Flexibility Analysis for Multi-Energy Microgrid and Distribution System Operator under a Distributed Local Energy Market Framework

Abstract

Increasing the penetration rate of microgrids (MGs) for Local Energy Market (LEM) participation creates new challenges for the market-clearing process under a large number of requests for energy transactions. The market-clearing process for decentralized market frameworks is dependent on participants’ flexibility in negotiations for bilateral energy transactions. Multi-energy microgrids (MEMGs) include combined heat and power units which can be less dependent on electricity prices because of energy conversion equipment, gas infrastructure, and combined heat and power loads. In this regard, to evaluate prosumers’ flexibility role in market negotiations, a new analysis based on energy scheduling of MEMG considering a Demand-Response Program (DRP) model is executed under a distributed market structure. Moreover, two new flexibility indexes for market participants with attention to prosumers’ adaption capabilities are proposed. The results show that, under a 9.35% flexibility index improvement for the entire system, the social welfare function improved by 2.75%. Moreover, the results show that the DRP model for changeable and shiftable loads can improve the flexibility of the entire system by 35.82%. Combined heat and power load are considered as the resource of flexibility for system evaluations.

1. Introduction

1.1. Motivation and Aims

Traditionally, power systems were composed of large centralized generators usually operated in a radial form to feed large and small customers. However, these days generation can be owned by companies or individual customers such as MGs, which are not operated by Distribution System Operators (DSOs) [1]. These independent prosumers can participate in local energy markets or ancillary service markets to gain financial profits and support DSO from price fluctuations of the upstream market [2]. These new energy-trading opportunities would create new challenges for local markets because a large number of independent prosumers would increase the computation burden of the market-clearing process [3]. The flexibility of prosumers would have an intensive effect on the market-clearing process, as it would be simpler to match more flexible players to achieve an agreement on energy-trading values. In this context, by establishing reliable two-way communication systems between distributed independent prosumers, a new aspect of flexibility would be considered based on the adaptability features of each prosumer. How can this kind of flexibility, however, be measured? Generally, flexibility is calculated for energy-generation units with evaluation metrics associated with their technical characteristics. Several researchers have studied the concept, effects, and measurement metrics to evaluate a single power plant’s flexibility [4,5]. However, loss of load probability and expected unsupplied energy with an attitude of preventing the demand exceeds from the available capacity, can not be more practical to evaluate a system with the need to predict the behaviors [6]. New market structures create new requirements for the metrics of the system that can evaluate the market participants’ behavior from a market adaptation point of view. So new metrics need to be provided in response to the flexibility requirements of the market-clearing process. The flexibility index of prosumers can be used by market operators as a new instrument to improve the social welfare of the system.

