Constrained Optimization as the Allocation Method in Local Flexibility Markets
Abstract
:1. Introduction
- RQ1: How is the optimization problem defined, including all necessary requirements and boundary conditions?
- RQ2: What parameters and constraints need to be considered to reach the optimization goal?
- RQ3: How does the proposed approach differ from existing LFM matching designs?
- RQ4: Can the matching algorithm prove its applicability in a realistic situation?
2. Market Design of LFMs
2.1. Grid-Oriented Flexibility Allocation as Matching Markets
- The topological grid location of available flexibility is relevant to solving specific congestions and has to be integrated in the matching.
- Many flexibility calls are associated with boundary conditions.
- The reliability of the flexibility call is essential for the demand side: congestion management measures are defined as emergency measures. A market-based solution has to meet strong requirements in planning security.
- Offered price for flexibility, which can be individually specified by the plant operators for each time step in schedule offers (see Section 3.3.1).
- Available power for every 15 min slot of the contraction period (i.e., the next day), which is provided by the active marketers or determined by the aggregation algorithm for long-term contracted asset pools (see Section 3.3.1 and Section 3.3.2).
- Constraints and boundary conditions regarding power and call restrictions that can be further voluntarily indicated for schedule offers or are predefined by the platform as a condition of participation for long-term contraction (see Section 3.4).
- Effectiveness of flexibility offered to the congestion, which is defined as the impact of power adaption to the overloaded grid component by the resulting change in current or voltage. Therefore, an approach to determining a linearized relation between the congestion and flexible assets without the need of continuous load flow calculations and grid data was developed, as described in [8] (see Section 3.4).
- A regional order book assumes a constant effectiveness of all FOs on the congestion. According to [8], the effectiveness in a mid-voltage grid varies significantly and has to be integrated in the matching process.
- In a regional order book, the traded flexibility is the deviation from a baseline. In this case, it is not possible to consider restrictions of the supply side.
- From a system perspective, an optimal matching solution on the LFM must be found not for a specific point in time, but for a time period (i.e., the entire day of contraction with 96 time steps of 15 min each in a day-ahead market process), while considering the restrictions of flexibility offers and demands. Therefore, an iterative determination of the optimum combinations of flexibility offers is necessary to efficiently meet the demand.
2.2. Literature Review and Meta Study on Allocation Methods in Other LFMs
Platform | Project and Institutions Involved | Level of Application | Main Purpose | Flexibility Product Characteristics | Allocation Method | Time Frame | References |
---|---|---|---|---|---|---|---|
Flex4Energy | Storegio e.V. ENTEGA | DSO | Grid congestion management | Schedule- and limit-based | Continuous order book trading including local grid topology information | No specific trading time frame (up to 15 min before fulfillment) | [31] |
Flex2Market | Uni Wuppertal, SPIE SAG GmbH, E-Werk Schweiger OHG | DSO | Grid congestion management, voltage control, curtailment reduction | Schedule-based | Iterative techno- economical optimization | Intraday (max. 45 min before fulfilment) | [32,33] |
EMPOWER | Schneider Electric Norge AS | DSO and TSO | Grid congestion management, profitable local energy community | Schedule-based | Call auction, non-continous trading (Based on open limit order book) | Day-Ahead (23:00) and intraday | [22,34] |
iPower | Technical University of Denmark | DSO | Grid congestion management, voltage control | Limit-based | Two trading setups: merit order book with OPF check and economical optimization (minimization of DSO portfolio in- vestment risk) | Two different markets: reservation (year-ahead) and activation (day-ahead) | [35,36,37] |
Total Flex | ForskEL programme, Energinet.dk | DSO | Grid congestion management | Schedule-based | Economical optimization with geographical constraints | intraday and day-ahead | [38,39] |
