Transmission network tariff volatility assessment under UPFC-integrated system and N-1 contingency condition

In the restructured electricity markets, transmission usage, usage costs, and loss allocation are critical issues for recovering network embedded and maintenance costs from network users. However, because of the integration of the flexible alternating current transmission system (FACTS) and the occurrence of power system contingencies, this allocation is more complex and critical from the util-ity’s perspective, as it may cause volatility in transmission network costs. In this work, the unified power flow controller (UPFC) is utilized to show the effect of its integration on the system cost and cost allocation. Further, contingency conditions are common in power systems. Therefore, for determining usage, usage cost, and loss allocation volatility under UPFC-integrated system and N-1 contingency conditions, this work utilized a power flow tracing-based transmission usage allocation technique. Reliability factors are used to determine transmission line flows in the event of a failure. Furthermore, contingency line flows are employed to assess transmission tariff volatility in terms of risk premiums. The cost of transmission utilization is recovered using a modified MW-mile technique. The devised approach was put to the test on a 6-bus system and an IEEE 14-bus system.

loss allocation, and cost allocation for transmission utilization. 1 These fundamental concerns put transmission utilities in a difficult position. Moreover, because of its monopolistic structure; the transmission sector makes it difficult to establish competition. As a result, cost allocation among the many market players is typically at the core of issues with deregulation. 2 A sufficient resource allocation among market players must be preserved via the transmission pricing system and user-cost allocation. It is preferred that choices about new generating investment be unaffected by transmission pricing and payments. This must be done in a straightforward and equitable manner as well. Each nation has a different deregulation model depending on the features of its transmission infrastructure. 2 All generators are appropriately planned in the vertically integrated model in order to achieve the lowest system losses and associated cost of generation. Further generation, transmission, and distribution are all under the control of a single body, so there is no concern about their security, reliability, or competition. However, in a free market setting, every entity is a distinct participant, and generating schedules, which are created appropriately. 1 In addition, they are competing with one another to reap greater rewards. Each entity strives to get greater advantages by obtaining energy from less expensive sources. All of these activities cause the transmission system to become congested and overloaded, which might result in system failure. Therefore, in order to preserve the security of the system, an external entity required that monitors such activity. 3 This task is performed by the system operator (SO) in a deregulated environment. It offers fair and equal open access to all participants and administers the transmission network within its security and reliability constraints. All entities utilize the transmission network, thus it is necessary to know how each one uses it and how the system is doing in order to allocate charges fairly. Thus, the introduction of deregulation in the electrical supply business encourages the development of new models and the involvement of new players in order to provide fair and equal open access at all deregulation levels. Following sections provide a quick overview of various market models and new entities. 4 Many transmission pricing systems are utilized around the world to assign transmission charges to clients. Embedded cost and market-based pricing are the two most common pricing approaches (marginal and incremental methodologies). Embedded approaches (such as the postage stamp, contract path, and MW-Mile) are based on a transaction's actual network use. 1 It also covers charges for amenities, assets, and maneuvering and maintenance. The increased transmission cost associated with a single electrical transaction is the basis for market-based approaches (marginal/incremental). 2 Embedded cost pricing uses power flow tracing to produce cost allocation techniques. It gives a thorough description of the transmission cost allocation problem. Once the consumption allocation is established, it is simple to divide transmission charges between generators and loads. Furthermore, with the recent transmission technologies such as flexible alternating current transmission systems (FACTS) and the occurrence of power system contingencies, this allocation is more complex and critical from the utility perspective. In the developing countries, the electricity industry is still working in a regulated manner, so such pricing schemes are very important.