1.2. Literature Review

In a power system context, the term flexibility refers to diverse things ranging from the quick response times of generation units to the degree of efficiency or robustness of a given power market setup [7]. With more attention paid to market concepts, flexibility is defined by Euro Electric as the ability to adapt the generation or consumption pattern in response to an external signal, which would be a price signal or any other incentive or inhibitory parameter [8]. This concept distinguishes a feature of flexibility in the integration of energy scheduling and market structure for signal generation. MEMGs as a new emerging part of power systems have improved the flexibility of MG operation by using Combined Heat and Power units (CHP), energy converter equipment such as Heat Pumps (HPs), and electrical and thermal energy-storage devices [9]. Moreover, demand-response programs can provide a significant opportunity for MEMGs to enhance the flexibility aspects of the systems [10]. Ref. [11] denotes the demand-flexibility definition as shifting eligible loads across the hours of a day to off-peak periods and reshaping the daily load curve to reduce generation costs. Although the traditional DRP models can control a specific kind of demand, a more integrated formulation would be required for combined heat and power loads in multi-energy systems. Ref. [12] defines a combined model of loads for changeable demands, which can be consumed in a thermal or electrical model. However, the proposed model is restricted to the changeability feature of the combined loads, and the shift ability of the DRP is not considered in the article. MEMGs with various energy resources can provide new features for a system by postponing the use of energy under energy-storage devices and changing the kind of demand with energy-converting equipment. These capabilities can create a new model of demand responses for combined heat and power loads, which have not been studied in recent papers. Many articles have been written on the optimal energy scheduling of MEMGs, each of which considered some aspects of the issue, but none of them have studied the flexibility analysis of MEMGs considering the flexibility features for MEMGs for market participation. Ref. [13] propose an optimal energy management model for multi-microgrids considering DRP with only an electric energy carrier. To consider the effects of multi-energy systems, Ref. [14] presents the optimal short-term scheduling for an MEMG considering load uncertainty. However, the role of a Distribution System (DS) is not considered in this study. DSO can play the role of an aggregator for prosumers such as MGs or energy hubs to trade energy with TSO as an intermediate platform [15,16,17]. The role of DSO as an aggregator would prevent a high-dimensional optimization problem with a large number of small controllable elements, which need to be modeled individually [18]. However, the security constraints of the DS would influence the energy-trading schedule according to the bus voltage and line current restrictions [19]. So the proposed model would consider both sides of the model from MG and DSO points of view. Ref. [20] proposes a bi-level problem structure for the operation scheduling of MG with the interaction of the distribution system. Although this study considered the role of DSO in the interaction of MGs, the problem is formulated neglecting a flexibility analysis and energy-trading negotiations. To investigate the effects of heat power, Ref. [21] uses the time-of-use tariff released by the main grid as fixed prices for energy trading of multi-energy peers. Ref. [22] proposes an energy scheduling model for multi-energy systems under two separate coalitions for heat and power energy transactions. Ref. [23] proposes uniform pricing and a pay-as-bid strategy for energy trading. However, static pricing strategies are not able to dynamically consider the effects of market-clearing prices on energy transactions. So, these methods are not good solutions for flexibility analysis. To consider the capability of negotiations for energy transactions, Ref. [24] used the Alternating Direction Method of Multipliers (ADMM) method for bilateral energy trading. Although the proposed model considers the privacy of data for market participants, the study ignored the security constraints of the distribution system, which would decrease the practicality of the model in real operation. Ref. [25] used the ADMM method for heat and power energy trading. Although the proposed model considers the energy-trading negotiation possibility under the security constraints of the system, flexibility analysis is ignored and no evaluation metric is presented in the study. Ref. [26] proposes a Flexibility Index (FI) based on the comparison of the largest variation range of uncertainty and the target range within which the system can remain feasible under a given response time horizon [27]. Ref. [28] presents a detailed flexibility study to incorporate net load forecast errors. The proposed FIs are employed to evaluate the reserve capacity requirements to cover the uncertainty of generation. Ref. [29] provides three flexibility quantification metrics: expected unserved flexible energy, expected duration of insufficient flexibility, and expected flexibility index to design an appropriate DRP. Similarly, Ref. [30] introduces the average power flexibility during the peak period index to evaluate the energy flexibility of the DRPs. To provide demand-response services, Ref. [31] presents an FI, based on a probabilistic curve of the available power from the thermostatically controlled loads. Although the proposed indexes were suitable indicators to evaluate the reliability of the system for flexibility services, none of them can be used to predict the flexibility capability of a system for market participation. In [32], with a focus on the flexible energy of building energy systems, new FIs are proposed to show a system’s capabilities in delivering power and coordination capabilities of resources. Although the different types of demands are considered in this study, the conversion of loads from one carrier to the others is not considered. Ref. [33] proposes a stochastic economical flexibility-evaluation method to scrutinize the flexibility sensitivity to the storage facility capacity. The proposed model indicates that the proposed FIs can help network operators to be aware of the available capabilities of the system. Several metrics have been proposed to measure the flexibility of a system, but no metric has been presented up to now to measure the adaptability of a system for the coordination of an independent operator with the others. This is a feature that can be used in the market-clearing process to make a margin for a market operator for easier market settlement. Moreover, several FIs have been presented to quantify the individual flexibility of an overall system, but none of them are adapted to the market requirements. This is because it is dependent on several parameters and cannot be calculated under the summation of different indicators. For example, the system flexibility cannot be calculated by using a weighted sum of the values of the flexibility indicators for all generators, because there is a relation between the operating constraints of the system and cost with flexibility that restricts the overall flexibility [34].

