Reserve Capacity for Failure in Power Market Environment

Tan Lunnong, and Zhang Baohui, Senior Mernbel; IEEE

Abstract-In power market environment, the first goal of grid company is to maximize its profits, which is different from the traditional power system. The security and reliability of power system should be subordinate to this goal. This paper proposes that, in power market environment, the power interruption acceptable to both supply and demand sides should be regarded not as damage to secure and reliable operation, but as continuity of power supply. In this point of view, the paper proposes that the optimal failure reserve capacity (in economic sense) in power market environment should be determined in light of cost of failure reserve capacity and load-shedding. The simulated results of a reliability test system shows that the method is feasible and economic.

Index Terms- electric power market, .fault, power system, reserve capacity

1 . INTRODUCTION

N the deregulated environment of electric power system, the power transaction is carried out through interconnected power network. Buyers profit from the

price differential between wholesaling and retailing, and sellers profit from selling power at a price higher than production cost. The grid company, as a intermediary in electric power market, profits from the trade between supply energy companies and service energy companies. The grid company obtains transaction commission from both sellers and buyers, thus its profits is directly proportional to the trade volume. But transaction commission is not its net profits, for a grid company has to pay fees for not only the construction and maintenance of electric power network, but also its normal operation, such as the purchase of ancillary services. Different from traditional power system, as an independent economic entity, a grid company’s goal is to maximize profits, though it still has to be responsible for the normal operation of network. This means that its investment in construction and operation of network is determined by potential earnings. Of course, the damage of security and reliability will affect economic efficiency. If a grid company cannot maintain the normal operation of network, it will definitely receive no transaction commission. Furthermore, it has to pay reparations to supply energy companies and service energy companies for stopping service. Here the aim of a grid company is profit maximization, and to maintain normal operation of power system is only to ensure its own profit. In other words, reliability is higher than economy in traditional power system, but reliability serves economy in electric power market.

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Holding certain reserve capacity is one of the measures to ensure power system safety and stable operation. However, the above-mentioned changes of aim of grid companies will lead to different reserve capacity holding in electric power market. In light of this change, this paper proposes a possible dispatching method for failure reserve capacity in electric power market, that is, the economical failure reserve capacity can be obtained by synthetically analyzing cost of failure reserve capacity and load-shedding.

11 . DETERMINATION OF FAILURE RESERVE CAPACITY IN TRADITIONAL POWER SYSTEM

In traditional power system, because the chief demand is to ensure the reliability of power supply, reserve capacity is prescribed by regulation when scheduling generation in order to guarantee continuity of power supply during system fault. The amount of failure reserve capacity should be decided according to capacity of power system, the number of generating units, capacity of each generating unit, failure probability of generating unit, reliability of power system, et al. ‘Power System Technical Criteria’ [ 11 prescribes: failure reserve capacity should be about 10% of the system peak load, but not less than capacity of the largest generating unit. It is obvious that the decision of failure reserve capacity takes only operation reliability of system into account, and does not consider operation economic efficiency. Especially, it does not make quantitative analysis of reserve variation with different network structure, network losses, electricity price, et al. .

111. POSSIBLE MODEL FOR FAILURE RESERVE CAPACITY IN ELECTRIC POWER MARKET

In electric power market, reserve capacity is one of ancillary services bought by grid companies from supply energy companies. There are two relevant prices to be paid for it. One is the price paid for reserved capacity and the other is the price paid for energy that is dispatched under certain defined conditions [2]. So, as an independent economic entity with profit maximization as its first goal, a grid company, when making decision to buy reserve capacity, will makes a comparison between payment for purchasing reserve and possible cost without reserve, and the only criterion of purchasing reserve is whether this purchase can bring economic interests.

A. Security and Reliability of Power System in Electric

0-7803-7459-2/02/$17 00 0 2002 IEEE - 91 2,-

Power Market

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In traditional power system, continuity of power supply is an important index of a system's security and reliability. But in electric power market, as the goal pursued by a grid company is profits, to pay reparations for load-shedding will be more profit-efficient when the cost to buy reserve is higher than to pay reparations. Then, are there consumers prefer interrupted power supply and accept reparations? Consider that there are consumers in power system in just so-so operation and with energy cost accounting for a large proportion of its production cost. For example, for a corporation, every its $100 business income consists of $50 energy cost and $40 other costs (for instance, raw material cost, labor cost, depreciation of equipment and taxes), its net profits is only $10. Then, in theory, the power supply of this corporation can be interrupted if just 20% energy charge is paid by the grid company (for every $100 business income, it is $10). This interruption does not bring any losses to the corporation. If a grid company prefers to pay more reparations, this corporation will be very glad to be interrupted its energy supply. In view of this, it is necessary to redefine the security and reliability in elect& power market environment. The power interruption acceptable to both supply and demand sides should not be regarded as damage to secure and reliable operation, but as continuity of power supply. In fact, consumers' acceptation of power interruption is just like power reserve with good technical performance here (it can supply the power with capacity no less than its designed load at any moment energy is needed by power system). So, it is necessary to analyze the cost of failure reserve capacity and load-shedding synthetically to optimize failure reserve capacity in power market.

