A Novel Cost Allocation Mechanism for Local Flexibility in the Power System with Partial Disintermediation

Abstract

Electricity markets are going through a comprehensive transformation that includes the large-scale appearance of intermittent renewable generators (RGs). To handle the local effects of new RGs on the distribution grid, the more efficient utilization of distributed local flexibility (LF) resources is necessary. However, the optimal market design is not yet known for LF products. This paper investigates a novel cost allocation mechanism in the context of this market challenge. The mechanism is designed to provide several important advantages of peer-to-peer trading without creating barriers to practical application. It provides partial disintermediation. The acquisition of LF remains the responsibility of the DSO, while the financial costs of the transaction are covered on power exchanges (PXs). To provide this functionality, the clearing algorithm of the PX in question has to incorporate a novel feature we call the Payment Redistribution Technique. This technique allows the buyers’ expenses to be larger than the sellers’ income, and the difference is used to finance flexibility costs. Its mathematical formulation is presented and analyzed in detail, considering computational efficiency and accuracy. Afterward, a realistic case study is constructed to demonstrate the operation of the algorithm and its energy market effects.

1. Introduction

The market share of renewable electricity production is growing in the energy mix because of its contribution to improved environmental quality [1] and energy security [2]. However, the transition leads to technical difficulties. Solar and wind power are weather-dependent and intermittent in nature; therefore, their large-scale application requires the enhancement of power system flexibility [3]. Another complicating factor is that, unlike conventional power plants, renewable generators (RGs) are connected to the distribution grid in large numbers [4].

In the context of the liberalized power market, the best allocation mechanism of power system flexibility is an important field of research. It is a very diverse field due to the many different variants of flexibility products. (Reference [5] presents a literature review about flexibility products using ten main criteria.) The main focus of the current paper is local flexibility on the level of distribution grids, but the investigated questions are relevant for flexibility products in general.

Balancing capacity was the first category of flexibility products introduced to the market, even before the recent expansion of renewable generation. Consequently, some of the most basic questions about flexibility markets have originally been formulated for balancing capacity. One of these basic questions asks: who should pay for flexibility?

In practice, the usual answer is that the system operator covers flexibility costs. On the distribution level, this means that the distribution system operator (DSO) procures the needed local flexibility and then collects the corresponding costs from the customers using fixed tariffs (This process is called DSO procurement herein).

The literature provides two alternative approaches for cost allocation. One of them considers market actors according to their contribution to the need for flexibility and requires payment from them on this basis. To do this, the reliability of generators and consumers has to be quantified using a common metric, i.e., an uncertainty factor. A cost allocation method following this outline is presented in [6] based on agent-based modeling and stochastic unit commitment. For markets of the European type without unit commitment, Ref. [7] gives a potential solution using compulsory flexibility bids attached to energy orders and non-convex minimum surplus conditions.

The other main approach in the literature emerges from the observation that both the DSO procurement and the uncertainty-factorized allocation incorporate intermediaries into market transactions. The eventual payment is provided by power consumers in every case; the DSO and the factorized market agents are standing between them and the actual flexibility sources. Disintermediation through the use of peer-to-peer (P2P) trade platforms is expected to enhance transparency and reduce payment delays and transaction lead times [8]. A P2P flexibility market is proposed in [9] using distributed ledger technology and self-enforcing smart contracts as well as Oracles for the purpose of adequate bid matching. Although DSOs remain in this market as flexibility buyers, their role is partially taken over by aggregators who are able to both buy and sell flexibility. However, as is detailed in the conclusion of [9], the opportunities presented by P2P trading schemes are difficult to exploit in practice due to technological, regulatory, and organizational barriers.

Table 1. Most important properties of flexibility cost allocation mechanisms.

Flexibility Cost Allocation Mechanism	Applicability in Existing Market Designs	Possibility of Disintermediation
DSO procurement	✓
[6]	✓ 1
[7]	✓ 2
[9]		✓
present proposal	✓	partially

¹ For markets with unit commitment (North American type). ² For portfolio-bidding markets (European type).

summarizes the most important properties of the three approaches. The most important conclusion is that only the P2P trading mechanism is able to implement disintermediation, but its practical application is not feasible without substantial reforms in existing market designs. Our proposal is developed to provide the most important benefits of disintermediation with only small modifications to the market environment.

The proposed new flexibility cost allocation approach can be considered as a tradeoff mechanism between traditional DSO procurement and P2P trading in [9] with partial disintermediation of the flexibility procurement process. It links the problem to the daily operation of power exchanges (PX) and requires the PX clearing algorithm to include a novel feature: the Payment Redistribution Technique (PRT). The PRT makes it possible to redistribute a part of demand bidders’ expense on the energy market for the purpose of flexible cost financing. It is the only technical novelty of the proposal.

