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Day‐ahead flexibility market clearing mechanism for interactive collaboration of transmission and distribution system operators

Day‐ahead flexibility market clearing mechanism for interactive collaboration of transmission and... INTRODUCTIONOne most important reason for the growing tendency toward collaboration between the DSOs and TSOs is the increased number of RESs connected to the grid. These intermittent and uncertain resources have posed new challenges to the operation of power systems. In [1] the faced challenges by power system operators have been described and the necessity to foster collaboration between TSO and DSO to overcome these issues have been highlighted. One of the most important challenges is the need to provide more flexibility for the power system. From these perspectives, flexibility can be defined as the ability of the power system to reduce the adverse effects of predictable or unpredictable changes to any of the elements or parameters of the power system which in turn leads to increasing costs, endangering the power system security, or deteriorating any other security‐related index of the power system.The transmission and distribution grids are physically interconnected such that changes occurring in one system may affect the other one's performance as well. The separate operation of transmission and distribution grids leads to undesirable exploitation of the total potential flexibility capacity of the entire power system. Thus, the coordinated operation of TSO‐DSO enhances the technical and economic efficiency of the whole power system. The flexibility sources are classified based on the supply source type, grid connection location, planning period, technical specifications such as energy amount, power capacity, and ramping capacity, and also their applications, including balancing power at transmission grid, balancing power at distribution grid and distribution grid management [2–4]. These resources are available at the transmission and distribution levels. Purposeful use of these resources for better use of the power system can be useful.While the motivations of TSOs and DSOs toward flexibility procurement for their corresponding grids might differ, however, enhancing flexibility improves the entire system performance facing RES uncertainties. In [5], utilization of the power system flexibility potential for reinforcement investment deferral of the distribution grid in the presence of DERs is regarded as the most significant multi‐year motivation of DSOs. These investments focus on the installation of new lines and transformers. In addition to long‐term contracts of off‐market flexibility procurement, the existence of a market for the flexibility provided in the presence of other buyers improves the overall welfare. With the increase in renewable energy production and distributed energy resources (DER), flexibility markets are developed to aid the performance of evolving power systems [6].These markets are more suitable for providing flexibility to meet DSO's short‐term goals. The short‐term goals of DSOs to use the flexibility services may include power balancing within the distribution grid, congestion management, and voltage management. These goals can be achieved to some extent by the resources available at the distribution level, provided that these resources are economically motivated. Therefore, one of the most essential DSOs’ goals is the direct or indirect access of flexible generation sources to free energy markets. The existing sources at the distribution level can be employed to procure the flexibility services of the entire power system. These sources usually have a reasonable response speed to the net load variations of the grid. The economic operation of these sources in a local or centralized market can increase their motivations to procure flexible services [7–9]. Each market, either local or centralized, faces its respective benefits and drawbacks. A local market in the presence of retailers offers low liquidity and high market power and, consequently, attracts little interest for the participation of small sources. Still, the local market fulfils the high‐priority DSO needs while reducing the computational burden. In [10], establishing the unique flexibility markets for TSO and DSO service procurement and avoiding the local markets has been recommended.Depending on the user and the purpose of the usage, the flexibility resources could match the various needs or potentially cause conflict themselves. Therefore, it is crucial to establish an appropriate market framework to benefit from the flexible resources of the entire grid [11, 12].An alternate approach seems to be the existence of a centralized market with separate operators for each grid. In other words, from the TSOs’ viewpoint, the DSO's grid is seen as an aggregated generator or flexible load that can deliver its services to the upstream grid. This model is more consistent with the current structure of existing markets. As an example, [13] presents a hierarchical market to incentivize the participation of multiple microgrids (MGs) in the balancing markets. An economic comparison suggests that the TSO‐DSO interaction is favourable for both MGs and transmission systems.Existing markets are primarily focused on flexible ramp product (FRP) procurement. TSO requests FRP to overcome the increased uncertainty in net demand. These services, which are traded in times close to real‐time (RT), use the flexible units to help the traditional units as a reserve, rapidly and without occupation of the production capacity [14].Generally, strict ramping limitations are not imposed in distribution grids [13]. Thus, DSO can help establish the power balance using the flexible resources in the distribution grids. Depending on the user and the purpose of the usage, the flexibility resources could match the various needs or potentially cause conflict themselves. Therefore, it is crucial to establish an appropriate market framework to benefit from the flexible resources of the entire grid [14, 15].While FRP is currently presented for RT markets only, its procurement prediction in DA or intraday (ID) markets is imperative. This leads to risk reduction for generators revenue under DA price. FRP can be optimized simultaneously with energy and ancillary services. From the NYISO perspective, ramp procurement in the RT market entails no cost. The shortage pricing methodology, currently used for operation and regulation reserve, is applied for ramp [15]. To ensure power balance, considered FRP should be larger than the predicted value. In [16], the ramp modelling has been elaborated in the existing markets. A drawback to current methods is that they only address the ramp of existing sources and neglect the ramp amount needed by the entire system. This might compromise system reliability and lead to price fluctuations and mathematically infeasible solutions to the problem. One strategy to overcome this issue is to consider the entire system's ramp in the DA market. Such a market is exploited in this paper for DSO flexibility service procurement at the transmission level. An overview of the market framework for the latter is shown in Figure 1. In this figure microgrids (MGs) are identified as an inseparable part of recent distribution systems. MGs usually supply part of the demands of a local network. This amount of energy is provided by MGs for economic reasons or to increase consumer reliability. In addition, MGs can be a good resource for providing system flexibility. However, using MGs can be challenging. From a market perspective, the role of the DSOs varies depending on the MGs’ ownership. If the MGs belong to a DSO, the goal is to maximize the total profit of the MGs. The DSO, therefore, acts as an aggregator. Conversely, if the DSO does not own the MGs, each MG seeks to maximize its profits, while the DSO can be brought up as a local operator. Therefore, providing flexibility by MGs increases the complexity of the market‐clearing process, which is rarely addressed in the presented papers in the area. So, in this paper, the effect of MGs under DSO ownership on flexibility procurement is investigated.1FIGUREOverview of the market frameworkHere, the DA market sources are scheduled based on the robust adaptive approach to encounter the predicted uncertainties. Clearing of DA markets with high penetration of RESs is performed in a two‐ or multi‐stage fashion. In the first stage, the sources’ ‐DA dispatch costs are obtained using the scheduled or predicted values. The second stage calculates the real‐time expected balancing cost based on the system's uncertainties. This method considers a sufficient amount of flexibility to overcome system uncertainty in real‐time. In [17] and [18], four techniques are presented to clear such a market based on the market design philosophy.However, currently in most existing DA markets, the flexibility required by the system is provided through the ancillary services market, especially the reserve market. But the impact of this market on the flexibility of the power system has not been well studied. For example, power plant units may be reserved to provide load capacity changes. If this amount of reserve is determined regardless of the amount of ramp load, it may cause more problems for the system. In [19], the utilization of spinning reserve for FRU procurement through the DA market is proposed. In the paper, it was assumed that the spinning reserve is present, and its value is given beforehand; however, a DA market mechanism for its provision is not stated.Therefore, it can be understood that the amount of reserve affects the ability of the system to cope with changes. For this reason, this article examines the reserve impact on flexibility procurement for the power system.Various metrics are introduced for the quantitative measurement of flexibility [20–24]. These metrics are most beneficial for the planning studies of the power systems, as the adjustment points of sources might change during operation at each time interval, depending on the operator's current decisions. For this reason, some available research in the area, for example, ref. [25] presents the online metrics to estimate the system flexibility. On the whole, defining these metrics is to predict the system capability against the existing uncertainties in RESs and loads [26]. Since the grid flexibilities have various spectra and applications, defining a single metric is insufficient to describe the grid flexibility. For instance, a grid may effectively react to an increase in wind power but not a decrease of the same amount. Thus, in this paper, several flexibility metrics, including flexible power‐up (FPU), flexible power‐down (FPD), flexible ramp‐up (FRU), flexible ramp‐down (FRD), and spilled wind power, are taken into account [27].The postulated market in this article is of energy‐only type. In energy‐only markets, the reserve is not traded as a separate commodity; instead, it is achieved as a by‐product of the energy market clearing. In this case, there is no need to estimate the reserve amount, and also, no price bid for reserve. Therefore, no extra cost is paid for a reserve that has not been converted to energy. A fundamental flaw of this method is the uncertainty of the revenue generated from such reserves [28]. However, by applying risk management methods or introducing financial participants, the providers’ profit drop can be minimized.Accordingly, this paper examines the DSO's resources impact on flexibility procurement for the power system. To the best authors, knowledge, the main contributions of this paper with respect to the available research in the area can be summarized as follows:-Two‐stage clearing of DA market mechanism based on a robust adaptive approach is presented to meet the flexibility demands of the entire system in DA market using existing sources in both transmission and distribution levels. Using existing resources at the transmission and distribution levels, this paper examines the provision of required flexibility for the entire power system. The flexibility is provided in the DAM because of the uncertainty at the load buses. Accordingly, based on the predicted values of the loads, the amount of power generation and ramping of the units are determined in the first step. According to the worst‐case scenario, the second stage modifies the values obtained from the first stage. That is, the operators adjust the scheduled values according to the predicted values, but they are also prepared to deal with the worst‐case scenario. At times being close to RT, the system maybe does not require any additional flexibility. Fast‐ramping units are therefore less stressed as a result. Consequently, the first‐ and second‐stage reservations, such as frequency control reservations, are no longer necessary. Furthermore, the market‐clearing mechanism should simultaneously fulfil TSO and DSO restrictions. Accordingly, one solution is to use a central market framework. With global optimization, this market makes full use of flexibility. This type of market, however, runs slowly because of the volume of information while the DSO´s information should also be fully observable by the TSO. The method also has the disadvantage of not prioritizing network flexibility for TSOs or DSOs. It is no longer possible to use these services if the TSO urgently needs flexibility, while the DSO has already purchased them. A distributed MILP formulation based on primal problem solving is used to overcome this issue. In this model, TSOs and DSOs agree on exchanging the power and price through an iterative process.-Flexible sources at distribution level are aggregated by DSOs to present in the upstream markets for TSOs’ flexibility procurement. Generally, strict ramp limitations are not imposed in distribution grids [25]. Thus, DSO can help to support the power balance using its available flexible resources. Therefore, even though distribution‐level flexibility resources have a small size, they can react quickly. Thus, these sources, which can be either DGs or MGs, are suitable for the fast‐ramping requirements of the grid. Using an appropriate market mechanism, it is possible to increase the economic incentive for these resources to participate in providing flexibility. In contrast, since there are so many resources, their participation must be coordinated through an aggregator. In this paper, the distribution network with flexible resources is considered as a controllable load from TSO's viewpoint. Accordingly, TSO is notified by DSOs about maximum, minimum, and ramp values. When the TSO does not need additional flexibility, it exchanges the same predetermined values with the DSO. If not, buying flexibility from DSO will increase TSO operating costs. This may increase overall operating costs, but it increases the profitability of DGs and MGs and reduces RES output spillage. Thus, distribution resources are motivated to provide flexibility at the transmission level.