Research motivation
Due to the fact that both generators and loads needed a transmission network to transfer and receive their energy, the emergence of the deregulated electricity market brought transmission consumption cost allocation, loss cost allocation under normal and contingency condition into the spotlight. 3 For the transmission embedded cost allocation, many strategies have recently been devised. Because they accurately depict how a transmission system actually operates, embedded cost approaches are given special consideration in this article. Due to the complete cost recovery provided by flow tracing, these methods predominate over marginal participation approaches. Additionally, it is dependent on Kirchhoff current laws and easy to apply at huge power systems. Additionally, it is far less volatile than marginal participation techniques. It also offers consistency and fairness in charge distribution because it is based on the system's real usage. 2 The research developed a new method for usage-based fixed cost allocation under both normal and contingency conditions based on power flow tracking. Additionally, transmission loss and reliability margin were allotted by the proposed method. Furthermore, new reliability indices are established to take contingency's impacts on use and cost allocation into account. The developed work also takes into account the impact of FACTS devices on newly restructured electricity market concerns including transmission usage allocation, cost allocation, and loss allocation because they are a crucial component of the power transmission system. 4

Related work
Several researchers used various techniques to address usage and cost allocation issues in the deregulated power system. First attempt to follow power flows, Bialek and Tam. 3 presented topological generation distribution factors-based power flow tracing, laying out the approach for tracing generator output. Strbac 4 proposed the notion of domains, commons, and interconnections as part of a power flow tracing method based on the comparative sharing hypothesis. Conejo et al. 5 proposed a Z-bus matrix-based approach for allocating network charges. The short-term pricing effects and CO 2 cost pass-through transmission mechanism in China were documented by Ma et al. 6 The authors described the features of locational uncertainty marginal pricing for associated uncertainties of variable renewable supply and needs in Reference 7 From the perspective of distributed generation (DG) owners, Avar and Sheikh-El-Eslami 8 proposed an optimal DG placement in energy markets, taking into account the influence of transmission costs. Brooks and Lesieutre 9 established the locational marginal price for variable power injections in energy and regulating markets. Based on marginal power network use in the spot market, Yang et al. 10 suggested an efficient transmission cost allocation. Xie et al. 11 provided an improved incidence matrix-based power flow tracing methodology in terms of graph theory-based approaches.
Because the number of participants on the electric grid has expanded as a result of deregulation, transmission line reliability margins have shrunk. In addition, reliability margins are reduced in fault conditions. As a result, transmission embedded cost allocation approaches should account for transmission reliability margin when calculating costs. A transmission reliability margin feature should be incorporated into the transmission pricing process to address this issue. As a result, the strategy proposed in Reference 12 takes into account transmission network function under both normal and contingency conditions while dispersing dependability costs to consumers. In Reference 13 , the authors provided a transmission loss and cost allocation index as well as a co-operative game theory approach. Several strategies for assigning dependability contributions to market participants are proposed in References 14, 15. Vijay Venu and Verma 16 suggested a new probabilistic transmission pricing approach that takes transmission reliability margin into account. Monsef and Jaefari 17 presented a mechanism for allocating transmission costs that considers the dependability margin in the event of a contingency.

Research gap
Various manuscripts tried to address the issues of transmission usage, usage cost, and loss allocation by utilizing different methods, but still, the impact of integration of the transmission components, such as the FACTS controller, is not incorporated. Furthermore, the impact of the N-1 contingency condition on transmission usage allocation, usage cost, and loss is still not well described.

Contribution
The following is the contribution of the proposed work: 1. A unified power flow controller (UPFC), integrated transmission network load flow was performed to compute the usage and losses. 2. The effects of the UPFC on the transmission usage, usage cost, and loss are computed. 3. Unified methodology for transmission usage, loss and Cost allocation is presented. 3. Different power system security assessment factors are utilized to compute the power flow under contingency conditions. 4. Under the N-1 contingency, transmission usage, usage cost, and loss are computed. 5. Different cost recovery methods such as full cost and partial cost, N-1 contingency recovery cost are also proposed.

Organization of the manuscript
The manuscript is organized as follows: Section 2 discussed the developed methodology utilized in this work. Section 3 presented the various results obtained by the proposed method. Further, a critical discussion of computed results is also presented in this section. Section 4 provides the conclusion of the article.

