S C I E N T I F I C - T E C H N I C A L P A P E R S

N U C L E A R P O W E R P L A N T S W I T H W A T E R - M O D E R A T E D

W A T E R - C O O L E D R E A C T O R S I N P O W E R S Y S T E M S :

A D A P T A T I O N M E T H O D S

V. A. Khrustalev UDC 621.311.25:621.039.524.44

In planned power systems with a probable high percentage of nuclear power plants (NPP), the problem arises of seeking

compromise methods for the control of daily, weekly, and seasonal load-schedule irregularities. In the examination of the various

modes of such NPP operation, it is necessary to observe optimal circuit-parameter characteristics and an equal energy effect as

well as engineering constraints. One of the determining constraints in the direct unloading of a multiunit NPP is the total

limiting control range, which is a function of the time and nature of the annual distribution of fuel recharging in the reactors.

According to the conditions of the 135Xe transient period, this factor is important for daily control, is less-important for weekly

control, and has practically no effect on loading when control is less-frequent. Analysis of the data of various organizations has

provided a basis for proposing a general-purpose approximation of the total control range of an NPP with a daily load cycle [1]:

A N Z = exp (a - b A t i) ~'ki(1 - "tki) c-dA t i 1, (I)

where At i is the time of smooth load variation of the i-th unit, in h; tki is the relative operating period (stationary fuel cycle);

and a, b, c, and d are coefficients, which are equal to 3.06, 0.132, 1.15, and 0.075 for the VVI~R-1000 water-moderated water-

cooled power reactor (WMWCPR).

Calculations by formula (I) have shown that with a conservative approach (alternate reloading in periods of maximum

inflow to hydroelectric plants in spring or minimal energy deficit in summer), NPP units with VVI~R-1000 reactors do not

provide even the moderate optimal control ranges established earlier [2]. This circumstance as well as the well-known economic

disadvantage of direct NPP unloading, owing to the smaller fuel component than that of a heat power plant, make it necessary

to investigate alternative methods for coverage of schedule irregularities. The main methods are listed in Table 1 and are well-

known in principle.

The initial conditions and formulas for the transmitted-energy balance in all power complexes follow from the methods

load-schedule coverage. Many of the proposed schedule-filling methods have been studied in detail - - for example, optimal

schemes, parameters, and realization methods for NPPs with WMWCPRs have been analyzed and generalized [1]. We shall

discuss method II, which is less-known in the literature and in which combines variation of the power of a unit by unloading at

valleys and spiking at peaks in the schedule. In this version, it is potentially possible to eliminate the shortcomings of direct

unloading. At the same time, along with reduction of capital outlays for NPPs due to the low power established in the power

system, additional expenditures for spiking of all elements of the unit are taken into account. The reduction of this version to a

single ecological effect consists of estimation of the additional cost of storage of excess enriched fuel in a cooling pond and the

isolation of a large area of land for a safety zone. More details on this version can be found elsewhere [I] or from the experience

of American NPPs with PWRs [3].

Versions I, It, and Ill combine an absence of generation of intermediate storable energy and, therefore, losses in its

transmission, as is observed in versions IV-VII. Losses are caused by energy dissipation (versions V and VI) as well as by losses

of potential performance due to lower efficiency of the peak circuit (version IV) or peak superstructure (version VII). In these

versions, the peak power is expressed in terms of the intermediate-generation power by means of the coefficients K/. in Table 1.

Saratov Polytechnic Institute. Translated from Atomnaya l~nergiya, Vol. 71, No. 6, pp. 551-555, December, 1991.

Original article submitted December 4, 1990.

0038-531X/91/7106-1013512.50 �9 Plenum Publishing Corporation 1013

T A B L E 1. Ana lys i s o f Ve r s ions of C o v e r a g e of Schedu le I r r egu la r i t i e s Us ing a N u c l e a r P o w e r P l an t

Coverage method (type of 1 irregularity)

Formulas

I. Direct unloading

AN = ANse p

(daily, weekly, seasonal)

II. Unloading-spiking

AN= AN s RANsep Idaily, weekly, seasonal)

aN= ANGTP+ AN NPP

(daily, weekly, seasonal)

IV. Combinatio- of NPP and phase transition storage devices

( r-~ v ) "0 a N =ANpc; K- . t v t l p c q f

( daily )

V. Power complex: NPP and HSPP

T-t v ..MV = AN + cgAN-h~ K=

dis ~v ~IHSPP

Idailv)

Vl. NPP with off-peak su~p 1 y

T - x v K

r v rl f qelc

(daily)

VII. Power complex: NPP and system for hydrogen production and consump- tion

AN = ANHs " AN~PP " s '

T--T V K=

qel 7 dn

( d a i l y )

14B(Tj-Zv'A'%[) qv QO ZI(T:-~v~N)

