A New Transmission Cost Allocation Method Considering Power Flow Duration Time in Smart Grid

Transcription

1 1 A New Transmission Cost Allocation Method Considering Power Duration Time in Smart Grid Xi Jia, Student Member, IEEE, Qing Xia, Senior Member, IEEE, and Qixin Chen, Member, IEEE Abstract The efficiency of asset utilization is one of the core contents of Smart Grid. This paper proposes the line Power Duration Curve (PFDC) as a tool in the process of transmission cost allocation. The impact of the power flow duration time on the transmission asset utilization can be taken into account effectively. An implementation mechanism is designed. The case studies based on the IEEE 30-bus and 118-bus system demonstrate that the transmission cost can be allocated much more reasonably by the proposed method. Index Terms Transmission cost allocation, line power flow duration curve (PFDC), power flow duration time, efficiency of asset utilization, Smart Grid. I. INTRODUCTION DUE to the rapid development of Smart Grid that has brought forward a huge demand of investment, the efficiency of transmission asset utilization has aroused more and more concern, because the investmenn transmission assets accounts for a large proportion of the whole investment in Smart Grid. Hence, is not only necessary but also important to improve the efficiency of transmission asset utilization through design and implementation of reasonable price mechanism. The transmission cost typically consists of four components, the fixed cost, the operation cost (including the transmission losses cost), the opportunity cost (including the congestion cost) and the expansion cost [1]. The key stage in transmission pricing is to allocate the total transmission cost fairly and reasonably among all the users (including generators and consumers) based on their different usage of time and locations. Existing methods include the accounting-based comprehensive cost method, the economics-based marginal cost method, and the hybrid methods that combines these two methods [2]. In this paper, we focus on the first method. There are various of methods to allocate the accounting-based comprehensive cost. In absence of the power flow calculation, the Postage Stamp Method and the Contract Path are well known with the simplicity from the computational point of view, but they cannot reflect the efficiency of transmission asset utilization [3] [5]. Besides, some methods are based on the power flow This work is supported by China National High-Tech Research and Development Program (863 Scheme, No.2010AA ). Xi Jia, Qing Xia and Qixin Chen are with the State Key Lab of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing , China ( s: gux02@mails.thu.edu.cn, qingxia@tsinghua.edu.cn, qxchen@tsinghua.edu.cn). calculation, such as the Boundary Method [6], the MW- Mile Method [7], the Distribution Factors Method [8], the AC Sensitivity Indices Method [9], the Transaction Assessment Method [10], and the Power Tracing Method [11]. These methods can reflect the utilization of the transmission line capacity to some extent. However, is far from enough because these methods only rely on the DC or AC power flow in a snapshot. The difference of power flow between different periods of time and the persistence effect across several periods of time are not taken into account effectively. Actually, for each specific transmission line in any time period, a Power Duration Curve (PFDC) could be obtained by sorting the power flow value in the transmission line. The higher the power flow level, the larger transmission capacity is needed; the longer a power flow level lasts, the higher its efficiency of transmission capacity to transfer the power is, and the fewer the capacity cost per unit energy per unit time is. Usually, the peak load in power systems dose not last long, which means a low efficiency of transmission asset utilization, and the energy transferred during this time should pay a high capacity price. This pricing principle will help to achieve peak power flow shifting which would shave the peak flow effectively, postpone unnecessary transmission expansion and improve the efficiency of asset utilization. This paper proposes a new transmission cost allocation method. The remaining of this paper is organized as follows. Section II introduces the concept and formulation of the line Power Duration Curve. Section III designs an implementation mechanism for further practical application. Then, the case studies based on the IEEE 30-bus system and 118- bus system are conducted and its promising resuls shown in Section IV. Section V concludes this paper. II. FORMULATION Based on Section I, a reasonable method to allocate the transmission cost should cover two important factors, i.e. the numerical value and the duration time of power flow. The former shows the transmission line capacity actually used by users, while the latter shows the efficiency of asset utilization just for the capacity in the former. With these two factors, this paper proposes a novel method and mechanism to allocate the transmission cost according to the efficiency of lines asset utilization. First, calculate the PFDC for each transmission line;

