6. Estimation of market power in deregulated electricity market

In this final section, the application of cubic spline technique has been illustrated in the field of deregulated electricity market. In this market, market power issues predominantly spoil the basic idea of maintaining equilibrium within the market players.

Market power is the ability of showing one's monopolistic nature on the price of the commodities in the market. This has become a challenging issue in the context of the present electricity market and will become more challenging and play a significant role when private generation companies start participating in buying/selling the power [5]. Due to the increase in demand and the regulatory policies, private parties have started investing in the power sector, especially in the renewable energy sources. Thus, it is inevitable for the independent system operator (ISO) to estimate market power for taking crucial decisions [6].

#### 6.1. Market power indices

#### 6.1.1. Herfindahl-Hirschman index

The Herfindahl-Hirschman index (HHI) is used to measure the market concentration that will reflect the number of players in the market and also the inequality in their market shares. The HHI is defined as the sum of the squares of market shares of all the players as given in Eq. (25)

$$\text{HHI} = \sum\_{i=1}^{N} S\_i^2\\\text{HHI} = \sum\_{i=1}^{N} \mathbf{S}\_i^2 \tag{25}$$

Step 5. Repeat step 4 for calculating NMRS for the remaining generators on each load.

Step 9. Plot NMRS of a generator against the maximum generation of other generators.

Step 8. Calculate the NMRS for all the generators using the conventional method as discussed

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Step 10. Connect two points at a time using cubic spline interpolation technique (piecewise polynomial) using MATLAB built-in function, that is, for example, a = spline (b, c, de) and ff = spline (b, c) where 'a' gives the interpolated values which correspond to the query points in

The application of cubic's spline interpolation for calculating the respective market power of generation companies on all busses for any given load or operating condition is implemented on a sample IEEE 14 bus test system. This system consists of four generator busses and an additional slack generator at bus number 1 in addition to the nine load busses. The intercon-

In Figure 8, the operating condition is such that the total load is increased by 10% from the base case. The fast and accurate calculation of the market power at any given operating point of the generator may serve or help the principal purposes of various bodies like the GENCOs, DISCOs and ISOs. The knowledge of market power for any given operating condition will enable these above bodies to take suitable actions to change their own operating points in

nection of the system is accomplished with 20 transmission lines.

Figure 8. Normal case versus increase in load by 10%.

Step 6. Repeat steps 4 and 5 for various cases.

Step 7. End.

in steps–7.

de [9].

where N is the number of players and Si is the ith player market share in percentage [7].

#### 6.2. Lerner index

It measures or indicates the proportional deviation of the price at the firm's profit-maximizing output from the firm's marginal cost at that output. It is defined as shown in Eq. (26)

$$\mathrm{LI\_i} = \frac{(\rho\_{\mathrm{i}} - \mathrm{mc\_i})}{\rho\_{\mathrm{i}}} = \frac{1}{\varepsilon\_{\mathrm{i}}^{\mathrm{d}}} \mathrm{LI\_i} = \frac{\rho\_{\mathrm{i}} - \mathrm{mc\_i}}{\rho\_{\mathrm{i}}} = \frac{1}{\varepsilon\_{\mathrm{i}}^{\mathrm{d}}} \tag{26}$$

where LIi is the Lerner index for a given firm i, r<sup>i</sup> and mc<sup>i</sup> are the price and marginal cost, respectively, and ε<sup>d</sup> <sup>i</sup> is the elasticity of demand felt by the firm.

#### 6.3. Nodal must run share

This index reflects the impact of load variation on market power and geographic difference of market due to network constraints. Must run share (MRS) represents the effect of load variation and nodal must run share (NMRS) represents the geographical difference of market powers. The equation for NMRS is shown in Eq. (27)

$$\text{NMRS}\_{\text{k,i}} = \frac{\text{Pg}\_{\text{k,i}}^{\text{must}}}{\text{Pd}\_{\text{i}}} \text{NMRS}\_{\text{k,i}} = \frac{\text{Pg}\_{\text{must}\_{\text{k,i}}}}{\text{Pd}\_{\text{i}}} \text{i} = 1,2,... \text{N} \tag{27}$$

where N is the number of busses in a power system, Pdi is the load at bus i, and Pgmust k,i Pdi Pgmustk,<sup>i</sup> is the contribution of the must run generator k to Pdi. The background calculation of NMRS is available in Ref. [7].

Steps involved in estimation of market power using NMRS [5, 8].

Step 1. Define the number of generators and their active power limits.

Step 2. Determine Pgmust <sup>k</sup> of generator k

Step 3. Calculate distribution matrix [M�<sup>1</sup> ]

Step 4. Calculate NMRS of generator 1 on load 1.

Step 5. Repeat step 4 for calculating NMRS for the remaining generators on each load.

Step 6. Repeat steps 4 and 5 for various cases.

Step 7. End.

6.1. Market power indices

144 Topics in Splines and Applications

6.2. Lerner index

respectively, and ε<sup>d</sup>

available in Ref. [7].