The scientific contribution of the present paper is twofold:

• The exact formulation of the proposed flexibility cost allocation mechanism (including the PRT) is presented and explained in detail. The most important properties of the PRT are highlighted and investigated using an illustrative clearing example.
• The simulation of a realistic application is conducted to demonstrate the expected energy market effects of the proposed PX clearing algorithm in different trading scenarios. The accuracy, feasibility, and practical viability of the new model are discussed in light of the simulation results.

Section 2 presents the proposed cost allocation method along with the mathematical details and most important characteristics of the PRT. Section 3 describes numerical case studies to investigate the market effect of our proposal. The discussion of the remaining research questions and the paper’s conclusion can be found in Section 4 and Section 5, respectively.

2. Materials and Methods

2.1. The Improved Allocation of Local Flexibility Costs

The requirements for future power systems are expected to follow three key principles: decarbonization, decentralization, and digitalization, with an emphasis on the active participation of consumers [10]. These trends are closely connected, and they pose considerable challenges for system operators and customers alike.

As described in the introduction, the growing market share of carbon-neutral RGs leads to the increased need for system flexibility. Furthermore, regulations and centralized routines of DSOs have to be altered to handle the local effects of RGs adequately. This necessity is one of the reasons behind the increased research attention on decentralized autonomous energy systems and supporting market designs [11].

Local flexibility markets lie at the junction of decarbonization and decentralization. While the primary purpose of system-wide flexibility services is usually to secure the systemic energy balance in the presence of RG uncertainty, local flexibility is needed to handle location-dependent technical problems introduced by RGs on the distribution grid, such as network congestion and voltage limit violations [12]. The search for the best market design of local flexibility is a field of intense research with several proposals for allocation methods [13] and regulatory reforms [14]. In general, it is expected that local and regional factors lead to significant differences in market design choices as no “one size fits all” solution exists [4].

The question of allocation mechanisms is also greatly affected by the third overall trend mentioned above: digitalization. Historically, the liberalization of electricity markets was facilitated by the availability of efficient and reliable computation, especially optimization techniques. From energy market clearing [15] through microgrid management [16] to the determination of bidding strategies [17], optimization algorithms have become standard tools for power system actors. Nonetheless, any large-scale application of optimization practically requires a centralized structure. For example, market clearing (bid matching) algorithms operate on previously collected bid parameters and send back the optimal allocation results to participants. This scheme is not appropriate for a decentralized setting with local autonomy. In the case of flexibility procurement, it has already been demonstrated that there can be conflicting interests between local and system-wide flexibility utilization [18].

In contrast, an alternative organizational model emerged in recent years based on direct peer-to-peer (P2P) transactions and digital blockchain technology. P2P trading turns passive customers into active market participants who engage in trading their available energy resources [19]. P2P transactions eliminate all intermediaries; therefore, they can be considered as an ultimate tool of decentralization. However, the existing organization of electricity markets, along with technological and legal obstacles, make the integration of P2P applications difficult. Most of the blockchain projects in Europe’s energy systems fail [20]. As a consequence, there is little interest in local P2P flexibility trading among European regulators [14]. The main focus for them remains on procurement by the DSO to meet the needs of its network.

This paper presents the algorithmic background of a tradeoff proposal between centralized DSO procurement and the P2P trading of local flexibility. Figure 1 illustrates the two extreme cases.

If the procurement process is managed entirely by the DSO, then the DSO in question has to collect additional long-term fees from customers to finance its flexibility purchases. The quality of supplied electric power is enhanced in return. On the other hand, if P2P trading is considered, the customers themselves buy local flexibility from service providers directly. In this scheme, the only role of the DSO is to provide motivation for the purchase, i.e., to specify technical requirements for customers about the needed flexibility. (The DSO should also be involved in the eventual activation of flexibility. Figure 1 is about procurement; the process of activation is not shown).

The compromise is illustrated in Figure 2. It provides partial disintermediation. The technical side of the procurement process, i.e., the operation of the auction platform, remains the responsibility of the DSO. This setup acknowledges the unique technical knowledge of DSOs and mirrors the ancillary service procurement process of transmission system operators (TSOs). On the other hand, it makes any direct blockchain application impossible. To provide the most important advantages of successful P2P applications (the reduction of payment delays and transaction lead times [8]), the proposal does not give any active role to the DSO in the financial settlement. Instead of paying additional monthly or yearly fees to the DSO, power system customers finance local flexibility through the daily clearing process of power exchanges (PXs). The DSO provides only the summarized daily flexibility cost while the corresponding funds are allocated by the redistribution of demand bidders’ expenses on the energy market. Hence, further burdens on the local grid tariff are eliminated. The location where the flexibility costs originate can be adequately represented using a more refined zonal network model, e.g., if each DSO network has its own bidding zone. Furthermore, the PX clearing algorithm in question must include a novel feature: the payment redistribution technique (PRT). The PRT is the only technical novelty in the whole design.

