MW-Mile Method Considering the Cost of Loss Allocation for Transmission Pricing

Avinash D.

M. Tech. student, Electrical Engineering Department National Institute of Technology, Kurukshetra

Haryana, India avinash.6474@yahoo.co.in

B. Chalapathi Assi. Prof., Department of Electrical and Electronics

Engineering GPREC, Kurnool, AP, India

chalam212@gmail.com

Abstract— Since the evolution of MW-Mile method there

have been so many new methods for transmission pricing were

developed but still it is been used in most of the places

throughout world because of its simplicity. However this method

does not provide fair pricing for the users since it is lacking in the

provision of cost component for loss and power factor. This

paper tries to provide a mathematical model so that the cost

component of loss and power factor can be added in the

transmission pricing.

Keywords—MW-Mile Method , Cost of Loss Component, Power

Factor, Transmission pricing

I. INTRODUCTION

The restructuring of power system in many parts of the world caused changes in transmission pricing and there have been so many methods proposed. Initially the transmission capacity allocation and cost of services is proposed in [1] based on magnitude of electric power and the length of line this is nothing but referred as MW-Mile method, which is a kind of embedded pricing method and this is the first method proposed based on actual usage of transmission network, before this there was an existing method known as Pro rata method/Postage stamp method which was modeled using only the magnitude of the power involved in a transaction [2]

The total transmission pricing methods can be categorized into 3 types 1) Embedded cost methods 2) Incremental cost methods 3) Marginal cost based methods. In these embedded cost methods are mostly used because of its simplicity. Further these embedded cost methods are divided into 4 types known as 1) Postage stamp method 2) Rated contract path method 3) MW-Mile method 4) Power flow based MW-Mile method [3],[4].

Nodal pricing is another approach for transmission pricing which is based on the concept of differences of the marginal prices of nodes but if the network is loss less and there is no congestion then all the prices at all nodes become equal making the revenue zero. The main drawback of this method is that it cannot generate the actual cost of transmission service cost there by creates loss to the transmission service provider. There has been several modifications proposed for

nodal pricing methods to increase the revenue but still the MW-Mile method gives the better cost allocation so as to recover the operation and investment cost. The two methods both embedded and marginal have their own advantages and disadvantages, embedded methods can recover the transmission cost but they are not providing any economical signal to the users where as marginal price methods can provide economical signals and they are having some mathematical basis but still they cannot fully recover the transmission cost. In literature several authors tried to solve this problem by combining both the above methods known as hybrid methods [5],[6]. Using Ramsay pricing concept the nodal method has been modified so that it can recover the transmission cost up to some extent in [7], and to create the nodal price differences a concept of generation and nodal injection penalties is introduced in [8]

Using Z bus the cost allocation of transmission service is presented in [9] but in this the shunt branches of the transmission lines were not modeled and recently there have been so many methods proposed based on game theory, which gives some important concepts, models and methods which can be used to access the behavior of the agents participated in the market, optimal power flow tracing, min-max fairness algorithm using optimization based real power tracing. In [10] principle of bilateral exchanges is used, where it assigns some part of generator generation for each load and some part of load for each generator on proportional basis, which removes some of the drawbacks of the other methods,

Use of dispersed slack bus is discussed in [11] so as to remove the difficulty in selection of slack bus in case of marginal pricing methods which are more sensitive to the selection of slack bus. There have been several methods developed to consider the cost component of power factor by using reactive power parameters, in [12] and [13] papers point to point method is proposed, in [14] a correction factor is introduced to account for the cost of power factor to improve MW-Mile method but it does not consider the cost of loss component and it mainly relates the change in current component because of power factor change. This paper is aimed to consider both the effects of power factor and loss

cost components in the conventional MW-Mile method for providing better economical signal to the users. This paper is organized into 3 sections: section 2 describes about basic MW-Mile method, section 3 presents the proposed methodology and section 4 gives the conclusion.

II. MW-MILE METHOD

This method of transmission pricing is proposed based on the magnitude of electric power transacted and the length of the line [1] which is widely used since it gives the measure of actual usage of transmission line. This method can be represented as follows

��� = ∑ ����,��

���� (1)

Where ��� Transmission cost to user n;

� Number of transmission lines;

�� Cost in $/MW-mile or $/MW-Km which is already defined; �� Length of line i;

��,� Power flow in line i, because of the user n

��� Power capacity of line i in MW;

Here the total cost for a user n is the summation of cost components for providing transmission lines which are involved in the transaction.

