Investigating the impact of distributed energy resources on market power of strategic utility corporation

Market participants may employ potential market power improperly in energy trading. On the other hand, integrations of distributed energy resources (DER) are highly complex since it entails the optimal coordination of a diverse portfolio of DER under multiple sources of uncertainty. A large number of possible stochastic realisations that arise can lead to complex operational models that become problematic in real-time market environments. Although recent works have explored the impacts of DER on numerous aspects of grid operation and planning, its role in imperfect competitive energy markets has not been investigated nonetheless. This article proposes the theoretical and quantitative analysis of the withholding strategies for the utility corporations with the integration of DERs for the first time and the corresponding market power effects on utility corporation's profits and market prices. The quantitative demonstration is supported by a bi-level model with the optimal company profit for the upper level and the market clearing for the lower level. This bi-level problem can be solved directly when a single-level problem is obtained with a mathematical program with equilibrium constraints (MPEC). Numerical studies are implemented on a wholesale market with the day-ahead horizon and hourly resolution.


Research motivation
Market participants such as generation corporations and transmission corporations may be able to manipulate market prices away from their competitive levels and benefit from it, i.e. market power abuse. Evaluating market power has never been a simple task, particularly in energy markets. Certain market issues that arise from specific characteristics of energy such as restricted demand response (DR), time-and volume bounds and restrictive entry barriers, make exercising market power in energy markets notably possible and detecting it extraordinarily difficult [1].

Literature review
Market deregulation back within the past decades has transformed energy market. The results of this transformation are emerging of organised marketplaces. An organised energy market is a centralised platform where market participants can trade energy in a direct manner and pay or receive money for the delivered power. Most trades are implemented with power exchanges (PX) or brokers. With the growing integrations of renewable resources, the majority of trading went from the long-term to short-term such as day ahead and real-time market. The day ahead market is one of the major areas of energy trading where sales and buy contracts are created between seller and buyer for the delivery of power for the following day. Market participants submit their orders electronically through the trading platforms after which supply and demand are compared and the market price is calculated for every hour of the following day. In addition, PXs enable intraday market (ID) for improving participants' position, which can be implemented as continuous trading or auction. ID offers market participants the opportunity to trade energy hourly or in other products up to a few minutes prior to delivery. On the other hand, some PXs offer ID auctions where the market participants can submit additional supply offers or demand bids and after the market clearing time, the results are obtained by economic optimal order principle [2]. Energy markets are better described in terms of imperfect competitive instead of perfect competition. Utility corporations hold generations considering strategic bidding in the power grid are able to affect the market prices like locational marginal pricing and increase their profits beyond the fully competitive equilibrium levels. This exercise of market power leads to higher price levels and loss of social welfare [3]. One of the recently developed strategies for exercising market power was on ramp-rate in the way of adjusting the generation bids [4]. On the other hand, if there is a line congestion in the transmission system, the final clearing price may increase accordingly as well [5].
The feature of the emerging smart grid paradigm involves the integration of a large number of distributed energy resources (DER), such as flexible loads, renewable, and controllable microgenerators and energy storage (ES) units, in order to support the economic operation of the future low-carbon power system. However, the large number, small individual size, and inherent stochasticity characterising these DER have complicated system scheduling and market coordination. In the meanwhile and in line with the emerging smart grid paradigm, a high penetration of DERs in distribution network is observed [6]. Previous study has shown that DR can limit generation corporations' ability to exercise market power when market prices are high in the way of reducing or shifting load in the imperfect energy market [7][8][9]. However, the single time period modelling of those works are not suitable for analysing the integration of DERs, due to its time coupling and power coupling with renewable resources. Various works have evaluated the benefits of DERs on numerous aspects of power grid operation and planning [10][11][12][13][14][15][16][17][18] and indicated the potential benefit in the market environment in the near future [19][20][21][22]. To the best of author's knowledge, however, the market power, especially the effects on market prices, caused by the integration of DER in the imperfect competitive energy markets has not been investigated nonetheless.