This approach of partial disintermediation is available only because PXs are liquid trading platforms and are also generally much larger than local flexibility markets. Furthermore, an ever larger share of energy trade takes place on these platforms. Several attempts have been made to utilize PX liquidity to support other market platforms. For example, the coupling of national PXs in Europe provides a critical contribution to the efficient allocation of network transmission rights [21]. On the other hand, US markets incorporate balancing capacities and the associated constraints into the PX bidding and clearing processes [22], and there are proposals along similar lines for energy-reserve co-optimization in Europe [23]. The financing of local flexibility costs can be considered another entry in this list.

The tradeoff mechanism and the PRT have been developed during the course of the INTERRFACE H2020 research project funded by the European Union [24]. A short description of the project is given in Appendix A.

2.2. Power Exchange Clearing with Payment Redistribution

The PRT makes it possible for the PX operator to define flexibility costs in each bidding zone. It is assumed that the cost values are provided by the corresponding DSOs. A part of the demand bidders’ expense is removed from the market and dedicated to cover these external costs. This setup is possible because the demand bidders’ overall expense is allowed to be larger than the supply bidders’ summarized income, i.e., demand and supply can have different clearing prices. Otherwise, the allocation rules of submitted orders and the equations of network congestion management remain intact; they are not modified or compromised in any way by the payment redistribution.

The energy markets of PXs are substantially larger than local flexibility markets. Nonetheless, degenerated or erroneous instances can be constructed with overly high external costs that cannot be financed on the PX. The algorithm is designed to provide feasible results in these cases as well. The remaining unpaid costs are assumed to be settled using an external source. External contribution (XCON) variables are introduced for this purpose.

For the sake of brevity and easier understanding, the PRT is incorporated into a simplified PX clearing algorithm herein. The market consists of only simple step bids of energy in a single trading hour. The transmission network is represented by multiple bidding zones with congestion management based on Available Transfer Capacities (ATCs).

In the following equations of the clearing model, the notations of decision variables are presented in uppercase, while the parameters are in lowercase.

$$max\left\{{\displaystyle \sum }_{d}A{Q}_d\cdot p_d-{\displaystyle \sum }_{s}A{Q}_s\cdot p_s-{\displaystyle \sum }_{z}fcos{t}_z-pfactor\cdot {\displaystyle \sum }_{z}XCO{N}_z\right\}$$

(1)

$\forall z:$

$${\displaystyle \sum }_{z_d=z}A{Q}_d-{\displaystyle \sum }_{z_s=z}A{Q}_s={\displaystyle \sum }_{t{o}_l=z}T{Q}_l-{\displaystyle \sum }_{fro{m}_l=z}T{Q}_l$$

(2)

$${\displaystyle \sum }_{z_d=z}F{P}_d+XCO{N}_z=fcos{t}_z$$

(3)

$$XCO{N}_z\ge 0$$

(4)

$\forall l:$

$$-atcne{g}_l\le T{Q}_l\le atcpo{s}_l$$

(5)

$$MC{P}_{t{o}_l}-MC{P}_{fro{m}_l}>0\to T{Q}_l=atcpo{s}_l$$

(6)

$$MC{P}_{fro{m}_l}-MC{P}_{t{o}_l}>0\to T{Q}_l=-atcne{g}_l$$

(7)

$\forall d:$

$$0\le A{Q}_d\le q_d$$

(8)

$$A{Q}_d>0\to CC{P}_{z_d}\le p_d$$

(9)

$$A{Q}_d<q_d\to CC{P}_{z_d}\ge p_d$$

(10)

$$A{Q}_d>\frac{q_d}{2}\to F{P}_d=\left(CC{P}_{z_d}-MC{P}_{z_d}\right)\cdot q_d$$

(11)

$$A{Q}_d\le \frac{q_d}{2}\to F{P}_d=0$$

(12)

$\forall s:$

$$0\le A{Q}_s\le q_s$$

(13)

$$A{Q}_s>0\to MC{P}_{z_s}\ge p_s$$

(14)

$$A{Q}_s<q_s\to MC{P}_{z_s}\le p_s$$

(15)