EcoGrid 2.0 | Danish Energy Association | TSO and DSO | Grid congestion management, aggregated inclusion of DERs | Schedule- and limit-based, Scheduled or conditional activation | Regionalized merit order books | Days to months ahead | [40,41] |
Flex-DLM | Universidad Carlos III de Madrid | DSO | Grid congestion management using demand side flexibility | Schedule-based | OPF-based techno- economical optimization | Day-ahead | [23] |
GOPACS/ ETPA | TenneT, Stedin, Liander, Enexis Groep and Westland Infra | TSO and DSO | Grid congestion management, link to ETPA intraday energy market, TSO-DSO coordination | Buy-sell congestion spread product (IDCONS) | Automated continuous order book | Intraday | [29,42] |
ReFlex | C/sells, EnergieNetz Mitte | DSO | Grid congestion management, voltage control | Schedule- and limit-based | Techno- economical optimization with network calculation | Day-ahead (by 15:00) | [9,10,28] |
comax | C/sells, TenneT | DSO and TSO | Grid congestion management | Schedule-based | Bottom-up techno- economical optimization | Day-ahead (by 14:30) with intraday changes up to 15 min before delivery | [9,10,28] |
enera market | enera | DSO and TSO | Grid congestion management, TSO-DSO coordination | Schedule-based | Continuous regionalized order books | intraday (6 h before up until 5 min before) | [12] |
nodes | Nodes AS and Nodes Market Limited | DSO and TSO | Grid congestion management, TSO-DSO coordination, integration of flexibility in intraday market | Schedule-based (Availability and activation products) | Continuous order book trading including local grid topology information | Day-ahead, intraday | [43,44] |
ENKO | NEW 4.0 | DSO | Grid congestion management, curtailment reduction | Schedule-based | Merit-order book with sensitivity- analysis by DSO | Day-ahead (by 14:00) | [45] |
WindNode platform | WindNode | TSO and DSO | Grid congestion management, curtailment reduction | Schedule-based | Bottom-up, iterative techno- economical optimization | intraday (2 h before) and day-ahead (until 18:00) | [10,46] |
3. Matching Flexibility Demand and Supply through Optimization
- Reverse auctions are characterized by the inverse roles of sellers and buyers compared to a traditional auction. Here, the sellers constitute the bidders, while a buyer wants to acquire a resource for the lowest possible cost.
- Multi-attribute auctions are required, because in addition to the price, flexibility bids are characterized by the aforementioned constraints, i.e., effectiveness, available power, and boundary conditions.
- Double-sided auctions typically feature multiple buyers and sellers. Concerning regionalized LFMs, the buyer side involves several DSOs demanding flexibility for congestion management.
3.1. Optimization Goal
- Minimize operating costs: The goal is to minimize the overall operating costs. This is represented by the objective function where the sum of all operational costs is minimized, while
- Simultaneously meeting as much of the demand for flexibility as possible: By only minimizing costs, it is impossible to reach a satisfying market result, as the cheapest option would always be not contracting anything at all and therefore resulting in costs equal to zero. However, attempting to always exactly match flexibility demand might result in disproportionately high costs. Therefore, demand fulfillment is not formulated as an equality constraint but rather incorporated into the objective function via a penalty factor. This approach is valid as flexibility demand includes a certain degree of elasticity. In the case of critical network conditions, DSOs have other contingency measures for resolving grid congestion available to them, which are independent of the flexibility offers. Accordingly, they are not forced to draw disproportionately expensive FOs.
3.2. Flexibility Demand
3.3. Flexibility Offers and Products
3.3.1. Schedule Offers
3.3.2. Long-Term Contraction and Aggregated Offers
3.4. Boundary Conditions
3.4.1. Technical Boundary Conditions of Flexibility Options
3.4.2. Call Restrictions of Flexibility Offers
3.4.3. Consideration of Localities via Effectivity Values
3.5. Definition of the Optimization Problem
- Consideration of the effectiveness evaluation by conversion of offered flexibility in at the point of supply into a change of current in or voltage in , separately, at the congestion (Section 3.4).