Table 1. Literature review.

	Index Feature	Properties	Reason	Effects
[4]	Power capacity	Available power and ramp rate	Variability and uncertainty	Comparison of generators
[5]	Technical weighted Index	Operational range, ramp rate, start-up and shut-down times, minimum up and down times	Frequent and larger variations in the net load	Comparison of generators
[26]	Uncertainty coverage capability	Available power	Uncertainty	Measure the flexibility of power system
[27]	Expected unserved ramping	Unserved ramping	Variability and uncertainty	Risk management
[28]	Insufficient ramping resource expectation, loss of load expectation, flexibility residual indexes	Ramp rate, loss of load	Load forecast errors	Reserve requirements
[29]	Unserved flexibility service	Unserved energy, duration of insufficient flexibility	Renewable generation integration	Design appropriate DRP, formulate operational policies
[30]	Flexibility during peak period	Energy flexibility of the demand-response programs	Uncoordinated DRP	Determines the best strategy for operation planning
[32]	Electricity-providing capability, time durations of services	Forced flexibility factor, delayed flexibility factor	Advanced energy conversions	Demand side management, control strategy
[35]	Response time	Time duration	Generation outage	Contingency analysis
C.P	Rescheduling capability	Energy-trading changes/power-trading changes	Evaluation of prosumers’ adoption	Comparison of market participants, market-clearing development

reports a summary of FIs. It can be cocluded that there is no FI that could reflect the adaptability of a system according to a received signal such as prices for market participation. This is a new metric for evaluating the adoption of prosumers that can be used for the market-clearing process or ranking of prosumers in future market-clearing designs.

1.3. Contribution and Innovations

In this paper, a new model of energy scheduling for MEMGs is presented under the flexibility analysis for bilateral market energy transactions. MEMGs with electricity and gas infrastructure can provide a specific percentage of their demand from both gas and electricity energy carriers. In this regard, a new model of DRP is proposed in this paper for combined heat and power demands, which can be adapted to the market prices according to each energy carrier’s cost. According to recent studies, it can be deduced that, despite paying a lot of attention to the concept of flexibility and energy scheduling separately, no quantitative index has been presented up to now to evaluate the flexibility of prosumers according to the market negotiations. In this regard, this paper proposes a new index of flexibility for prosumers based on capabilities to change the bids/offers submitted to the local energy markets. A local energy market based on a distributed market framework is executed, which runs the market for a distribution system operator and connected multi-energy micro grid to study the effects of the flexibility of prosumers in energy-trading negotiations. By using a two-directional structure for market negotiations, the proposed indexes are evaluated from the market-clearing process point of view. As the effects of DRP on the improvement of flexibility are investigated in several types of research [36], MEMGs are employed for flexibility analysis with a new model of DRP for combined loads. In this way, the most prominent features of the current work are as follows:

• Providing a new model of energy scheduling for multi-energy microgrids under the employment of a demand-response program for changeable and shiftable loads;
• Providing new indexes to quantitatively evaluate the flexibility of prosumers under market negotiations;
• Analysis of the operation schedule, market-clearing process, and energy-trading negotiations from the flexibility point of view;
• Providing an integrated demand-response program model for combined heat and power loads.

1.4. Paper Arrangement

This article is arranged as follows:

A comprehensive mathematical formulation for the operation scheduling of MEMGs and DSO is provided in Section 2. Section 2.3 describes the centralized and proposed distributed solution approaches for bilateral energy. The results of the two structures are compared in the analysis of Section 3. Section 3.2 provides a flexibility assessment of the proposed demand-response program in MEMGs. It also defines two flexibility indexes to evaluate the prosumer adjustment capability in energy-trading negotiations. Finally, Section 4 provides a comprehensive summary of the work carried out.

