A Framework of Electricity Market Based on Two-Layer Stochastic Power Management for Microgrids

This Article Develops a Novel Multi-Microgrids (MMGs) Participation Framework in the Day-Ahead Energy and Ancillary Services, i.e. Services of Reactive Power and Reserve Regulation, Markets Incorporating the Smart Distribution Network (SDN) Objectives Based on Two-Layer Power Management System (PMS). A Bi-Level Optimization Structure Is Introduced Wherein the Upper Level Models Optimal Scheduling of SDN in the Presence of MMGs While Considering the Bilateral Coordination Between Microgrids (MGs) and SDN’s Operators, i.e. Second Layer’s PMS. This Layer Is Responsible for Minimizing Energy Loss, Expected Energy Not-Supplied, and Voltage Security as the Sum of Weighted Functions. In Addition, the Proposed Problem Is Subject to Linearized AC Optimal Power Flow (LAC-OPF), Reliability and Security Constraints to Make It More Practical. Lower Level Addresses Participation of MGs in the Competitive Market Based on Bilateral Coordination Among Sources, Active Loads and MGs’ Operator (First Layer’s PMS). The Problem Formulation Then Tries to Minimize the Difference Between MGs’ Cost and Revenue in Markets While Satisfying Constraints of LAC-OPF Equations, Reliability, Security, and Flexibility of the MGs. Karush–Kuhn–Tucker Method Is Exploited to Achieve a Single-Level Model. Moreover, a Stochastic Programming Model Is Introduced to Handle the Uncertainties of Load, Renewable Power, Energy Price, the Energy Demand of Mobile Storage, and Availability of Network Equipment. The Simulation Results Confirm the Capabilities of the Suggested Stochastic Two-Layer Scheme in Simultaneous Evaluation of the Optimal Status of Different Technical and Economic Indices of the SDN and MGs.


I. INTRODUCTION
To Achieve Clean Energy Supply Conditions in the Power System and Prevent Early Exhaustion of Fossil Fuels, the Utilization of Environmentally-Friendly Technologies Such as Electric Vehicles (EVs) and Renewable Distribution Generations (RDGs) Placed at Consumption Sites Is a Promising Solution [1]. Thanks to Their Low Emission Level, Non-RDGs (NRDGs), Such as Fuel Cells and Microturbine, Are Widely Used at Consumption Points to Supply Energy as Concentrated Power Plants [1]. In This Regard, Energy Storage Systems (ESSs) and Demand Response Programs (DRPs) Are Highly Potential Choices [1]. Nevertheless, Achieving Desirable Environmental Conditions Besides Improving Technical and Economic Situations of Energy Networks Requires Appropriate Energy Management of These Elements Within the Network. Hence, the First Step Is to Integrate These Elements in Different Coordinating Forms Like Micro-Grids (MGs) [2]. Following This, a Distribution Network Is Expected to Consist of Several MGs. In This Scheme, an MG Is Composed of a Specific Number of Sources, Storages, and Consumers, Each With Its Local Controller. Moreover, the MG Itself Has a Central Controller Known as the MG Operator (MGO). By Executing Smart and Communication Infrastructure in the MG, It Is Expected That Bilateral Coordination Is Met Among Sources, Storages, and Consumers With the MGO [3]. In This Case, by Adopting an Energy Management System (EMS) or Power Management System (PMS) in the Second Step, an MG With Various Capabilities in Economic and Technical Terms Such as Operation, Reliability, and Security Can Be Obtained [4]. Additionally, Several MGs or Multi-MGs (MMGs) Have Bilateral Coordination With the Distribution System Operator (DSO) in This Scheme; Thus, It Is Predicted That a Suitable Situation From DSO's Viewpoint Is Obtained for the Distribution Network in These Conditions [5].
A Great Deal of Research Has Been Conducted on the Management of the Operation of Distribution Networks or MGs. To Exploit a Mixture of Active and Reactive Power Control Capabilities of EVs, a Model Is Introduced in [6] to Manage These Powers Simultaneously in an Smart Distribution Network (SDN   Condition to Use the KKT and Other Methods to Transform the Multi-Level Problem Into a Single-Level One. Since the Mentioned Problem Is Subject to AC-OPF Constraints, It Is Non-Convex [15], [16] t∈O OH