24B(Tj- ~v j AN) 8 s . v qs ZI (T)- t v,i AN)

C.~v~ [1-n~ (D/rv)-i)(l-m~ c .248

24B(T]-t v j)AN q0 ns .C nQ~ rlGTP

• (~/tvj-i)(1-O-~)] +

+ k GTPk. (1-(x -A~)) ] sp

Ch~ v [ l - - a N

24s~24- ~d A~) n y v AN

+ (24/'l'dY "1) ~-='[- ] +

~f 8pc -

A.~" I , kPCk"

J sp k* 1

E+E~ [ k NPP(I-AN)+ sp

zjG-x v~at0

AN (24/'t v --i) 1 --

k*l § r

E+ E a

Zdy(24-~.. q A ~/) sp k*l

AN I -

B (24-T v &'~) n0

x 1 - + sp k§ k+l

+ " p

Z. (24-I vZ~g)(k+l) dy

C 2 v [ . I - A N

s 24B (24 -x v AN) rlav

( E + E a) [ k NPP x L sp

Z (24-t v AN) dy

§ .3 f i sh_ + sp L 24-x ~N (k + I

241T v -I ] § E§ a

q0 ~y (24--x v AN)

x k NPP sp * A3e.coEAZeco

CnXv ( l _ A N qo] * E*E~

24B (24-T v ATe) [" ~ ) / Zdy(24-Tv &~)

x ksp 1 - ksp - A 3 sep.

1014

pecks/ I- (kU-h)

1,1

1,o

Version i- i J

z '/,

I i I

0,05 0,/ o,15

l

i i / < ?"~ I

1

i I 1221 ousand fuel units

kc I __ I a

O.Z AN

Fig. 1. Specific reduced expenditures of versions I-III for coverage of variable load schedules at C n = 800 (1),

500 (2), and 300 rubles/kg UO 2 (3), spiking range AN s = 0.5AN (dashed curves), and NPP cost rise by 8%

(dot---dash curve).

E~ ko- pecks/ (kW' h)

Lq5 ,

i

i Lq~

/.55 .--

I,Y~-

1,2S t- 1 i

Version /V

TS;v ~Z ~,

/

o t ! i

. - ' ~ , ~ . ,§ 2/.

C

8 i Z,§

~-: f , ~ L- Z E

~ y

C a b q.21 . . . . . .

0.C5 0./ 8 : 5 .'LZ ,SV

Fig. 2. Specific reduced costs of versions IV, VI, and VII for coverage of variable load sched-

ules at ks PC = 100 (2') and 40 rubles/kW (2") and ~ e i ~ i = 15 rubles/thousand fuel units (la);

1, 3, 3) see Fig. 1.

We shall also discuss the generation and delivery of useful electrical energy according to a given schedule from a system

of NPPs and hydroelectric storage power plants (HSPP). This version involves reduced system expenditures, switching of the

NPP exclusively to the base part of the schedule, and the production of high (discharge) peak powers. Today, however, such one-

sided analysis is unacceptable: the ecological consequences of the HSPP must be taken into account. In addition, unsuitable

1015

E, kopecks/(kW'h)

J

bE,

Version_ / iii/v

j '

I I I a

$

i

O, 0g 0, I 0,15 0,2 zltr

lillion rub] es/yr

7

b I I

E. million rubles/year

f00 f

760

86'

~0

C

I I I

Fig. 3. Specific reduced expenditures of version V (a) and differences for versions I-II (b) and

I-V (c); 2', 2") without allowance tor ecological factors; I, 2, 3) see Fig. 1.

terrain and geological conditions increase the specific expenditures for the HSPP and the building of large high-head reservoirs

next to NPP sites whose safety is in doubt. The losses associated with the additional damage to soil (flooding) and fishing are

considerable in this case.

In versions VI and VII, in accordance with general principles of systems analysis, the closing costs for the production of

hydrogen, oxygen, and heat must be considered the most-favorable of the known individual methods. This refers chiefly to the

structure of the reduced costs of each of the versions. The initial data for today and for the future are calculated on their basis.

Qualitative analysis shows that, in principle, all versions could be competitive under conditions of daily irregularities but

only versions I, II, and III are suitable for weekly and seasonal irregularities, The following designations are used in the formulas

of Table 1: r/v, r/0, r/s and r/s are the efficiencies of NPP generation in the valley and base parts of the schedule and at minimum

and maximum loads under conditions of spiking; Zj is the annual number of load-variation cycles; and k NPP, k ~ k HsPP, k Pc sp ' sp , and ks PH are the specific capital outlays for an NPP, GTP, HSPP, a peak circuit n which an NPP is combined with phase-

transition storage devices, and a peak hydrogen superstructure.