2. Operation Scheduling

2.1. Multi-Energy Microgrid

MEMGs have electrical and heat demands that can be supplied using MG sources or energy trading with the distribution system. MGs in this study include CHP, Microturbines (MTs), Boilers (Bo’s), HP, Electrical Energy Systems (EESs), and Thermal Energy Systems (TESs). In this section, the mathematical model of the operation scheduling for MEMGs is presented. Figure 1 shows the different components of each MEMG.

2.1.1. Objective Function

The energy generation cost in an MG is the central part of the objective function in the problem. The results of energy management in an MG include generation scheduling for each resource, making decisions about the amount of power trading with DS, and implementation of DRP for load management. In this paper, it is assumed that a specific percent of each MG load includes combined electrical and heat demands that are changeable, and can be shifted to another time following the marginal cost of electricity and heat. Equation (1) defines the objective function of each MEMG.

$$\begin{gathered} Min \\ {C}_{{MG}_i}=\sum _t^T{(C}_{i,t}^{CHP}+C_{i,t}^{MT}+C_{i,t}^{Bo}-R_{i,t}) \end{gathered}$$

(1)

2.1.2. Constraints

a.

CHP

The electrical and thermal output power of CHP are dependent on each other and form a closed curve called FOR. In this model, the convex form of the CHP model is used [37]. Equation (2) indicates the constraints for electrical and thermal power generation of CHP units concerning the Feasible Operating Region (FOR) zones. Equations (3) and (4) consider the minimum cost of on/off for CHP units. Finally, in accordance with the start-up/shut-down costs and the amount of electrical and thermal power generated, the total cost function of CHP is calculated in Equation (5).

$${\{P}_{i,t}^{CHP},H_{i,t}^{CHP}\}\in {FOR}_i^{CHP}$$

(2)

$$C_{i,t}^{CHP,SU}\ge {\rho }_i^{CHP,SU}\left(x_{i,t}^{CHP}-x_{i,t-1}^{CHP}\right);\forall i,t$$

(3)

$$C_{i,t}^{CHP,SD}\ge {\rho }_i^{CHP,SD}\left(x_{i,t}^{CHP}-x_{i,t-1}^{CHP}\right);\forall i,t$$

(4)

$$C_{i,t}^{T,CHP}=\frac{\left(P_{i,t}^{CHP}+H_{i,t}^{CHP}\right){\lambda }_t^{NG}}{{\eta }_i^{CHP}}+C_{i,t}^{CHP,SU}+C_{i,t}^{CHP,SD};\forall i,t$$

(5)

b.

Microturbine

The MT unit has been used to generate electric power. Equation (6) refers to the maximum power output of an MT unit. Equation (7) shows the cost function for power generation.

$$P_{i,t}^{MT}\le P_i^{MT,max};\forall i,t$$

(6)

$$C_{i,t}^{T,MT}=\frac{P_{i,t}^{MT}{\lambda }_t^{NG}}{{\eta }_i^{MT}};\forall i,t$$

(7)

c.

Heat Pump

An MT HP works like a demand converter that can protect the MEMG from natural gas price fluctuations. Equation (8) determines the maximum value of heat generation, and Equation (9) indicates the maximum heat power generation for an HP.

$$H_{i,t}^{HP}\le H_{i,t}^{HP,max};\forall i,t$$

(8)

$${H_{i,t}^{HP}=\alpha P}_{i,t}^{HP};\forall i,t$$

(9)

d.

Boiler

Equation (10) presents the heat-generation range of the boiler. Equation (11) shows the boiler cost function. Boiler operation constraints and cost functions are in accordance with [38].

$$H_{i,t}^{Bo}\le H_{i,t}^{Bo,max};\forall i,t$$

(10)

$$C_{i,t}^{T,Bo}=\frac{H_{i,t}^{Bo}{\lambda }_t^{NG}}{{\eta }_i^{Bo}};\forall i,t$$

(11)

e.