-The impact of MGs under DSO ownership to procure flexibility is modelled and studied. DSO faces challenges in leveraging the potential of MGs to provide flexibility. If, as assumed in this article, DSO also acts as an aggregator, then ownership of MGs becomes a serious issue. If the DSO owns the MGs, its goal is either to maximize profits or to enhance RES uptake or any other objective function. In contrast, if the DSO does not own the MGs, each MG tries to maximize its profits, while the DSO tries to maintain the scheduled values at the CCP. Therefore, the DSO problem becomes one of the Stackelberg games with multiple leaders and followers. MGs are lower‐level problems, while DSO is the upper level. Accordingly, the upstream TSO market announces hourly prices for DSOs. Based on these prices, CCP power is exchanged. Regarding centralized market execution, we face a tri‐level problem. Furthermore, this model over‐complicates the problem in addition to the disadvantages cited for the centralized market. Therefore, this paper employs the distributed MILP method to overcome this issue. Essentially, the tri‐level problem becomes a bi‐level problem, much less complex than before. By publishing the price by TSO, then DSO and MG decide the amount of power to be exchanged. Once the amount of the power to be exchanged has been determined, TSO announces the updated prices to DSO by re‐launching the upstream market. This trend continued until the price equilibrium and convergence of the TSO‐DSO power exchange is reached at the CCP.-The effect of the reserve on the flexibility procurement process is modelled and investigated. Currently, in the existing DA markets, the flexibility is traded through ancillary service markets, especially the reserve market. Although, some references offer ramps during close to RT operation, the reserve market by its nature does not include ramp restrictions. On the other hand, flexibility markets can also provide the necessary reservation based on the system's needs. In other words, this market can simultaneously supply the energy, power, and ramping requirements of the system. Therefore, in this paper, the effect of system reserve on the proposed market of this paper is investigated. The postulated market here is of energy‐only type. In energy‐only markets, the reserve is not traded as a separate commodity; instead, it is achieved as a by‐product of the energy market clearing. In this case, there is no need to estimate the reserve amount and present the price bid for reserve. Therefore, no extra cost is paid for a reserve that has not been called for energy. A fundamental flaw of this method is the uncertainty of the revenue generated from such reserves [28]. However, by applying risk management methods or introducing financial participants, the providers’ profit drop can be minimized.In summary, this paper provides the required flexibility of the power system in the face of RES uncertainties using the resources available at the distribution level and in cooperation with the TSO on the DAM framework. The effect of DSO´s ownership on MGs and reservation amount on power system flexibility have also been investigated.The remainder of this paper is organized as follows: Section 2 presents the TSO‐DSO collaboration problem formulation in detail. In Section 3, simulation results and discussion are presented and Section 4 concludes the paper.TSO‐DSO COLLABORATION PROBLEM FORMULATIONIn this section, the problem formulation of the proposed TSO‐DSO framework for procurement of flexibility services in the power system in the day‐ahead market (DAM) is expressed.TSO modelEquations (1)–(49) demonstrate the mathematical formulation to model TSO and market clearing. The TSO objective function, given in (1), includes the social welfare (SW) maximization or operation cost minimization for a situation where predicted values of wind units are at their highest deviation. Equation (2) gives the units dispatch cost in the first stage with expected or scheduled values, and (3) calculates the re‐dispatch costs in the second stage, that is, balancing stage.1costTSO=minΘDAcostDA+maxΔwminΘBScostBS\begin{equation}\mathop {\cos t}\nolimits^{TSO} = \mathop {\min }\limits_{\mathop \Theta \nolimits_{DA} } {\rm{\ }}\left\{ {{\rm{cos}}{t^{DA}} + \mathop {\max }\limits_{\Delta w} {\rm{\ }}\left[ {\mathop {\min }\limits_{\mathop \Theta \nolimits_{BS} } {\rm{\ }}\left( {{\rm{cos}}{t^{BS}}} \right)} \right]} \right\}\end{equation}2costDA=∑i,tci.pi,tDA+ci,tsu+ci,tsd+ciRu.Ri,tU+ciRd.Ri,tD+∑q,tcq.wq,tfc−∑j,tLj,tfc.uj,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} {\rm{cos}}{t^{DA}} = \displaystyle\mathop \sum \limits_{i,t} \left({c_i}.p_{i,t}^{DA} + c_{i,t}^{su} + c_{i,t}^{sd} + c_i^{Ru}.R_{i,t}^U + c_i^{Rd}.R_{i,t}^D\right)\\[14pt] \qquad\qquad+\, \displaystyle\mathop \sum \limits_{q,t} \left({c_q}.w_{q,t}^{fc}\right) - \displaystyle\mathop \sum \limits_{j,t} \left(L_{j,t}^{fc}.{u_{j,t}}\right) \end{array} \end{equation}3costBS=∑i,tciu.ri,tu−cid.ri,td+∑q,tcq.wq,t−wq,tfc−wq,tspill+∑j,t.vollj.Lj,tshed−uj,td.Lj,td+uj,tu.Lj,tu\begin{equation}{\rm{cos}}{t^{BS}} = \left\{ \def\eqcellsep{&}\begin{array}{l} {\rm{\ }}\displaystyle\mathop \sum \limits_{i,t} c_i^u.r_{i,t}^u - c_i^d.r_{i,t}^d\\[12pt] + \displaystyle\mathop \sum \limits_{q,t} {c_q}.\left( {{w_{q,t}} - w_{q,t}^{fc} - w_{q,t}^{spill}} \right)\\[15pt] + \displaystyle\mathop \sum \limits_{j,t} .vol{l_j}.L_{j,t}^{shed} - u_{j,t}^d.L_{j,t}^d + u_{j,t}^u.L_{j,t}^u \end{array} \right\}\end{equation}4∑i∈Inpi,tDA+∑q∈Qnwq,tFC−∑j∈JnLj,tFC−∑m∈Mn1xmn.δn,t0−δm,t0+∑sεSnPs,tTM,DA−Ps,tPM,DA=0,∀n,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} \displaystyle\mathop \sum \limits_{i \in {I_n}} p_{i,t}^{DA} + \displaystyle\mathop \sum \limits_{q \in {Q_n}} w_{q,t}^{FC} - \displaystyle\mathop \sum \limits_{j \in {J_n}} L_{j,t}^{FC} - \displaystyle\mathop \sum \limits_{m \in {M_n}} \frac{1}{{{x_{mn}}}}.\left( {\delta _{n,t}^0 - \delta _{m,t}^0} \right)\\[15pt] \quad + \displaystyle\mathop \sum \limits_{s\epsilon {S_n}} \left( {P_{s,t}^{TM,DA} - P_{s,t}^{PM,DA}} \right) = 0{\rm{,}}\forall n,t \end{array} \end{equation}51xmn.δn,t0−δm,t0≤fn,mmax,∀m,n,t\begin{equation}\frac{1}{{\mathop x\nolimits_{mn} }}.\left(\mathop \delta \nolimits_{n,t}^0 - \mathop \delta \nolimits_{m,t}^0 \right) \le \mathop f\nolimits_{n,m}^{\max } ,\forall m,n,t\end{equation}6pi,tDA+Ri,tU≤vi,t.pimax,∀i,t\begin{equation}p_{i,t}^{DA} + R_{i,t}^U \le {v_{i,t}}.p_i^{max},\forall i,t\end{equation}7pi,tDA−Ri,tD≥vi,t.pimin\begin{equation}p_{i,t}^{DA} - R_{i,t}^D \ge {v_{i,t}}.p_i^{min}\end{equation}8ciSU≥ciSU0.vi,t−vi,t−1\begin{equation}c_i^{SU} \ge c_i^{SU0}.\left( {{v_{i,t}} - {v_{i,t - 1}}} \right)\end{equation}9ciSD≥ciSD0.vi,t−1−vi,t\begin{equation}c_i^{SD} \ge c_i^{SD0}.\left( {{v_{i,t - 1}} - {v_{i,t}}} \right)\end{equation}10pi,tDA−pi,t−1DA≤RUi.vi,t−1\begin{equation}p_{i,t}^{DA} - p_{i,t - 1}^{DA} \le R{U_i}.{v_{i,t - 1}}\end{equation}11pi,t−1DA−pi,tDA≤RDi.vi,t\begin{equation}p_{i,t - 1}^{DA} - p_{i,t}^{DA} \le R{D_i}.{v_{i,t}}\end{equation}12∑t=1Tiuvi,t≤Tiu\begin{equation}\mathop \sum \limits_{t = 1}^{T_i^u} {v_{i,t}} \le T_i^u\end{equation}13∑t′=tt+Tiu−1vi,t′≥Tiu.yi,t,Tiu<t≤T−Tiu+1\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^{t + T_i^u - 1} {v_{i,t^{\prime}}} \ge T_i^u.{y_{i,t}},T_i^u &lt; t \le T - T_i^u + 1\end{equation}14∑t′=tTvi,t′−yi,t≥0,T−Tiu+1<t≤T\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^T {v_{i,t^{\prime}}} - {y_{i,t}} \ge 0,T - T_i^u + 1 &lt; t \le T\end{equation}15∑t=1Tidvi,t=0\begin{equation}\mathop \sum \limits_{t = 1}^{T_i^d} {v_{i,t}} = 0\end{equation}16∑t′=tt+Tid−11−vi,t′≥Tid.zi,t,Tid<t≤T−Tid+1\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^{t + T_i^d - 1} 1 - {v_{i,t^{\prime}}} \ge T_i^d.{z_{i,t}}{\text{\ \ }},{\text{\ \ }}T_i^d &lt; t \le T - T_i^d + 1\end{equation}17∑t′=tT1−vi,t′−zi,t≥0T−Tiu+1<t≤T\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^T 1 - {v_{i,t^{\prime}}} - {z_{i,t}} \ge 0{\text{\ \ \ \ \ \ }}T - T_i^u + 1 &lt; t \le T{\rm{\ }}\end{equation}18PTs,tDA=σs,tT.QTs,tDA\begin{equation}PT_{s,t}^{DA} = \sigma _{s,t}^T.QT_{s,t}^{DA}\end{equation}19PPs,tDA=σs,tP.QPs,tDA\begin{equation}PP_{s,t}^{DA} = \sigma _{s,t}^P.QP_{s,t}^{DA}\end{equation}20vols,tDA,u=vols,t−1DA,u+QPs,tDA−QTs,tDA\begin{equation}vol_{s,t}^{DA,u} = vol_{s,t - 1}^{DA,u} + QP_{s,t}^{DA} - QT_{s,t}^{DA}\end{equation}21vols,tDA,l=vols,t−1DA,l−QPs,tDA+QTs,tDA\begin{equation}vol_{s,t}^{DA,l} = vol_{s,t - 1}^{DA,l} - QP_{s,t}^{DA} + QT_{s,t}^{DA}\end{equation}22vols,tDA,u≥vols,t0,u\begin{equation}vol_{s,t}^{DA,u} \ge vol_{s,t}^{0,u}\end{equation}23vols,tDA,l≥vols,t0,l\begin{equation}vol_{s,t}^{DA,l} \ge vol_{s,t}^{0,l}\end{equation}Equations (24)–(47) describe the constraints of the second stage. Equation (24) shows the power balance at this stage. Equations (30), (31) convey the increasing or decreasing power limitations based on the pre‐specified reserve values. Equations (32)–(37) model the flexible loads. Relation (32) displays the lowest daily amount of energy required for shiftable loads. Equations (38)–(47) formulate the pumped‐storage power plants in the second stage.24∑i∈Inri,tu−ri,td+∑j∈JnLj,tshed+Lj,tu−Lj,td+∑q∈Qnwq,t−wq,tfc−wq,tspill−∑m∈Mn1xmnδn,t−δn,t0−δm,t−δm,t0+∑s∈SnΔPTs,t−ΔPPs,t=0,∀n,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} \displaystyle\mathop \sum \limits_{i \in {I_n}} r_{i,t}^u - r_{i,t}^d + \displaystyle\mathop \sum \limits_{j \in {J_n}} L_{j,t}^{shed} + L_{j,t}^u - L_{j,t}^d\\[15pt] + \displaystyle\mathop \sum \limits_{q \in {Q_n}} {w_{q,t}} - w_{q,t}^{fc} - w_{q,t}^{spill} \\[15pt] - \displaystyle\mathop \sum \limits_{m \in {M_n}} \frac{1}{{{x_{mn}}}}\left[ {\left( {{\delta _{n,t}} - \delta _{n,t}^0} \right) - \left( {{\delta _{m,t}} - \delta _{m,t}^0} \right)} \right]\\[15pt] + \displaystyle\mathop \sum \limits_{s \in {S_n}} \Delta P{T_{s,t}} - \Delta P{P_{s,t}} = 0{\rm{\ ,}}\forall n,t \end{array} \end{equation}251xmn.(δn,t−δm,t)≤fn,mmax,∀m,n,t\begin{equation}\frac{1}{{\mathop x\nolimits_{mn} }}.(\mathop \delta \nolimits_{n,t} - \mathop \delta \nolimits_{m,t} ) \le \mathop f\nolimits_{n,m}^{\max } ,\forall m,n,t\end{equation}26wq,tspill≤wq,t\begin{equation}w_{q,t}^{spill} \le {w_{q,t}}\end{equation}27pi,t=pi,tDA+ri,tu−ri,td\begin{equation}{p_{i,t}} = p_{i,t}^{DA} + r_{i,t}^u - r_{i,t}^d\end{equation}28pi,t−pi,t−1≤RUi.vi,t−1\begin{equation}\mathop p\nolimits_{i,t} - \mathop p\nolimits_{i,t - 1} \le R{U_i}.{v_{i,t - 1}}\end{equation}29pi,t−1−pi,t≤RDi.vi,t\begin{equation}\mathop p\nolimits_{i,t - 1} - \mathop p\nolimits_{i,t} \le R{D_i}.{v_{i,t}}\end{equation}30ri,tu≤Ri,tu\begin{equation}r_{i,t}^u \le R_{i,t}^u\end{equation}31ri,td≤Ri,td\begin{equation}r_{i,t}^d \le R_{i,t}^d\end{equation}32∑tLj,t≥Ejday\begin{equation}\mathop \sum \limits_t {L_{j,t}} \ge E_j^{day}\end{equation}33Lj,t−Lj,t−1≤Ljpiu\begin{equation}{L_{j,t}} - {L_{j,t - 1}} \le L_j^{piu}\end{equation}34Lj,t−1−Lj,t≤Ljdrp\begin{equation}{L_{j,t - 1}} - {L_{j,t}} \le L_j^{drp}\end{equation}35Lj,t=Lj,tfc+Lj,td−Lj,tu−Lj,tshed\begin{equation}{L_{j,t}} = L_{j,t}^{fc} + L_{j,t}^d - L_{j,t}^u - L_{j,t}^{shed}\end{equation}36Lj,td≤Dj,t+\begin{equation}L_{j,t}^d \le D_{j,t}^ + \end{equation}37Lj,td≤Dj,t+\begin{equation}L_{j,t}^d \le D_{j,t}^ + \end{equation}38PTs,t=σs,tT.QTs,t\begin{equation}\mathop {PT}\nolimits_{s,t} = \sigma _{s,t}^T.\mathop {QT}\nolimits_{s,t} \end{equation}39PPs,t=σs,tP.QPs,t\begin{equation}\mathop {PP}\nolimits_{s,t} = \sigma _{s,t}^P.\mathop {QP}\nolimits_{s,t} \end{equation}40vols,tu=vols,t−1u+QPs,t−QTs,t\begin{equation}vol_{s,t}^u = vol_{s,t - 1}^u + \mathop {QP}\nolimits_{s,t} - \mathop {QT}\nolimits_{s,t} \end{equation}41vols,tl=vols,t−1l−QPs,t+QTs,t\begin{equation}vol_{s,t}^l = vol_{s,t - 1}^l - \mathop {QP}\nolimits_{s,t} + \mathop {QT}\nolimits_{s,t} \end{equation}42vols,tu≥vols,t0,u\begin{equation}vol_{s,t}^u \ge vol_{s,t}^{0,u}\end{equation}43vols,tl≥vols,t0,l\begin{equation}vol_{s,t}^l \ge vol_{s,t}^{0,l}\end{equation}44volsu,min≤vols,tu≤volsu,max\begin{equation}vol_s^{u,min} \le vol_{s,t}^u \le vol_s^{u,max}\end{equation}45volsl,min≤vols,tl≤volsl,max\begin{equation}vol_s^{l,min} \le vol_{s,t}^l \le vol_s^{l,max}\end{equation}46QTs,t≤QPsmax\begin{equation}Q{T_{s,t}} \le QP_s^{max}\end{equation}47QPs,t≤QPsmax\begin{equation}Q{P_{s,t}} \le QP_s^{max}\end{equation}DSO modelThis paper addresses DSO participation to procure required flexible services of the grid. To this end, four prominent scenarios are considered for DSO modelling. Here, each DSO is assumed to consist of multiple MGs.Scenario 1: As for the inflexible loads, DSO aggregates MGs and other demands and presents its bid and available power to the market. These values are, in fact, the results of the economic dispatch (ED) program, according to (48)–(60), that DSO implements on an hourly basis with the objective of SW maximization or operation costs minimization. In fact, in this case, the DSO can act as an aggregator.Equation (48), that is, the objective function shows the total DSO's operation costs. λ is the locational marginal price (LMP) of the TSO's bus to which the DSO is connected. Equations (49) and (50) show the operation costs of DGs and DR, respectively. Equation (51) expresses the power balance relationship for each DSO bus, (52) and (53) the distribution limits of distribution lines and DGs. Equations (54) and (55) present the constraints of DR blocks. Equations (56)–(59) represent the equations for electrical storage. Finally, Equation (60) shows the power balance relationship of each MG.48minΘDSO∑mg∑dgC(pdg,t)+ptgrid.λt+cmg,tDR,∀t\begin{equation}\mathop {\min }\limits_{\mathop \Theta \nolimits^{DSO} } \sum_{mg} {\left\{ {\sum_{dg} {C(\mathop p\nolimits_{dg,t} ) + \mathop p\nolimits_t^{grid} .\mathop \lambda \nolimits_t + \mathop c\nolimits_{mg,t}^{DR} } } \right\}}, \quad \forall t\end{equation}49C(pdg,t)=αdg+βdg.pdg,t+γdg.pdg,t2\begin{equation}C ( {{p_{dg,t}}}) = {\alpha _{dg}} + {\beta _{dg}}.{p_{dg,t}} + {\gamma _{dg}}.{p_{dg,t}}^2\end{equation}50Cmg,tDR=∑zcmg,z.qmg,z,tDR.umg,z,tDR\begin{equation}C_{mg,t}^{DR} = \sum_z {{c_{mg,z}}} .q_{mg,z,t}^{DR}.u_{mg,z,t}^{DR}\end{equation}51ptgrid+∑m∈Mn1xmn(δn,t−δm,t)=pn,tload−∑mg∈MGnpmg,tsell−pmg,tbuy,∀n,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} \mathop p\nolimits_t^{grid} + \displaystyle\sum_{m \in \mathop M\nolimits_n } {\frac{1}{{\mathop x\nolimits_{mn} }}} (\mathop \delta \nolimits_{n,t} - \mathop \delta \nolimits_{m,t} ) \\[15pt] \quad =\,\mathop p\nolimits_{n,t}^{load} - \displaystyle\sum_{mg \in \mathop {MG}\nolimits_n } {\left(\mathop p\nolimits_{mg,t}^{sell} - \mathop p\nolimits_{mg,t}^{buy} \right)}, \quad \forall n,t \end{array} \end{equation}521xmn.