The indices of demand bids, supply bids, network interconnections, and bidding zones are denoted by d, s, l, and z, respectively. AQ_k, p_k, q_k, and z_k are the allocated quantity, bid price, bid quantity, and bidding zone of any demand or supply bid k (both d and s can stand in the place of k). XCON_z is the necessary XCON in bidding zone z. The penalty factor for XCONs is denoted by pfactor. FP_d is the flexibility payment (FP) of demand bid d, while fcost_z is the zonal flexibility cost. Each network interconnection l has a nominal direction in the model. Considering this fact, atcpos_l and atcneg_l can be interpreted as their ATCs in the positive and negative direction, while from_l, to_l, and TQ_l are their starting zone, ending zone, and transferred quantity, respectively. CCP_z and MCP_z are the zonal clearing prices for demand and supply bids: the consumer clearing price (CCP) and the market clearing price (MCP). Notations are summarized in Appendix B.

These equations and variables are formulated in a way that follows the structure of the COSMOS algorithm [25]. COSMOS is an important precursor of the current pan-European clearing algorithm, EUPHEMIA [26].

We will demonstrate the operation of the PRT with a small example later in this section. Nonetheless, a basic explanation for each equation is presented herein.

The objective function (1) of the clearing algorithm is called social welfare (SW). Market clearing algorithms usually define SW as the difference between the overall utility of demand (the first summation in (1)) and the overall cost of supply (the second summation in (1)) [23]. The subtraction of the third term is included because flexibility costs are covered by bid surplus removal, while the fourth term is needed to minimize XCON variables, i.e., to maximize the portion of flexibility costs that are covered by actors on the market. The freely selected pfactor must be large enough to achieve this target.

The zonal balance of demand and supply allocations is enforced by (2). The exact value of the flexibility cost as the sum of contributions (FPs and XCONs) is specified in (3) for each zone. This equation ensures that every bidder contributes only to the flexibility cost of its own zone. Zonal XCONs are constrained to be non-negative (4) to prevent any attempts of the solver to increase SW by misusing the penalty term in (1).

The transmission limits of network interconnections are formulated in (5). As (6) and (7) dictate, price differences along an interconnection are possible only if the ATC in the direction pointing to the more expensive bidding zone is fully exploited. Note that MCPs provide the basis for this comparison. CCPs have no role in congestion management.

Marginal allocation rules are specified in (8)–(10) for demand bids and in (13)–(15) for supply bids using the corresponding clearing prices. The FPs of demand orders are determined in (11) and (12) using an approximation. The exact FP definition formulas contain bilinear terms, i.e., products of decision variables on the right side of the equality.

$\forall d:$

$$F{P}_d=\left(CC{P}_{z_d}-MC{P}_{z_d}\right)\cdot A{Q}_d$$

(16)

The bilinear terms are both continuous and non-convex; therefore, their presence makes these equations unavailable in any efficient optimization algorithm. The approximate calculation of (11) and (12) is accurate if the bid in question is fully accepted or fully rejected; it leads to inaccuracy if the bid is partially accepted.

2.3. Clearing Example

Consider a simple market with the submitted orders specified in

Table 2. Parameters of submitted orders in the clearing example.

Name	Side	Quantity (MWh)	Price (EUR/MWh)
DO1	demand	15	120
DO2	demand	50	70
DO3	demand	15	40
DO4	demand	30	35
SO1	supply	60	20
SO2	supply	15	30
SO3	supply	25	60
SO4	supply	10	80

. This market has a single bidding zone with a 900 EUR flexibility cost.

The price curves of this small example are drawn in the diagram of Figure 3. Demand and supply bid curves are shown in blue and red, respectively. Flexibility payments are highlighted in magenta.

Without the flexibility cost and the PRT, the optimal clearing solution would be trivial: the intersection point of demand and supply curves would provide the total allocated quantity (75 MWh) and the appropriate MCP (40 EUR/MWh). SW would be 4050 EUR.

In our case, the optimal solution is different because the 900 EUR external flexibility cost is financed by the FPs of energy demand bids as specified in the proposed clearing formulation (1)–(15). This allocation is shown in Figure 3. The total allocated quantity is only 65 MWh, and the prices for demand and supply bids deviate considerably. The CCP is 43.846 EUR/MWh, while the MCP equals 30 EUR/MWh. As shown in the diagram, the 13.846 EUR/MWh price difference for the 65 MWh quantity is adequate to cover the 900 EUR flexibility cost. The SW is only 3050 EUR, partly because the flexibility cost is subtracted from the earlier value and partly because the surpluses of the bids between the 65 MWh and 75 MWh allocated quantities are lost.

It is worth noting that although the flexibility cost is financed by the FPs of demand bids, the supply side has its implicit contribution. In this example, CCP is higher than in the case without PRT, but the MCP is also modified: it is lower. The curtailments of demand and supply surpluses both contribute to the payment of the flexibility cost.