Electrical Energy Storage

Due to the impossibility of simultaneous charging and discharging of EES units, relations (12) and (13) are formulated by considering the binary variable $x_{i,t}^{EES}$. Equation (14) shows the amount of energy stored in the storage in accordance with the charges and discharges of each hour. Equation (15) represents the energy balance equation for an EES unit. Equation (16) indicates the state of the charge range of the storage unit.

$$H_{i,t}^{Ch,TES}\le H_i^{Ch,TES,max}{x}_{i,t}^{TES};\forall i,t$$

(12)

$$H_{i,t}^{dCh,TES}\le H_i^{dCh,TES,max}\left(1-x_{i,t}^{TES}\right);\forall i,t$$

(13)

$${SOC}_{i,t}^{TES}={SOC}_{i,t-1}^{TES}+H_{i,t}^{Ch,TES}{\eta }_i^{Ch,TES}-\frac{H_{i,t}^{dCh,TES}}{{\eta }_i^{dCh,TES}};\forall i,t$$

(14)

$${SOC}_{i,1}^{TES}={SOC}_{i,24}^{TES};\forall i$$

(15)

$${SOC}_{i,t}^{TES,min}\le {SOC}_{i,t}^{TES}\le {SOC}_{i,t}^{TES,max};\forall i,t$$

(16)

f.

Thermal Energy Storage

Constraints (17)–(21), similar to the EES, represent the operational constraints for TES.

$$H_{i,t}^{Ch,TES}\le H_i^{Ch,TES,max}{x}_{i,t}^{TES};\forall i,t$$

(17)

$$H_{i,t}^{dCh,TES}\le H_i^{dCh,TES,max}\left(1-x_{i,t}^{TES}\right);\forall i,t$$

(18)

$${SOC}_{i,t}^{TES}={SOC}_{i,t-1}^{TES}+H_{i,t}^{Ch,TES}{\eta }_i^{Ch,TES}-\frac{H_{i,t}^{dCh,TES}}{{\eta }_i^{dCh,TES}};\forall i,t$$

(19)

$${SOC}_{i,1}^{TES}={SOC}_{i,24}^{TES};\forall i$$

(20)

$${SOC}_{i,t}^{TES,min}\le {SOC}_{i,t}^{TES}\le {SOC}_{i,t}^{TES,max};\forall i,t$$

(21)

g.

Demand-Response Program

In this paper, by considering a specific percent of the MEMG loads which can be changed between the electrical and heat model, a new model of DRP for combined heat and power loads is proposed. It is based on the proposed model in accordance with the changeability and shiftability feature of the combined loads, which can be scheduled based on the price of electricity and gas energy carrier to reduce the operating cost. The DRP model for changeable loads considers consumption scheduling so that by maintaining consumption values for combined loads over 24 h, electricity and gas consumption on-peak price time durations are shifted to lower-priced hours of an energy carrier under the new time-of-use DRP model. Equation (22) shows the model of changeable load over 24 h. Equation (23) indicates the maximum changeable electrical load, and Equation (24) refers to the maximum changeable heat load. Although a small percentage of an MG load can be considered as combined heat and electrical demand, these values can be significant at peak times.

$$\sum _{t=1}^{24}{(ech}_{i,t}+{hch}_{i,t})=0;\forall i$$

(22)

$${{-Ch}_{i,t}^{MG,max}\le ech}_{i,t}\le {Ch}_{i,t}^{MG,max};\forall i,t$$

(23)

$${{-Ch}_{i,t}^{MG,max}\le hch}_{i,t}\le {Ch}_{i,t}^{MG,max};\forall i,t$$

(24)

h.

Energy Trading with DSO

MEMGs can trade power in LEM in a connected mode of operation. Equation (25) represents the revenue of power trading with DSO. As the output power of the network on the two sides of the transformer connecting the MEMGs to the DS is different, Equation (26) makes a difference in generating power and final power value for selling. Equation (26) assumes the power output of the transformer as the sales power of the MEMG and also prevents simultaneous buy and sell bid generation for an MG.

$$R_{i,t}=\left(P_{i,t}^{Sell}-P_{i,t}^{Buy}\right){\lambda }_{i,t};\forall i,t$$

(25)

$$P_{i,t}^{Sell}=P_{i,t}^{{Sell’}^{}}.{\eta }_i^{trans};\forall i,t$$

(26)

i.

