Impact of FACTS devices on exercising market power in deregulated electricity market

Abstract

In power system studies, congestion in transmission lines and utilization of flexible alternating current transmission system (FACTS) devices are closely associated. These devices are very important due to their role in power delivery system enhancement. It is to be noted that the generation companies can exercise their market power which depends on the line flows, line constraints, generators’ location and its share to the individual loads. This issue cannot be overlooked as it creates monopoliness which is against the deregulated market policy. The objective of this paper is to study the impact of market power when FACTS devices like thyristor controlled switching capacitor (TCSC) and thyristor controlled phase angle regulator (TCPAR) are used under steady state operation. The market power is determined using nodal must-run share (NMRS) index for the standard IEEE 14-bus system with and without the above FACTS devices and the results obtained are compared. All the above simulations are conducted in a MATLAB 7.9-R2009b environment.

Keywords

flexible alternating current transmission system (FACTS) / thyristor controlled switching capacitor (TCSC) / thyristor controlled phase angle regulator (TCPAR) / market power / must-run generation (MRG) / nodal must-run share (NMRS)

Introduction

For the past few decades, flexible alternating current transmission system (FACTS) devices have been adopted for controlling power and enhancing the usable capacity of present, as well as new and upgraded transmission lines under normal condition and congestion [1]. The research has concentrated on the location/sizing of these devices with various objectives and different control strategies.

Congestion management is one of the most important issues for secure and reliable system operations in deregulated electricity market [2]. Congestion management is said to occur in a power system whenever the system state of the grid is characterized by one or more violations of the policy constraints under which the grid operates in the normal state or in any one of the contingency cases in a set of specified contingencies. In Ref. [2], Singh and David have suggested a simple and efficient model for optimizing the location of FACTS devices used for congestion management by controlling the parameters of the device. They have proposed performance index sensitivity factor for finding the optimal location of FACTS devices. It is an effective way of determining the optimal location in a deregulated environment.

If there is no congestion, the placement of FACTS devices, from the static point of view, can be decided based on reducing losses but this approach is inadequate when congestion occurs. A method based on the real power flow performance index (PI) has been considered because of security and stability considerations [3]. There is a possibility that several lines are suitable for the placement of FACTS devices. In Ref. [2], the choice used is based on the reduction of congestion cost.

In Ref. [4], a loss sensitivity approach has been proposed for placement of series capacitors, phase shifters and static var compensators. Applications of these devices for improving the dynamic performance of the system are also well documented in Refs. [5-7]. Rajaraman et al. [8] have used continuation power flow for obtaining the size and locations of series compensators to increase the loadability limit of the system. After placement of series compensation in each line, the loadability with a uniform loading factor at each bus is computed with the help of the continuation power flow technique. In large power systems where load change is not uniform, it is difficult to decide the optimal location of series compensation. Paterni et al. [9] have developed a genetic algorithm to determine the best location of phase shifters in the French network based on the cost factors of the device. In Refs. [10,11], the optimal locations of FACTS devices have been obtained by solving the economic dispatch problem plus the cost of these devices, making the assumption that all lines, initially have these devices. In the presence of bilateral/multilateral contracts, it would be difficult to use this objective. Moreover, these papers involve complex method for determining the optimal location in a deregulated environment.

The restructuring of the electricity supply industry that normally accompanies the introduction of competition provides a fertile ground for the growth of embedded generation [12]. For the country like India, owing to the enormous gap between the generation and demand, and lack of transmission corridor to import power, the generation companies can show its dominance on the market. This anti-competitive practice may prevent competition in the electric power industry, especially in generation in the form of market power [13]. Market power exists in restructured power systems when any of a generation companies exerts its influence on market pricing or on the availability of electric power. Market power may be defined as owning the ability by a seller, or a group of sellers, to drive price over a competitive level, control the total output or exclude competitors from a relevant market for a significant period of time [13]. It reduces the competitiveness, quality and the impact of development in the field of technology. There is always a doubt that market power is being exercised regularly in many electricity markets [14]. Many researchers have come out with various indices to measure market power. Herfindahl-Hirschman index (HHI), Lerner index, must-run ratio (MRR), must-run share (MRS), nodal must-run share (NMRS) and expected nodal must-run share (ENMRS) are some of them. Each index has its own limitations. MRS, NMRS and ENMRS are the indices which reflect the impact of load variation, transmission constraints and random failures on the market power respectively. In this paper MRS and NMRS are used to measure the market power.