PROPOSED METHODOLOGY
The methodology utilized in this work is presented in Figure 1. This work proposes a unified methodology to solve transmission use and loss allocation problems with the UPFC-integrated transmission network and under an N-1 contingency condition. Total five steps are utilized to perform the proposed research. System modeling is performed under step 1. Newton-Raphson load flow analysis is performed to get the load low of the system in Step 2. Transmission line flows and losses are computed with UPFC and under N-1 contingency condition in Step 3. A modified Kirchhoff matrix is developed to allocate transmission usage and losses with UPFC and under N-1 contingency condition in Step 4. Further the cost is allocated under Step 5. Under both the scenarios, the tracing process is completed and used for transmission consumption, loss allocation, and cost. 11 Furthermore, transmission usage and loss are assessed in conjunction with power system security assessment factors under contingency conditions. For that purpose, system security assessment parameters have been developed. A modified MW-Mile methodology is employed for full and partial recovery of transmission usage and loss cost, and an algorithm given in Reference 18 is adapted for maximum flow conditions under contingency conditions.

Allocation under base case
For a simple graph G of n vertices, an n by n matrix called the Kirchhoff matrix Where k ij represent the elements of Kirchhoff matrix, d − (v i ) represents the diagonal elements of the Kirchhoff matrix, and −x ij represents the off-diagonal elements of the Kirchhoff matrix. The power flow matrix ( PF ij ) has been created is as follows: Here, −pf ij and pf ij represent the off-diagonal elements of the power flow matrix, while p Ti represents the diagonal element of the power flow matrix. The modified Kirchhoff matrix of a power network is denoted as K m = ( k m−ij ) n×n , the elements of the modified Kirchhoff matrix are given by Equation (3): Here, k m−ij represents the elements of the modified Kirchhoff matrix. Kirchhoff loss matrix may now be created using the above-updated Kirchhoff matrix: where kl ij represents the elements of the Kirchhoff loss matrix. p l ij represents the losses in line i−j, while flow in the direction of i to j bus. Similarly, p l ji represents the losses in line i−j, while flow in the direction of j to i bus. Further, p l ij = p ij + p ji , and p l ji = p ji + p ij .

Features of modified Kirchhoff matrix
1. The active load power at bus j is equal to the sum of all entries in row j of a modified Kirchhoff matrix, that is, 11 where U represents the identity matrix and P L represents the load matrix. 2. The total active power of generators at bus j is equal to the sum of all entries in column j of the modified Kirchhoff matrix, that is, 11 Here, P G represents the generation matrix.
The following is a rewrite of Equation (11): From Equations (5) and (7), 11 Equation (9) can be rewritten as follows: 11 The inverse of the modified Kirchhoff matrix is produced from the aforementioned matrix and is utilized for power flow tracing and loss allocation. The technique for power flow tracking and loss allocation is given in the next section.

Transmission usage allocation
The tracing approach described in 11 is used in this study, with transmission loss and reliability margin allocation adjusted. 1. Model for usage allocation Let ln = 1. … e represents the total number of lines in the system, G n = 1. … .g is total number of generators and D = 1 … … d is the total number of loads in the system. Again represents generation in diagonal matrix. Thus, 11 By combining Equations (11) and (8) The supply factor matrix (SFM) is matrix P GG K −1 m . The matrix of supply factors is denoted by SFM = , that is, And from Equation (9) where, t ij P Lj denotes the active power contribution of generator situated at bus i to the load at bus j.
The usage allotted to the generator at bus i on the s−b line is provided by, The same approach is used to calculate load shares in line flows and generated power: Considering dual of Equation (9) where the diagonal matrix ) T is the extraction factor matrix (EFM) of loads to generators. 11