L

Min(C c,A4 ( P I ) , = I

(4" + ~ ( P ) ) - U , f U , ( G , c o s S , , + 1'1

B, sinS,) = 0 (i = 1,2,...,n) n

Q, - U , C U , ( G , sinS,, - B,J COSS,) = 0 J = I

( i = 1,2,...,n) (i is the load bus) '4 5 Qtma

U,,,, < U , I U , , , (i=1,2;..,n) ,e,,,, IQ, IQ,,, (i=L&... ,n)

B. Cost of Reserve Capacity

The cost of reserve capacity includes capacity cost and energy cost. Capacity cost can be easily obtained according to the amount of reserve capacity needed by a grid company and the bids given by each supply energy company. It can be written as follows:

= Z a , P (1) ,= I

where J; is the capacity cost; a, is the unit capacity cost at time i ; P is the amount of reserve capacity bought by a grid

company.

And the energy cost of reserve capacity can be obtained only after the dispatched probability has been taken into account. The dispatched probability of reserve is mainly determined by the failure probability of generating units. Thus the energy cost paid by a grid company for purchasing the reserve in one day can be written as follows (in this paper, the cases of two or more generating units fault simultaneously are

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not considered) :

f ? . ( p ) = ? f i l ~ P J p ) f ( p ) I=! J = 1 ( 2 )

where fz is the energy cost; G is the total number of generating units in power system; p J is the failure probability of generating unit j ;

PJ, is the dispatched reserve capacity when generating

/?, is-the unit energy cost at time i . unit j fault at time i and reserve capacity is P ;

Then, the total cost for failure reserve capacity is as follows:

f (PI = f ; ( P > + fz (PI (3) where f is the total cost for failure reserve capacity.

C. Cost for Load-shedding

In the case of generating unit faults and being out of service, the system will be in a state of insecurity if there is no or insufficient reserve capacity in power system. Therefore, a grid company must adopt load-shedding to ensure the system operating securely, or the system may be in a state of insecurity and lead to more economic losses. So no or insufficient reserve capacity will result in a reparation paid by a grid company to service energy companies for load-shedding.

hp,(P) is the amount of load-shedding in node i when

M,, is the acceptable maximum of load-shedding in node

CO is the nodal infections of active power in node i when

U, and 6, are the voltage magnitude and phase angle

the reserve capacity is P ;

i ;

the power system is in normal operation;

respectively; 6, = 6, -6, ;

Cy and By are the real and imaginary parts of the nodal

U,,, and U,,,, are the maximum and minimum of nodal

Q,,, andQ,,,, are the maximum and minimum of nodal

admittance matrix;

voltage respectively;

injections of reactive power.

After the amount of load-shedding has been obtained, the reparation paid by a grid company to service energy companies for load-shedding is as follows:

74 I: r

where f 3 ( P ) is reparation for load-shedding, and when P = 0 ,

G is the number of generating unit in power system; L is the number ofload node in power system; p , is the failure probability of generating unit i ; c Z is the unit reparation for load-shedding in node j at

is the amount of load-shedding in node j for the

there is no reserve capacity;

time k ;

failure of generating unit i at time k .

D. Decision of Failure Reserve Capacity in Power Market Environment

Analyzing Equ. (3) and (9, we can find that the cost for reserve capacity f( P ) increases with increasing reserve capacity P , and the reparation for load-shedding f, ( P ) decreases with the increasing reserve capacity P . In order to maximize its profits, the grid company will make a synthetic analysis of f(P) and f, ( P ) to determine an efficient reserve capacity P . This optimal problem can be described as follows:

where F ( P ) is the total cost for purchasing failure reserve

Pmi, and P,, are the minimum and maximum of reserve capacity and paying load-shedding reparation;

capacity that can be dispatched.

Equ. (6) can be show in Figure 1 : Where Pois the reasonable reserve capacity based on the

principle of profits maximization. When P is less than Po , P is too small, and the reparation for load-shedding will be larger than the cost for increasing reserve capacity; when P is larger than Po, P is too large, and the cost for reserve capacity will be larger than the reparation for load-shedding, and the failure reserve capacity can be decreased so as to increase profits.