The results of the comparative analysis are shown in Figs. 1-3. Typical irregularities, which are determined by the ratio

Tj/Tvj , are as follows: 2.4-4 daily, 4-6 weekly, and 6-10 seasonally. Version I (the worst) and version II (the best) were found to

be polar opposites. Version II is the most-efficient when the entire control range AN (up to 20%) is covered by an NPP without

additional expenditures for its support (curve 1 of Fig. 1, version II).

In the compound process of irregularity coverage partially by unloading and spiking (AN s = 0.5AN) with allowance for

the increased NPP cost (A,~sp = 8%), the E value is increased appreciably. For example, it is apparent from Fig. 1 (version II)

that the rise is up to 13-15% in the first case and up to 4-6% in the second at C n = 300 rubles/kg UO 2 and AN = 0.2. The

method is most-efficient at 7)/r v = 6-10, which corresponds to weekly and seasonal irregularities. For all versions except for V,

the specific expenditures are typically reduced by 10-12% or more when C n is reduced from 800 to 300 rubles/kg UO 2.

In version III with a GTP that uses costly organic fuel, the dependence of Tj/T v on expenditures is reversed: the shorter

the peak period, the higher the efficiency of combining NPPs and GTPs. At Cf < 25 rubles/thousand fuel units, however, the

effect of lower GTP costs prevails, the effect of the ratio 7)/r v is the same as in versions I and II, and the efficiency is increased

by 11-12%. It is apparent from Fig. 1 that Cf = 35-40 rubles/thousand fuel units, versions III and I are economically equivalent,

but an NPP with a GTP is more-efficient that direct unloading with daily and weekly irregularities (but less-efficient with

seasonal irregularities).

Versions IV-VII are economically justified only for the control of daily irregularities, since the capital outlays for storage

devices rise sharply with prolonged load cycles. Version IV, in which an NPP is combined with a peak circuit of phase-transition

storage devices, is situated economically between direct unloading and spiking. In the case of daily cycling, a reduction in the

specific cost for a peak circuit from i00 to 40 rubles/kW (zones 2 and 2' at C n = 500 rubles/kg UO2) corresponds to an

efficiency increase by 1.5-2% for this method.

1016

Versions VI and VlI are in many ways dependent on the costs of separate replacement production. In version VI, for ,- AEv el example, a reduction ol - - s e p from 30 to 15 rubles/thousand fuel units impairs the efficiency of the method by 1.3-1.5% at ~ =

0.2 and ~:v = 10 h. If more-costly fuel is used, the saving from replacement of solid fuel, even at Cf = 30-40 rubles/thousand fuel

units and T j # v = 4-6, raises the competitiveness of version VI over that of version IV (Fig. 2a).

Version VII (Fig. 2c) for off-peak supply is more-efficient than direct unloading as well as an NPP with GTP when

costly organic fuel is used but is inferior to all other versions except V (Fig. 3a). Here, as in version VI (Fig. 2b), the costs refer

to the initial given desired delivery of energy to the consumer.

The specific costs of version V with HSPP with allowance for ecological factors (Fig. 3, curve 3 ') are increased by a

factor of 3.2-3.3 at ~ = 0.2, which attests to the total inefficiency of this version. Ground rent for the additional alienated

territory and direct annual expenses for the fishing industry are proportional to the energy consumed and distributed by the

HSPP.

The cost savings in the operation of an NPP with WMWCPR with the load schedules for versions II and I are compared

in Fig. 3b. For 0 _< C n < 800 rubles/kg UO 2 and 0.05 _< AN _< 0.2, the saving is from 2.8 to 14 million rubles per year for a unit

power of 1000 MW. In Fig. 3c, the expected loss for HSPP construction is compared with that direct unloading of the NPP. At

0.05 < AN _< 0.2 and 2.4 _< T/ t v <__ 6, the annual cost overrun can rise from 22 to 210 million rubles for a 1000-MW system.

Analysis of the possible versions with NPP participation in the control of load schedules allows versions II and IV and

sometimes I to be recommended for more-detailed development. The timely preparation for typical NPP load situations will

make it possible to develop most efficiently and optimally and operate safely and reliable plant equipment and power systems in

the future.

LITERATURE CITED

1.

2.

3.

R. Z. Aminov, V. A. Khrustalev, A. S. Dukhovenskii, and A. I. Osadchii, Nuclear Power Plants with Water-Cooled

Water-Moderated Reactors: Operating Conditions, Characteristics, Efficiency [in Russian], l~..nergoatomizdat, Moscow

(1989).

V. A. Khrustalev, "On optimal participation of heat and nuclear power plants in the coverage of variable load sched-

ules," in: Use of Low-Grade Solid Fuel in Energy Technology and Protection of the Environment [in Russian], Saratov

Polytechnic Inst. (1988), pp. 1(}4-107.

V. A. Khrustalev, "Increasing the power of nuclear power plant units with pressurized-water reactors in the United

States," At. Tekh. Rubezh., No. 5, 10-13 (1988).

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