Methodology and contributions
The contributions of this paper are summarised fourfold as follows.
(i) Theoretical model of impact of DERs on market power exercised by utility companies considering generation capacity withholding, which includes physical and economical. (ii) Proposed a bi-level model for the imperfect competitive energy market, the upper level problem represents the strategic utility corporation optimising profit while the lower level problem represents the electricity market clearing process considering the integration of DERs. (iii) Quantitative studies are implemented in a day head market to demonstrate the benefits of DERs in reducing the utility company's profit increase. (iv) The market power effects on utility corporation's profits and market prices with the integration of DERs is analysed for the first time.

Paper organisation
The rest of this paper is organised as follows. Section 2 describes models of supply and demand for market power exercise. Section 3 proposes a theoretical decision modelling of the utility corporation as the bi-level optimisation problem. Section 4 formulates the solution for the bi-level problem. Case studies and illustrative results are presented in Section 5. Finally, Section 6 discusses conclusions of this work. Fig. 1 shows the background of the power system configuration. Generally, storage value can be obtained in the way of providing the greater part of additional balancing required by stochastic wind power outputs. Storage can be used to store generation excesses during windy hours and low demand by charging while releasing the energy by discharging. Similarly, the storage can serve as a regulation resource and enable it to compensate for the variability of solar PV generation. Thus, coupling solar PV and storage will enable more effective power grid management. In this regards, it is necessary to investigate the market power of storage in the integrations of DER in an energy market environment.

Utility company's market power
The major utility company strategic market power exercise is generation capacity withholding, which includes physical and economical ones. The physical capacity withholding implies the amendment within the quantity of energy supplied. The producers hold the quantity of energy they provide, leading to distinct aggregated supply curve and the obtained market price raise. On the other hand, the economical withholding represents the supply prices are higher than the marginal cost (MC) of the generating units. Such strategies are risky because there is no guarantee that the proposed offer will be accepted and, therefore, trade can be implemented. In most cases, the market clearing price is lower than the proposed offer price from a generation corporation [23].
For the generation units, we assume that every utility corporation i holds a single generator, the MC function reported to the system operator, power output P it , and capacity upper bound P i max and lower bound P i min are presented in (1) and (2), respectively: Following the economical withholding model employed in [9], the strategic marginal cost (SMC) function is described by (3), where the value of the decision variable α it ≥ 1 represents the economical withholding strategy employed by utility corporation i at hour t. On the other hand, the physical withholding strategy is developed in (4), the decision variable is set up as β it ≤ 1, represents the physical withholding strategy employed by Utility Corporation i at hour t.
If α it = 1 and β it = 1, utility corporation i participates in the market competitively in the way of reporting its actual marginal costs and quantity of power supplied to the market operator at hour t. If α it > 1, utility corporation i will apply the strategies and reveals higher marginal costs than its actual ones to the market operator at t. If β it < 1, utility corporation i will apply the strategies and reveals lower power quantity than its actual ones supplied to the market at hour t. In this regard, utility corporation i is supposed to set the values of α it and β it by considering the balance between higher market clearing price and lower clearing amount. Moreover, a higher α it and lower β it , will result in raising the market clearing price. In the meanwhile, it will lead to the lower amount sold by utility corporation i, since if corporation supply lower power amount, it may replace i in the merit order and / or the load side and the DER may decrease the demand load at hour t.

Load-side benefit
Following [9], the benefit B t obtained by the load side at hour t is represented by a quadratic function in (5) with the load level D t . The marginal benefit (MB) or willingness to pay the electricity is thus presented as a linearly decreasing function in (6) which expressed the impact of load's self-price elasticity, i.e. the energy consumers are willing to pay a lower price when the load level raises; on the other hand, power purchased by the consumers will decrease when the market price is high. The limits in the load level at hour t are described by (7). The coefficients in (5) and the upper load level bound are time-specific parameters, capturing the differentiated preferences of energy consumers across various hours in the day ahead market [24].

