem is explained by the fact that cladding material creep modeling under the conditions corresponding to real operational variable load modes is inconvenient or impossible as such tests can last for years. As a rule, the real FE operational conditions can be simulated in such tests very approximately only, not taking into account all the variety of possible exploitation situations (Semishkin, 2007).

The code FEMAXI analyzes changes in the thermal, mechanical and chemical state of a single fuel rod and interaction of its components in a given NR power history and coolant conditions. The code analytical scope covers normal operation conditions and transient conditions such as load-following and rapid power increase in a high-burnup region of over 50 MWd/kg-U.

In the creep model used in the code, irradiation creep effects are taken into consideration and rate of equivalent cladding creep strain pe is expressed with a function of cladding stress, temperature and fast neutron flux (MATPRO-09, 1976):

Pe = K-Ф(+ B ■ exp (C-tf^exp (-Q / R ■ T )т~°’5 , (11)

where pe is biaxial creep strain rate, s-1 ; K, B, C are known constants characterizing the cladding material properties; Ф is fast neutron flux (E > 1.0 MeV), 1/m2 s; oe is circumferential stress, Pa; Q = 104 J/mol; R = 1.987 cal/mol K; T is cladding temperature, K; т is time, s.

According to (11), creep strain increases as fast neutron flux, cladding temperature, stress and irradiation time increase.

For creep under uniaxial stress, cladding and pellet creep equations can be represented as (Suzuki, 2010):

Pe = f (e (H’T >ф >F), (12)

where pe is equivalent creep strain rate, c1; de is equivalent stress, Pa; £H is creep

hardening parameter; F is fission rate, 1/m3 s.

When equation (12) is generalized for a multi-axial stress state, the creep strain rate vector { p } is expressed as a vector function { в } of stress and creep hardening parameter:

{p } = {e(M’fH)} , (13)

where T, Ф and F are omitted because they can be dealt with as known parameters.

When a calculation at time tn is finished and a calculation in the next time increment Atn+1 is being performed, the creep strain increment vector is represented as

{APn+a} = Atn+1 {Pn+e}={ P{tfn+e},£]H+e } , (14)

where К+Л = (-e)°n}+^{tfn+a} ; ^+6 =((-0)-єПН + в-£п+і ; 0 ^ 9 ^ 1

In order to stress importance of numerical solution stability, 0 = 1 is set.

Then, when the (r+1)-th iteration by the Newton-Raphson method is being performed after completion of the (r)-th iteration, the creep strain rate vector is expressed (Suzuki, 2010).

As shown in Fig. 1, the analysis model includes a 2-dimensional axisymmetrical system in which the entire length of a fuel rod is divided into AS, and each AS is further divided into concentric ring elements in the radial direction.

Upper plenum

Segment M

Segment M-1

Pellet

Cladding

Segment 2

Segment 1

Lower plenum

Fig. 1. Analysis model.

In this system, stress/strain analysis is performed using FEM with quadrangular elements having four degrees of freedom, as is shown in Fig. 2.

Fig. 2. Quadrangular model element with four degrees of freedom.

Fig. 3 shows relationship between mesh division and degree of freedom for each node in an AS.

zu Z1	4	zu Z3 ……….	z^ .. ^9	ZU z10			4	7U z12	zu z13	7U z14
’ r r2	’ r{ r3	* r{ …….. ‘9	► r і ‘lO	> r< ‘ll	r ( 42	і ri 43	1 у К 44	1 r,	1 у ( 46
— •— 4	*2	*3 …………	zL ‘ Z9	ZL Z10	і	к	zh zi2	ПЗ	zL Z14
		pellet						cladding

gap

Fig. 3. Mesh division of FEM (for one AS).

In Fig. 3, the number of mesh divisions in the radial direction of pellet and cladding is fixed at 10 and 4, respectively. The inner two meshes of a cladding (11, 12) are metal phase, and the outer two meshes (13, 14) are oxide layer (ZrO2). The model used in the code takes into account that the oxide layer mesh and metal mesh are re-meshed and change their thickness with the progress of corrosion.

The fuel temperature calculation was carried out with the difference between the numerical solution and analytical solution not exceeding 0.1 %. The numerical error arising in the form of residue from iterative creep calculation on each time step, was not estimated as in most cases this error is exceeded by other uncertainties, first of all by thermal conductivity model error (Suzuki, 2010).

Denoting the number of daily load NR power cycles as N, using the CET-model, the dependence A (N), as well as the borders of characteristic creep stages (unsteady, steady and rapid creep) for zircaloy cladding were obtained for the WWER daily load cycle (16 h — 100 %; 6 h — k100 %), where k = 1; 0.75; 0.5; 0.25. Hence the number of daily cycles Ne,0 that the cladding can withstand prior to the rapid creep stage beginning could be calculated. The conclusion was made that the calculated value of Ao is not constant for a given material and depends on the operating mode of multiple cyclic power changes (Pelykh, 2008).