Problem definition

In the deregulated environment, FACTS devices play a vital role in solving various power system problems, specifically under congestion. None of the researchers have given a concrete relation between the usage of FACTS devices and their implication in market power issues. The aim of this paper is to find the impact of the FACTS devices on executing market power by the generation companies and hence the location, size and the selection of FACTS devices are beyond the scope. The optimum location and the devices, namely thyristor controlled switching capacitor (TCSC) (with X_c = 0.0132 pu) and thyristor controlled phase angle regulator (TCPAR) (with phase angle (δ) = -3.95°), are taken for the analysis as proposed in Refs. [2,15]. The market power is assessed using the MRS and NMRS index proposed by Wang et al. [16] and a complete study has been made on the standard IEEE 14 bus system.

Methodology

The static modeling of TCSC is shown in Fig. 1. The power injection method is used for the static modeling of FACTS devices. Let the complex voltages at bus-i and bus-j in Fig. 1 be denoted by V_i|{\delta }_i and V_j|{\delta }_j respectively.

The complex power flowing from bus-i to bus-j can be expressed as

(1)S_{ij}^{\ast }=P_{ij}-\text{j}{Q}_{ij}=V_i^{\ast }{I}_{ij}

=V_i^{\ast }[(V_i-V_j)Y_{jj}+V_i({\text{j}{B}_{}}_{\mathrm{c}})]

(2)=V_i^{\mathrm{2}}[G_{ij}+\text{j}(B_{ij}+{B_{\mathrm{c}}}_{})]-V_i^{\ast }{V}_j(G_{ij}+\text{j}{B}_{ij}),

where

(3)G_{ij}+\text{j}{B}_{ij}={\displaystyle \frac{\mathrm{1}}{r_{ij}+{\mathrm{j}x}_{ij}}}.

The real power flow from bus-i to bus-j without series compensation can be written as

(4)P_{ij}=V_i^{\mathrm{2}}{G}_{ij}-V_i{V}_j[G_{ij}\cos ({\delta }_{ij})+B_{ij}\sin ({\delta }_{ij})].

The real power flow from bus-j to bus-i without series compensation can be written aswhere {\delta }_{ij}={\delta }_i-{\delta }_j.

The real power flow with series capacitance c from bus-i to bus-j (P_{ij}^{\mathrm{c}}) and from bus-j to bus-i (P_{ij}^{\mathrm{c}}) of a line having series impedance z_{ij}=r_{ij}+\text{j}{x}_{ij} and a series reactance (-\text{j}{x}_{\mathrm{c}}) are

(6)P_{ij}^{\mathrm{c}}=V_i^{\mathrm{2}}{G}_{ij}^{\text{'}}-V_i{V}_j[G_{ij}^{\text{'}}\cos ({\delta }_{ij})+B_{ij}^{\text{'}}\sin ({\delta }_{ij})],

(7)P_{ji}^{\mathrm{c}}=V_j^{\mathrm{2}}{G}_{ji}^{\text{'}}-V_i{V}_j[G_{ij}^{\text{'}}\cos ({\delta }_{ij})-B_{ij}^{\text{'}}\sin ({\delta }_{ij})],

where

(8)G_{ij}^{\text{'}}+\text{j}{B}_{ij}^{\text{'}}={\displaystyle \frac{\mathrm{1}}{R_{\mathrm{L}}+X_{\mathrm{L}}-{\mathrm{j}X}_{\mathrm{c}}}}.

Here L and C are the inductance and capacitance of a line between i and j. The change in power flow due to series capacitance is represented as a line without series capacitance with additional power (complex) injections at receiving and sending (S_{i\text{c}}) ends respectively.