Mathematical model
Recently, [25] discussed the strategy for a DER aggregator in the market environment. In addition, the game-theoretical approach was utilised in [26,27] to model the bidding strategy of DER. Moreover, a distribution company is considered to participate in market trading through strategic bidding [28]. A framework for the day-ahead trans-active market is proposed which includes end-toend power system participants starting from the bulk power ISO and ending at DSO [29]. A transactive energy scheme based on multi-factor evaluation and contract net protocol is proposed to determine energy trading strategies among prosumers in the distribution network [30]. Here, the market-based operation of strategic utility corporations is proposed as the bi-level optimisation model (8)- (25). The framework of the proposed bilevel model is shown in Fig. 2. The optimal offering strategies are employed by utility corporations in order to maximise the profit in upper level model. The maket price λ nt in (8) is subject to the lower level model which is representing the day ahead market clearing process. Thus, the two problems are coupled with market price λ nt . The economical withholding and physical withholding offering strategies in the upper level problem will have the impact on the objective function of the lower level problem. On the other hand, the generation bid obtained by the upper level model will affect the objective function of the lower level model. The objective function (8) of the upper level problem expresses the profit of the utility corporations, i ∈ Ψ n identifies the strategic utility company i located at bus n. This objective is subject to the bounds of the strategic offer variables (9) and (10) and the lower level model (11)- (25). The latter represents the market clearing process at every hour t, maximising the social welfare (11), subject to the constraints including economical withholding strategy (12), physical withholding strategy (13), power balance (14) (the Lagrangian multipliers of which represent the market clearing prices), strategy generation, non-strategy generation, and load limits (15)- (17), m ∈ Θ n identifies the buses m connected to bus n at all hours. The ES is considered as the representation for DER since it can charge or discharge to formulate bidirectional power flow to the grid, the operational constraints of DERs are expressed in (18)-(22), including energy balance in an ES, the energy capacity limits, the charge and discharge capacity limits, and the final state of charge (SOC) requirement. The power flow capacity limits, bus phase angle limits, and reference bus requirement are outlined in (23)- (25).

Model transformation
Recently, complementarity theory is appealing to tackle bi-level model problem in electricity market [31,32], which can transform the bi-level problem into a single level MILP problem. Therefore, this paper follows the similar approach to solve the proposed bilevel model within the manner of the lower level problem is represented by its KKT optimality conditions that is enabled by the continuity and convexity of the lower level model. As shown in Fig. 3, the lower level model may be utterly replaced by its KKT conditions and enclosed as constraints of the upper level model. This converts the bi-level problem to a single level MPEC [33] that is developed as follows in (26)-(56).
where u is an auxiliary 0 − 1 variable and M is a big enough positive integer.
(ii) Linearisation of Bilinear Terms: The primal problem, dual problem and the strong duality equality are utilised to obtain the exactly equivalent linear term of the bilinear term ∑ i ∈ Ψ n t λ tn P it S .
The linearised representation corresponding to the original bilinear term is expressed in (58), and all the items on the right hand side of the equation are linear combinations. Then a linear objective function is presented in (59).

Case studies
A modified IEEE 6-bus power system shown in Fig. 4 is used to demonstrate the performance of the proposed model. DR and ES are included here as the DER. The proposed optimisation model can be expressed as a MILP problem. A highly efficient commercial solver CPLEX [34] is employed to solve the developed model. Table 1 provides data for the generations presented in this case study. Each column refers to a particular generation unit. The first row expresses the type of utility corporations, i.e. 'S' represents generations belonging to the strategic utility corporations and 'O' represents generations of non-strategic utility corporations. The second row contains the power capacity of each generator with their associated production cost. Table 2 provides demand data for each period of time (1 to 24). The first column outlines the bids (energy and price) with their associated forecasted load in the second column. Total load is shared among the buses as 20%, 40, and 40% for bus 3, bus 4, and bus 5, respectively. The assumed values of the ES operational parameters are modified from [35] and given in Table 3.