2 2 P max P max t n P n P n E n,n E n P n-1 P 1 P n-1 P 1,n-1 Fig. 1. curve t n t n-1 Time Duration Time Formulation of the PFDC for line k from the sequential power flow t 1 Fig. 2.,1 t 1 t n t n-1 Duration Time The horizontal segmentation on the PFDC of line k Second, obtain the capacity cost for one more unincremental power flow by horizontal segmentation along the value of power flow; Third, calculate the allocation rate of the transmission cost for different time by vertical accumulation. The calculation process is described in more detail as below: A. Formulation of the PFDC of Line k A PFDC is a curve showing the duration on which the power flow in a specific transmission line equals or exceeds a given value within a specific time window. And it can be converted from the sequential power flow curve conveniently, as shown in Fig. 1, in which on the lefs the sequential power flow curve of line k, where is the sampling time interval. On the righs the PFDC of line k, where the represents the duration time when power flow equals or exceeds P i, and the label i is sorted by the value of power flow from small to big. Assuming that the maximal power flow in line k in the time window [0 t 1 ] is Pmax, and the total cost of line k needs allocating during the time window [0 t 1 ] is. Given two adjacent discrete points P n and P n 1 on the PFDC, whose duration time is t n and t n 1 respectively, then the following equations can be obtained: P n P n 1 = (1) t n t n 1 = (2) On the sequential power flow curve, assuming that the energy transferred by power flow P n in slot is (the shaded part shown in the left of Fig. 1), its corresponding part on the PFDC is shown as the shaded part on the right of Fig. 1. And the following equation can be obtained: B. Horizontal Segmentation = P n (3) As shown in Fig. 2, can be divided into n strips from bottom to top along the value of power flow in the horizontal direction, which are denoted as,1,,2,...,,n 1,,n. Assuming that the allocated cost on,i (i = 1,2,...,n) in line k is F n,i. F n,n is taken as an example to demonstrate the process for calculating the F n,i as follows. When the power flow increases from P n 1 to P n, the corresponding energy increase ise n (the shaded part shown in Fig. 1). Simultaneously, the required transmission line capacity will increase by F n in order to satisfy the increase of the power flow, which is: F n = Pmax Then the allocation rate C n of the transmission cost corresponding to E n is: C n = F n = Pmax 1 t n = (4) Pmax t n (5) Comparing Fig. 1 and Fig. 2, it can be noted that,n is the overlap of and E n, then F n,n can be obtained as follows: F n,n = C n,n = C. Vertical Accumulation Pmax = Pmax t n (6) According to (6), the allocated cost F n,i corresponding to energy,i (i = 1,2,...,n), can be calculated as follows: F n,i = P i Pmax i = 1,2,...,n (7) Then the allocated cost F n corresponding to energy, could be obtained by accumulation of F n,i one by one in the vertical direction: F n = F n,i (8) Then the allocation rate of the transmission cost C k n corresponding to the power flow level P n in the sequential power flow curve of line k, can be calculated from (3), (7) and (8) as follows: Cn k = F n = Pmax P n ( 1 P i ) (9) Is demonstrated by (9) that the allocation resuls not only related to the value but also the duration time of power flow.

3 3 There is positive and negative power flow in transmission lines, and if the allocation rate of the transmission cost for negative power flow C k n is set to be zero [12], which means all the cost F n obtained from (8) should be allocated to the positive power flow, then (9) can be modified as follows: C k n,+ = F n = Pmax P n,+ ( 1 P i ) (10) P n,+ represents the summation of the absolute value of all the positive power flow in line k. D. Calculation of the allocation rate of the transmission cost for nodes According to (10), if power flow P tn j,k in line k is generated by the power injection of node j at t n, then the unit energy transferred should afford the transmission cost allocation rate Cn,+ k. Assuming that the lines ses K, then C tn j, the allocation rate of transmission cost for node j at t n, can be calculated through weighted average of each Cn,+ k (k K), where the weight coefficients depend on the power flow in each line generated by the power injection of node j. C tn j = (Cn,+ k P tn j,k )/ P tn j,k (11) k K k K III. MECHANISM DESIGN In order to put the proposed method into practice, there are still three important problems to be solved: First, how to obtain the PFDC for each transmission line through a reasonable method in advance; Second, how to determine the interval for horizontal segmentation and the density of allocation rate along the timeline; Third, how to take into account and deal with the gap between the transmission cost actually collected and the theoretically calculated value in presence of the forecast error. In order to address these problems, an in-depth mechanism design is conducted as follows: A. Annual Typical PFDC A year is taken as an illustrative time window to form the PFDC. Based on the analysis of the operating modes on different typical days throughout the year, an approximate annual PFDC of each line could be obtained by superposition and reasonable extrapolation on power flow curves on these typical days. Then, the approximate annual PFDC is used as the basis for the cost allocation throughout the year. A typical day can be selected seasonally, monthly or weekly, which depends on the actual system operating conditions. If month is selected as the interval to form typical days, the typical power flow distribution of each line during the month and distribution factors of each generation node and load node with transmission lines could be obtained from weighted average on typical peak and off-peak operating modes corresponding to the high-load day and low-load day each month. Then a cluster of typical PFDC could be obtained, and each curve approximately describes the flow in a specific line throughout the year. For any line k, the total annual transmission cost could be allocated according to the typical PFDC mentioned before, forming the transmission cost allocation rate of line k in different time, based on which the allocation rate actually implemented could be calculated. Generally, the typical PFDC should remain unchanged as a basis of calculation. In order to improve the flexibility of the mechanism, some modifications on PFDC are also acceptable if an unexpected big change happens in the system power flow distribution. B. Liquidation and carry-over for annual payment In order to ensure that the total annual consumers payment is equal to the theoretical value and reflects the actual efficiency of transmission asset utilization, the liquidation and carry-over annually would be needed since the typical PFDC are only an approximate estimation of the actual PFDC. A simple way for implementation is to carry-over the deviation of cost annually. At the end of each year, the cost allocation rate could be calculated according to actual PFDC based on the operating data throughout the year, and the theoretical payment for each node could be calculated according to the power flow in each line caused by the injection at each node. The deviation is defined as the difference between the theoretical and actual payment, while shortage should be paid by consumers and surplus should be refunded to consumers. For convenience, the balancing account of payment for the transmission cost should be established for each user(especially for generators and large consumers), with charging some fees in advance as a deposit, and the annual debit/credit would be settled into account. Users should add money up to the deposit level when the balance is below a certain limit, and would get surplus part back when the balance is above a certain limit. IV. CASE STUDY In order to verify the validity of the proposed method, two case studies are conducted, assuming that all the transmission lines are at the same voltage level. The simulation is by Matpower [13] on the Matlab R2009a platform. The transmission coss allocated only to the positive power flow in the transmission lines. The generalized generation shift distribution factor (GGSDF) [14] is adopted to eliminate the impact of the choice of slack bus. A. Case study I The first case is based on the IEEE 30-bus system, and the construction cost for each line is shown in Table I. The bus generation and load data are extended to 8760 snapshots to represent the data throughout the year. Then the sequential curve of transmission cost allocation for each bus can be calculated. Bus 1(Generation) and Bus 20(Load) are taken as examples shown in Fig. 3. It s obvious that the difference of transmission cost allocation rate between the two buses is significant, and the