The real power injections due to series capacitor at bus-i(P_{\text{jc}}) and bus-j(P_{\text{jc}}) are

(9)P_i^{\mathrm{c}}=P_{ij}^{}-P_{ij}^{\mathrm{c}}=V_i^{\mathrm{2}}\Delta G_{ij}^{\text{'}}-V_i{V}_j[\Delta G_{ij}^{\text{'}}\cos ({\delta }_{ij})+\Delta B_{ij}^{\text{'}}\sin ({\delta }_{ij})],

(10)P_j^{}=P_{ji}-P_{ji}^{\mathrm{c}}=V_i^{\mathrm{2}}\Delta G_{ij}^{\text{'}}-V_i{V}_j[\Delta G_{ij}^{\text{'}}\cos ({\delta }_{ij})-\Delta B_{ij}^{\text{'}}\sin ({\delta }_{ij})].

The reactive power injection into the system has no effect on any of the market power concepts which will be discussed in the sections below and hence the reactive power expressions are not discussed. Similarly, the static model for TCPAR is taken from Ref. [2] for which the market power of Gencos is determined under both cases, i.e. with and without these devices.

Must-run generation (MRG)

The MRG of a generator is defined as the minimum capacity which must be provided by a generator to supply system load considering generation and transmission constraints. It is obtained for a generator by solving the optimization problem using linear programming. It is denoted by P_{gk}^{\text{must}}. The MRG of each unit is determined by solving the optimization problem given below.\min {\displaystyle \sum _{k\in A}{P}_{\mathrm{g}k}}

The total MRG then can be found by

(11)P_A^{}={\displaystyle \sum _{k\in A}{P}_{\text{g}k}}.

So, for a given generation unit, the MRG is equal to

(12)\min P_{\text{g}k}

such that

(13)\begin{array}{ll}{e}_{}(P_{\text{g}}-P_{\text{d}})=\mathrm{0}& (\mathrm{Power}\mathrm{balance}\mathrm{equations}),\end{array}

(14)\begin{array}{ll}\mathrm{0}\le P_{\text{g}}\le P_{\text{g}\max }& (\mathrm{Generator}\mathrm{output}\mathrm{limits}),\end{array}

(15)\begin{array}{ll}-P_{\text{g}\max }\le F(P_{}-P_{\text{g}})\le P_{\text{d}\max }& (\mathrm{Transmission}\mathrm{line}\mathrm{limits}),\end{array}

where P_d is the demand vector, e_{\mathrm{T}} is a vector with all ones; P_{\mathrm{g}}, the generation vector; , the line limit; and F, distribution factor.

MRS

The MRS of a generator represents the minimal market share required for generator k in a power market to supply a given market load. In a perfect market, the MRS of each generator is expected to be zero for fair competition. It is denoted by {\mathrm{MRS}}_k, and defined as

(16){\mathrm{MRS}}_k=\frac{P_{\mathrm{g}k}^{\mathrm{must}}}{P_{\mathrm{d}}}

where P_{\mathrm{d}} is the total demand in the power market; and P_{\text{g}k}^{\text{must}} the MRG of a generator.

NMRS

The NMRS represents the minimum capacity that must be provided by the must-run generator k to supply a given load at node i. It is denoted by{\text{NMRS}}_{k,i}, and defined as

(17){\text{NMRS}}_{ki}=\frac{P_{\text{g}ki}^{\text{must}}}{P_{\text{d}i}}=\frac{{\left[M^{-1}\right]}_{ik}{P}_{\text{g}k}^{\text{must}}}{{\displaystyle \sum _{j\in N}{\left[M^{-1}\right]}_{ij}}{P}_{\text{g}j}}

where N is the number of buses; P_{\text{d}i}, the load at bus i; j, the bus which is directly connected to bus i through transmission lines; and [M]; the distribution matrix which is used to show how the power supplied at a node is contributed from all the generators in a system explained in Ref. [16].

Simulation and results

The IEEE 14 bus system is analyzed to illustrate how the exercise of the market power of Gencos (assuming all the 5 generating units available at bus numbers 1, 2, 3, 6 and 8 as individual companies and denoting them with the respective bus number as subscript) on the loads (loads are positioned at bus numbers 2, 3, 4, 5, 6, 9, 10, 11, 12, 13 and 14 and they are denoted with the respective bus number as subscript). The maximum generation limits (active power in MW) of the Gencos are suitably assumed to be 32, 88, 63, 72 and 31 MW respectively.