III. PROPOSED METHODOLOGY

The power flow capacity of a line when its resistance is neglected depends up on the voltages at the ends and the reactance of the line. Since we use DC load flow in calculation of MW-Mile method we can assume that the both ends of the voltages are equal. The equation of power handling capacity can be written as follows

�� = V�sin ��� (2)

Where δ Angular difference between the two ends in degrees; x reactance of the line per unit length; V Operating voltage of the line in kV; Assuming unity power factor the current carrying capacity of the line �can be calculated as follows

� = ��

√3#(3)

By substituting (2) in (3) we get

� = # sin �√3�� (4)

The power loss corresponding to the maximum power capability in a 3 phase system can be written as follows

��%&& = 3( �)�'�(5)

By substituting (4) in (5) the expression for ��%&& modifies to

��%&& = #� (sin �)�

���� (6)

Therefore the percentage of power loss expressed in terms of the power handling capacity of line is as follows

%��%&& = 100��%&&�� =100' sin �

� (7)

Considering the stability mostly δ is limited to certain value hence by assuming � = 30∘ the equation (7) can be re written as follows

%��%&& = 50/�'0

(8)

For a particular voltage level of a line the /230 ratio will be

known to the system operator and there by the percentage of power loss can be calculated. Since this loss component is in terms of the power handling capacity we cannot use this parameter directly in the allocation of cost component of line loss.

The loss in a line is depending on the actual power flow of the line, to take this into consideration we introduce a

correction factor for the calculation of��%&&which is given by

4 = 5��6

7�(9)

With this modification the power loss in a line can be expressed as

��� = 4��%&&(10) The loss component mentioned above can be added to power flow component which we get by DC load flow so as to account for the losses. Hence by applying this method the transmission cost for a user n can be expressed as follows

��� = 9����(��,� + ���,�)���

�

���(11)

In [14], a method is proposed to consider the effect of power factor by introducing a coefficient �; by which the above equation can be written as

��� = �; ∑ ���(�,�<=�,�)�

���� (12)

This modified formula considers both the power factor and the loss to allocate the transmission pricing. In the calculations it is assumed that the length of the line is proportional to the impedance. For a given system initially the full capacities of

the lines are calculated, based on /230 ratios the loss

percentages are evaluated and then for a particular transaction the flows in all the lines are found using DC power flow, based on these flows and using the correction factor K we can adjust the flows to represent loss component.

IV. RESULTS

IEEE 14 bus system is considered as the test system and dc power flow is used to find the power flows. The data is taken from [4], two transactions T1 and T2 are considered as in [15] which are given below T1: Transaction of 20 MW from bus 1 to bus 5 T2: Transaction of 20 MW from bus 2 to bus 14 because of these two transactions the power flow changes through all the lines, which can be determined by using Power Transfer Distribution Factors (PTDFs) and also the change in power flow in each line due to a particular transaction can be found [16]. Figure I show the PTDFs for transactions T1 and T2 respectively.

Fig. 1. PTDF variations for transactions T1 and T2

In calculating the cost of each transaction the cost per p.u MW mile is taken as 50 $/p.u MW-mile as in [14]. The length of the transmission lines is taken on the basis of impedance of the lines and also the negative counter flows are not considered that gives to an assumption that the transactions are always increasing the power flow irrespective of their direction. Table I gives the details of power flows in all the cases such as base case and base case with transactions.

TABLE I. DETAILS OF POWER FLOWS IN IEEE 14 BUS SYSTEM

Lines Base case (MW)

Base case with T1 (MW)

Base case with T2 (MW)

1-2 147.87 160.08 143.98 1-5 71.11 78.90 75.00

2-3 70.04 72.11 73.21 2-4 55.22 59.53 61.85

2-5 40.90 46.73 47.21

3-4 -24.15 -22.09 -20.98

4-5 -62.33 -56.30 -64.05

4-7 28.98 29.20 36.30 4-9 16.63 16.75 20.83

5-6 42.08 41.74 50.55

6-11 6.30 6.09 6.88

6-12 7.54 7.51 9.29

6-13 17.03 16.92 23.17

7-8 0 0 0

7-9 28.98 29.20 36.30

9-10 6.19 6.40 5.61

9-14 9.92 10.05 22.02

10-11 -2.80 -2.59 -3.38

12-13 1.44 1.44 3.20 13-14 4.97 4.82 12.87

Table II gives the cost of transactions considering several cases such as without loss component, with loss component, and the case with power factor variation. The power factors at load points in the transactions considered are 0.8 and 0.9 (lag) where as the reference power factor is kept at 0.85 as in [14]. The effect of power factor variation is considered including the cost of loss component.

TABLE II. COST OF TRANSACTIONS WITH DIFFERENT CASES

T1 T2

Cost without loss component ($/hr)

88.93 554.84

Cost with loss component ($/hr)

90.00 597.09

Cost at 0.8 pf ($/hr)

95.62 634.41

Cost at 0.9 pf ($/hr)

85.00 563.89

It can be seen from Table II that the cost component of loss is less when compared with the cost component of power factor and also the transaction T2 utilizes most of the transmission lines from bus 2 to bus 14 hence its transaction cost is very high compared with the transaction cost of T1. This shows the dependence of this method on the physical nature of the network.

V. CONCLUSIONS

In this paper the effect of counter flows arising because of simultaneous multi transactions is not considered. When the counter flows are negative they benefit the transmission system provider by increasing the transmission system capacity and also reducing the power loss hence this factor plays main role in deciding the cost component for losses hence further work can be done to include negative counter flows in cost of loss allocation.

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