Contingency-based usage allocation
In this study, transmission consumption costs are distributed to customers. Under contingency conditions, the following models are used to apportion transmission usage costs to users. Otherwise. Otherwise. where where PF k,out m presents the power flow in line k under outage in line m. P k,opt presents the flow in line k under contingency condition. P k,Cap represents the capacity of the line k, P c k,max is maximum capacity of line k under contingency condition.
This research proposed Equations (20)-(22) by developing reliability indices. After evaluating outage flow in lines, Equation (22) is used to compute the power flows under contingency conditions. The cost of transmission is then distributed to the user using these flows in the next stage.
2. Usage cost allocation under contingency Transmission consumption costs are assigned to customers in this section based on base capacity, rated capacity, and capacity under N-1 contingency condition.
(a) Full Recovery Model From the previous section transmission usage cost allocated to users (generators only) is given by FTUC Here, PF i→s−b presents the power flow in line s−b, contributed by generator i. P base s−b presents the base case flow in line Similarly partial recovery model to users (generators only) is given by PTUC Here, PF i→s−b presents the power flow in line s−b, contributed by generator i. P rbase s−b presents the reduced capcityof (c) Under N-1 Contingency Recovery Model Now with the help of proposed algorithm, transmission usage cost is allocated to users with reference to maximum flow under N-1 contingency condition is given by CTUC Here

Allocation of loss and cost under N-1 contingency
Transmission flows in other lines may vary due to outages in any line. Therefore, line losses also vary under such conditions. For allocating losses under such conditions, two factors, that is, line outage loss impact factor (LOLIF) and line outage loss distribution factor (LOLDF), are proposed. These factors are defined as follows: 1. Line outage loss distribution factor (LOLDF) It is the ratio of difference between transmission loss occurred in line i when j is faulty and the losses occurred in normal condition in faulty line j. Otherwise.
Here, pl i,out j represents the power loss in line i, when line j is out. pl i and pl j represent the power losses in line i and line j under base case condition. 1. Line outage loss impact factor (LOLIF) It provides the effect on transmission losses of healthy line i with respect to the outages in other lines. It is the ratio of difference between transmission loss occurring in line i when j is faulty and the losses occurring in normal condition in line i.
Maximum flows in lines under contingency conditions are estimated once all of these parameters have been determined using Equations (28)-(30).
where pl i,out j is transmission losses in line i when line j is out, pl i is transmission losses in line i in normal condition, pl j is transmission losses in line j in normal condition, pl j max is transmission losses in line j in all outages (n−1) and pl i max transmission losses in line i in all outages (n-1). plk, out m is power loss in line k when line m is faulty, PLk,max is maximum loss of line k, PL c k,max is maximum loss under contingency condition. The transmission loss cost (TLC) of a line is allocated to consumers using Equations (31) and (32) with these optimal losses under contingency condition are as follows.
Here, PL i→s−t present the power loss in line s-t, contributed by the generator i. PL k,base presents the power loss in line k under base case condition. PL k,max presents the maximum power loss in line k under all contingency conations. CL k represents the loss cost of line k.

Usage, usage cost and loss allocation with integration of UPFC
In this work UPFC is utilized in the transmission network to enhance the power transfer capability of the system. For the placement of the UPFC, a minimum loss criterion is utilized. 22 The effect of cost characteristics of the UPFC is also incorporate to allocate the transmission usage, usage cost and loss allocation in the transmission system. 23 For modeling of the UPFC, Newton-Raphson load flow Jacobian matrix is modified with the parameters of the UPFC. 24 The following formulation is utilized to allocate the usage, usage cost and loss to the generators.
1. Model for usage and cost allocation Generator situated at bus i share to the line s − b with UPFC (PF UPFC(i→s−b) ) is given by equation (33).
Here, pf UPFC(s−b) represents the power flow in line s−b with UPFC. Similarly for load situated at bus j share to the line s − b is given by For cost allocation, For generator G i full recovery model is given by FTUC Here, pf UPFC(base s−b) shows the base power flow in s−b line with UPFC. Similarly partial recovery model is given by PTUC With the help of the above equations, transmission usage costs are allocated to generators with UPFC devices. In the next step, the UPFC installation cost is calculated and allocated to generators and loads in proportion to the usage generated or utilized. Therefore, the UPFC installation cost (IC UPFC ) allocated to the generator situated on the bus i using the full recovery model is given by Total Transmission Lines Cost IC UPFC .
Similarly for partial recovery model Total Transmission Lines Cost IC UPFC .