(δn,t−δm,t)≤fn,mmax,∀m,n,t\begin{equation}\frac{1}{{{\rm{ }}{x_{mn}}}}.({\delta _{n,t}} - {\delta _{m,t}}) \le {\rm{ }}f_{n,m}^{\max },\forall m,n,t\end{equation}53pdgmin≤pdg,t≤pdgmax\begin{equation}p_{dg}^{min} \le {p_{dg,t}} \le p_{dg}^{max}\end{equation}54∑zqmg,z,tDR.umg,z,tDR≤pmg,tload\begin{equation}\sum_z {q_{mg,z,t}^{DR}} .u_{mg,z,t}^{DR} \le p_{mg,t}^{load}\end{equation}55umg,z,tDR≥umg,z−1,tDR,∀z≥2\begin{equation}u_{mg,z,t}^{DR} \ge u_{mg,z - 1,t}^{DR},\forall z \ge 2\end{equation}560≤pes,tch≤pes,tch,max\begin{equation}0 \le p_{es,t}^{ch} \le p_{es,t}^{ch,max}\end{equation}570≤pes,tdis≤pes,tdis,max\begin{equation}0 \le p_{es,t}^{dis} \le p_{es,t}^{dis,max}\end{equation}58soces,t=soces,t−1+η.pes,tch−1η.pes,tdis\begin{equation}so{c_{es,t}} = so{c_{es,t - 1}} + \eta .p_{es,t}^{ch} - \frac{1}{\eta }.p_{es,t}^{dis}\end{equation}590≤soces,t≤soces,tmax\begin{equation}0 \le so{c_{es,t}} \le soc_{es,t}^{max}\end{equation}60pmg,tload−pmg,tbuy+pmg,tsell−∑dg∈mgpdg,t−∑es∈mgpes,tdis−pes,tch−DRmg,t=0,∀mg,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} p_{mg,t}^{load} - p_{mg,t}^{buy} + p_{mg,t}^{sell} - \displaystyle\sum_{dg \in mg} {{p_{dg,t}}} \\[15pt] - \displaystyle\sum_{es \in mg} {\left( {p_{es,t}^{dis} - p_{es,t}^{ch}} \right)} - D{R_{mg,t}} = 0,\forall mg,t \end{array} \end{equation}Scenario 2: Similar to a flexible load in transmission level, DSO places a bid for flexibility services procurement. This bid includes the maximum and minimum powers and the procurable ramp by the specification of the marginal costs. In this scenario, DSO obtains the above values by aggregation of all existing sources in its grid. In other words, in this scenario, the DSO acts as a flexible service provider (FSP). As before, the primary objective function of DSO is the SW maximization or operation cost minimization, considering the constraints on the distribution grid and MGs based on the provided formulations.Equation (48) is rewritten to obtain the aggregated values of the objective function. Generally, the sources present in the distribution grid are unable to satisfy the distribution grid loads completely. To achieve the maximum (minimum) value of the absorbable power by distribution grid in TSO‐DSO common coupling point (CCP), the DSO objective function is to maximize (minimize) the receivable power from the grid (Ptgrid). Marginal cost (MC) or, in this scenario, marginal utility (MU) is obtained using Equations (61)–(63). These MUs demonstrate the maximum energy value for DSO during a load increase or decrease. Equation (62) is used for scenarios whose objective function is the same as (48), and equality function (63) relates to the circumstances that their objective function, rather than (48), is the maximization/minimization of Ptgrid value. In this scenario, since Ptgrid is at its highest or lowest values possible, the MC is not definable; thus, the mean cost concept is utilized according to (63). As can be seen from this equation, the mean cost is the total DSO's operation cost to the power absorbed by the DSO grid. If the problem is not infeasible, the value of the mean cost is very close to the MC. The difference in the power grid in Equation (62) is equal to unity, unlike in (63).61costtDSO=∑mg∑dgεMGcpdg,t+ptgrid.λtfc+cmg,tDR,∀t\begin{equation}{\rm{cos}}t_t^{DSO} = {\rm{\ }}\mathop \sum \limits_{mg} \left\{ {\mathop \sum \limits_{dg\epsilon MG} c\left( {{p_{dg,t}}} \right) + p_t^{grid}.\lambda _t^{fc} + c_{mg,t}^{DR}} \right\}{\rm{,}}\forall t\end{equation}62MUtDSO=costtDSOptgrid−costtDSOptgrid−1\begin{equation}MU_t^{DSO} = {\rm{cos}}t_t^{DSO}\left| {_{p_t^{grid}}} \right. - {\rm{cos}}t_t^{DSO}\left| {_{_{\left( {p_t^{grid} - 1} \right)}}} \right.\end{equation}63U¯tDSO=costtDSOptgrid\begin{equation}\bar{U}_t^{DSO} = \frac{{{\rm{cos}}t_t^{DSO}}}{{p_t^{grid}}}\end{equation}In this scenario, DSO submits the maximum and minimum power receivable from the grid along with MUs to the TSO. After evaluating the bids, TSO announces the cleared values to the participants.Scenarios 3 and 4 account for the situations where DSO owns MGs or not, respectively. If DSO lacks MGs, the objective function minimizes operating costs by considering penalties for scheduled power exchange deviation. Nevertheless, DSO owns MG; there is a bi‐level problem. The objective function is to maintain the cleared power values at the upper level and maximize MGs profit at the lower level. This is done by DSO by offering LMPs at the distribution level. In other words, by announcing LMPs, DSO encourages MGs to fulfil the expected power [16]. Equations (64), (65), (66) and (52) are the objective function and the upper‐level constraints, and the Equations (67) and (53)–(60) are the objective function and the lower‐level constraints, respectively. Equation (64), that is, the upper‐level objective function, minimizes the sum of deviations from the scheduled powers at DAM. Equations (65), (66) guarantee that the deviation values are positive. Equation (67), that is, the objective function of lower‐level, is comparable to Equation (48).64MinΘDSOupper−level.∑tΔptccp\begin{equation}\mathop {{\rm{Min}}}\limits_{\mathop \Theta \nolimits^{DSO} }^{upper - level} .{\text{\ \ \ }}\mathop \sum \limits_t \Delta p_t^{ccp}\end{equation}65Δptccp≥ptcl−ptccp\begin{equation}\Delta p_t^{ccp} \ge p_t^{cl} - p_t^{ccp}\end{equation}66Δptccp≥−ptcl+ptccp\begin{equation}\Delta p_t^{ccp} \ge - p_t^{cl} + p_t^{ccp}\end{equation}67MinΘMGlower−level∑t∑DG∈MGcdg,p.pdg,t+λmg,t.pmg,tbuy−pmg,tsell+cmg,tDR,∀MG∈DSO\begin{equation}\mathop {{\rm{Min}}}\limits_{\mathop \Theta \nolimits^{MG} }^{lower - level} {\rm{\ }}\mathop \sum \limits_t \left\{ \def\eqcellsep{&}\begin{array}{l} \displaystyle\mathop \sum \limits_{DG \in MG} \left( {{c_{dg,p}}.{p_{dg,t}}} \right) \\[15pt] + {\lambda _{mg,t}}.\left( {p_{mg,t}^{buy} - p_{mg,t}^{sell}} \right) + c_{mg,t}^{DR} \end{array} \right\},\quad \forall MG \in DSO\end{equation}Uncertainty modellingUncertainty due to wind units’ power adopts different values in different hours and geographical places. In this paper, an uncertainty range is applied according to linearized Equations (68)–(74), which is suitable for solving problems using a robust adaptive approach [26]. Equation (72) indicates that the sum of wind power at each moment is below a specific value. Given the dependency of units’ productions to their geographical place of installation, it is expectable that the sum of wind units’ generated powers are bound to a specific value. This relation models the interdependency of the wind units and is not applied to the individual wind units. For example, the maximum number of hours in which the unit output has the highest deviation from the predicted value is a particular value for a wind power plant. This limitation can be applied via (73). Noticeably, Equations (72) and (73) describe the spatiotemporal constraints and dependencies of the uncertainty of wind units.68wq,t=wq,tfc+Δwq,t\begin{equation}{w_{q,t}} = w_{q,t}^{fc} + \Delta {w_{q,t}}\end{equation}69wq,t≤wq,tfc+Δwq,tmax\begin{equation}{w_{q,t}} \le w_{q,t}^{fc} + \Delta w_{q,t}^{max}\end{equation}70wq,t≥wq,tfc−Δwq,tmax\begin{equation}{w_{q,t}} \ge w_{q,t}^{fc} - \Delta w_{q,t}^{max}\end{equation}71Δwq,t=Δwq,t+−Δwq,t−\begin{equation}\Delta {w_{q,t}} = \Delta w_{q,t}^ + - \Delta w_{q,t}^ - \end{equation}72∑qΔwq,t++Δwq,t−Δwq,tmax≤Γt\begin{equation}\mathop \sum \limits_q \frac{{\Delta w_{q,t}^ + + \Delta w_{q,t}^ - }}{{\Delta w_{q,t}^{max}}} \le {{{\Gamma}}_t}\end{equation}73∑tΔwq,t++Δwq,t−Δwq,tmax≤Γq′\begin{equation}\mathop \sum \limits_t \frac{{\Delta w_{q,t}^ + + \Delta w_{q,t}^ - }}{{\Delta w_{q,t}^{max}}} \le {{\Gamma}}_q^{\rm{^{\prime}}}\end{equation}74Δwq,t+,Δwq,t−≥0\begin{equation}\Delta w_{q,t}^ + ,\Delta w_{q,t}^ - \ge 0\end{equation}DAM clearing and solution methodAs previously pointed out, market clearing is a two‐stage process. In the first stage, the unit scheduling is performed using predicted values, assumed identical to the actual values. By taking the worst‐case uncertainty parameters, the second stage adjusts the newly calculated values and obtained values in the previous stage. This ensures that the scheduled values cover the maximum uncertainty present (worst‐case scenario). There is some consideration about market clearing mechanism and solution methodology as follows:-The Benders decomposition method is applied to solve the market‐clearing equations considering the transmission constraints. In this method, the first stage is regarded as the main problem, and the dual problem of the second stage is taken as the sub‐problem. Due to the multiplication of uncertain values, Δw, by dual variables, the outer approximation, a linearized method based on Taylor expansion, is employed [29].-A percentage of power in each unit can be allocated to the reserve to cover the RES uncertainties. In this case, each unit submits its reserve bid to the TSO. An alternate approach is to regard the market as energy‐only. That means it only considers the reserve cost that has been delivered to the grid as energy.By aggregating its grid flexibilities, DSO determines the maximum and minimum powers consumed or generated and the ramping limits of power procurement in the CCP. This paper hypothesizes that the DER units installed on the DSO grid are capable of rapid ramping procurement. This CCP ramping value is different from the algebraic sum of all units’ ramping because the transmission lines may not transmit the intended power variations. It should be noted that the values of maximum (minimum) power and maximum ramping in CCP will vary concerning time. Therefore, the ED for each DSO should be executed according to Equations (48)–(60) hourly. To avoid the problem's complexity, DSO can present the maximum and minimum powers and their corresponding prices to the TSO. After the market clearing, DSO should solve the above equations again for updated information and submit the scheduled power values and nodal prices of the distribution grid to each MG. In particular, DSO announces the new offered deals based on the values from the TSO market‐clearing outcome, until convergence to an appropriate bid price, to minimize the DSO's price prediction error (using the objective function (67) and constraints (48)–(60)). Conclusively, DSO determines the new power values of its grid sources using the placed prices by TSO to maintain the cleared power values in the CCP with the minimum cost.The TSO‐DSO price convergence is based on a decentralized method presented in reference [30]. The use of primal space instead of dual problem space is one of the major advantages of this method. Convexity is the only requirement for convergence. All the equations in this paper are convex, so convergence of the problem is guaranteed. This method replaces the objective function (1) with Equation (75).75minΘTSO,αcostτTSO+∑dαd,τ\begin{equation}\mathop {\min }\limits_{\mathop \Theta \nolimits^{TSO} ,\alpha } \left\{ {\mathop {\cos t}\nolimits_\tau ^{TSO} + \sum_d {\mathop \alpha \nolimits_{d,\tau } } } \right\}\end{equation}76Eq.2−Eq.47\begin{equation}{\rm{Eq}}{\rm{.}}\;2 - {\rm{Eq}}{\rm{.}}\;47\end{equation}77αd,τ≥LBd,τ\begin{equation}\mathop \alpha \nolimits_{d,\tau } \ge \mathop {LB}\nolimits_{d,\tau } \end{equation}78Δptgrid,τ=Ptgrid−Lj,tfc+Lj,td−Lj,tuτ:π1\begin{equation}\mathop {\Delta p}\nolimits_t^{grid,\tau } = \mathop {\left( {\mathop P\nolimits_t^{grid} - \left(L_{j,t}^{fc} + L_{j,t}^d - L_{j,t}^u\right)} \right)}\nolimits_\tau \;:\;\mathop \pi \nolimits_1 \end{equation}79Δδt,τ=δn,t,τTSO−δv1,t,τDSO:π2\begin{equation}\Delta \mathop \delta \nolimits_{t,\tau } = \mathop \delta \nolimits_{n,t,\tau }^{TSO} - \mathop \delta \nolimits_{v1,t,\tau }^{DSO} \;:\;\mathop \pi \nolimits_2 \end{equation}80minΘDSO,β,γ,λcostd,τDSO+KPEN(βΔptgrid,τ+γΔδt,τ)+λt(Δptgrid,τ−Δδt,τ)\begin{equation}\mathop {\min }\limits_{\mathop \Theta \nolimits^{DSO} ,\beta ,\gamma ,\lambda } \left\{ \def\eqcellsep{&}\begin{array}{l} \mathop {\cos t}\nolimits_{d,\tau }^{DSO} + \mathop K\nolimits^{PEN} ({{\bm \beta }}\mathop {\;\Delta p}\nolimits_t^{grid,\tau } + {{\bm \gamma }}\;\Delta \mathop \delta \nolimits_{t,\tau } )\\[6pt] + \mathop \lambda \nolimits_t (\mathop {\Delta p}\nolimits_t^{grid,\tau } - \Delta \mathop \delta \nolimits_{t,\tau } ) \end{array} \right\}\end{equation}81LBd,τ=minΘDSO,β,γ,λcostd,τDSO+KPEN(βΔptgrid,τ+γΔδt,τ)−π(Δptgrid,τ−Δδt,τ)\begin{equation}\mathop {LB}\nolimits_{d,\tau } = \mathop {\min }\limits_{\mathop \Theta \nolimits^{DSO} ,\beta ,\gamma ,\lambda } \left\{ \def\eqcellsep{&}\begin{array}{l} \mathop {\cos t}\nolimits_{d,\tau }^{DSO} + \mathop K\nolimits^{PEN} ({{\bm \beta }}\mathop {\;\Delta p}\nolimits_t^{grid,\tau } \\[6pt] + {{\bm \gamma }}\;\Delta \mathop \delta \nolimits_{t,\tau } ) - {{\bm \pi }}\;(\mathop {\Delta p}\nolimits_t^{grid,\tau } - \Delta \mathop \delta \nolimits_{t,\tau } ) \end{array} \right\}\end{equation}82Eq.49−Eq.60\begin{equation}{\rm{Eq}}{\rm{.}}\;49 - {\rm{Eq}}{\rm{.}}\;60\end{equation}83UBd,τ=costτ−1TSO+costd,τDSO+KPEN(β.Δptgrid,τ+γ.Δδt,τ)\begin{eqnarray} \mathop {UB}\nolimits_{d,\tau } = \mathop {\cos t}\nolimits_{\tau - 1}^{TSO} + \mathop {\cos t}\nolimits_{d,\tau }^{DSO} + \mathop K\nolimits^{PEN} ({{\bm \beta }}.\mathop {\Delta p}\nolimits_t^{grid,\tau } + {{\bm \gamma }}.