1) UPPER LEVEL PROBLEM
The Formulation of the Upper-Level Problem Is Given in (1)- (12). The Objective Function of the Problem as Shown in (1) [6]. However, Since the Difference Between Voltage Angles of Both Nearand Far-End Buses of the Distribution Line in the Distribution Network Is Generally Less Than 6 • , the Terms cos ϕ b − ϕ j and sin ϕ b − ϕ j Can Be Approximated to 1 and ϕ b − ϕ j [25], [26] (4) and (5) [25]. The Operation Constraints of the SDN Are Given in (7) [1]. It Is Not Formulated in Equation (13). Constraints (4)-(12) Holds for MGs as Well, so They Are Presented in (14). Active and Reactive Power Balance Constraints in Different Buses of MGs in the Presence of Sources, Storages, and Responsive Loads Will Be as (15) and (16) [27], [31], [32]. Moreover, the Probability of the Selected Values for Load and Energy Price Parameters Is Calculated in Each Scenario Using the Normal Probability Distribution Function (PDF) [1]. The Probability of Values of Renewable Power for Wind and Photovoltaic Systems Are Specified Based on Weibull and Beta PDFs, Respectively [1]. The Probability of Values for Parameters of EVs Is Found Using Rayleigh PDF [27], and It for the Three Last Uncertainties Calculates Based on Bernoulli PDF [24]. The Probability of Occurrence of an Event in Each Scenario (π 0 ) Is Equal to the Multiplication of the Probabilities of Uncertainty Parameters in That Scenario. In the Next Step, the SBM Chooses a Small Number of the Generated Scenarios and Applied Them to the Proposed Problem. It Should Be Noted That Scenarios With a Small Distance From Each Other Are Selected in This Method. The Probability of New Scenario (π) Is Equal to Rate of Its π 0 and Sum of π 0 for All Scenarios Obtained by SBM. The Detailed Information About the Formulation of the Mentioned Method Is Accessible in [33].

III. SINGLE-LEVEL MODEL OF THE PROPOSED PROBLEM
Reaching a Single-Level Model Is a Necessity to Find an Optimal Solution for the Problem (1)-(27) by Using TRaditional Solvers [27]. Since That This Problem Includes Linear Formulation, Thus, It Includes a Convex Model. Hence, the KKT Is Employed as Follows. The y ∈ arg min F 2 = f T y Subject To: g 1 y = h 1 : ρ (31) We Need to Use the Constrained Found Using the KKT of the Lower-Level Problem in the Upper-Level Problem, Aiming to Find the Single-Objective Model of the Problem Being Discussed [27]. One Solution Is to Find the Lagrangian Function (L) of the Lower Level Problem (33). The Objective Function and Penalty Functions Related to the Problem Constraints Are Put Together to Find the Lagrangian Function.
The Penalty Function for Constraints a ≤ b and a = b Are Given by µ.max(0, a -b) and ρ.(b -a), Respectively [27].
The Constraints Found by KKT Are in Proportion to Making Derivative of the Lagrangian Function Equal to Zero by Differentiating It With Respect to Its Variables (y, µ, and ρ) [27]. As a Result, the Single-Level Formulation of the Problem (28) Finally, the Flowchart of the Problem Solving Is as Fig. 2.

A. CASE STUDIES
The Proposed Scheme Is Implemented on a 33-Bus Radial SDN [34]- [36] With Three MG1, MG2, and MG3 Microgrids, as Shown in Fig. 3. The Peak Load Data and Specifications of Distribution Lines and Substation of the SDN Are Reported in [13], and This Data for MGs Is Given in [16].       the Results Concerning This Range of EENS max Are Not Depicted in Fig. 5(b).   on the Mentioned Networks. Based on Table 6, by Proper Management of Sources, Storages, and Responsive Loads