Power Equality

Equation (27) shows the electrical power equality, and Equation (34), similarly, states the equality constraint for heat generation and consumption in an MEMG.

$$P_{i,t}^{CHP}+P_{i,t}^{MT}+P_{i,t}^{dCh,EES}+P_{i,t}^{Buy}=P_{i,t}^{MG}+P_{i,t}^{HP}+P_{i,t}^{Ch,EES}+P_{i,t}^{{Sell’}^{}}+{ech}_{i,t};\forall i,t$$

(27)

$${H_{i,t}^{HP}+H}_{i,t}^{CHP}+H_{i,t}^{Bo}+H_{i,t}^{dCh,TES}=H_{i,t}^{MG}+H_{i,t}^{Ch,TES}+{hch}_{i,t};\forall i,t$$

(28)

2.2. Distribution System

2.2.1. Objective Function

The DSO optimizes its objective function intending to provide its demand with the lowest cost and maximize the profit of energy trading with MGs. Equation (29) presents the revenue function for DSO as costs of supplying demand through DGs, the revenue of energy trading with MGs, and the revenue achieved via power trading with the upstream grid as TSO.

$$\begin{gathered} \mathrm{M}\mathrm{a}\mathrm{x} \\ {R}_{DSO}=\sum _{i=1}^N\sum _{t=1}^T\left({\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Sell}-{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}\right)\times {}_{i,t}+\sum _{t=1}^T\left(P_{b1,t}^{Sell,TSO}{\lambda }_t^{Sell,TSO}-P_{b1,t}^{Buy,TSO}{\lambda }_t^{Buy,TSO}\right)-\sum _{b=1}^{N_b}\sum _{t=1}^T{\lambda }_b^{DG}{P}_{b,t}^{DG} \end{gathered}$$

(29)

2.2.2. Problem Constraints

The following equations are formulated according to the load flow model presented in reference [39], under the radial and active structure of the distribution network. Figure 2 shows a typical radial structure of the distribution system. Equation (30) expresses the voltage limits of the buses. Equation (31) considers the effects of transformer efficiency on energy generation for selling. Equations (32) and (33) present the active and reactive power balance constraints for each bus, respectively. Equation (34) calculates the voltage of each bus based on the previous bus voltage and the voltage drop across the two bus connections. Equation (35) defines the maximum power generation for DG at the distribution system.

$$V^{min}\le V_{b,t}\le V^{max};\forall t,\forall b$$

(30)

$${\widehat{P}}_{b,t}^{Sell}={\widehat{P}}_{b,t}^{Sell’}\eta .{}_i^{trans};\forall t,\forall b{\pi }_i$$

(31)

$$P_{b,bp,t}+P_{b,t}^{Buy,TSO}+P_{b,t}^{DG}+{\widehat{P}}_{\begin{array}{c}b,t\\ b\in {\pi }_i\end{array}}^{Buy}=\sum _{bp\in {\pi }_b}{P}_{bp,k,t}+P_{bp,t}+P_{b,t}^{Sell,TSO}+{\widehat{P}}_{\begin{array}{c}b,t\\ b\in {\pi }_i\end{array}}^{{Sell’}^{}};\forall t,\forall b$$

(32)

$$Q_{b,bp,t}+Q_{b,t}^T=\sum _{k\in {\pi }_b}{Q}_{bp,k,t}+Q_{bp,t};\forall t,\forall b$$

(33)

$$V_{bp,t}=V_{b,t}-\frac{r_{b,bp,t}{P}_{bp,t}+x_{b,bp,t}{Q}_{bp,t}}{V_{ref}};\forall t,\forall b$$

(34)

$$P_{b,t}^{DG}\le P_{b,t}^{DG,max};\forall t,\forall b\in {\pi }_d$$

(35)

2.3. Solution Approach

2.3.1. Centralized Model

In this section, without considering the possibility of negotiations between the players, under a central control structure, the social welfare is modeled in accordance with Equation (36).