4 4 TABLE I THE TRANSMISSION COST OF 41 LINES IN THE IEEE 30-BUS SYSTEM Transmission Allocation Rate (Bus 1) Fig. 3. Line NO. Transmission Transmission Line NO. Cost(10 4 $) Cost(10 4 $) Bus 1 (Generator) Bus 20 (Load) Transmission Cost Allocation Rate, Case I maximum price for Bus 1 is more than 9.8 times of that for Bus 20, which is reasonable considering that the base value of power injection at Bus 1 is 23.54MW whereas it s only 2.2MW at Bus 20. Furthermore, with the variation of power flow along the time line, significant peaks appears when the power flow level is high in both the two sequential curves, which reflects the impact of the efficiency of transmission asset utilization effectively. B. Case study II The second case is based on the IEEE 118-bus system with 186 lines, and the transmission cost of each line is assumed under the same rules as case I. The bus generation and load data are extended to 720 snapshots to represent the data throughout a month. Bus 10(Generator) and Bus 69(Generator) are taken as examples. Although the output of Bus 69 (516.4MW) is larger than Bus 10 (450MW), the result of cost allocation rates is just the opposite. Furthermore, as shown in Fig. 4, when the outputs of the two are increased by 1MW respectively, the Transmission Allocation Rate (Bus 20) 0.5 Difference of Transmission Allocation Rate 4.0E-4 2.0E-4-2.0E-4-4.0E-4-6.0E-4-8.0E-4-1.0E-3-1.2E E E+0 Bus 10 (Generator) Bus 69 (Geneartor) Average Value Of Bus 10 Average Value Of Bus E E E-5 5.4E-5 5.3E-5 5.2E-5 5.1E-5 5.0E E-05 Fig. 4. Variations of Transmission Cost Allocation Rate with 1MW More Output, Case II variations of their cost allocation rates are totally different. Refer to the left vertical axis, the variation of the rate at Bus 69 is always positive, and increases significantly during peak flow periods, while that at Bus 10 is positive during valley flow periods and negative during peak flow periods. At the same time, refer to the right vertical axis, the average value of the variations for Bus 10 ( ) is larger than that for Bus 69 ( ), which explains why the cost allocation rate of Bus 10 is larger than Bus 69 numerically. Actually, the basic reason might be the different locations of the two buses in this large system. As shown in Fig. 5, Bus 69 is near to the load centers while Bus 10 is far away. Is well recognized that power plants which are built near load centers would improve the utilization of transmission lines for less construction costs, less transmission losses, and more usage, and the transmission cost should be a important factor in the generation expansion planning [15]. The result calculated above could be a clear signal for investors to build power plants as near as possible to load centers. V. CONCLUSION As one of the core contents of Smart Grid, is required to take efficiency of asset utilization into consideration of electricity pricing, forming more reasonable price signals and promoting the efficient utilization of asset. It has been a long time for the transmission cost allocation to take the usage of line capacity based on power flow in a snapshonto account, without considering the difference of efficiency caused by different duration time of power flow in some periods. Moving forward from this point, the main contributions of this paper are: First, with an overall consideration of the value and the duration time of power flow, a novel transmission cost allocation method is developed, based on the PFDC of transmission lines. Power flow duration time is taken into account for the efficiency of asset utilization by horizontal segmentation on the PFDC along the value of power flow; and then the different 4.9E-5 Average Value of the Difference

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