The general procedure to calculate the NMRS of a generator at node i is

Step 1 Determine P_{\text{g}k}^{\text{must}}of generator k.

Step 2 Calculate the distribution matrix[M^{-\mathrm{1}}].

Step 3 Calculate the NMRS_i.

Step 4 Go to step 1 and continue the process for all the generators.

Repeat the above steps for the base case, with the TCSC and TCPAR.

Eq. (12) is solved using linear programming with the help of all the constraints as specified in Eqs. (13)-(15). Various combinations of MW generation are achieved for different generators, out of which the minimum value is given by the MRG. The MRG is calculated without FACTS devices and is tabulated in Table 1.

Similarly, after the placement of the TCSC and TCPAR in the system, the MRG of various generators are listed in Tables 2 and 3 respectively.

The NMRS of each generator to supply each load located at various busses are calculated and tabulated in Table 4 (without any FACTS devices) and Table 5 (with TCSC in the 13th line).

Table 4 shows the NMRS of each generator for a specific load such that the total load and the constraints are met without any FACTS devices. i.e. the market power of the generators in terms of their share in meeting the load.

Similarly, the NMRS of each generator to supply all loads located at various buses are calculated and tabulated in Table 5 (with TCSC in the 13th line) and in Table 6 (with TCPAR in the 19th line).

Figure 2 shows the share of the generator at bus 1 to the loads has slightly increased when compared to the base case. It is also observed that the share of this generator to load at bus 5 is increased from 12.7% to 13.5%. Whereas when the TCPAR is placed in the 19th line, it is observed that the share of this generator to load at bus 2, 3, 4, 5 is increased to 11.9%, 5.9%, 27.6% and 41.5% from 0%, 0.6%, 6.1% and 12.7%, respectively. The blue bar graph represents the share of generator 1 without any FACTS devices. In all the figures, the loads on respective buses are taken in the abscissa and presented in Table 7.

Figure 3 shows that the market power of the generator at bus 2 is not much altered with respect to TCSC. They are almost similar to the base case because the change in MRG is almost negligible and is almost equal to the maximum capacity of that generator. In the case of TCPAR, it is observed that the share has been reduced on the load at bus 3 from 58% to 30.6%.

Figure 4 shows that the share of the generator at bus 3 is totally met by the load at the same bus, so that the share of MRG to the other loads is zero. This is because the load at bus 3 is more than the generation capacity of the generator at bus 3. In the case of TCSC, the generator share to the load has increased from 41.3% to 41.7%. In the case of TCPAR, the generator share has increased from 41.3% to 61.7%.

Figure 5 shows that in the case of TCSC, as the generator at bus 6 is very near to the 13th line where TCSC is placed, there are more shares from this generator to the loads which are near to this line. This shows the dominance of this generator over these loads and it can exercise its market power on these loads. Similarly, in the case of TCPAR, there are more shares from this generator to the loads nearest to that of the generator as well as to the 19th line where the device is placed.

Figure 6 shows that the share of the generator at bus 8 to the load at bus 9 has increased from 43% to 44% whereas, for TCPAR, the share has increased to 78.1%.

Conclusions

In this paper, the impact of FACTS devices on the market power of the generator has been clearly illustrated using IEEE 14 bus system. From the results, it is inferred that when the generator is far away from the line in which FACTS devices are placed, the nearby loads to that generator suffer from the market power exercised by the respective generators.

It is observed that when the FACTS devices are included in the system, the transmission congestion is relieved which in turn affects the power flowing through the transmission lines. When the power flow changes, the MRG of each generator gets affected. It is worth noting that the transmission constraints, generation limits and power flows on the transmission lines play a vital role in deciding the NMRS of a generator. In other words, the geographical location of the generation company is a deciding factor of a Genco to exercise its market power. Though FACTS devices are placed to improve the system performance, it indirectly aids the generation company to exercise its market power which is by nature, an anti-competitive act. It is therefore suggested to consider the market power as one of the important constraints in locating the FACTS devices optimally.

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