\Delta \mathop \delta \nolimits_{t,\tau } )\nonumber\\ \end{eqnarray}84(UBd,τ−LBd,τ)≤ε\begin{equation}(U{B_{d,\tau }} - L{B_{d,\tau }}) \le \varepsilon \end{equation}where in (75), the cost of TSOs and the total sum of the costs of DSOs are minimized in each iteration. Δptgrid,τ${{\Delta}}p_t^{grid,\tau }$and Δθtgrid,τ${{\Delta}}\theta _t^{grid,\tau }$in Equations (78) and (79) show the difference between the power and angle of the TSO‐DSO at the CCP for each iteration τ. Equation (80) expresses the objective function of the subproblem, i.e., the DSO problem. It is evident from this equation that TSO‐DSO boundary constraints can be relaxed to make DSO problems feasible. The non‐negative variables β and γ guarantee the feasibility of the DSO problem. TSO nodal prices are indicated by λt. KPEN represents the penalty coefficient of non‐equality of TSO and DSO parameters at the CCP. Equation (81) shows the lower bound of the subproblem's objective function. In this equation, π is a vector of dual variables of boundary constraints and consists of π1 and π2. Equation (83) indicates the upper bound of the DSOs' objective function. Equation (84) also takes into account the stopping condition. ε represents the stopping threshold of the proposed solution method. The overall flexibility procurement process is summarized in Figure 2.2FIGUREFlexibility procurement processSIMULATION RESULTS AND DISCUSSIONIn this paper, a modified 118‐bus grid is used for modelling TSO with data drawn from [13]. Four wind power plants with a nominal capacity of 560 MW are considered in this grid. These units are located at buses 17, 56, 94 and 100. Ten 33‐bus distribution systems, each with multiple MGs, are connected to the transmission grid as a DSO‐operated grid. These DSOs are located at buses 10, 20, …, 100. The data corresponding to distribution grids along with MG specifications are extracted from [10].To investigate the effect of providing flexibility by DSO, in one case DSO is considered without flexibility, that is, as a fixed load. In another case, the DSO is regarded as flexible demand from the TSO point of view. To study the effect of the reserve, in one case the amount and cost of the reserve are considered and in the other case, this amount of the reserve is not considered. In these two cases, the effect of the reserve on the amount of system flexibility is measured. Two conditions are also considered to examine the effect of DSO ownership on MGs. In one case, all MGs are assumed to belong to the DSO. In this case, the DSO offers energy or flexibility to the market from these MGs. Otherwise, MGs compete with each other for more profit. The equilibrium of this competition is where changes in the output power of each MG do not increase its profit [31].There are eight specific cases considering the reserve and the four DSO‐related scenarios. These cases are summarized in the following:Case 1: The reserve and its costs are not included. DSO flexibility is not provided. DSO owns the MGs.Case 2: The reserve and its costs are included. DSO flexibility is not provided. DSO owns the MGs.Case 3: The reserve and its costs are not included. DSO flexibility is provided. DSO owns the MGs.Case 4: The reserve and its costs are included. DSO flexibility is provided; however, ramping procurement cost is not considered separately. DSO owns the MGs.Case 5 to 8: The same as cases 1 to 4, except that in these cases, the DSO does not own the MGs. Therefore, the DSO's problem becomes a bi‐level problem.As mentioned previously, in all the above cases, TSO returns the market‐clearing results to the DSOs for better decision‐making. It will result in lowering the DSO's bid error. The simulation results are presented in Table 1. As can be comprehended from this table, in terms of market efficiency, the highest SW is related to the case in which DSO delivers its flexible sources to the DA market. In fact, DSO aggregates demand with higher MU rather than TSO, which increases overall SW. In other words, by providing a range of flexibility, DSO gives TSO the opportunity to compensate for changes in net bus loads at a lower cost. This range of flexibility is shown in Figure 3. As this figure shows, DSO can generate or consume variable output or input power at any time. Of course, the cost of each DSO operating point is different. Figure 4 shows the costs associated with each operating point. As shown in this figure, the cost of providing optimal DSO power is the lowest. That is, in normal network operation, the optimal DSO power values are selected and therefore the cost of operating the whole system is reduced.1TABLEComparison of simulation results by casesCasesSWTSOCostDSOΣ(BenefitMGs)Wspil [MW]FPU [MW]FPD [MW]FRU [MW/h]FRD [MW/h]Case17986536041411298639551353844413373427Case2754851600994572747550833845315133421Case37992146035211298625559403876822514054Case4759293600784586685560163890523234499Case57986536027911925639551353844413373427Case67548516011111884747550833845315133421Case77992146049211925625559403876822514054Case87592936020011890685560163890523234499FPU: flexible power‐up; FPD: flexible power‐down, FRU: flexible ramp up; FRD: flexible ramp down.3FIGUREAggregated flexible demand of DSO4FIGUREThe aggregated marginal cost of DSO flexibilityIn other operating modes where the need for DSO flexibility increases, TSO can utilize this flexibility at an additional cost.Figures 3 and 4 show the power values taken from the grid and the marginal prices corresponding to each case for a DSO. As shown in Figure 3, the flexible demand of case 3 is presented as the maximum value (p_max), the minimum value (p_min), and the optimal value (p_opt) with the lowest cost. Moreover, the prices corresponding to the powers are shown in Figure 4.The imposition of any extra cost such as reserve causes to reduce SW. Whereas it is costly to procure reserve for the entire system, it is not paid until it is deployed. Nevertheless, the reserve cost contributes to increased total revenue from generating units.Transmission reserve reduces MGs’ profit in the cases that DSO lacks MGs (cases 2 and 4). However, if DSO owns MGs (cases 6 and 8), the MGs’ profit value rises tangibly.The marginal cost of transmission reserve is less than the marginal cost of distribution units. So, in the former case, the former DSO tends to increase the amount of TSO imported instead of increasing the production of MGs. On the other hand, by increasing the amount of power input from the TSO, there may be a violation of the planned amount of power and thus increase the cost of input power in RT. Therefore, the best thing to do for DSO is to request the purchase of the right amount of transmission reserve in the first stage. This reserve value is determined based on load forecasting values ​​or probabilistic planning. In this paper, the adaptive robust approach is used to determine the amount of reserve. In the latter case, the DSO seeks to increase the profitability of MGs in addition to reducing operating costs. An increase in MGs profit is subject to an increase in the nodal prices. The increase in the nodal prices occurs if there is a violation of the planned amount of power.This contradicts the original purpose of the DSO. Therefore, DSO goals are at two different levels and a compromise must be reached between these goals. In other words, in the former, the DSO objective function is to meet the scheduled power with the least amount of deviation. At the same time, in the latter, in addition to the goal mentioned at the upper level, maximizing the profit of microgrids at the lower level is considered. Concerning the spilled wind power, the lowest value is attributable to the case with DSO flexible sources. The more the flexibility of DSO sources, the less will be the amount of spilled wind power. This reveals as if the flexibility of DSO has been employed to alleviate the consequences of the uncertainty of TSO. Of course, this has come at the cost of increasing operating costs. The higher the RES penetration, the lower the price increase. In other words, the value of flexibility for such power systems is greater.The reserve consideration causes an increase in Wspill because a percentage of flexible capacity of sources is being sold as the reserve. In Table 1, FPU (FPD) and FRU (FRD), as regards flexibility indices, are represented as the sum of remaining (curtailable) power capacity, and ramp‐up (down) of all units, respectively.The flexibility metrics vary depending on the direction of the net load increase or decrease. The simulation results prove that all system flexibility metrics are improved for a flexible system when considering the reserve. That is, the system readiness—to handle net load variations due to prediction error or contingency cases—increases.Considering reserve for an inflexible system causes a reduction in the FPD flexibility metric while increasing other metrics. Here, the actual wind power was higher than the predicted value, and for this reason, a percentage of units capacity is allocated to this unpredicted wind power. Thus, FPD decreases as FPU increases. With FPD reduction, Wspill reduces as well. However, the other ramp metrics have increased. This suggests that the wind power variation slope has not caused a severe limitation. As shown by Table 1, existing reserve in the transmission system leads to profit reduction for MGs connected to the distribution grid because it is assumed that DSO does not participate in reserve procurement. The DSO problem can be transformed into a bi‐level problem according to relations (72)–(76) to overcome this issue. Doing so will guarantee MGs profit, which is well demonstrated by the results of cases 5 to 8. For cases where DSO flexibility (items 3–4 and 7–8) serves the TSO, the amount of flexibility indexes increases significantly. This means that the sum of the TSO and DSO flexibility is available to the entire power system. Of course, it should be noted that due to network limitations, this will not be an algebraic sum. Simultaneous transmission reserve and distribution flexibility increase the flexibility of the entire power system. For example, transmission reserve increases the FRU by 176 units (differences between items 1 and 2). Distribution flexibility also increases the index by 914 points (differences in items 1 and 3). The sum of these two is more than the simultaneous effect of transmission reserve and DSO flexibility (differences between cases 4 and 1). This reflects the interaction between transmission reserve and distribution flexibility. This is due to CCP restrictions. The results in Table 1 show that DSO ownership of DGs has no effect on flexibility indexes. It only slightly increases operating costs. This cost increase is due to the DSO compromise between the deviation of power transfer from the CCP and the profit of the MGs. Using transmission reserve reduces DSO costs. Because the marginal cost of transmission reserve is less than the marginal cost of producing MGs. In all of the above cases, the income of the microgrids and the cost of the loads are entirely dependent on the nodal prices. Figure 5 shows the nodal prices for CCP1 (connection point of DSO1 to the transmission network) for the third case. As can be seen from this figure, the trend of market price changes of the first stage (DA) and the second stage (BS) are similar. When the share of wind power supplied from CCP increases, the BS price is higher than the DA price. In this case, the flexibility of the system is used to provide sufficient power and ramps. This flexibility costs the same as the DA and BS price difference. At these times (t1–t3, t10–t12, and t14–t24) the amount of actual wind power is higher than forecasted. During t5–t9 times, adequate power reduction by flexible network sources reduced the BS price relative to the DA.5FIGUREThe locational marginal cost of DA and BS in CCP1CONCLUSIONIn this paper, the collaboration between TSOs and DSOs in DAM to provide power system flexibility was investigated. The distribution grid can act fully flexible to procure the grid's flexibility. That means when a higher ramping capability is required, this grid can meet the extra demand by altering the adjustment values of DERs, which comes at the price of receding from the optimal operation point of units. Furthermore, in situations where net load variations on the bus bar are low, DER adjustments can provide higher power values. This indicates the flexibility of DSO control in procuring flexible services of the entire system. The extraction of DSO flexibility to deal with the effects of variability and uncertainty of RESs on the entire power system was investigated with the robust approach.The simulation results showed that the deployment of flexible resources, located at the DSO level, enhances the technical and economic metrics of the entire power system. In this regard, DSO has a key role in the provision of more flexible resources at the distribution level. It was assumed here that each DSO also included some MGs. If the MGs are under DSO's ownership, it acts either as a local operator or an aggregator. So, the DSO's problem became a bi‐level that ensured the profitability of MGs.Reserve services affect the flexibility of the system and, for a flexible system, improve the flexibility metrics of the overall system. Lack of participation of DSO in reserve procurement reduces the profit of its connected MGs. To resolve this issue, the DSO problem is solved as a bi‐level problem by considering MGs profit. The reserve affects the system flexibility by enhancing the metrics for a flexible system while causing them to reduce for an inflexible system.FUNDING INFORMATIONNoneCONFLICT OF INTERESTNoneDATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.ACKNOWLEDGEMENTThe authors thank Dr. Hanna Niemelä for her assistance with proofreading of the paper and comments that greatly improved the manuscript.NOMENCLATURE0Initial value (state)ASets and IndicesBAbbreviations and superscriptsBSBalancing stageCConstantsc(.)Marginal cost [$/MWh]c(.)SU0,SD0Up/down reserve cost [$/MWh]c(.)u/dUp/down reserve cost [$/MWh]CCPCommon coupling pointChChargeCLCleareddIndex of DSODVariablesD+/‐Maximum up/down DR [MW]DADay‐aheadDayDailydgIndex of distributed generationDisDischargeDRDemand responsedrpDrop‐downEdayShiftable energy [MW]fMaximum line flow [MW]fcForecastedFSPFlexible service provideriIndex of generatorsInSet and of generators connected to bus njIndex of loadsJnSet and of loads connected to bus nLLoad [MW]LBLower boundm,nIndices of busesmgIndex of microgridsMGnSet of microgrids connected to bus nMnSet of buses connected to bus nP(.)(.)PowerpiuPick‐upPMPump modePP(s,t)Power consumption in pump modePT(s,t)Power production in turbine modeqIndex of wind turbine unitsQMaximum water flow [m3/s]qDR(mg,z,t)Quantity of zth(DR) block [MW]QnSet and of wind turbine units connected to bus nQP(s,t)Water flow in pump modeQT(s,t)Water flow in turbine modeRdDown reserveRDMaximum ramp‐down limit [MW/h]RD(i,t)Down‐reserverd(i,t)Deployed down‐reserveRuUp reserveRUMaximum ramp‐up limit [MW/h]RU(i,t)Up‐reserveru(i,t)Deployed up‐reservesIndex of pumped‐storage unitsSDShut‐downShedLoad sheddingSnSet of pumped‐storage units connected to bus nSUStart‐upt,t´Index of timeTMTurbine modeTu/dMinimum (up/down) timeUUp, upper levelUBUpper boundUu/dUp/down marginal utility [$/MWh]v(i,t)On/off state of unitsVol(s,t)Volume of reservoirVOLLValue of lost load [$/MWh]w(q,t)Actual wind power outputwFCForecasted RES output [MW]wspill(q,t)Spilled wind power outputxPer‐unit line reactancey(i,t)Binary variable of starting up at the beginning of the periodzIndex of demand response blocksz(i,t)Binary variable of shutting down at the beginning of the periodα, β, γCoefficients of generation cost functionΓConservation factorδ(.,t)Phase angleΔw(q,t)Deviation of wind power outputΔw+/‐(q,t)Up/down‐ward deviation of RESΔwmaxMaximum deviation [MW]ηCharge efficiencyΘSet of decision variablesλ(.,t)Marginal costσConversion factor water flowREFERENCESZegers, A., Brunner, H: TSO‐DSO interaction: An overview of current interaction between transmission and distribution system operators and an assessment of their cooperation in Smart Grids. 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Day‐ahead flexibility market clearing mechanism for interactive collaboration of transmission and distribution system operators

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© 2022 The Institution of Engineering and Technology.