2.4. Demonstration of Non-Convexity

The investigated market does not allow the use of non-convex order types such as blocks or complex orders [26]. Still, the clearing formulation (1)–(15) does not define a convex mathematical problem. The objective function is linear but the constraints presented as logical consequences, i.e., (6), (7), (9)–(12), (14) and (15), assume the incorporation of discrete variables.

For the sake of easier understanding, the discrete auxiliary variables are not explicitly specified in the formulation. They appear when the logical conditions are transformed into linear constraints as needed by the solver algorithm. The transformation uses the bigM technique that introduces variables to indicate the truth values of logical premises. The indicator variables are, therefore, discrete binaries, i.e., they equal either one or zero (A more detailed description of the bigM technique can be found in the appendix of [23]). The clearing model (1)–(15) belongs to the category of mixed integer linear problems (MILPs).

It would be advantageous if the same functionality could be formalized as a much simpler continuous and convex linear problem (LP). However, this task is not possible. To verify this impossibility, we demonstrate the non-convexity of the clearing example.

In this example, the overall FP of demand bids can be calculated in three steps for any allocated quantity:

• It has to be noted that supply and demand allocations are the same because there is only a single bidding zone without network interconnections (2).
• The CCP and the MCP are determined from the bid allocations as (8)–(10) and (13)–(15) dictate.
• Bid FPs are calculated using the formula in (16) and then summarized. This way, the potential inaccuracy of (11) and (12) is avoided in this analysis.

The results of this calculation are presented in Figure 4 for each relevant allocated quantity (magenta line). For allocations above 75 MWh, the overall FP values are not shown because they are negative and, therefore, irrelevant in this assessment. Vertical sections of the magenta curve are the consequences of the fact that certain allocations can correspond to different CCPs and MCPs, and, therefore, there are indeterminacies in the total FP as well.

One of the main insights coming from the diagram in Figure 4 is that the overall FP has a maximal value. If 60 MWh is allocated with a CCP of 70 EUR/MWh and an MCP of 20 EUR/MWh, then a flexibility cost of 3000 EUR is covered. However, if the external cost is specified to be larger than 3000 EUR, then no allocation exists to finance it entirely. This is the reason why XCON variables are necessary: without them, a large flexibility cost parameter would make the whole clearing problem infeasible. Although the PRT is intended for applications where market liquidity is abundant and overly large flexibility costs appear only in erroneous cases, the certain delivery of feasible solutions, even in these cases, is very important.

The other crucial insight from Figure 4 can be contemplated if one considers the actual flexibility cost of the clearing problem (900 EUR), as highlighted in grey. The points where the 900 EUR line intersects the flexibility payment curve are where (3) is satisfied. Intersection happens four times: at total allocations of 9 MWh, 15 MWh, 18 MWh, and 65 MWh. Since (5)–(7) are ineffective due to the lack of network interconnections, (3) is the last constraint to take into account. This means that all four points are equally feasible, and the 9 MWh, 15 MWh, and 18 MWh points are ignored in the end only because the 65 MWh allocation—as presented in Figure 3—provides the largest SW.

The emergence of four discontinuous feasible points proves and demonstrates the non-convexity of the clearing example. Considering this non-convexity, any LP formulation of the problem is impossible. On the other hand, the MILP of (1)–(15) can be viewed as an efficient mathematical model because MILPs are reliably solved by state-of-the-art solvers such as CPLEX [27] and Gurobi [28].

2.5. Inaccuracy Assessment

In the original clearing example, the approximate FP calculation of (11) and (12) yields the same result as the exact formula (16) because none of the demand bids are accepted partially. To inspect a case when inaccuracy occurs, the example must be altered: flexibility cost is reduced from 900 EUR to 600 EUR.

The smaller flexibility cost leads to a larger SW (3450 EUR), as expected. The corresponding optimal allocation is illustrated in Figure 5 in a layout similar to Figure 3. The CCP is lower than in the original case (40 EUR/MWh), while the MCP is higher (32.5 EUR/MWh). In general, the allocation is closer to the solution without external cost, i.e., to the intersection point of demand and supply price curves.

The bid called DO3—the one at the 40 EUR/MWh price level—is accepted partially in the optimal solution: 10 MWh of its 15 MWh quantity is allocated. Since the acceptance ratio is larger than 1/2, (11) determines FP as if the bid would be fully accepted. (For the same reason, (12) is inactive.) The FP of DO3 is calculated to be 112.5 EUR despite the fact that the actual available payment is only 75 EUR.