- Boundary conditions for the flexibility offers, i.e.,
4. Altdorfer Flexmarkt (ALF) Case Study
- Access to existing small-scale flexibilities (i.e., heat pumps, electric vehicles, or small PV systems) and development of suitable flexibility products.
- Market entry for unused flexibility: integration of flexibilities without market access today.
- Technical realization of the process chain: the project intends to show the proof of concept of the technical setup and the performance of the smart meter infrastructure [56].
4.1. Field Test Setup and Application on Medium-Voltage Grid in the Project Region
4.2. Implementation Example
- In the first time step, the three FOs are activated according to the merit order. This results in FO 1 and FO 2 operating at maximum capacity, while the more expensive FO 3 only contributes around 51% of its available power.
- For the second time step, a decrease in flexibility demand can be observed. As a result, FO 2 is no longer required and can be switched off.
- In the third time step, the result deviates from the merit order, as one of the constraints becomes active. Considering its total call duration, is limited to four time steps and FO 1 is switched off by the matching algorithm, as its contribution is most dispensable at this moment compared to the other time steps.
- During the fourth time step, the operator of FO 3 suddenly increases the cost to 100 /. For the example, the penalty factor was chosen so that underfulfillment of the flexibility demand occurred. In this case, the DSO would have to resort to contingency measures beyond the flexibility platform to resolve the congestion.
- In the last time step, the costs of FO 3 reduce to its default level and the power ramps up again to full capacity. The flexibility demand cannot be met 100% because the third constraint becomes active. forces FO 2 to be switched off after two subsequent time steps of operation, so that its capacity is unavailable when resolving the congestion.
5. Critical Review
- The matching algorithm currently neglects the energy component of the flexibility offers. Although this aspect is intercepted via additional boundary conditions, energy constraints may offer added value, especially for storage facilities.
- Penalization of demand over- and underfulfillment is still defined by a uniform value. In order to adapt to realistic market and demand behavior, a differentiation between allowed overfulfillment and avoidable underfulfillment may be beneficial.
- Furthermore, a limitation on maximum costs has not yet been implemented. Limiting maximum costs to avoid exorbitant costs may be realized by an additional constraint, setting a cap on the costs of the activated power of all FOs per time step and demand. This cap can prevent price gouging by a supplier possessing market power due to a lack of alternative solutions to a given congestion.
- The general potential for market manipulation due to market design inconsistency and market power tendencies needs to be observed. The potential of mitigation measures within LFM were discussed previously (see [59,60]). Nevertheless, a consistent evaluation of dynamic market behavior still demands further research.
- As typical for a day-ahead process, uncertainty remains in the forecast of the demand and the offers. Therefore, it is possible that the result of the matching does not perfectly fit the actual grid load:
- -
- From a demand perspective and the grid operator’s point of view, this topic is not critical: an LFM is an additional tool in the congestion management of the grid operators. The already established mechanisms remain as emergency measures.
- -
- For the flexibility offers, it is conceivable that a prequalification process (e.g., balancing power) is integrated in the LFM as part of the registration. Furthermore, a penalty for non-fulfillment can be considered. The described project focused on the technical proof of concept and does not provide detailed settlement processes.
- Flexibility on the LFM is highly regulated and there is no real competition with other use cases. In this case, the LFM can be seen as an additional tool for the grid operators with regulated, cost-based pricing.
- The LFM competes with other use cases. This opens the door to strategic bidding (and possible inc-dec gaming; see [59] for a detailed discussion).