$$\begin{gathered} \mathrm{M}\mathrm{i}\mathrm{n} \psi \\ \psi =\sum _{i=1}^N{C}_{{MG}_i}-R_{DSO} \\ =\sum _{i=1}^N\sum _t^T{\left(\right(C}_{i,t}^{T,CHP}+C_{i,t}^{T,MT}+C_{i,t}^{T,Bo})+\left(P_{i,t}^{Buy}-P_{i,t}^{Sell}\right){\lambda }_{i,t})-\sum _{i=1}^N\sum _{t=1}^T\left({\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Sell}-{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}\right)\times {\lambda }_{i,t} \\ -\sum _{t=1}^T\left(P_{b1,t}^{Sell,TSO}{\lambda }_t^{Sell,TSO}-P_{b1,t}^{Buy,TSO}{\lambda }_t^{Buy,TSO}\right)+\sum _{b=1}^{N_b}\sum _{t=1}^T{\lambda }_b^{DG}{P}_{b,t}^{DG}=\sum _{i=1}^N\sum _{t=1}^T{(C}_{i,t}^{T,CHP}+C_{i,t}^{T,MT}+C_{i,t}^{T,Boiler}) \\ -\sum _{t=1}^T\left(P_{b1,t}^{Sell,TSO}{\lambda }_t^{Sell,TSO}-P_{b1,t}^{Buy,TSO}{\lambda }_t^{Buy,TSO}\right)+\sum _{b=1}^{N_b}\sum _{t=1}^T{\lambda }_b^{DG}{P}_{b,t}^{DG} \end{gathered}$$

(36)

s.t. (2)–(28) and (30)–(35)

$$P_{i,t}^{Buy}={\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Sell};\forall i,\forall t,\forall b\in {\pi }_i$$

(37)

$$P_{i,t}^{Sell}={\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy};\forall i,\forall t,\forall b{\pi }_i$$

(38)

By solving the problem in a centralized manner under Equation (36), and in consideration of coupling constraints (37) and (38), the optimal value for the social welfare function of the system can be calculated. However, by eliminating the parameters related to energy trading as global variables, it will not be possible to calculate the price of power trading for MEMGs and DS. On the other hand, due to the separate ownership concept for the MGs and data privacy issues, it will not be possible to use a centralized model for a decentralized problem structure. Therefore, in the next section, using an ADMM method, the problem will be solved in a distributed manner to maintain data privacy for market participants and calculate the flexibility indexes for MEMGs.

2.3.2. Distributed Model of Market Negotiation

Using the ADMM decomposition method, the problem is broken down into two parts which, after repeating and receiving feedback from each other, finally reach convergence and an optimal solution [40]. The ADMM solution method is used in this paper as a dynamic framework to submit the updated bids to the market in response to the received signals, which can be used to determine the effects of the flexibility of prosumers on energy-trading negotiations and the market-clearing process.

a.

The upstream problem for MEMGs

Considering the penalty function of the ADMM solution approach, the objective function of MEMG is defined as in Equation (39).

$$\begin{gathered} \mathrm{M}\mathrm{i}\mathrm{n} \\ \sum _{t=1}^T{(C}_{i,t}^{T,CHP}+C_{i,t}^{T,MT}+C_{i,t}^{T,Bo})+\left(P_{i,t}^{Buy}-P_{i,t}^{Sell}\right){\lambda }_{i,t}+(\frac{\rho }{2})\sum _{t=1}^T{‖{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}-P_{i,t}^{Sell}+{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}-P_{i,t}^{Sell}‖}_2^2 \end{gathered}$$

(39)

s.t. (2)–(28).

b.

The sub-problem on the DSO side

$$\begin{gathered} \mathrm{M}\mathrm{a}\mathrm{x} \\ \sum _{i=1}^N\sum _{t=1}^T\left({\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Sell}-{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}\right)\times {\lambda }_{i,t}+\sum _{t=1}^T\left(P_{b1,t}^{Sell,TSO}{\lambda }_t^{Sell,TSO}-P_{b1,t}^{Buy,TSO}{\lambda }_t^{Buy,TSO}\right)-\sum _{b=1}^{N_b}\sum _{t=1}^T{\lambda }_b^{DG}{P}_{b,t}^{DG} \\ -(\frac{\rho }{2})\sum _{i=1}^N\sum _{t=1}^T{‖{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}-P_{i,t}^{Sell}+{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}-P_{i,t}^{Sell}‖}_2^2 \end{gathered}$$

(40)

s.t. (30)–(35).