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10.1049/gtd2.12474
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Abstract

INTRODUCTIONOne most important reason for the growing tendency toward collaboration between the DSOs and TSOs is the increased number of RESs connected to the grid. These intermittent and uncertain resources have posed new challenges to the operation of power systems. In [1] the faced challenges by power system operators have been described and the necessity to foster collaboration between TSO and DSO to overcome these issues have been highlighted. One of the most important challenges is the need to provide more flexibility for the power system. From these perspectives, flexibility can be defined as the ability of the power system to reduce the adverse effects of predictable or unpredictable changes to any of the elements or parameters of the power system which in turn leads to increasing costs, endangering the power system security, or deteriorating any other security‐related index of the power system.The transmission and distribution grids are physically interconnected such that changes occurring in one system may affect the other one's performance as well. The separate operation of transmission and distribution grids leads to undesirable exploitation of the total potential flexibility capacity of the entire power system. Thus, the coordinated operation of TSO‐DSO enhances the technical and economic efficiency of the whole power system. The flexibility sources are classified based on the supply source type, grid connection location, planning period, technical specifications such as energy amount, power capacity, and ramping capacity, and also their applications, including balancing power at transmission grid, balancing power at distribution grid and distribution grid management [2–4]. These resources are available at the transmission and distribution levels. Purposeful use of these resources for better use of the power system can be useful.While the motivations of TSOs and DSOs toward flexibility procurement for their corresponding grids might differ, however, enhancing flexibility improves the entire system performance facing RES uncertainties. In [5], utilization of the power system flexibility potential for reinforcement investment deferral of the distribution grid in the presence of DERs is regarded as the most significant multi‐year motivation of DSOs. These investments focus on the installation of new lines and transformers. In addition to long‐term contracts of off‐market flexibility procurement, the existence of a market for the flexibility provided in the presence of other buyers improves the overall welfare. With the increase in renewable energy production and distributed energy resources (DER), flexibility markets are developed to aid the performance of evolving power systems [6].These markets are more suitable for providing flexibility to meet DSO's short‐term goals. The short‐term goals of DSOs to use the flexibility services may include power balancing within the distribution grid, congestion management, and voltage management. These goals can be achieved to some extent by the resources available at the distribution level, provided that these resources are economically motivated. Therefore, one of the most essential DSOs’ goals is the direct or indirect access of flexible generation sources to free energy markets. The existing sources at the distribution level can be employed to procure the flexibility services of the entire power system. These sources usually have a reasonable response speed to the net load variations of the grid. The economic operation of these sources in a local or centralized market can increase their motivations to procure flexible services [7–9]. Each market, either local or centralized, faces its respective benefits and drawbacks. A local market in the presence of retailers offers low liquidity and high market power and, consequently, attracts little interest for the participation of small sources. Still, the local market fulfils the high‐priority DSO needs while reducing the computational burden. In [10], establishing the unique flexibility markets for TSO and DSO service procurement and avoiding the local markets has been recommended.Depending on the user and the purpose of the usage, the flexibility resources could match the various needs or potentially cause conflict themselves. Therefore, it is crucial to establish an appropriate market framework to benefit from the flexible resources of the entire grid [11, 12].An alternate approach seems to be the existence of a centralized market with separate operators for each grid. In other words, from the TSOs’ viewpoint, the DSO's grid is seen as an aggregated generator or flexible load that can deliver its services to the upstream grid. This model is more consistent with the current structure of existing markets. As an example, [13] presents a hierarchical market to incentivize the participation of multiple microgrids (MGs) in the balancing markets. An economic comparison suggests that the TSO‐DSO interaction is favourable for both MGs and transmission systems.Existing markets are primarily focused on flexible ramp product (FRP) procurement. TSO requests FRP to overcome the increased uncertainty in net demand. These services, which are traded in times close to real‐time (RT), use the flexible units to help the traditional units as a reserve, rapidly and without occupation of the production capacity [14].Generally, strict ramping limitations are not imposed in distribution grids [13]. Thus, DSO can help establish the power balance using the flexible resources in the distribution grids. Depending on the user and the purpose of the usage, the flexibility resources could match the various needs or potentially cause conflict themselves. Therefore, it is crucial to establish an appropriate market framework to benefit from the flexible resources of the entire grid [14, 15].While FRP is currently presented for RT markets only, its procurement prediction in DA or intraday (ID) markets is imperative. This leads to risk reduction for generators revenue under DA price. FRP can be optimized simultaneously with energy and ancillary services. From the NYISO perspective, ramp procurement in the RT market entails no cost. The shortage pricing methodology, currently used for operation and regulation reserve, is applied for ramp [15]. To ensure power balance, considered FRP should be larger than the predicted value. In [16], the ramp modelling has been elaborated in the existing markets. A drawback to current methods is that they only address the ramp of existing sources and neglect the ramp amount needed by the entire system. This might compromise system reliability and lead to price fluctuations and mathematically infeasible solutions to the problem. One strategy to overcome this issue is to consider the entire system's ramp in the DA market. Such a market is exploited in this paper for DSO flexibility service procurement at the transmission level. An overview of the market framework for the latter is shown in Figure 1. In this figure microgrids (MGs) are identified as an inseparable part of recent distribution systems. MGs usually supply part of the demands of a local network. This amount of energy is provided by MGs for economic reasons or to increase consumer reliability. In addition, MGs can be a good resource for providing system flexibility. However, using MGs can be challenging. From a market perspective, the role of the DSOs varies depending on the MGs’ ownership. If the MGs belong to a DSO, the goal is to maximize the total profit of the MGs. The DSO, therefore, acts as an aggregator. Conversely, if the DSO does not own the MGs, each MG seeks to maximize its profits, while the DSO can be brought up as a local operator. Therefore, providing flexibility by MGs increases the complexity of the market‐clearing process, which is rarely addressed in the presented papers in the area. So, in this paper, the effect of MGs under DSO ownership on flexibility procurement is investigated.1FIGUREOverview of the market frameworkHere, the DA market sources are scheduled based on the robust adaptive approach to encounter the predicted uncertainties. Clearing of DA markets with high penetration of RESs is performed in a two‐ or multi‐stage fashion. In the first stage, the sources’ ‐DA dispatch costs are obtained using the scheduled or predicted values. The second stage calculates the real‐time expected balancing cost based on the system's uncertainties. This method considers a sufficient amount of flexibility to overcome system uncertainty in real‐time. In [17] and [18], four techniques are presented to clear such a market based on the market design philosophy.However, currently in most existing DA markets, the flexibility required by the system is provided through the ancillary services market, especially the reserve market. But the impact of this market on the flexibility of the power system has not been well studied. For example, power plant units may be reserved to provide load capacity changes. If this amount of reserve is determined regardless of the amount of ramp load, it may cause more problems for the system. In [19], the utilization of spinning reserve for FRU procurement through the DA market is proposed. In the paper, it was assumed that the spinning reserve is present, and its value is given beforehand; however, a DA market mechanism for its provision is not stated.Therefore, it can be understood that the amount of reserve affects the ability of the system to cope with changes. For this reason, this article examines the reserve impact on flexibility procurement for the power system.Various metrics are introduced for the quantitative measurement of flexibility [20–24]. These metrics are most beneficial for the planning studies of the power systems, as the adjustment points of sources might change during operation at each time interval, depending on the operator's current decisions. For this reason, some available research in the area, for example, ref. [25] presents the online metrics to estimate the system flexibility. On the whole, defining these metrics is to predict the system capability against the existing uncertainties in RESs and loads [26]. Since the grid flexibilities have various spectra and applications, defining a single metric is insufficient to describe the grid flexibility. For instance, a grid may effectively react to an increase in wind power but not a decrease of the same amount. Thus, in this paper, several flexibility metrics, including flexible power‐up (FPU), flexible power‐down (FPD), flexible ramp‐up (FRU), flexible ramp‐down (FRD), and spilled wind power, are taken into account [27].The postulated market in this article is of energy‐only type. In energy‐only markets, the reserve is not traded as a separate commodity; instead, it is achieved as a by‐product of the energy market clearing. In this case, there is no need to estimate the reserve amount, and also, no price bid for reserve. Therefore, no extra cost is paid for a reserve that has not been converted to energy. A fundamental flaw of this method is the uncertainty of the revenue generated from such reserves [28]. However, by applying risk management methods or introducing financial participants, the providers’ profit drop can be minimized.Accordingly, this paper examines the DSO's resources impact on flexibility procurement for the power system. To the best authors, knowledge, the main contributions of this paper with respect to the available research in the area can be summarized as follows:-Two‐stage clearing of DA market mechanism based on a robust adaptive approach is presented to meet the flexibility demands of the entire system in DA market using existing sources in both transmission and distribution levels. Using existing resources at the transmission and distribution levels, this paper examines the provision of required flexibility for the entire power system. The flexibility is provided in the DAM because of the uncertainty at the load buses. Accordingly, based on the predicted values of the loads, the amount of power generation and ramping of the units are determined in the first step. According to the worst‐case scenario, the second stage modifies the values obtained from the first stage. That is, the operators adjust the scheduled values according to the predicted values, but they are also prepared to deal with the worst‐case scenario. At times being close to RT, the system maybe does not require any additional flexibility. Fast‐ramping units are therefore less stressed as a result. Consequently, the first‐ and second‐stage reservations, such as frequency control reservations, are no longer necessary. Furthermore, the market‐clearing mechanism should simultaneously fulfil TSO and DSO restrictions. Accordingly, one solution is to use a central market framework. With global optimization, this market makes full use of flexibility. This type of market, however, runs slowly because of the volume of information while the DSO´s information should also be fully observable by the TSO. The method also has the disadvantage of not prioritizing network flexibility for TSOs or DSOs. It is no longer possible to use these services if the TSO urgently needs flexibility, while the DSO has already purchased them. A distributed MILP formulation based on primal problem solving is used to overcome this issue. In this model, TSOs and DSOs agree on exchanging the power and price through an iterative process.-Flexible sources at distribution level are aggregated by DSOs to present in the upstream markets for TSOs’ flexibility procurement. Generally, strict ramp limitations are not imposed in distribution grids [25]. Thus, DSO can help to support the power balance using its available flexible resources. Therefore, even though distribution‐level flexibility resources have a small size, they can react quickly. Thus, these sources, which can be either DGs or MGs, are suitable for the fast‐ramping requirements of the grid. Using an appropriate market mechanism, it is possible to increase the economic incentive for these resources to participate in providing flexibility. In contrast, since there are so many resources, their participation must be coordinated through an aggregator. In this paper, the distribution network with flexible resources is considered as a controllable load from TSO's viewpoint. Accordingly, TSO is notified by DSOs about maximum, minimum, and ramp values. When the TSO does not need additional flexibility, it exchanges the same predetermined values with the DSO. If not, buying flexibility from DSO will increase TSO operating costs. This may increase overall operating costs, but it increases the profitability of DGs and MGs and reduces RES output spillage. Thus, distribution resources are motivated to provide flexibility at the transmission level.