Bidding method for wind generation company in nodal power market

In recent years, the increasing integration of wind power has become a critical issue in power system. Owing to the randomness and intermittency of wind generation, it is a big challenge to incorporate wind power into power market operation fairly. To address this challenge, a novel method is presented for wind generation companies to bid in a nodal power market. Wind power output is comprised of two parts, i.e. reliable energy part and uncertain energy part. In the nodal power market, reliable energy bids in single price mode. On the other hand, uncertain energy bids in two-part price mode, which contains adjustment price and energy price. According to the above remarkable features, the authors’ research develops the mathematical model for wind power bidding and design the corresponding market clearing mechanism. Also, the impact of their method on wind power accommodation and social benefit is deeply analysed. Numerical results indicate that the proposed method enables the fair competition among renewable energy generation company in the electricity market; thus, could enhance the integration of wind power while alleviating on providing a subsidy.

Abstract: In recent years, the increasing integration of wind power has become a critical issue in power system. Owing to the randomness and intermittency of wind generation, it is a big challenge to incorporate wind power into power market operation fairly. To address this challenge, a novel method is presented for wind generation companies to bid in a nodal power market. Wind power output is comprised of two parts, i.e. reliable energy part and uncertain energy part. In the nodal power market, reliable energy bids in single price mode. On the other hand, uncertain energy bids in two-part price mode, which contains adjustment price and energy price. According to the above remarkable features, the authors' research develops the mathematical model for wind power bidding and design the corresponding market clearing mechanism. Also, the impact of their method on wind power accommodation and social benefit is deeply analysed. Numerical results indicate that the proposed method enables the fair competition among renewable energy generation company in the electricity market; thus, could enhance the integration of wind power while alleviating on providing a subsidy.
Nomenclature N w number of wind generating units in the system N tr number of traditional generating units in the system N l number of load in the system C w,i offer price of wind generating unit i C tr,i offer price of traditional generating unit i P w,i wind power output of wind generating unit i P l,k power of forecasted load k P max The intensification of environmental problems leads to the rapid development of wind power generation. Since wind is free and inexhaustible fuel without any emissions, it is regarded as a perfect alternative to traditional fossil fuels. According to the statistics, the total installed global capacity of wind power reached 486.8 GW at the end of 2015 [1]. However, certain issues should be considered seriously for high penetration of wind power has a great impact on the operation of power system. Integration of wind power poses a great risk to the reliability of power system and power market, because of its uncertainty and variability.
Researchers explore numerous strategies in order to fully utilise wind generation and reduce wind curtailment which is described in [2]. A new method for wind power forecasting based on Gaussian process is proposed to reduce the uncertainty of wind power output and enhance the stability of power system [3]. Since the contribution of improving prediction accuracy is limited due to the restriction of mathematical technique, researchers and power system operators try new ways from another perspective. Energy storage system (ESS) attracts increasing attention, because the combination of wind generation and ESS can lead to various benefits to power system [4,5].
However, only a small number of researches concentrate on the market-based approach to solve this issue promoting wind power consumption. The market is a fair and effective way to some extent. In traditional energy markets, wind power generations do not participate in the market, and it is treated as a negative nonresponsive load. We call these wind power generations 'price taker', i.e. they have no market power to influence price formation, while accepting the price derived from the energy market. To prevent the wind power generation companies from not meeting power balance of system, researchers propose a new approach called risk-limiting dispatch by considering the stochastic nature of wind [6]. This approach has a great issue to be taken into account, i.e. it will be unreasonable to assume that the wind generation companies have no market power when their penetration is high. Wind generation companies must bid in energy markets such as other classical power generations to form a proper price in this condition.
To design an appropriate market mechanism becomes a critical problem operators have to solve. In [7][8][9], researchers study the design of an energy market and the formation of energy price. However, all of these papers concentrate on the classical generation, renewable energy such as wind power is rarely involved.
We note that increasing wind generations installed lead to power system transmission congestion in addition to power balance problem. Locational marginal price (LMP) is an effective method to solve this problem; it consists of energy cost, congestion cost and loss cost. The different buses have its own LMPs, the differences between buses can relieve transmission congestion naturally. It is beneficial for wind generation company to be allowed to participate in LMP-based markets (nodal markets), from an economical perspective and reliability perspective [10]. The New York Independent System Operator (ISO) and the Midwest ISO take their own measures to allow operators optimise the dispatch of wind generation based on security and economics of power system [11,12].
In this paper, a novel bidding method for wind generation companies in nodal power market is proposed and this paper designs the operation of LMP-based adjustment energy market. Results proved that this new method can reduce operation cost and utilise wind power effectively.
This paper is organised as follows. Section 2 mainly discusses why we should divide wind output into two parts and how we design an adjustment energy market based on LMP. In Section 3, how wind generation companies bid in the energy market and the operation of LMP-based adjustment market. Section 4 shows results of analysis of the proposed model. Conclusions are drawn in Section 5.