It was found, that the calculated equivalent creep strain pe for zircaloy cladding, for all daily load modes, gradually increases and a hysteresis decrease of pe can be seen at the last creep stage beginning. Then, after the hysteresis decrease, pe starts to grow fast and achieves considerable values from cladding reliability point of view. At the rapid creep beginning, the equivalent stress ae decrease trend changes into the ae increase trend, at the same time pe decreases a little, that is there is a "hysteresis loop", when the pe increase has got a phase delay in comparison with the ae increase. It should be noted, that the cause of the pe hysteresis decrease effect must be additionally studied as pe is expected to continuously increase unless the cladding is subjected to significant compressive creep stresses during the cycle and that this had been properly included in the creep material model.

The following new NR power daily maneuver algorithm was proposed in (Maksimov et al.,

2009) . It is considered that a nuclear unit is working at the nominal power level (100 %),
unwanted xenon oscillations are suppressed by the NR control group movement. At first, boric acid solution is injected so that the NR capacity decreases to 90 %, while the NR inlet coolant temperature is maintained constant at the expense of the Main Steam Line (MSL) pressure rise. To guarantee suppression of xenon oscillations, the optimal instantaneous Axial Offset (АО) is maintained due to the NR control group movement. Further the NR power is lowered at the expense of poisoning. The NR capacity will reach the 80% level in 2-3 h and the capacity will be stabilized by intake of the "pure distillate". The NR capacity will be partly restored at the expense of depoisoning starting after the maximal iodine poisoning. To restore the nominal NR power level, the "pure distillate" is injected into the NR circuit and the MSL pressure is lowered, while the NR coolant inlet temperature is maintained constant. The optimal instantaneous AO to be maintained, the control rod group is extracted from the active core. The automatic controller maintains the capacity and xenon oscillations are suppressed by the control group movement after the NR has reached the nominal power level.

The proposed algorithm advantages: lowering of switching number; lowering of "pure distillate" and boric acid solution rate; lowering of unbalanced water flow; improvement of fuel operation conditions. Also, the proposed NR capacity program meaning the NR inlet coolant temperature stability, while the MSL pressure lies within the limits of 5.8-6.0 MPa and the NR capacity changes within the limits of 100-80 %, has the advantages of the well known capacity program with the first circuit coolant average temperature constancy.

The capacity program with the first circuit coolant average temperature constancy is widely used at Russian nuclear power units with WWER-reactors due to the main advantage of this program consisting of the possibility to change the unit power level when the reactor control rods stay at almost constant position. At the same time, as the MSL pressure lies within the procedural limits, the proposed algorithm is free of the constant first circuit temperature program main disadvantage consisting of the wide range of MSL pressure change. Two WWER-1000 daily maneuver algorithms were compared in the interests of efficiency (Maksimov et al., 2009):

1. The algorithm tested at KhNPP ("Tested") on April 18, 2006: power lowering to 80 % within 1 h — operation at the 80 % power level within 7 h — power rising to 100 % within 2 h.

2. The proposed algorithm ("Proposed"): power lowering to 90 % by boric acid solution injection within 0.5 h — further power lowering to 80 % at the expense of NR poisoning within 2.5 h — operation at the 80 % power level within 4 h — power rising to 100 % within 2 h.

Comparison of the above mentioned daily maneuver algorithms was done with the help of the "Reactor Simulator" (RS) code (Philimonov and Mamichev, 1998). To determine axial power irregularity, AO is calculated as

N — N, N ‘

where Nu, Ni, N are the core upper half power, lower half power and whole power, respectively.

The instantaneous АО corresponds to the current xenon distribution, while the equilibrium АО corresponds to the equilibrium xenon distribution. Having used the proposed method
of cladding failure estimation for zircaloy cladding and WWER-type NR, dependence of the irreversible creep deformation accumulated energy from the number of daily load cycles is calculated for the "Tested" and "Proposed" algorithms, and efficiency comparison is fulfilled — see Table 3.

	Easy of NR power field stabilization		The number of daily cycles Ne,0 that cladding can withstand prior to the rapid creep beginning, eff. days
Algorithm	Divergency of instantaneous and equilibrium АО diagrams	Amplitude of АО change during the maneuver	CF
"Tested"	considerable divergency	considerable amplitude	0.929	705
"Proposed"	slight divergency	amplitude is more than 10 times less	0.942	706

Table 3. Efficiency comparison for two daily maneuvering algorithms.

For the "Proposed" algorithm, taking into account the lower switching number necessary to enter "pure distillate" and boric acid solution during the maneuver, slight divergency of the instantaneous and equilibrium АО diagrams, the lower amplitude of АО change during the maneuver, the higher turbo-generator efficiency corresponding to the higher CF, as well as in consideration of practically equal cladding operation times for both the algorithms, it was concluded that the "Proposed" algorithm was preferable (Maksimov et al., 2009).

Using this approach, the complex criterion of power maneuvering algorithm efficiency for WWER-1000 operating in the mode of variable loading, taking into account FE cladding damage level, active core power stability, NR capacity factor, as well as control system reliability, has been worked out (Pelykh et al., 2009). Also the Compromise-combined WWER-1000 power control method capable of maximum variable loading operation efficiency, has been proposed and grounded (Maksimov and Pelykh, 2010).