6. Conclusions and Outlook
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ALF | Altdorfer Flexmarkt |
CM | Congestion Management |
CAP | Combinatorial Auction Problem |
DSO | Distribution System Operator |
EEG | German Renewable Energy Sources Act |
FO | Flexibility Option |
LFM | Local Flexibility Market |
MIP | Mixed Integer Problem |
MINLP | Mixed-Integer Nonlinear Problem |
OPF | Optimal Power Flow |
PV | Photovoltaics |
TSO | Transmission System Operator |
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Variable | Meaning |
---|---|
Costs for positive flexibility of FO i at time period j | |
Costs for negative flexibility of FO i at time period j | |
Contracted power increase for FO i at time period j | |
Contracted power reduction for FO i at time period j | |
Penalty costs for non-fulfilment of the demand l | |
Auxiliary variable for the absolute value of non-fulfillment of demand l at time period j |
Equation | Description |
---|---|
Simulation of non-fulfillment of demand considering specific effectivities. | |
The sum over all state switches plus the state of the FO in the first as well as the last time step must not exceed twice the number of allowed calls. | |
After activation, a FO can remain switched on for a maximum time period. The first condition covers the case that the FO is activated in the first time step, while the second condition deals with later activations. | |
Depending on the moment of activation, the two conditions ensure that FOs remain activated for a minimum defined time period. | |
After a call of a FO has occurred, the FO in question must remain deactivated for a defined blocking time. The second condition extends this constraint to blocking times remaining from the previous day. | |
The total call duration per day must not exceed a defined limit. The factor accounts for 15-min intervals. | |
In the case that FOs do not feature continuous power modulation, discrete switch settings (e.g., 0–30–60–100%) must be considered. | |
In the case of continuous power modulation, minimum and maximum power restrictions must not be violated. The four conditions cover the lower and upper bounds for power increase and power decrease. | |
Parameter | Meaning |
---|---|
I | Set of FOs, |
J | Set of time periods, (default: 96) |
L | Set of demands, |
Indicator of a state switch of FO i at time period j | |
S | Set of percentages, |S| = q (default: 4) |
Flexibility demand l at time period j | |
Maximum number of calls of FO i per day (default: 96) | |
Total call duration per day (h) (default: 24) | |
Maximum call duration per call (h) (default: 24) | |
Minimum call duration per call (h) (default: 0.25) | |
Minimum time between two calls (h) (default: 0) | |
Remaining blocking time of the previous day (h) (default: 0) | |
Indicator of the state of the FO i at time period j | |
Auxiliary variable for the restriction to a percentage | |
Maximum available power | |
Minimum available power | |
Effectivity factor | |
Auxiliary constant (large enough) | |
Possible shares of power (default: ) | |
Indicator for P (continuous or restricted to power steps) | |
Indicator for zero demand for a flexibility demand l at time period j |
Time | Baseline | Power− | Power+ | Energy− | Energy+ | Price− | Price+ | Partial Call | Max. Num- ber of Calls Per Day | Max. Dura- tion Per Day, h | Blocking Time be- tween Two Calls, h | Max Call Dura- tion, h | Min Call Dura- tion, h |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0:00 | |||||||||||||
0:15 | |||||||||||||
0:30 | |||||||||||||
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ||||||
23:45 |
Time Step | Flexibility Demand in A | FO 1 40 KW 10 €/MWh | FO 2 30 KW 20 €/MWh | FO 1 50 KW 5 €/MWh |
---|---|---|---|---|
1 | 40 | 50 | ||
2 | 0 | 50 | ||
3 | 0 | 3 | 50 | |
4 | 40 | 30 | 0 | |
5 | 40 | 0 | 50 |
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Zeiselmair, A.; Köppl, S. Constrained Optimization as the Allocation Method in Local Flexibility Markets. Energies 2021, 14, 3932. https://doi.org/10.3390/en14133932
Zeiselmair A, Köppl S. Constrained Optimization as the Allocation Method in Local Flexibility Markets. Energies. 2021; 14(13):3932. https://doi.org/10.3390/en14133932
Chicago/Turabian StyleZeiselmair, Andreas, and Simon Köppl. 2021. "Constrained Optimization as the Allocation Method in Local Flexibility Markets" Energies 14, no. 13: 3932. https://doi.org/10.3390/en14133932