The consequence of this inaccuracy is that the solver falsely perceives that the flexibility cost is covered. Meanwhile, an imbalance, i.e., a sum of missing money, appears (37.5 EUR) that is not paid by anyone on the market. In this case, 6.25% of the external cost has to be drawn from a special dedicated fund.

The modified clearing example leads to a large inaccuracy compared to the size of the market (the missing sum is more than 1% of the SW). Fortunately, under realistic circumstances, inaccuracy is expected to be much smaller than in this example. The reason for this expectation is that real markets handle a large number of submitted demand bids and each of these realistic bids contains only a small fraction of the overall demand quantity. In most cases, either zero or one of them is accepted partially due to marginal allocation; therefore, the ignored partial allocation is small compared to the whole market.

3. Simulation Results

3.1. The Inspected Market

The simulation assumes the introduction of a new electricity trading platform in Romania. This daily trading platform divides the Romanian grid into eight sectors according to the territories of the eight DSOs and includes one bidding zone for the market actors in each sector (see Figure 6). As suggested in the introduction, this setup makes it possible to identify the source locations of flexibility costs.

Historical market data are obviously not available for this new market. The data of real submitted bids of Romanian day-ahead (DAM) and intra-day (IDM) markets have been used to construct the simulation. The clearing results will be analyzed for a quarter-hour between 19:00 and 19:15 on 1 June 2019.

Since the DAM and the IDM consider Romania as a single bidding zone, the main challenge was to assign the bids to one of the eight new zones. For the DAM bids, this task is performed in three steps:

• The bids are sorted according to the bid prices (supply and demand are handled separately).
• Bid quantities are broken up into pieces smaller than 1 MWh. Small bids are created from these pieces.
• The price-sorted small bids are distributed among bidding zones using a fixed sequence repeatedly.

This procedure is designed to create zones that have similar market structures but characteristic deviations in prices. The overall quantity of IDM bids is much smaller; therefore, they are assigned to bidding zones randomly (according to uniform distribution).

In the absence of functional markets of local flexibility, real external cost parameters are not available. Nonetheless, zonal cost parameters are calculated from real market data as well. Instead of local flexibility, submitted bids of the Romanian balancing capacity markets (mFRR and RR) have been used for this purpose. Costs are calculated for the case when half of the reserve supply is allocated. Reserve suppliers are assigned to bidding zones randomly (with uniform distribution again) along with the corresponding costs. Since suppliers have substantially different bid quantities on reserve markets, this assignment leads to unequal distribution of flexibility costs.

Network interconnections are included between bidding zones that correspond to neighboring DSO sectors (see the white lines in Figure 6). In the absence of real data on transmission limits, the ATC of every interconnection is fixed to 10 MWh in both directions.

The constructed order book contains 526 and 578 bids on the supply and demand sides, respectively. The 8 bidding zones are linked by 14 interconnections. The clearing algorithm is implemented in AMPL [29].

3.2. Results of the First Scenario: Basic Settings

The optimal SW of the basic scenario is 75,189.8 EUR. Other main results are presented in

Table 3. Main clearing results of the first simulated scenario.

Bidding Zone	Z1	Z2	Z3	Z4	Z5	Z6	Z7	Z8
Allocated supply (MWh)	74.25	73.8	72.31	72.25	72.08	70.80	69.96	69.68
Allocated demand (MWh)	68.00	68.43	71.56	71.42	73.71	73.56	74.26	74.19
Market clearing price (EUR/MWh)	50.95	50.95	50.95	50.95	50.95	50.95	50.95	50.95
Consumer clearing price (EUR/MWh)	52.83	51.94	51.39	51.82	50.97	61.83	51.01	51.06

.

The allocated quantities of supply and demand show that the bidding zones are constructed to be similar in size. Furthermore, the characteristic zonal deviations of bid prices are also visible: Z1–Z4 are exporting energy while Z5–Z8 are importing energy.

Every bidding zone has the same MCP: 50.95 EUR/MWh. This is possible because network transmission limits are not binding in this case. As Figure 7 illustrates, the transmitted quantities are smaller than 10 MWh on every interconnection. (Dotted lines denote the interconnections with zero transmission.) However, even without congestion, the demand bidders pay substantially different CCPs in different bidding zones because zonal flexibility costs are financed using the PRT. Figure 8 shows that the differences between CCPs and MCPs are strongly correlated to flexibility costs. This is expected because the allocated demand quantity is similar in the eight zones (see Table 3).

3.3. Results of the Second Scenario: Zero Flexibility Costs

To investigate the market effects of flexibility cost financing (and its implementation with the PRT), a modified scenario has been created with zero flexibility costs. All the other parameters of the basic scenario remain the same, including the quantities and prices of submitted bids and the limits on network transmission.