Solution analysis
The locational marginal prices (LMP) for each bus and hour for this case are presented in Fig. 4. As it can be seen from Fig. 5, the peak hours are from 10th hour to the 23rd hour during the day.
The generation physical and economical withholding are shown in Figs. 6 and 7, respectively. As it can be seen for Fig. 7, the economical withholding parameter has the same identical pattern with LMP while the physical withholding parameters are ranging from 0.7 to 1.
The operations of ES are expressed in Fig. 8 and the charge and discharge of ES are shown over the 24 h. To the best of knowledge, the Lerner index (60), formalised in 1934 by Abba Lerner [36], is the only one which can show the market power effects on corporation's profits and market prices caused by the integration of DERs, i.e. profitably raise the market price of electricity over marginal cost. Other market power-related indexes, e.g. Herfindahl-Hirschman Index [37], can only serve as an indicator of the amount of competition among market participant, which is out of the scope of this paper. In this regards, the Lerner index is utilised here to evaluate the market power of strategic utility company. P is the market price set by the firm and MC is the firm's marginal cost. The index ranges from a high of 1 to a low of 0, with higher numbers implying greater market power. For a perfectly competitive firm (where P = MC), L = 0; such a firm has   no market power. When MC = 0, Lerner's index is equal to unity, indicating the presence of monopoly power. The Lerner index for company 1 is depicted in Fig. 9. It is shown that the LMPs, Economical withholding parameter Gamma, and Lerner index have the almost same daily patterns, i.e. the market power of strategic company is higher when the LMPs are high. The resulting profit and power dispatches are shown in Table 4. It is shown that strategic company achieved significant profit compared with non-strategic companies if there is no cap on the economic withholding parameters.

Sensitivity analysis
The exercise of market power by the supply side in the way of economical withholding and physical withhold raises its profit while it reduces the production of strategic utility company since the LMP rise with the market power. Tables 5 and 6 illustrate the increment of the supply side's hourly profit and the decrement of the power outputs driven by the exercise of market power (as determined by the solution of the MPEC problem). Different scenarios of ES capacity are reported in Table 7. Due to the charging activities, ES increases the hourly generation profit. These effects are enhanced when the size of ES capacity is higher. Due to the fact that the negative impact of ES, a control or management strategy is needed in the exercise of market power, which is out of the scope of this paper. We change the transmission capacity limit of lines 1-4 from 80-120 MW. For this lower transmission capacity case, the solution of problem shows that the strategic corporations offer to congest lines 1-4 at some time periods so that strategic corporation    can sell its energy at higher prices. As shown in Table 8, the production of the strategic corporation drops compared to the less congested case while the LMP and market power increase. Due to high LMP, the traded energy of strategic unit drops in the market.

Conclusion
This paper proposes the theoretical and quantitative analysis of the withholding strategies for the utility corporations with the integration of DERs for the first time and the corresponding market power effects on utility corporation's profits and market prices. The quantitative demonstration is supported by a bi-level model with the optimal company profit as the objective for the upper level and the market clearing for the lower level. This bi-level problem can be solved directly when a single-level problem is obtained with a mathematical program with equilibrium constraints (MPEC). Numerical studies are implemented on a wholesale market with the day-ahead horizon and hourly resolution have quantitatively demonstrated the impacts of withholding strategies and the integrations of DERs on the market power in the way of observing market price and production of utility corporations. An increasing storage capacity has been shown to increase the generation profit made by the exercise of market power, a strategy is needed with the coordination of DR, which will be the future work for this study.

Acknowledgments
This work was supported by a Washington State University ESIC seed grant.