-The impact of MGs under DSO ownership to procure flexibility is modelled and studied. DSO faces challenges in leveraging the potential of MGs to provide flexibility. If, as assumed in this article, DSO also acts as an aggregator, then ownership of MGs becomes a serious issue. If the DSO owns the MGs, its goal is either to maximize profits or to enhance RES uptake or any other objective function. In contrast, if the DSO does not own the MGs, each MG tries to maximize its profits, while the DSO tries to maintain the scheduled values at the CCP. Therefore, the DSO problem becomes one of the Stackelberg games with multiple leaders and followers. MGs are lower‐level problems, while DSO is the upper level. Accordingly, the upstream TSO market announces hourly prices for DSOs. Based on these prices, CCP power is exchanged. Regarding centralized market execution, we face a tri‐level problem. Furthermore, this model over‐complicates the problem in addition to the disadvantages cited for the centralized market. Therefore, this paper employs the distributed MILP method to overcome this issue. Essentially, the tri‐level problem becomes a bi‐level problem, much less complex than before. By publishing the price by TSO, then DSO and MG decide the amount of power to be exchanged. Once the amount of the power to be exchanged has been determined, TSO announces the updated prices to DSO by re‐launching the upstream market. This trend continued until the price equilibrium and convergence of the TSO‐DSO power exchange is reached at the CCP.-The effect of the reserve on the flexibility procurement process is modelled and investigated. Currently, in the existing DA markets, the flexibility is traded through ancillary service markets, especially the reserve market. Although, some references offer ramps during close to RT operation, the reserve market by its nature does not include ramp restrictions. On the other hand, flexibility markets can also provide the necessary reservation based on the system's needs. In other words, this market can simultaneously supply the energy, power, and ramping requirements of the system. Therefore, in this paper, the effect of system reserve on the proposed market of this paper is investigated. The postulated market here is of energy‐only type. In energy‐only markets, the reserve is not traded as a separate commodity; instead, it is achieved as a by‐product of the energy market clearing. In this case, there is no need to estimate the reserve amount and present the price bid for reserve. Therefore, no extra cost is paid for a reserve that has not been called for energy. A fundamental flaw of this method is the uncertainty of the revenue generated from such reserves [28]. However, by applying risk management methods or introducing financial participants, the providers’ profit drop can be minimized.In summary, this paper provides the required flexibility of the power system in the face of RES uncertainties using the resources available at the distribution level and in cooperation with the TSO on the DAM framework. The effect of DSO´s ownership on MGs and reservation amount on power system flexibility have also been investigated.The remainder of this paper is organized as follows: Section 2 presents the TSO‐DSO collaboration problem formulation in detail. In Section 3, simulation results and discussion are presented and Section 4 concludes the paper.TSO‐DSO COLLABORATION PROBLEM FORMULATIONIn this section, the problem formulation of the proposed TSO‐DSO framework for procurement of flexibility services in the power system in the day‐ahead market (DAM) is expressed.TSO modelEquations (1)–(49) demonstrate the mathematical formulation to model TSO and market clearing. The TSO objective function, given in (1), includes the social welfare (SW) maximization or operation cost minimization for a situation where predicted values of wind units are at their highest deviation. Equation (2) gives the units dispatch cost in the first stage with expected or scheduled values, and (3) calculates the re‐dispatch costs in the second stage, that is, balancing stage.1costTSO=minΘDAcostDA+maxΔwminΘBScostBS\begin{equation}\mathop {\cos t}\nolimits^{TSO} = \mathop {\min }\limits_{\mathop \Theta \nolimits_{DA} } {\rm{\ }}\left\{ {{\rm{cos}}{t^{DA}} + \mathop {\max }\limits_{\Delta w} {\rm{\ }}\left[ {\mathop {\min }\limits_{\mathop \Theta \nolimits_{BS} } {\rm{\ }}\left( {{\rm{cos}}{t^{BS}}} \right)} \right]} \right\}\end{equation}2costDA=∑i,tci.pi,tDA+ci,tsu+ci,tsd+ciRu.Ri,tU+ciRd.Ri,tD+∑q,tcq.wq,tfc−∑j,tLj,tfc.uj,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} {\rm{cos}}{t^{DA}} = \displaystyle\mathop \sum \limits_{i,t} \left({c_i}.p_{i,t}^{DA} + c_{i,t}^{su} + c_{i,t}^{sd} + c_i^{Ru}.R_{i,t}^U + c_i^{Rd}.R_{i,t}^D\right)\\[14pt] \qquad\qquad+\, \displaystyle\mathop \sum \limits_{q,t} \left({c_q}.w_{q,t}^{fc}\right) - \displaystyle\mathop \sum \limits_{j,t} \left(L_{j,t}^{fc}.{u_{j,t}}\right) \end{array} \end{equation}3costBS=∑i,tciu.ri,tu−cid.ri,td+∑q,tcq.wq,t−wq,tfc−wq,tspill+∑j,t.vollj.Lj,tshed−uj,td.Lj,td+uj,tu.Lj,tu\begin{equation}{\rm{cos}}{t^{BS}} = \left\{ \def\eqcellsep{&}\begin{array}{l} {\rm{\ }}\displaystyle\mathop \sum \limits_{i,t} c_i^u.r_{i,t}^u - c_i^d.r_{i,t}^d\\[12pt] + \displaystyle\mathop \sum \limits_{q,t} {c_q}.\left( {{w_{q,t}} - w_{q,t}^{fc} - w_{q,t}^{spill}} \right)\\[15pt] + \displaystyle\mathop \sum \limits_{j,t} .vol{l_j}.L_{j,t}^{shed} - u_{j,t}^d.L_{j,t}^d + u_{j,t}^u.L_{j,t}^u \end{array} \right\}\end{equation}4∑i∈Inpi,tDA+∑q∈Qnwq,tFC−∑j∈JnLj,tFC−∑m∈Mn1xmn.δn,t0−δm,t0+∑sεSnPs,tTM,DA−Ps,tPM,DA=0,∀n,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} \displaystyle\mathop \sum \limits_{i \in {I_n}} p_{i,t}^{DA} + \displaystyle\mathop \sum \limits_{q \in {Q_n}} w_{q,t}^{FC} - \displaystyle\mathop \sum \limits_{j \in {J_n}} L_{j,t}^{FC} - \displaystyle\mathop \sum \limits_{m \in {M_n}} \frac{1}{{{x_{mn}}}}.\left( {\delta _{n,t}^0 - \delta _{m,t}^0} \right)\\[15pt] \quad + \displaystyle\mathop \sum \limits_{s\epsilon {S_n}} \left( {P_{s,t}^{TM,DA} - P_{s,t}^{PM,DA}} \right) = 0{\rm{,}}\forall n,t \end{array} \end{equation}51xmn.δn,t0−δm,t0≤fn,mmax,∀m,n,t\begin{equation}\frac{1}{{\mathop x\nolimits_{mn} }}.\left(\mathop \delta \nolimits_{n,t}^0 - \mathop \delta \nolimits_{m,t}^0 \right) \le \mathop f\nolimits_{n,m}^{\max } ,\forall m,n,t\end{equation}6pi,tDA+Ri,tU≤vi,t.pimax,∀i,t\begin{equation}p_{i,t}^{DA} + R_{i,t}^U \le {v_{i,t}}.p_i^{max},\forall i,t\end{equation}7pi,tDA−Ri,tD≥vi,t.pimin\begin{equation}p_{i,t}^{DA} - R_{i,t}^D \ge {v_{i,t}}.p_i^{min}\end{equation}8ciSU≥ciSU0.vi,t−vi,t−1\begin{equation}c_i^{SU} \ge c_i^{SU0}.\left( {{v_{i,t}} - {v_{i,t - 1}}} \right)\end{equation}9ciSD≥ciSD0.vi,t−1−vi,t\begin{equation}c_i^{SD} \ge c_i^{SD0}.\left( {{v_{i,t - 1}} - {v_{i,t}}} \right)\end{equation}10pi,tDA−pi,t−1DA≤RUi.vi,t−1\begin{equation}p_{i,t}^{DA} - p_{i,t - 1}^{DA} \le R{U_i}.{v_{i,t - 1}}\end{equation}11pi,t−1DA−pi,tDA≤RDi.vi,t\begin{equation}p_{i,t - 1}^{DA} - p_{i,t}^{DA} \le R{D_i}.{v_{i,t}}\end{equation}12∑t=1Tiuvi,t≤Tiu\begin{equation}\mathop \sum \limits_{t = 1}^{T_i^u} {v_{i,t}} \le T_i^u\end{equation}13∑t′=tt+Tiu−1vi,t′≥Tiu.yi,t,Tiu<t≤T−Tiu+1\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^{t + T_i^u - 1} {v_{i,t^{\prime}}} \ge T_i^u.{y_{i,t}},T_i^u &lt; t \le T - T_i^u + 1\end{equation}14∑t′=tTvi,t′−yi,t≥0,T−Tiu+1<t≤T\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^T {v_{i,t^{\prime}}} - {y_{i,t}} \ge 0,T - T_i^u + 1 &lt; t \le T\end{equation}15∑t=1Tidvi,t=0\begin{equation}\mathop \sum \limits_{t = 1}^{T_i^d} {v_{i,t}} = 0\end{equation}16∑t′=tt+Tid−11−vi,t′≥Tid.zi,t,Tid<t≤T−Tid+1\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^{t + T_i^d - 1} 1 - {v_{i,t^{\prime}}} \ge T_i^d.{z_{i,t}}{\text{\ \ }},{\text{\ \ }}T_i^d &lt; t \le T - T_i^d + 1\end{equation}17∑t′=tT1−vi,t′−zi,t≥0T−Tiu+1<t≤T\begin{equation}\mathop \sum \limits_{t^{\prime} = t}^T 1 - {v_{i,t^{\prime}}} - {z_{i,t}} \ge 0{\text{\ \ \ \ \ \ }}T - T_i^u + 1 &lt; t \le T{\rm{\ }}\end{equation}18PTs,tDA=σs,tT.QTs,tDA\begin{equation}PT_{s,t}^{DA} = \sigma _{s,t}^T.QT_{s,t}^{DA}\end{equation}19PPs,tDA=σs,tP.QPs,tDA\begin{equation}PP_{s,t}^{DA} = \sigma _{s,t}^P.QP_{s,t}^{DA}\end{equation}20vols,tDA,u=vols,t−1DA,u+QPs,tDA−QTs,tDA\begin{equation}vol_{s,t}^{DA,u} = vol_{s,t - 1}^{DA,u} + QP_{s,t}^{DA} - QT_{s,t}^{DA}\end{equation}21vols,tDA,l=vols,t−1DA,l−QPs,tDA+QTs,tDA\begin{equation}vol_{s,t}^{DA,l} = vol_{s,t - 1}^{DA,l} - QP_{s,t}^{DA} + QT_{s,t}^{DA}\end{equation}22vols,tDA,u≥vols,t0,u\begin{equation}vol_{s,t}^{DA,u} \ge vol_{s,t}^{0,u}\end{equation}23vols,tDA,l≥vols,t0,l\begin{equation}vol_{s,t}^{DA,l} \ge vol_{s,t}^{0,l}\end{equation}Equations (24)–(47) describe the constraints of the second stage. Equation (24) shows the power balance at this stage. Equations (30), (31) convey the increasing or decreasing power limitations based on the pre‐specified reserve values. Equations (32)–(37) model the flexible loads. Relation (32) displays the lowest daily amount of energy required for shiftable loads. Equations (38)–(47) formulate the pumped‐storage power plants in the second stage.24∑i∈Inri,tu−ri,td+∑j∈JnLj,tshed+Lj,tu−Lj,td+∑q∈Qnwq,t−wq,tfc−wq,tspill−∑m∈Mn1xmnδn,t−δn,t0−δm,t−δm,t0+∑s∈SnΔPTs,t−ΔPPs,t=0,∀n,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} \displaystyle\mathop \sum \limits_{i \in {I_n}} r_{i,t}^u - r_{i,t}^d + \displaystyle\mathop \sum \limits_{j \in {J_n}} L_{j,t}^{shed} + L_{j,t}^u - L_{j,t}^d\\[15pt] + \displaystyle\mathop \sum \limits_{q \in {Q_n}} {w_{q,t}} - w_{q,t}^{fc} - w_{q,t}^{spill} \\[15pt] - \displaystyle\mathop \sum \limits_{m \in {M_n}} \frac{1}{{{x_{mn}}}}\left[ {\left( {{\delta _{n,t}} - \delta _{n,t}^0} \right) - \left( {{\delta _{m,t}} - \delta _{m,t}^0} \right)} \right]\\[15pt] + \displaystyle\mathop \sum \limits_{s \in {S_n}} \Delta P{T_{s,t}} - \Delta P{P_{s,t}} = 0{\rm{\ ,}}\forall n,t \end{array} \end{equation}251xmn.(δn,t−δm,t)≤fn,mmax,∀m,n,t\begin{equation}\frac{1}{{\mathop x\nolimits_{mn} }}.(\mathop \delta \nolimits_{n,t} - \mathop \delta \nolimits_{m,t} ) \le \mathop f\nolimits_{n,m}^{\max } ,\forall m,n,t\end{equation}26wq,tspill≤wq,t\begin{equation}w_{q,t}^{spill} \le {w_{q,t}}\end{equation}27pi,t=pi,tDA+ri,tu−ri,td\begin{equation}{p_{i,t}} = p_{i,t}^{DA} + r_{i,t}^u - r_{i,t}^d\end{equation}28pi,t−pi,t−1≤RUi.vi,t−1\begin{equation}\mathop p\nolimits_{i,t} - \mathop p\nolimits_{i,t - 1} \le R{U_i}.{v_{i,t - 1}}\end{equation}29pi,t−1−pi,t≤RDi.vi,t\begin{equation}\mathop p\nolimits_{i,t - 1} - \mathop p\nolimits_{i,t} \le R{D_i}.{v_{i,t}}\end{equation}30ri,tu≤Ri,tu\begin{equation}r_{i,t}^u \le R_{i,t}^u\end{equation}31ri,td≤Ri,td\begin{equation}r_{i,t}^d \le R_{i,t}^d\end{equation}32∑tLj,t≥Ejday\begin{equation}\mathop \sum \limits_t {L_{j,t}} \ge E_j^{day}\end{equation}33Lj,t−Lj,t−1≤Ljpiu\begin{equation}{L_{j,t}} - {L_{j,t - 1}} \le L_j^{piu}\end{equation}34Lj,t−1−Lj,t≤Ljdrp\begin{equation}{L_{j,t - 1}} - {L_{j,t}} \le L_j^{drp}\end{equation}35Lj,t=Lj,tfc+Lj,td−Lj,tu−Lj,tshed\begin{equation}{L_{j,t}} = L_{j,t}^{fc} + L_{j,t}^d - L_{j,t}^u - L_{j,t}^{shed}\end{equation}36Lj,td≤Dj,t+\begin{equation}L_{j,t}^d \le D_{j,t}^ + \end{equation}37Lj,td≤Dj,t+\begin{equation}L_{j,t}^d \le D_{j,t}^ + \end{equation}38PTs,t=σs,tT.QTs,t\begin{equation}\mathop {PT}\nolimits_{s,t} = \sigma _{s,t}^T.\mathop {QT}\nolimits_{s,t} \end{equation}39PPs,t=σs,tP.QPs,t\begin{equation}\mathop {PP}\nolimits_{s,t} = \sigma _{s,t}^P.\mathop {QP}\nolimits_{s,t} \end{equation}40vols,tu=vols,t−1u+QPs,t−QTs,t\begin{equation}vol_{s,t}^u = vol_{s,t - 1}^u + \mathop {QP}\nolimits_{s,t} - \mathop {QT}\nolimits_{s,t} \end{equation}41vols,tl=vols,t−1l−QPs,t+QTs,t\begin{equation}vol_{s,t}^l = vol_{s,t - 1}^l - \mathop {QP}\nolimits_{s,t} + \mathop {QT}\nolimits_{s,t} \end{equation}42vols,tu≥vols,t0,u\begin{equation}vol_{s,t}^u \ge vol_{s,t}^{0,u}\end{equation}43vols,tl≥vols,t0,l\begin{equation}vol_{s,t}^l \ge vol_{s,t}^{0,l}\end{equation}44volsu,min≤vols,tu≤volsu,max\begin{equation}vol_s^{u,min} \le vol_{s,t}^u \le vol_s^{u,max}\end{equation}45volsl,min≤vols,tl≤volsl,max\begin{equation}vol_s^{l,min} \le vol_{s,t}^l \le vol_s^{l,max}\end{equation}46QTs,t≤QPsmax\begin{equation}Q{T_{s,t}} \le QP_s^{max}\end{equation}47QPs,t≤QPsmax\begin{equation}Q{P_{s,t}} \le QP_s^{max}\end{equation}DSO modelThis paper addresses DSO participation to procure required flexible services of the grid. To this end, four prominent scenarios are considered for DSO modelling. Here, each DSO is assumed to consist of multiple MGs.Scenario 1: As for the inflexible loads, DSO aggregates MGs and other demands and presents its bid and available power to the market. These values are, in fact, the results of the economic dispatch (ED) program, according to (48)–(60), that DSO implements on an hourly basis with the objective of SW maximization or operation costs minimization. In fact, in this case, the DSO can act as an aggregator.Equation (48), that is, the objective function shows the total DSO's operation costs. λ is the locational marginal price (LMP) of the TSO's bus to which the DSO is connected. Equations (49) and (50) show the operation costs of DGs and DR, respectively. Equation (51) expresses the power balance relationship for each DSO bus, (52) and (53) the distribution limits of distribution lines and DGs. Equations (54) and (55) present the constraints of DR blocks. Equations (56)–(59) represent the equations for electrical storage. Finally, Equation (60) shows the power balance relationship of each MG.48minΘDSO∑mg∑dgC(pdg,t)+ptgrid.λt+cmg,tDR,∀t\begin{equation}\mathop {\min }\limits_{\mathop \Theta \nolimits^{DSO} } \sum_{mg} {\left\{ {\sum_{dg} {C(\mathop p\nolimits_{dg,t} ) + \mathop p\nolimits_t^{grid} .\mathop \lambda \nolimits_t + \mathop c\nolimits_{mg,t}^{DR} } } \right\}}, \quad \forall t\end{equation}49C(pdg,t)=αdg+βdg.pdg,t+γdg.pdg,t2\begin{equation}C ( {{p_{dg,t}}}) = {\alpha _{dg}} + {\beta _{dg}}.{p_{dg,t}} + {\gamma _{dg}}.{p_{dg,t}}^2\end{equation}50Cmg,tDR=∑zcmg,z.qmg,z,tDR.umg,z,tDR\begin{equation}C_{mg,t}^{DR} = \sum_z {{c_{mg,z}}} .q_{mg,z,t}^{DR}.u_{mg,z,t}^{DR}\end{equation}51ptgrid+∑m∈Mn1xmn(δn,t−δm,t)=pn,tload−∑mg∈MGnpmg,tsell−pmg,tbuy,∀n,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} \mathop p\nolimits_t^{grid} + \displaystyle\sum_{m \in \mathop M\nolimits_n } {\frac{1}{{\mathop x\nolimits_{mn} }}} (\mathop \delta \nolimits_{n,t} - \mathop \delta \nolimits_{m,t} ) \\[15pt] \quad =\,\mathop p\nolimits_{n,t}^{load} - \displaystyle\sum_{mg \in \mathop {MG}\nolimits_n } {\left(\mathop p\nolimits_{mg,t}^{sell} - \mathop p\nolimits_{mg,t}^{buy} \right)}, \quad \forall n,t \end{array} \end{equation}521xmn.