Model for transmission loss allocation
The transmission losses of line s − b allocated to generator situated at bus i with UPFC device is given by Here, p l UPFC(s−b) is the power loss in line s−b with UPFC. Similarly for load situated at bus j is given by P l UPFC(j→s−b) : From the above equations, losses are allocated to generators and loads with UPFC devices, respectively.

Cost Characteristics of UPFC Device
Installation of UPFC devices is very costly, so their cost allocation in the restructured market is a very important issue. Therefore, in this work, after incorporating the UPFC devices into the load flow, their costs are also allocated to users in proportion to their usage allocation.
The investment cost of the UPFC (C UPFC ) devices can be formulated as follows 24 : The operating range S of UPFC (S UPFC ) device is determined from the following equation, Here, Q 1 and Q 2 are the sending and receiving end buses reactive power.
Once the operating range of UPFC is found, the corresponding C UPFC is calculated from the above equations. So the overall investment cost IC UPFC is

RESULT AND DISCUSSION
This section discussed the various results obtained under the scenarios of UPFC-integrated transmission network and N-1 contingency condition. The proposed work is implemented on Sample 6 bus 20 and IEEE 14 bus test systems. 20 A laptop with configuration of 64-bit operating system, 4 GB RAM, Intel(I) Core(TM) i5-3230M CPU@2.60 GHz processor is utilized to perform this work. Mathematical models are coded in MATLAB R2018a scenario in the MATPOWER tool box version 7.0 to perform the proposed method.

Allocation of usage and usage cost under N-1 contingency condition
Under contingency analysis, cost allocation for transmission usage needs fair dealing because the pattern of transmission usage is determined by the questions of how much power flows during an outage and which generator supplied it. Furthermore, even in contingency conditions, customers will not fully utilize the reliability margin because transmission infrastructure' capacity is typically more than the maximum flow through them. Models for transmission consumption cost allocation under contingency are explored in this article.

Sample 6 bus system
The results for transmission use cost allocation under contingency conditions for a six-bus system are now shown. The capacities of several lines are shown in Table 1 under N-1 contingency scenarios. For computing the line capacities under N-1 contingencies, four different system security factors LOIF, LODF, LOIFM, and LODFM are utilized.
Transmission usage cost is calculated and it is 100% allocated to generators as presented in Table 2, due to all four factors. Transmission usage cost allocation due to LOIF to G1 for lines 1-2 for a 6-bus system is 85.24 Rs/hr, 87.98 Rs/hr due to LODF, 125.53 Rs/hr due to LOIFM, and 128.07 Rs/hr due to LODFM. In this way, transmission usage costs are allocated for all generators and all lines. The cost of the line is proportional to the impedance of the line. Table 2 presents the comparison between cost allocation to generators using LOIF and LODF.
Similarly, Table 3 shows the cost of transmission utilization for generators utilizing LOIFM and LODFM. From the results, it is clear that under contingency conditions, maximum recovery is possible by using developed power security indices such as LODFM and LOIFM. The results show that LODFM and LOIFM are used to allocate the highest transmission usage cost in all four scenarios. As a result, the utility should deploy LODFM and LOIFM to maximize transmission cost recovery under contingency conditions. The entire transmission consumption cost allotted to all generators is shown in Figure 2. The results show that the maximum usage cost is assigned in all four scenarios using the maximum line outage impact factor, i.e. LODFM.
It is clear from the figure that the cost allocated due to LODFM is more than LOIFM, LODF, and LOIF. Thus, during an outage condition, LODFM provides maximum transmission usage cost recovery. Similar findings are achieved for transmission usage cost allocation to loads. Tables 4 and 5 show the cost allocation to loads as a result of all four system security factors. It is obvious from the preceding tables that using LODFM allows for the largest recovery of transmission usage costs in the event of a contingency. Figure 3 shows a graphical comparison of total transmission use charges assigned to loads for a six-bus system, which shows the maximum recovery is possible from the LODFM factor.
2. IEEE 14 bus system Under the contingency flow, transmission lines are different as compared to the base case condition. Hence, usage cost allocation is also different in this condition. By using a developed algorithm, transmission line flow under contingency conditions is calculated by four different indices. In comparison to, 20 in which LODF is used to find contingent line flows, developed indices provide more recovery. Table 6 shows the results of line flows for the modified IEEE 14 bus system under contingency conditions. Table 6 presented the line capacities under N-1 contingency condition for IEEE 14 bus system.
For computing the line capacities under N-1 contingencies, four different system security factors, LOIF, LODF, LOIFM, and LODFM, are utilized. The cost of transmission is then assigned to generators and demands using the above-calculated line flows. Table 7 shows the transmission usage cost allocation to generators in the IEEE 14 bus system.
Transmission line flows, obtained by all four security factors, are allocated to the two generators available in the IEEE 14 bus system.   Figure 4 shows that by employing LODFM, maximum transmission usage cost recovery may be achieved.
Under N-1 contingency conditions, Figure 5 demonstrates that the entire transmission consumption cost for the IEEE 14 bus system is allotted to different loads. As shown in Figure 5, LODFM gives the maximum allocation to loads.

