**3. Simulation Results**

We evaluate the proposed method in the case of a simple, single-period market clearing scenario, where supply and demand bids are submitted to energy and positive and negative reserve markets. SRDBs are created for uncertain energy bids and the market is cleared according to the rules described in Section 2.2. We assume that no network capacities or other limitations constrain the trading (in other words we assume a one-node market). We use the reference bid set described in Appendix B.

As the positive and negative uncertainty upper bounds *u*<sup>+</sup> and *u*<sup>−</sup> define the set of uncertain bids (as described in Section 2.1), decreasing these parameters from a sufficiently large value (which initially implies no uncertain bids) may be viewed also as gradual introduction of the uncertain bidder pays principle to the market. In this section, for the sake of simplicity, we assume that *u*<sup>+</sup> = *u*<sup>−</sup> = *u* and analyze the effect of decreasing *u*.

#### *3.1. Social Welfare of the Sub-Markets*

Figure 2 shows how the TSW values of the energy and reserve sub-markets changes as the parameter *u* is decreased from 30% to 1% in 1% steps. As energy bids with uncertainty values over *u* are considered as uncertain bids, the decrease of this parameter implies an increasing number of uncertain bids. When a bid becomes uncertain, it is submitted with the respective SRDBs and the MSCs come into play. Even if the MCPs do not change, it can happen that, thanks to the newly occurring expenses of SRDBs, a formerly accepted energy bid does not meet the MSC conditions and will be rejected.

Regarding the energy sub-market it can be said that decreasing *u* adds additional constraints to the optimization problem (implied by the SRDBs and corresponding MSCs), thus the decreasing TSW in the first plot of Figure 2 is perfectly plausible.

Regarding the reserve sub-markets, the increase of the TSW depicted in the second plot of Figure 2 may be explained with the increasing number of demand bids. As more and more energy bids are classified as uncertain, more and more SRDBs appear in the markets.

As reserve bids do not correspond to physical production but to the allocation of potential production, usually the bid prices are lower compared to energy bids. This is also reflected in the bid set used for the example and described in Appendix B—the prices of reserve bids are lower. Considering that the volume traded on the reserve markets is also lower, this naturally results in a lesser value of social welfare compared to the energy sub-market.

**Figure 2.** (**a**) Total social welfare of the energy sub-market (*TSW<sup>E</sup>*) as the parameter *u* is decreased. (**b**) Total social welfare of the reserve sub-markets as the parameter *u* is decreased. *TSWR*<sup>+</sup> and *TSWR*− denote the total social welfare of the positive and the negative reserve market respectively
