**1. Introduction**

Although modern renewable generators do have improved controllability properties compared to earlier solutions, they still exhibit a higher level of supply uncertainty compared to non-renewable generators. In addition, uncertainty is present in several forms in the power grid. First of all, in addition to renewable sources with fundamental characteristics of production uncertainty (of some level), conventional power plants are also naturally subject to failures and technological issues, which may limit their output from time to time. Furthermore, significant part of the demand corresponds to domestic consumers, the schedule of whom may be predicted only with limited accuracy [1,2].

As supply-demand imbalance causes frequency shift in the power network, certain forms of ancillary services (or 'reserves' to put it shorter) are needed for frequency stability. Activating these reserves in the appropriate time restores power balance and thus network frequency. Ancillary markets [3] are specialized energy-economical platforms, in which commodities connected to ancillary services are traded. Although there is a broad spectrum of ancillary service and reserve types, in this paper we consider reserves used for frequency control. In a typical ancillary market, reserve providers are paid for allocating the required reserves and an additional fee is paid if the reserve is activated as well. According to this, in the current paper (regarding reserves) we consider capacity-allocation paymen<sup>t</sup> (and we are not interested if later the reserve is activated or not and do not consider these activation payments).

Reserves may be classified furthermore into non-event and event driven resources. While non-event driven resources are used to compensate production-consumption imbalances, event driven resources are used in reaction to contingencies and power plant or line outages. In the current article we focus on non-event driven resources and their allocation.

As maintaining the frequency stability of the power grid is the responsibility of the system operator (The terminology may differ as the expressions TSO (transmission system operator) and ISO (independent system operator) are also used for this player. In our case, as reserves will be allocated in the integrated power-reserve auction, we will assume that the operator is in charge not only of the transmission system but also of the auction, so we will use ISO.), it is its task to ensure the allocation of the required amount of reserve via long-term contracts or from the ancillary markets. Ensuring the necessary reserves via long term contracts is by nature more inflexible, as the actual power mix resulting from day ahead power exchanges and its uncertainty properties can not be taken into account. Either the system operator takes a conservative (and costly) approach and allocates a high amount of reserves in long term contracts or uses a mix of long term and short term solutions to account for the actual reserve requirements.

Regarding the general issues of reserve allocation, Reference [4] formulates two general questions: How much reserve should be allocated and who should pay for it? The first problem, in addition to the simple approach presented in the same paper [4], has been a subject to several articles. Following the lead idea of Reference [4], namely that reserve should be purchased up to the point where the marginal cost of providing reserve is equal to the marginal value of this reserve, the article [5] considers the customer outage cost to determine the marginal value of reserve. Regarding more recent approaches, motivated by the increasing market share of renewable sources, stochastic unit commitment based reserve procurement procedure for power systems including wind farms is described in Reference [6], while more or less the same problem is approached by a different solution in Reference [7]. Reference [8] contributes to the same topic by applying a chance-constrained optimization to determine the required amounts of reserve capacity. A robust optimization based method of joint determination of day-ahead energy and reserve dispatch is described in Reference [9]. Allocation of reserve-related costs is however not discussed in detail in these articles.

Regarding the allocation of these costs, which is discussed less in the literature, the original paper [4] gives two approaches: In addition to the most simple solution, namely '*all consumers should pay a share of the cost of reserve on the basis of their consumption*', it also adds that on the other hand '*the cost of reserve should be shared among the generators on the basis of their contribution to the need for reserve*'. It also discusses the possible scenario when generators forward these cost to their consumers. Regarding the allocation of reserve-related balancing and ramping costs, Reference [10] proposes a unit commitment-based approach, applying the principle of pareto-optimality for the problem. Reference [11] aims to distribute the reserve cost among the most appropriate consumers, applying agent-based modelling and simulation approach. A somewhat similar agent-based approach combined with stochastic unit commitment for the reserve cost allocation problem is presented in Reference [12]. The two latter papers both use the concept of *demand factors* (first defined in Reference [13]) to characterize the reliability level of customers.

In the current article we follow the second principle formulated in Reference [4] and aim to put the burden of reserve allocation costs to market participants whose activity significantly contributes to the need of reserve allocation. In the context of portfolio-bidding markets, the '*who pays for*' question is typically answered by the principle that the accepted demand bids cover the costs of products, thus we need to introduce any cost-allocation policy in the form of demand bids. This principle can be considered promising as it fits into the official market development plans of the European Union. It is stated in the Clean Energy Package that '*all market participants shall be responsible for the imbalances they cause in the system*' and this imposition includes variable renewable energy producers [14]. However, the explicit regulation concerns only balancing markets while the more liquid day-ahead trading platform may remain free of uncertainties. This gap could be filled using a model developed in the current article.

In order to facilitate European market development, the created clearing formulation has to be adjusted to the usual European approach. Thus, in contrast to previous results, which analyzed the problem in a unit commitment framework [15], we consider self-scheduling generators and a purely portfolio-bidding market based framework, consisting energy and reserve markets. We define the concept of supplementary reserve demand bids, which ensure that the owner of any uncertain energy bid, in the case of acceptance, will also automatically contribute to the costs of reserve allocation as well. While uncertainty characterization in the majority of previous literature was focussing to either power plants or customers, in the proposed approach we consider the potential uncertainty of both side of the energy market—both uncertain supply and demand energy bids are considered. Furthermore while previous methods use computationally demanding agen<sup>t</sup> based modelling (as References [11,12]) or include quadratic constraints [10] (or their semidefinite relaxation), we formulate the suggested method as a simple mixed integer linear problem (MILP), which can be efficiently solved, for example, via Benders-decomposition [16] and/or the branch-and-bound algorithm [17]. (Both techniques are widely used to solve problems in the power sector [18–20].) In addition, the method suggested in the current paper uses a single scalar parameter according to which the set of uncertain/not uncertain energy bids are defined. Decreasing this parameter from a sufficiently large value, the market implementation of the method presented may be introduced to the market incrementally.

For the aim of simplicity and clarity, we introduce the proposed concept assuming a period decoupled market, in which no multiperiod block orders or minimum income condition (MIC) orders are present, thus every period may be dispatched independently of the others. This means that it is enough for us to define the framework for a single period and introduce the concepts in this context. Later, in Section 4, we discuss the principles according to which the proposed concepts may be implemented in markets using multi-period block orders or MIC orders.

## **2. Materials and Methods**