Proposed methodology
One of the most critical factors that influence the utility of wind power is its stochastic output. The deviations between expectation and actual output can lead trouble to the operation of power system. While not all of the wind powers are random, i.e. certain part of wind generation output is reliable, especially in some regions with rich wind resources, wind power output can ensure a minimum value. From Fig. 1, we can see that different output blocks divided by red line have a different value in the same period for their various reliabilities. Moreover, the same output level has a different value in different periods. We divided wind generator output into two parts in this paper for convenience without any other impacts to the proposed model's feasibility.
Since the reliable output is deterministic just such as classical generation, it would not do harm to the power system. We can define that this part of wind power has a high quality, and reliable part and uncertain part must be treated differently. Power with high quality is supposed to get a high price, and vice versa. In [13], Du and Wang show us a novel method to estimate the value of different parts of wind power output by layer. The proposed meticulous approach is somewhat sophisticated to use in the energy market. This paper simplifies it and designs corresponding adjustment market.
This proposed adjustment market is unique and based on LMP. Although many markets such as pennsylvania-new jersey-maryland (PJM) and UK electricity market, which have their approaches to solve the power balancing problem, while they have their own limitations. For instance, the UK electricity market keeps power balancing by 'offer and bid'. However, this method cannot deal with the transmission congestion problem. So, this paper takes congestion cost into account and build an adjustment market based on LMP.
The designed market consists of day-ahead (DA) market and the proposed adjustment market. In DA market, wind generation companies offer only reliable part such as other classical generations. The operators need not consider deviations in DA market. Moreover, in adjustment market, wind generation company can nearly determine the accurate output. At this time, wind generation company only offers added output compared with DA reliable part. According to the above statement, the uncertain part deserves the lower price. To balance the added power, traditional generation will reduce their own output by returning some of the money they got in DA market. Wind power can be utilised fully and the operation cost of the power system will be cut through this way.
Subject to: The load demand that is supposed to be inelastic is forecasted before the day: (ii) Transmission power constraint (iii) Constraints of generating units In the calculation of transmission power, we use T called transfer factor matrix which represents the connection between bus power and line power. Moreover, the formula is shown in (5) LMP will be available by solving the linear programming model LMP expression is composed of λ and μ k . After the solvation of this model, these Lagrange multipliers can be available. Since this Loss cost part of LMP is shown in (7). (∂P Loss )/(∂P Gi ) are called incremental transmission losses, which can be calculated by AC flow model. Owing to space limitations, the process of specific speculation is not discussed in this paper.

Adjustment market
In adjustment market, the definition of LMP is different from that in DA market though the calculation model is similar In (8), S i is the profit wind generator except for uncertain part of output and B j is what traditional generators are supposed to return to market because it reduces its power. Subject to: (ii) Transmission power constraint (iii) Constraints of generating units We note that (9) is somewhat different from (2). In (2), the formula means the balance between all generators' power and load, while in (9) the balance is between the added power of wind generations and reduced power over traditional generations. The LMP expression in adjustment market is similar to what in DA market.
We proposed some assumptions in the model without any effect on its universality: (i) Deviations between DA forecast load and real-time load are zero, i.e. the forecasted results are accurate. (ii) In adjustment market, the maximum power wind generator company bid is supposed as real as its real output. Moreover, in the case, we assume that uncertain power of wind generator is about 40% of the reliable part. This proportion would not have an impact on the conclusion.

Case study
In this section, we prove the feasibility and economy of this paper's proposed model and present a case study based on a simple threebus system [14].
In this case, we assume the adjustment cost at a level and based on that wind generators and traditional generators all can get some profit. The assumption has no effect on the model's general applicability.
The three-bus system as shown in Fig. 2 is composed of four conventional generators and a wind generator located at bus 3. Moreover, we can see the detailed data of these generators in Table 1. Wind power generation company has cheap cost for it nearly does not have any operation margin cost. For comparison, traditional generators are also divided into cheap cost generators and expensive generators. Adjustment cost means the cost that the generator expects if you want it to change its output cleared in DA market. Apparently, wind generator wants to raise its output, so the adjustment cost is positive, whereas the traditional generator's adjustment cost is negative, because traditional generators reduce its output and should return some profit it got in DA market.
In Table 2, we can see detailed transmission line parameters. In this case, we concentrate on the benefit of adjustment market, so we lose sight of power loss in power system.
To illustrate the benefits of the method proposed in this paper in the nodal market, we run two simulations in a single period. The first only considers DA market, the second is composed of DA market and adjustment market (AJ market). Tables 3 and 4 show us the results of the case. Note that cleared power of traditional generating unit in AJ market is negative and wind generating power is positive. The power purchase fee in DA market is $31.9667, while after the running of AJ market, the operation cost, i.e. the power charge reduced to $30.9617. It means that   we cut down the operation cost of the system and relieve the uncertainty of wind power in a market method. The price in Table 4 takes account not only the energy part, but also the congestion part of operation cost.

Conclusion
This paper proposed a novel method that wind generation companies bid in nodal market and design corresponding market mechanism.
The uncertainty nature of wind power is a critical problem for power system operators. The case study results illustrate that the method in this paper can effectively alleviate the problems: (i) It relieves the impacts that high penetration of wind generation has on the operation of power system in a market measure. (ii) It can reduce the operation cost of the power system to some extent and alleviate government's pressure on providing a subsidy. (iii) More wind power can be consumed by this design market mechanism.
It is worth mentioning that wind generation company is likely to bid more power than it can provide deliberately to get more profits. So, a penalty mechanism is needed in this market.

Acknowledgment
This work was supported by the Science and Technology Project of Northwest Branch of State Grid Corporation China (no. 52993216000H).