The optimal SW, in this case, is larger: 76,293.7 EUR. Since only costs are removed from the basic problem, this larger value is expected. Other main results are summarized in

Table 4. Main clearing results of the second simulated scenario.

Bidding Zone	Z1	Z2	Z3	Z4	Z5	Z6	Z7	Z8
Allocated supply (MWh)	73.97	73.93	73.99	72.25	72.08	69.35	69.96	69.68
Allocated demand (MWh)	68.05	68.43	71.56	71.42	73.71	73.59	74.26	74.19
Market clearing price (EUR/MWh)	50.95	50.95	50.95	50.95	50.95	50.95	50.95	50.95
Consumer clearing price (EUR/MWh)	50.95	50.95	50.95	50.95	50.95	50.95	50.95	50.95

in a layout similar to Table 3.

The most conspicuous difference compared to Table 3 is that CCPs are equal to MCPs in all bidding zones. Otherwise, the results of the two scenarios are quite similar: the uniform MCP of 50.95 EUR/MWh remains the same, and the export-import pattern of the bidding zone does not change either. Zonal allocated quantities are slightly modified in several cases. The general takeaway is that the overall flexibility cost of this market is relatively small, i.e., it can be easily covered by the PRT without severely disturbing the energy market.

Since the MCP is identical in the first and second scenarios, the overall surplus of the supply side is identical, too. The differences in allocated supply quantities belong to at-the-money bids; therefore, they do not affect bid surpluses. This result means for the first scenario that—in contrast to the modified clearing example of Figure 5—the surplus of the demand side covers all of the flexibility costs.

In general, the distribution of surplus reduction mainly depends on the price elasticity of order curves. The more elastic the order curve is, the less surplus is taken away by the PRT. For the simulated Romanian market, the presence of at-the-money supply bids means that the supply is perfectly elastic (allocated quantities can be changed even without altering the price); therefore, the surplus of the supply side remains intact. For the small clearing example of Section 2, both the supply and demand curves are inelastic at certain relevant quantities (at 75 MWh and 65 MWh, respectively); therefore, the surplus reduction is shared.

The inelastic nature of the demand curves leads to solutions in which the CCP intersects demand curves at vertical sections, i.e., individual demand bids are not accepted partially. Without partially accepted demand bids, the approximate Equations (11) and (12) are equivalent to the exact formula (16). Thus, the solutions of all three simulated scenarios are entirely accurate.

3.4. Results of the Third Scenario: Network Congestion

In the first basic scenario, the transmission capacity of the network was large enough to allow the uniformity of MCPs across all bidding zones. To investigate the phenomenon of network congestion and its potential interference with the PRT, the third scenario prescribes smaller transmission capacities. Instead of 10 MWh values for all ATCs, the new problem uses 2.5 MWh values. All of the other parameters are identical to their equivalents in the first scenario.

SW is reduced compared to the basic variant: it equals 75,185.5 EUR. The reduction is expected because transmission limits, i.e., a subset of the optimization constraints, became stricter. Other clearing results are presented in

Table 5. Main clearing results of the third simulated scenario.

Bidding Zone	Z1	Z2	Z3	Z4	Z5	Z6	Z7	Z8
Allocated supply (MWh)	73.05	73.43	72.31	70.67	72.4	72.2	70.64	70.48
Allocated demand (MWh)	68.05	68.43	71.56	71.42	73.71	73.56	74.26	74.19
Market clearing price (EUR/MWh)	49.92	49.92	50.06	50.06	51.91	51.91	51.91	51.91
Consumer clearing price (EUR/MWh)	51.79	50.91	50.50	50.93	51.93	62.79	51.97	52.02

.

The three different MCP values imply that congestion happens on several lines in the optimal clearing solution. Figure 9 presents the details similarly to Figure 7. Congested interconnections are highlighted in red. The general direction of energy flow remains the same (from north to south), but network bottlenecks lead to higher prices in the southern bidding zones. In contrast, Z1–Z4 are cheaper than in the first scenario.

Do the changes affect the operation of the PRT? The other rows of Table 5 show that the effects are minimal. The allocated demand quantities are almost identical to the results in Table 3; the only difference is a very small increase in Z1. Consequently, since the flexibility cost is fixed, the difference between CCPs and MCPs is also very similar to basic results. Figure 8 is practically relevant for the third scenario as well as the first one because the deviation in the CCP-MCP price difference of Z1 is smaller than the rounding error.

4. Discussion

4.1. Comparison to Other Flexibility Cost Allocation Methods

The introduction of the present paper describes the research gap the proposed new flexibility cost allocation method attempts to fill. In addition to this theoretical basis, the advantages of the proposal compared to the alternatives should also be demonstrated with simulations and practical case studies. However, this demonstration lies outside the scope of the current paper. Our contribution herein is the introduction and preliminary analysis of partial disintermediation and the PRT. The case study in Section 3 is presented to justify its feasibility from the energy market point of view.