(δn,t−δm,t)≤fn,mmax,∀m,n,t\begin{equation}\frac{1}{{{\rm{ }}{x_{mn}}}}.({\delta _{n,t}} - {\delta _{m,t}}) \le {\rm{ }}f_{n,m}^{\max },\forall m,n,t\end{equation}53pdgmin≤pdg,t≤pdgmax\begin{equation}p_{dg}^{min} \le {p_{dg,t}} \le p_{dg}^{max}\end{equation}54∑zqmg,z,tDR.umg,z,tDR≤pmg,tload\begin{equation}\sum_z {q_{mg,z,t}^{DR}} .u_{mg,z,t}^{DR} \le p_{mg,t}^{load}\end{equation}55umg,z,tDR≥umg,z−1,tDR,∀z≥2\begin{equation}u_{mg,z,t}^{DR} \ge u_{mg,z - 1,t}^{DR},\forall z \ge 2\end{equation}560≤pes,tch≤pes,tch,max\begin{equation}0 \le p_{es,t}^{ch} \le p_{es,t}^{ch,max}\end{equation}570≤pes,tdis≤pes,tdis,max\begin{equation}0 \le p_{es,t}^{dis} \le p_{es,t}^{dis,max}\end{equation}58soces,t=soces,t−1+η.pes,tch−1η.pes,tdis\begin{equation}so{c_{es,t}} = so{c_{es,t - 1}} + \eta .p_{es,t}^{ch} - \frac{1}{\eta }.p_{es,t}^{dis}\end{equation}590≤soces,t≤soces,tmax\begin{equation}0 \le so{c_{es,t}} \le soc_{es,t}^{max}\end{equation}60pmg,tload−pmg,tbuy+pmg,tsell−∑dg∈mgpdg,t−∑es∈mgpes,tdis−pes,tch−DRmg,t=0,∀mg,t\begin{equation} \def\eqcellsep{&}\begin{array}{l} p_{mg,t}^{load} - p_{mg,t}^{buy} + p_{mg,t}^{sell} - \displaystyle\sum_{dg \in mg} {{p_{dg,t}}} \\[15pt] - \displaystyle\sum_{es \in mg} {\left( {p_{es,t}^{dis} - p_{es,t}^{ch}} \right)} - D{R_{mg,t}} = 0,\forall mg,t \end{array} \end{equation}Scenario 2: Similar to a flexible load in transmission level, DSO places a bid for flexibility services procurement. This bid includes the maximum and minimum powers and the procurable ramp by the specification of the marginal costs. In this scenario, DSO obtains the above values by aggregation of all existing sources in its grid. In other words, in this scenario, the DSO acts as a flexible service provider (FSP). As before, the primary objective function of DSO is the SW maximization or operation cost minimization, considering the constraints on the distribution grid and MGs based on the provided formulations.Equation (48) is rewritten to obtain the aggregated values of the objective function. Generally, the sources present in the distribution grid are unable to satisfy the distribution grid loads completely. To achieve the maximum (minimum) value of the absorbable power by distribution grid in TSO‐DSO common coupling point (CCP), the DSO objective function is to maximize (minimize) the receivable power from the grid (Ptgrid). Marginal cost (MC) or, in this scenario, marginal utility (MU) is obtained using Equations (61)–(63). These MUs demonstrate the maximum energy value for DSO during a load increase or decrease. Equation (62) is used for scenarios whose objective function is the same as (48), and equality function (63) relates to the circumstances that their objective function, rather than (48), is the maximization/minimization of Ptgrid value. In this scenario, since Ptgrid is at its highest or lowest values possible, the MC is not definable; thus, the mean cost concept is utilized according to (63). As can be seen from this equation, the mean cost is the total DSO's operation cost to the power absorbed by the DSO grid. If the problem is not infeasible, the value of the mean cost is very close to the MC. The difference in the power grid in Equation (62) is equal to unity, unlike in (63).61costtDSO=∑mg∑dgεMGcpdg,t+ptgrid.λtfc+cmg,tDR,∀t\begin{equation}{\rm{cos}}t_t^{DSO} = {\rm{\ }}\mathop \sum \limits_{mg} \left\{ {\mathop \sum \limits_{dg\epsilon MG} c\left( {{p_{dg,t}}} \right) + p_t^{grid}.\lambda _t^{fc} + c_{mg,t}^{DR}} \right\}{\rm{,}}\forall t\end{equation}62MUtDSO=costtDSOptgrid−costtDSOptgrid−1\begin{equation}MU_t^{DSO} = {\rm{cos}}t_t^{DSO}\left| {_{p_t^{grid}}} \right. - {\rm{cos}}t_t^{DSO}\left| {_{_{\left( {p_t^{grid} - 1} \right)}}} \right.\end{equation}63U¯tDSO=costtDSOptgrid\begin{equation}\bar{U}_t^{DSO} = \frac{{{\rm{cos}}t_t^{DSO}}}{{p_t^{grid}}}\end{equation}In this scenario, DSO submits the maximum and minimum power receivable from the grid along with MUs to the TSO. After evaluating the bids, TSO announces the cleared values to the participants.Scenarios 3 and 4 account for the situations where DSO owns MGs or not, respectively. If DSO lacks MGs, the objective function minimizes operating costs by considering penalties for scheduled power exchange deviation. Nevertheless, DSO owns MG; there is a bi‐level problem. The objective function is to maintain the cleared power values at the upper level and maximize MGs profit at the lower level. This is done by DSO by offering LMPs at the distribution level. In other words, by announcing LMPs, DSO encourages MGs to fulfil the expected power [16]. Equations (64), (65), (66) and (52) are the objective function and the upper‐level constraints, and the Equations (67) and (53)–(60) are the objective function and the lower‐level constraints, respectively. Equation (64), that is, the upper‐level objective function, minimizes the sum of deviations from the scheduled powers at DAM. Equations (65), (66) guarantee that the deviation values are positive. Equation (67), that is, the objective function of lower‐level, is comparable to Equation (48).64MinΘDSOupper−level.∑tΔptccp\begin{equation}\mathop {{\rm{Min}}}\limits_{\mathop \Theta \nolimits^{DSO} }^{upper - level} .{\text{\ \ \ }}\mathop \sum \limits_t \Delta p_t^{ccp}\end{equation}65Δptccp≥ptcl−ptccp\begin{equation}\Delta p_t^{ccp} \ge p_t^{cl} - p_t^{ccp}\end{equation}66Δptccp≥−ptcl+ptccp\begin{equation}\Delta p_t^{ccp} \ge - p_t^{cl} + p_t^{ccp}\end{equation}67MinΘMGlower−level∑t∑DG∈MGcdg,p.pdg,t+λmg,t.pmg,tbuy−pmg,tsell+cmg,tDR,∀MG∈DSO\begin{equation}\mathop {{\rm{Min}}}\limits_{\mathop \Theta \nolimits^{MG} }^{lower - level} {\rm{\ }}\mathop \sum \limits_t \left\{ \def\eqcellsep{&}\begin{array}{l} \displaystyle\mathop \sum \limits_{DG \in MG} \left( {{c_{dg,p}}.{p_{dg,t}}} \right) \\[15pt] + {\lambda _{mg,t}}.\left( {p_{mg,t}^{buy} - p_{mg,t}^{sell}} \right) + c_{mg,t}^{DR} \end{array} \right\},\quad \forall MG \in DSO\end{equation}Uncertainty modellingUncertainty due to wind units’ power adopts different values in different hours and geographical places. In this paper, an uncertainty range is applied according to linearized Equations (68)–(74), which is suitable for solving problems using a robust adaptive approach [26]. Equation (72) indicates that the sum of wind power at each moment is below a specific value. Given the dependency of units’ productions to their geographical place of installation, it is expectable that the sum of wind units’ generated powers are bound to a specific value. This relation models the interdependency of the wind units and is not applied to the individual wind units. For example, the maximum number of hours in which the unit output has the highest deviation from the predicted value is a particular value for a wind power plant. This limitation can be applied via (73). Noticeably, Equations (72) and (73) describe the spatiotemporal constraints and dependencies of the uncertainty of wind units.68wq,t=wq,tfc+Δwq,t\begin{equation}{w_{q,t}} = w_{q,t}^{fc} + \Delta {w_{q,t}}\end{equation}69wq,t≤wq,tfc+Δwq,tmax\begin{equation}{w_{q,t}} \le w_{q,t}^{fc} + \Delta w_{q,t}^{max}\end{equation}70wq,t≥wq,tfc−Δwq,tmax\begin{equation}{w_{q,t}} \ge w_{q,t}^{fc} - \Delta w_{q,t}^{max}\end{equation}71Δwq,t=Δwq,t+−Δwq,t−\begin{equation}\Delta {w_{q,t}} = \Delta w_{q,t}^ + - \Delta w_{q,t}^ - \end{equation}72∑qΔwq,t++Δwq,t−Δwq,tmax≤Γt\begin{equation}\mathop \sum \limits_q \frac{{\Delta w_{q,t}^ + + \Delta w_{q,t}^ - }}{{\Delta w_{q,t}^{max}}} \le {{{\Gamma}}_t}\end{equation}73∑tΔwq,t++Δwq,t−Δwq,tmax≤Γq′\begin{equation}\mathop \sum \limits_t \frac{{\Delta w_{q,t}^ + + \Delta w_{q,t}^ - }}{{\Delta w_{q,t}^{max}}} \le {{\Gamma}}_q^{\rm{^{\prime}}}\end{equation}74Δwq,t+,Δwq,t−≥0\begin{equation}\Delta w_{q,t}^ + ,\Delta w_{q,t}^ - \ge 0\end{equation}DAM clearing and solution methodAs previously pointed out, market clearing is a two‐stage process. In the first stage, the unit scheduling is performed using predicted values, assumed identical to the actual values. By taking the worst‐case uncertainty parameters, the second stage adjusts the newly calculated values and obtained values in the previous stage. This ensures that the scheduled values cover the maximum uncertainty present (worst‐case scenario). There is some consideration about market clearing mechanism and solution methodology as follows:-The Benders decomposition method is applied to solve the market‐clearing equations considering the transmission constraints. In this method, the first stage is regarded as the main problem, and the dual problem of the second stage is taken as the sub‐problem. Due to the multiplication of uncertain values, Δw, by dual variables, the outer approximation, a linearized method based on Taylor expansion, is employed [29].-A percentage of power in each unit can be allocated to the reserve to cover the RES uncertainties. In this case, each unit submits its reserve bid to the TSO. An alternate approach is to regard the market as energy‐only. That means it only considers the reserve cost that has been delivered to the grid as energy.By aggregating its grid flexibilities, DSO determines the maximum and minimum powers consumed or generated and the ramping limits of power procurement in the CCP. This paper hypothesizes that the DER units installed on the DSO grid are capable of rapid ramping procurement. This CCP ramping value is different from the algebraic sum of all units’ ramping because the transmission lines may not transmit the intended power variations. It should be noted that the values of maximum (minimum) power and maximum ramping in CCP will vary concerning time. Therefore, the ED for each DSO should be executed according to Equations (48)–(60) hourly. To avoid the problem's complexity, DSO can present the maximum and minimum powers and their corresponding prices to the TSO. After the market clearing, DSO should solve the above equations again for updated information and submit the scheduled power values and nodal prices of the distribution grid to each MG. In particular, DSO announces the new offered deals based on the values from the TSO market‐clearing outcome, until convergence to an appropriate bid price, to minimize the DSO's price prediction error (using the objective function (67) and constraints (48)–(60)). Conclusively, DSO determines the new power values of its grid sources using the placed prices by TSO to maintain the cleared power values in the CCP with the minimum cost.The TSO‐DSO price convergence is based on a decentralized method presented in reference [30]. The use of primal space instead of dual problem space is one of the major advantages of this method. Convexity is the only requirement for convergence. All the equations in this paper are convex, so convergence of the problem is guaranteed. This method replaces the objective function (1) with Equation (75).75minΘTSO,αcostτTSO+∑dαd,τ\begin{equation}\mathop {\min }\limits_{\mathop \Theta \nolimits^{TSO} ,\alpha } \left\{ {\mathop {\cos t}\nolimits_\tau ^{TSO} + \sum_d {\mathop \alpha \nolimits_{d,\tau } } } \right\}\end{equation}76Eq.2−Eq.47\begin{equation}{\rm{Eq}}{\rm{.}}\;2 - {\rm{Eq}}{\rm{.}}\;47\end{equation}77αd,τ≥LBd,τ\begin{equation}\mathop \alpha \nolimits_{d,\tau } \ge \mathop {LB}\nolimits_{d,\tau } \end{equation}78Δptgrid,τ=Ptgrid−Lj,tfc+Lj,td−Lj,tuτ:π1\begin{equation}\mathop {\Delta p}\nolimits_t^{grid,\tau } = \mathop {\left( {\mathop P\nolimits_t^{grid} - \left(L_{j,t}^{fc} + L_{j,t}^d - L_{j,t}^u\right)} \right)}\nolimits_\tau \;:\;\mathop \pi \nolimits_1 \end{equation}79Δδt,τ=δn,t,τTSO−δv1,t,τDSO:π2\begin{equation}\Delta \mathop \delta \nolimits_{t,\tau } = \mathop \delta \nolimits_{n,t,\tau }^{TSO} - \mathop \delta \nolimits_{v1,t,\tau }^{DSO} \;:\;\mathop \pi \nolimits_2 \end{equation}80minΘDSO,β,γ,λcostd,τDSO+KPEN(βΔptgrid,τ+γΔδt,τ)+λt(Δptgrid,τ−Δδt,τ)\begin{equation}\mathop {\min }\limits_{\mathop \Theta \nolimits^{DSO} ,\beta ,\gamma ,\lambda } \left\{ \def\eqcellsep{&}\begin{array}{l} \mathop {\cos t}\nolimits_{d,\tau }^{DSO} + \mathop K\nolimits^{PEN} ({{\bm \beta }}\mathop {\;\Delta p}\nolimits_t^{grid,\tau } + {{\bm \gamma }}\;\Delta \mathop \delta \nolimits_{t,\tau } )\\[6pt] + \mathop \lambda \nolimits_t (\mathop {\Delta p}\nolimits_t^{grid,\tau } - \Delta \mathop \delta \nolimits_{t,\tau } ) \end{array} \right\}\end{equation}81LBd,τ=minΘDSO,β,γ,λcostd,τDSO+KPEN(βΔptgrid,τ+γΔδt,τ)−π(Δptgrid,τ−Δδt,τ)\begin{equation}\mathop {LB}\nolimits_{d,\tau } = \mathop {\min }\limits_{\mathop \Theta \nolimits^{DSO} ,\beta ,\gamma ,\lambda } \left\{ \def\eqcellsep{&}\begin{array}{l} \mathop {\cos t}\nolimits_{d,\tau }^{DSO} + \mathop K\nolimits^{PEN} ({{\bm \beta }}\mathop {\;\Delta p}\nolimits_t^{grid,\tau } \\[6pt] + {{\bm \gamma }}\;\Delta \mathop \delta \nolimits_{t,\tau } ) - {{\bm \pi }}\;(\mathop {\Delta p}\nolimits_t^{grid,\tau } - \Delta \mathop \delta \nolimits_{t,\tau } ) \end{array} \right\}\end{equation}82Eq.49−Eq.60\begin{equation}{\rm{Eq}}{\rm{.}}\;49 - {\rm{Eq}}{\rm{.}}\;60\end{equation}83UBd,τ=costτ−1TSO+costd,τDSO+KPEN(β.Δptgrid,τ+γ.Δδt,τ)\begin{eqnarray} \mathop {UB}\nolimits_{d,\tau } = \mathop {\cos t}\nolimits_{\tau - 1}^{TSO} + \mathop {\cos t}\nolimits_{d,\tau }^{DSO} + \mathop K\nolimits^{PEN} ({{\bm \beta }}.\mathop {\Delta p}\nolimits_t^{grid,\tau } + {{\bm \gamma }}.