Step 2. Determine Pgmust

Step 3. Calculate distribution matrix [M�<sup>1</sup>

Step 4. Calculate NMRS of generator 1 on load 1.

6.3. Nodal must run share

6.1.1. Herfindahl-Hirschman index

The Herfindahl-Hirschman index (HHI) is used to measure the market concentration that will reflect the number of players in the market and also the inequality in their market shares. The HHI is defined as the sum of the squares of market shares of all the players as given in Eq. (25)

<sup>i</sup> HHI <sup>¼</sup> <sup>X</sup>

N

<sup>2</sup> (25)

i ¼ 1, 2, ::N (27)

k,i

Pdi Pgmustk,<sup>i</sup>

(26)

i¼1 Si

LIi <sup>¼</sup> <sup>r</sup><sup>i</sup> � mci ri

¼ 1 εd i

HHI <sup>¼</sup> <sup>X</sup> N

i¼1 S2

output from the firm's marginal cost at that output. It is defined as shown in Eq. (26)

<sup>i</sup> is the elasticity of demand felt by the firm.

LIi <sup>¼</sup> ð Þ <sup>r</sup><sup>i</sup> � mci ri

powers. The equation for NMRS is shown in Eq. (27)

NMRSk,<sup>i</sup> <sup>¼</sup> Pgmust

Steps involved in estimation of market power using NMRS [5, 8].

<sup>k</sup> of generator k

Step 1. Define the number of generators and their active power limits.

k,i Pdi

where N is the number of busses in a power system, Pdi is the load at bus i, and Pgmust

]

where N is the number of players and Si is the ith player market share in percentage [7].

It measures or indicates the proportional deviation of the price at the firm's profit-maximizing

where LIi is the Lerner index for a given firm i, r<sup>i</sup> and mc<sup>i</sup> are the price and marginal cost,

This index reflects the impact of load variation on market power and geographic difference of market due to network constraints. Must run share (MRS) represents the effect of load variation and nodal must run share (NMRS) represents the geographical difference of market

is the contribution of the must run generator k to Pdi. The background calculation of NMRS is

NMRSk:<sup>i</sup> <sup>¼</sup> Pgmustk,<sup>i</sup>

Pdi

¼ 1 εd i

Step 8. Calculate the NMRS for all the generators using the conventional method as discussed in steps–7.

Step 9. Plot NMRS of a generator against the maximum generation of other generators.

Step 10. Connect two points at a time using cubic spline interpolation technique (piecewise polynomial) using MATLAB built-in function, that is, for example, a = spline (b, c, de) and ff = spline (b, c) where 'a' gives the interpolated values which correspond to the query points in de [9].

The application of cubic's spline interpolation for calculating the respective market power of generation companies on all busses for any given load or operating condition is implemented on a sample IEEE 14 bus test system. This system consists of four generator busses and an additional slack generator at bus number 1 in addition to the nine load busses. The interconnection of the system is accomplished with 20 transmission lines.

In Figure 8, the operating condition is such that the total load is increased by 10% from the base case. The fast and accurate calculation of the market power at any given operating point of the generator may serve or help the principal purposes of various bodies like the GENCOs, DISCOs and ISOs. The knowledge of market power for any given operating condition will enable these above bodies to take suitable actions to change their own operating points in

Figure 8. Normal case versus increase in load by 10%.

order to fulfill their objectives. Figure 8 represents the interpolation plot for the case when load is increased by 10%.

References

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10.1109/TPWRS.2015.2477426

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[9] https://in.mathworks.com

Kerala, India. IEEE Xplore; 2012. pp. 299-303

actions on Power Systems. August 2004;19(3):1373-1379

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The interpolation is done between the five known operating points which are the maximum generation levels of Gen3, starting from 60 MW in steps of 10 MW. For these operating points, the NMRS values are calculated. As we increase the maximum generation level of a particular generator, it affects the NMRS of its neighboring generators. In this case, we have monitored the NMRS of Gen2 on bus 3 with the increase in the working range of Gen3 to demonstrate this fact. As a result, the base case plot for Gen2 tends to drop or go down as we keep increasing the generation level values for Gen3. As the load is increased by 10%, the NMRS plot shifts up. Thus, it represents an important observation that as the load goes up at a certain time of day in a particular region, then the GENCOs which lie in such a subsystem will have an increased market power. Due to the piecewise polynomials which are attained due to the application of cubic's spline interpolation between the operating points, GENCOs, DISCOs and ISOs can easily take suitable actions to not let anyone take undue advantage of the varying market power due to changes in operating conditions. Thus, it helps in attaining a zero market power. This work has been extended under various system conditions and an elaborate study is made in [10].

Inference: Market power reflects the amount of influence that a company has on the system in which it operates but in power systems Market power is the ability to maintain prices above the competitive levels for a significant period of time. Hence, it is of utmost importance to find the market power of the system under normal and abnormal condition that a system has to face.