The need for a study that compares the tradeoff mechanism of partial disintermediation to full DSO procurement provides an area of further inquiry. There are several immediate difficulties in this comparison:

• Since there are only a few operating local flexibility markets in the experimental phase of development, the simulation of full DSO procurement itself is a challenge. Trading platforms and algorithms suggested in the literature (such as [13]) might be used for this purpose.
• The lack of realistic bid data of local flexibility makes the exact results of any simulation questionable.
• To assess the performance of partial disintermediation, the flexibility cost allocation methods should be compared on the market design level, including several trading platforms and their potential interference. Thorough econometric investigations are probably needed to support this kind of assessment.

On the other hand, the direct comparison with the P2P flexibility markets (such as [9]) is not critical. The advantages of the tradeoff mechanism are adequately verified because incorporating the PRT into PX clearing is certainly easier to implement in practice than overcoming the many obstructions around P2P flexibility trade.

4.2. Additional Features for the Power Exchange Clearing Algorithm

In actual practice, PX clearing algorithms provide several additional features compared to the simplified trading platform investigated in this paper. In Europe, several non-convex order types, as well as flow-based congestion management, are incorporated in the pan-European day-ahead market clearing [26]. The use of non-convex order types, such as block orders, also implies that the algorithm will handle bids for an entire day instead of the hourly resolution assumed in this paper.

The equations of the PRT are compatible with most of the additional features if the mathematical formulation of the clearing problem follows the approach established by the COSMOS algorithm [25]. In the framework of COSMOS, the bid pricing rules are specified in “if-then” expressions similar to (6), (7), (9)–(12), (14) and (15) of the presented model. The available additions include complex orders with load gradient conditions [30], minimum income conditions in several versions [31], and unified purchase prices (UPPs), as well as flow-based transmission limits [32].

In essence, the UPP calculation of [32] is a precursor to the PRT presented herein. To allocate demand quantities according to a single clearing price (the UPP) in the case of network congestions, a redistribution of expenses from more expensive zones to cheaper zones is needed. Thus, this model already includes the separation of demand and supply prices and a different kind of payment redistribution in an energy-only trading environment.

Despite the mathematical compatibility of the listed market elements, their simultaneous inclusion may cause numerical difficulties for the clearing algorithm. Further development and relevant experiments are needed to finalize the common formulation with all features.

4.3. Other External Costs

The proposed algorithm, as described by (1)–(15), does not include any restriction that is specific to local flexibility. Accordingly, the PRT can be applied to provide funding for other products, too. The only condition is that the external costs must be small enough not to disturb the basic trading process of the PX in question. Due to the introduction of XCON variables, the algorithm is able to provide feasible solutions even in this case, but these solutions do not cover the full cost. Furthermore, the quality of these solutions is expected to be low from the viewpoint of the energy market.

A particular candidate for PRT financing may be the procurement of balancing capacity. Instead of the current practice of full TSO procurement, the alternative mechanism with partial disintermediation (similar to the scheme of Figure 2) may be applied for these services.

5. Conclusions

This paper has investigated a novel mechanism for local flexibility cost allocation considering overall power system trends as well as existing regulations and practices. The mechanism is a tradeoff between traditional centralized procurement and peer-to-peer trading. In the new scheme, the acquisition of flexibility remains the responsibility of the DSO while the financial side of the transaction is taken over by a daily PX trading platform, i.e., local flexibility costs are covered on PXs. High transaction lead times associated with DSO fees are alleviated in this mechanism.

To provide this functionality, the clearing algorithm of the PX in question has to incorporate a novel feature, the PRT. The PRT allows the clearing prices of demand and supply to deviate from the market. The expense of buyers is larger than the income of sellers, and the difference is used to finance the external costs. The mathematical formulation of the PRT has been presented and analyzed in detail.

A realistic case study has been constructed and described to demonstrate the operation of the PRT and to investigate its effects in the context of PX trading. It has been found that the distribution of flexibility cost to bidders is highly dependent on the actual bid curves, i.e., the new cost may lead to curtailments in both demand and supply surpluses. Since the external costs are expected to be small compared to the size of PXs, the PRT should have only minimal effects on energy trade and network transmission. This expectation is verified by the numerical simulation.

The remaining questions about the proposals in this paper have been discussed with special emphasis on the potential practical application in Europe. Promising research directions include the development of the clearing model to incorporate other European market features and the assessment of applying the PRT to finance other systemic costs.