S F

b- PO P

Fig. 1 Reserve capacity for failure in power market

h'. NUMERICAL RESULTS

The following shows the results obtained for a 5-node (total number of generating units is ll), 9-transmission lines test system [3]. Its single line diagram is shown in Figure 2:

Busl m 3 /// I f I

Bus3 &r& Bus4

Fig. 2 Single line diagram of the RBTS

The detailed data of generating units, loads and transmission lines in Figure 2 can be found in reference [3]. Let Bus 1 be a slack bus, Bus 2 be a PV bus, U , = U , = 1.05. Based on the results of power flow computation, the output of generating units in normal operation can be supposed as Table 1:

The mean time to repair for generating unit is always more than one day. But the failure probability used in this paper is

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Table I Output of generating units in normal operation (the system peak load is only 185MW), $7304, $3237 and $1286 can be saved every day at the above three different unit reparation for load-shedding, about 48.5 1%, 21.50% and 8.54% of total cost for failure reserve capacity prescribed in ‘Power System Technical Criteria’ respectively.

(2 ) Assume c = $350/MW , p and a are different

In these three cases, the optimal failure reserve capacity in is 9.1 ~ M W (for F~ ), 9. 1 ~ M W (for F~ ) and

Paper, $4299, $3237 and $2192 can be saved every day respectively, about 24.98%, 21.50% and 16.98% of total cost

values. Figure 4 can be obtained:

economic the failure probability occurring in one day, and the grid company doesn’t care about whether the failed generating unit will have been repaired or not thereafter. So the failure .

forced outage rate. It is decided by failure rate per year as follows:

probability of generating unit in this paper is different from 20.34MW (forF3 ) Using the method in this

Unit No 1 2 3

7 Unit No 5,6 Failure Probability 0 01644 0 01096

Failure Probability 0 00548 0 00822

p = L (7) I

365

4 0 01370 8,9,10,11 0 00658

for failure reserve capacity prescribed in ‘Power System Technical Criteria’ respectively.

where n is the failure rate per year.

generating units is in Bus 1. Fig. 4 Total coat in different reserve capacity price

(1) Assume the unit energy cost p = $35 I MW h ; the unit capacity cost a =$14/MW ; the unit reparation for (3) Assume p = $ 3 5 / W * h , a =$14fMW , load-shedding are 5, 10 and 15 times Of p respectively, that is, c = $ 3 5 0 / m and the failure probability of generating unit 2 175, 350 and $525/MW. Then we can obtain the results as is 0.00548, 0.01644 and 0.02740 respectively. The calculated shown in Figure 3: result is shown in Figure 5 :

I

x10 2.5 I

Fig. 3 Total cost in different load-shedding price

x10’

Fz : p2 =0.01644

. 19.18:j20.34 I , . P(MW

0 10 20 30 40

Fig. 5 Total cost in different failure probability of generator units

The optimal failure reserve capacity in economic sense are OMW, 19.18MW and 20.34MW for C = 175, 350 and 525$/MW respectivelv. All these three values are less than the

Here the optimal value is 19. 8MW (for p 2 =o.oo548),

=0.02740) l9.lSMW (for pz =0.01644) and 20.34MW 40MW failure reserve capacity prescribed in ‘Power System Technical Criteria’. In comparison, in this small power system

respectively. $3327, $3237 and $3 192 can be saved every day respectively, about 22.38%, 21.50% and 20.94% of total cost for failure reserve capacity prescribed in ‘Power System

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Technical Criteria’ respectively. e. The greater the failure probability of generating units, the

V . CONCLUSIONS larger the reasonable failure reserve capacity.

a. In electric power market environment, the security and reliability of power system should be redefined. The power interruption acceptable to both supply and demand sides should be regarded not as damage to secure and reliable operation, but as Continuity of power supply.

b.In power market environment, the first goal for a grid company is to maximize its profits. Both supply energy companies and service energy companies are its customers, and are in the same status. So purchasing failure reserve capacity and reparation for load-shedding can be both grid companies’ ways to ensure the normal operation of power system, and to choose which one depends on economic efficiency.

c. The lower the unit reparation, the more favorable the reparation for load-shedding, the smaller the reasonable failure reserve capacity. And vice versa.

f.The network construction affects network losses, thus affects the optimal failure reserve capacity indirectly.

VI. REFERENCES

[ I ]

[2]

Ministry of Water Resource & Power Industry. Power System Technical Criferia SD131-84. Beijing: Hydraulic and Electric Power Press. 1984 Harry Singh , Alex Papalexopoulos. “Competitive Procurement of Ancillary Services by an Independent System Operator”. IEEE Transactions on Power Systems, 1999, 14(2): 498-504 R. Billinton, S. Kumar, N. Chowdhury, et al. “A Reliability Test System for Educational Purposes-Basic Data”. IEEE Transactions on Power Systems, 1989,4(3): 1238-1244

[3]

VI1. Biographies

Tan Lunnong, was born in China in 1965. He is currently a Ph.D. candidate in the department of electrical engineering at Xi’an Jiaotong University. His research interests include power system operation and analysis.

Zhang Baohui, was born in China in 1953. He is a d.The lower the unit price of failure reserve capacity Professor with the department of electrical engineering at Xi’an Jiaotong - -

(including capacity cost and energy cost), the larger the reasonable failure reserve capacity.

University. His areas of interests include power system analysis, operation, control, and protection and communication.

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