\Delta \mathop \delta \nolimits_{t,\tau } )\nonumber\\ \end{eqnarray}84(UBd,τ−LBd,τ)≤ε\begin{equation}(U{B_{d,\tau }} - L{B_{d,\tau }}) \le \varepsilon \end{equation}where in (75), the cost of TSOs and the total sum of the costs of DSOs are minimized in each iteration. Δptgrid,τ${{\Delta}}p_t^{grid,\tau }$and Δθtgrid,τ${{\Delta}}\theta _t^{grid,\tau }$in Equations (78) and (79) show the difference between the power and angle of the TSO‐DSO at the CCP for each iteration τ. Equation (80) expresses the objective function of the subproblem, i.e., the DSO problem. It is evident from this equation that TSO‐DSO boundary constraints can be relaxed to make DSO problems feasible. The non‐negative variables β and γ guarantee the feasibility of the DSO problem. TSO nodal prices are indicated by λt. KPEN represents the penalty coefficient of non‐equality of TSO and DSO parameters at the CCP. Equation (81) shows the lower bound of the subproblem's objective function. In this equation, π is a vector of dual variables of boundary constraints and consists of π1 and π2. Equation (83) indicates the upper bound of the DSOs' objective function. Equation (84) also takes into account the stopping condition. ε represents the stopping threshold of the proposed solution method. The overall flexibility procurement process is summarized in Figure 2.2FIGUREFlexibility procurement processSIMULATION RESULTS AND DISCUSSIONIn this paper, a modified 118‐bus grid is used for modelling TSO with data drawn from [13]. Four wind power plants with a nominal capacity of 560 MW are considered in this grid. These units are located at buses 17, 56, 94 and 100. Ten 33‐bus distribution systems, each with multiple MGs, are connected to the transmission grid as a DSO‐operated grid. These DSOs are located at buses 10, 20, …, 100. The data corresponding to distribution grids along with MG specifications are extracted from [10].To investigate the effect of providing flexibility by DSO, in one case DSO is considered without flexibility, that is, as a fixed load. In another case, the DSO is regarded as flexible demand from the TSO point of view. To study the effect of the reserve, in one case the amount and cost of the reserve are considered and in the other case, this amount of the reserve is not considered. In these two cases, the effect of the reserve on the amount of system flexibility is measured. Two conditions are also considered to examine the effect of DSO ownership on MGs. In one case, all MGs are assumed to belong to the DSO. In this case, the DSO offers energy or flexibility to the market from these MGs. Otherwise, MGs compete with each other for more profit. The equilibrium of this competition is where changes in the output power of each MG do not increase its profit [31].There are eight specific cases considering the reserve and the four DSO‐related scenarios. These cases are summarized in the following:Case 1: The reserve and its costs are not included. DSO flexibility is not provided. DSO owns the MGs.Case 2: The reserve and its costs are included. DSO flexibility is not provided. DSO owns the MGs.Case 3: The reserve and its costs are not included. DSO flexibility is provided. DSO owns the MGs.Case 4: The reserve and its costs are included. DSO flexibility is provided; however, ramping procurement cost is not considered separately. DSO owns the MGs.Case 5 to 8: The same as cases 1 to 4, except that in these cases, the DSO does not own the MGs. Therefore, the DSO's problem becomes a bi‐level problem.As mentioned previously, in all the above cases, TSO returns the market‐clearing results to the DSOs for better decision‐making. It will result in lowering the DSO's bid error. The simulation results are presented in Table 1. As can be comprehended from this table, in terms of market efficiency, the highest SW is related to the case in which DSO delivers its flexible sources to the DA market. In fact, DSO aggregates demand with higher MU rather than TSO, which increases overall SW. In other words, by providing a range of flexibility, DSO gives TSO the opportunity to compensate for changes in net bus loads at a lower cost. This range of flexibility is shown in Figure 3. As this figure shows, DSO can generate or consume variable output or input power at any time. Of course, the cost of each DSO operating point is different. Figure 4 shows the costs associated with each operating point. As shown in this figure, the cost of providing optimal DSO power is the lowest. That is, in normal network operation, the optimal DSO power values are selected and therefore the cost of operating the whole system is reduced.1TABLEComparison of simulation results by casesCasesSWTSOCostDSOΣ(BenefitMGs)Wspil [MW]FPU [MW]FPD [MW]FRU [MW/h]FRD [MW/h]Case17986536041411298639551353844413373427Case2754851600994572747550833845315133421Case37992146035211298625559403876822514054Case4759293600784586685560163890523234499Case57986536027911925639551353844413373427Case67548516011111884747550833845315133421Case77992146049211925625559403876822514054Case87592936020011890685560163890523234499FPU: flexible power‐up; FPD: flexible power‐down, FRU: flexible ramp up; FRD: flexible ramp down.3FIGUREAggregated flexible demand of DSO4FIGUREThe aggregated marginal cost of DSO flexibilityIn other operating modes where the need for DSO flexibility increases, TSO can utilize this flexibility at an additional cost.Figures 3 and 4 show the power values taken from the grid and the marginal prices corresponding to each case for a DSO. As shown in Figure 3, the flexible demand of case 3 is presented as the maximum value (p_max), the minimum value (p_min), and the optimal value (p_opt) with the lowest cost. Moreover, the prices corresponding to the powers are shown in Figure 4.The imposition of any extra cost such as reserve causes to reduce SW. Whereas it is costly to procure reserve for the entire system, it is not paid until it is deployed. Nevertheless, the reserve cost contributes to increased total revenue from generating units.Transmission reserve reduces MGs’ profit in the cases that DSO lacks MGs (cases 2 and 4). However, if DSO owns MGs (cases 6 and 8), the MGs’ profit value rises tangibly.The marginal cost of transmission reserve is less than the marginal cost of distribution units. So, in the former case, the former DSO tends to increase the amount of TSO imported instead of increasing the production of MGs. On the other hand, by increasing the amount of power input from the TSO, there may be a violation of the planned amount of power and thus increase the cost of input power in RT. Therefore, the best thing to do for DSO is to request the purchase of the right amount of transmission reserve in the first stage. This reserve value is determined based on load forecasting values ​​or probabilistic planning. In this paper, the adaptive robust approach is used to determine the amount of reserve. In the latter case, the DSO seeks to increase the profitability of MGs in addition to reducing operating costs. An increase in MGs profit is subject to an increase in the nodal prices. The increase in the nodal prices occurs if there is a violation of the planned amount of power.This contradicts the original purpose of the DSO. Therefore, DSO goals are at two different levels and a compromise must be reached between these goals. In other words, in the former, the DSO objective function is to meet the scheduled power with the least amount of deviation. At the same time, in the latter, in addition to the goal mentioned at the upper level, maximizing the profit of microgrids at the lower level is considered. Concerning the spilled wind power, the lowest value is attributable to the case with DSO flexible sources. The more the flexibility of DSO sources, the less will be the amount of spilled wind power. This reveals as if the flexibility of DSO has been employed to alleviate the consequences of the uncertainty of TSO. Of course, this has come at the cost of increasing operating costs. The higher the RES penetration, the lower the price increase. In other words, the value of flexibility for such power systems is greater.The reserve consideration causes an increase in Wspill because a percentage of flexible capacity of sources is being sold as the reserve. In Table 1, FPU (FPD) and FRU (FRD), as regards flexibility indices, are represented as the sum of remaining (curtailable) power capacity, and ramp‐up (down) of all units, respectively.The flexibility metrics vary depending on the direction of the net load increase or decrease. The simulation results prove that all system flexibility metrics are improved for a flexible system when considering the reserve. That is, the system readiness—to handle net load variations due to prediction error or contingency cases—increases.Considering reserve for an inflexible system causes a reduction in the FPD flexibility metric while increasing other metrics. Here, the actual wind power was higher than the predicted value, and for this reason, a percentage of units capacity is allocated to this unpredicted wind power. Thus, FPD decreases as FPU increases. With FPD reduction, Wspill reduces as well. However, the other ramp metrics have increased. This suggests that the wind power variation slope has not caused a severe limitation. As shown by Table 1, existing reserve in the transmission system leads to profit reduction for MGs connected to the distribution grid because it is assumed that DSO does not participate in reserve procurement. The DSO problem can be transformed into a bi‐level problem according to relations (72)–(76) to overcome this issue. Doing so will guarantee MGs profit, which is well demonstrated by the results of cases 5 to 8. For cases where DSO flexibility (items 3–4 and 7–8) serves the TSO, the amount of flexibility indexes increases significantly. This means that the sum of the TSO and DSO flexibility is available to the entire power system. Of course, it should be noted that due to network limitations, this will not be an algebraic sum. Simultaneous transmission reserve and distribution flexibility increase the flexibility of the entire power system. For example, transmission reserve increases the FRU by 176 units (differences between items 1 and 2). Distribution flexibility also increases the index by 914 points (differences in items 1 and 3). The sum of these two is more than the simultaneous effect of transmission reserve and DSO flexibility (differences between cases 4 and 1). This reflects the interaction between transmission reserve and distribution flexibility. This is due to CCP restrictions. The results in Table 1 show that DSO ownership of DGs has no effect on flexibility indexes. It only slightly increases operating costs. This cost increase is due to the DSO compromise between the deviation of power transfer from the CCP and the profit of the MGs. Using transmission reserve reduces DSO costs. Because the marginal cost of transmission reserve is less than the marginal cost of producing MGs. In all of the above cases, the income of the microgrids and the cost of the loads are entirely dependent on the nodal prices. Figure 5 shows the nodal prices for CCP1 (connection point of DSO1 to the transmission network) for the third case. As can be seen from this figure, the trend of market price changes of the first stage (DA) and the second stage (BS) are similar. When the share of wind power supplied from CCP increases, the BS price is higher than the DA price. In this case, the flexibility of the system is used to provide sufficient power and ramps. This flexibility costs the same as the DA and BS price difference. At these times (t1–t3, t10–t12, and t14–t24) the amount of actual wind power is higher than forecasted. During t5–t9 times, adequate power reduction by flexible network sources reduced the BS price relative to the DA.5FIGUREThe locational marginal cost of DA and BS in CCP1CONCLUSIONIn this paper, the collaboration between TSOs and DSOs in DAM to provide power system flexibility was investigated. The distribution grid can act fully flexible to procure the grid's flexibility. That means when a higher ramping capability is required, this grid can meet the extra demand by altering the adjustment values of DERs, which comes at the price of receding from the optimal operation point of units. Furthermore, in situations where net load variations on the bus bar are low, DER adjustments can provide higher power values. This indicates the flexibility of DSO control in procuring flexible services of the entire system. The extraction of DSO flexibility to deal with the effects of variability and uncertainty of RESs on the entire power system was investigated with the robust approach.The simulation results showed that the deployment of flexible resources, located at the DSO level, enhances the technical and economic metrics of the entire power system. In this regard, DSO has a key role in the provision of more flexible resources at the distribution level. It was assumed here that each DSO also included some MGs. If the MGs are under DSO's ownership, it acts either as a local operator or an aggregator. So, the DSO's problem became a bi‐level that ensured the profitability of MGs.Reserve services affect the flexibility of the system and, for a flexible system, improve the flexibility metrics of the overall system. Lack of participation of DSO in reserve procurement reduces the profit of its connected MGs. To resolve this issue, the DSO problem is solved as a bi‐level problem by considering MGs profit. The reserve affects the system flexibility by enhancing the metrics for a flexible system while causing them to reduce for an inflexible system.FUNDING INFORMATIONNoneCONFLICT OF INTERESTNoneDATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.ACKNOWLEDGEMENTThe authors thank Dr. Hanna Niemelä for her assistance with proofreading of the paper and comments that greatly improved the manuscript.NOMENCLATURE0Initial value (state)ASets and IndicesBAbbreviations and superscriptsBSBalancing stageCConstantsc(.)Marginal cost [$/MWh]c(.)SU0,SD0Up/down reserve cost [$/MWh]c(.)u/dUp/down reserve cost [$/MWh]CCPCommon coupling pointChChargeCLCleareddIndex of DSODVariablesD+/‐Maximum up/down DR [MW]DADay‐aheadDayDailydgIndex of distributed generationDisDischargeDRDemand responsedrpDrop‐downEdayShiftable energy [MW]fMaximum line flow [MW]fcForecastedFSPFlexible service provideriIndex of generatorsInSet and of generators connected to bus njIndex of loadsJnSet and of loads connected to bus nLLoad [MW]LBLower boundm,nIndices of busesmgIndex of microgridsMGnSet of microgrids connected to bus nMnSet of buses connected to bus nP(.)(.)PowerpiuPick‐upPMPump modePP(s,t)Power consumption in pump modePT(s,t)Power production in turbine modeqIndex of wind turbine unitsQMaximum water flow [m3/s]qDR(mg,z,t)Quantity of zth(DR) block [MW]QnSet and of wind turbine units connected to bus nQP(s,t)Water flow in pump modeQT(s,t)Water flow in turbine modeRdDown reserveRDMaximum ramp‐down limit [MW/h]RD(i,t)Down‐reserverd(i,t)Deployed down‐reserveRuUp reserveRUMaximum ramp‐up limit [MW/h]RU(i,t)Up‐reserveru(i,t)Deployed up‐reservesIndex of pumped‐storage unitsSDShut‐downShedLoad sheddingSnSet of pumped‐storage units connected to bus nSUStart‐upt,t´Index of timeTMTurbine modeTu/dMinimum (up/down) timeUUp, upper levelUBUpper boundUu/dUp/down marginal utility [$/MWh]v(i,t)On/off state of unitsVol(s,t)Volume of reservoirVOLLValue of lost load [$/MWh]w(q,t)Actual wind power outputwFCForecasted RES output [MW]wspill(q,t)Spilled wind power outputxPer‐unit line reactancey(i,t)Binary variable of starting up at the beginning of the periodzIndex of demand response blocksz(i,t)Binary variable of shutting down at the beginning of the periodα, β, γCoefficients of generation cost functionΓConservation factorδ(.,t)Phase angleΔw(q,t)Deviation of wind power outputΔw+/‐(q,t)Up/down‐ward deviation of RESΔwmaxMaximum deviation [MW]ηCharge efficiencyΘSet of decision variablesλ(.,t)Marginal costσConversion factor water flowREFERENCESZegers, A., Brunner, H: TSO‐DSO interaction: An overview of current interaction between transmission and distribution system operators and an assessment of their cooperation in Smart Grids. 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Published: Jul 1, 2022

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