Transmission loss and cost allocation under N-1 contingency condition
When a transmission line goes down, power flows in other lines may change. This variation in power flow further varies losses in transmission lines. Therefore, losses that occur under contingency conditions are different as compared to base case conditions. For this purpose, four new reliability indices were developed. By using these indices, the line loss under the N-1 contingency condition is calculated. Further, by using Equations (26) and (30), transmission loss costs are allocated under base case and optimal line loss conditions.  Table 8 presented the transmission line losses under N-1 contingency condition for 6 bus system. For computing the line losses under N-1 contingencies, four different system security factors, LOLIF and LOLDF, are utilized. Further Table 8 presented the cost of loss, occurred in the particular line under N-1 contingency condition.
Based on the computation performed in Table 8, the cost of transmission loss is then distributed to generators using the LOLIF and LOLDF indices in the next phase. This allotment is shown in Table 9.
A graphical comparison between the total loss cost allocations to generators by using power system security factors under contingency condition is presented in Figure 6.
Under the N-1 contingency condition, more loss cost recovery is feasible by utilizing the line outage loss impact factor (LOLIF), as shown in Figure 6.

IEEE 14 Bus
Transmission loss cost allocation under contingency conditions is done in this section. The loss cost is allocated to generators after the losses under contingency are discovered. The transmission loss distribution to generators using LOLIF and LOLDF is shown in Table 10. Figure 7 depicts the percentage loss cost allocation owing to LOLIF and LOLDF in a contingency scenario. It is evident that utilizing LOLDF for IEEE 14 bus system loss cost allocation is more expensive than utilizing LOLIF.

Usage and cost allocation with UPFC
In the IEEE 14 bus system, UPFC connects between buses 9 and 14. The shunt branch is connected to bus 14 to control its voltage magnitude to 1 p.u. and to maintain the active and reactive powers leaving the UPFC toward bus 9 at 14 MW and 4 MVAr. With base case power flow, the total system usage for the IEEE 14 bus system is 649.05 MW, while with UPFC it increased to 651.34 MW.

Comparative analysis
The proposed wok is theoretically compared with the Reference 25. The following comparative analysis is obtained, which is mentioned in Table 12.

CONCLUSION
Transmission usage, usage cost, loss allocation under UPFC devices and N-1 contingency conditions are important issues in the deregulated power system. As a result, the authors proposed a unified strategy for allocating usage, usage costs, and losses in the scenarios discussed above. A novel N-1 contingency condition recovery model is proposed along with a full and partial recovery approach for cost allocation to different generators and demands. The transmission loss cost allocation under the UPFC-integrated transmission system and contingency circumstances was performed in this study. Power system security indicators were created for this purpose. The cost of transmission loss was apportioned to users based on these indicators. As a result, these indices are used to recover the maximum amount of transmission consumption and loss costs. The results for the sample 6 bus system and the IEEE 14 bus system were displayed.

CONFLICT OF INTEREST
Authors have no conflict of interest relevant to this article.

DATA AVAILABILITY STATEMENT
Research data are not shared.