In accordance with the Lagrange coefficient equation, the price update will be applied as follows on the DSO side:

$${\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}=\left\{{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Buy}|{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}>0\right\},{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}=\left\{{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}^{Sell}|P_{\begin{array}{c}b,t\\ b=i\end{array}}<0\right\}$$

(41)

$${\lambda }_{i,t}^{k+1}={\lambda }_{i,t}^k+\rho ({{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}}^{k+1}-{P_{i,t}}^{k+1})$$

(42)

The process of solving the method is described in the ADMM algorithm in accordance with Algorithm 1. At the first iteration, MGOs optimize their cost function with an initial assumption for energy-exchange price and power-trading suggestions to update the power-trading value. After that, the DSO receives all the suggestions from MGs; it optimizes its operation planning regarding received value. The power-trading results of DSO operation planning update the dual variable as trading price and send it back to the MGs to obtain the second feedback. This process is continued until the stopping condition is satisfied for dual variable deviations. Figure 3 shows the information-exchange procedure for DSO and MEMGs. Equation (43) presents the stopping condition of the algorithm.

$$\left|{\lambda }_{i,t}^{k+1}-{\lambda }_{i,t}^k\right|<\epsilon$$

(43)

Algorithm 1. Proposed distributed solution approach.
Synchronous Distributed Algorithm
1	Start:	K = 0, ${\widehat{P}}_{i,t}={\widehat{P}}_{i,t}^0,{\lambda }_{i,t}={\lambda }_{i,t}^0\forall N$
2	Repeat
3	At each individual MEMG
4	Repeat
5	Wait
6	Until receive update ${\widehat{\mathrm{P}}}_{\mathrm{b},\mathrm{t}}$ from DSO (1) solve local problem in (39) for optimal solution ${\mathrm{P}}_{\mathrm{i},\mathrm{t}}$
7	(2) send ${\mathrm{P}}_{\mathrm{i},\mathrm{t}}$ to the DS
8	At the DSO
9	Repeat
10	Wait
11	Until receive update ${\mathrm{P}}_{\mathrm{i},\mathrm{t}}$ from all MEMGs  (1) solve problem (40) for optimal solution ${\widehat{\mathrm{P}}}_{\mathrm{b},\mathrm{t}}$  (2) update dual variables (42): ${\lambda }_{i,t}^{k+1}={\lambda }_{i,t}^k+\rho ({{\widehat{P}}_{\begin{array}{c}b,t\\ b=i\end{array}}}^{k+1}-{P_{i,t}}^{k+1})$
12	(3) Send ${\widehat{P}}_{b,t},{\lambda }_{i,t}$ to all microgrids
13	$k\leftarrow k+1$
14	Until a stopping criterion is met Equation (43)

2.4. Flexibility Index

According to the definition provided for flexibility as the ability to adapt a generation or consumption pattern in response to an external signal, which would be a price signal or any other incentive or inhibitory parameter [8], two different metrics of flexibility are proposed in this paper as energy- and power-flexibility indexes. With two general points of view for energy and power-trading flexibility, it would be valuable to define specific indexes of flexibility for prosumers in accordance with market requirements and valid energy-trading deviations. In this paper, the changes in energy-trading values for the first power-trading bids, which are considered without any encouraging or preventative signals, in comparison to the last power-trading values, which are determined in response to any external signals, are considered as the flexibility of a prosumer in energy-trading negotiations. This definition can be used in many different ways and would be practical in both centralized and distributed market-clearing processes. For example, the index can be calculated by a prosumer via sensitivity analyses of energy trading in accordance with price signal changes. After the prosumer executes the sensitivity analysis, the index can be sent to the market operator as complementary data, which allows the market operator to lead the bids of prosumers in the direction of improving the social welfare of the entire system to achieve a greater margin for clearing the market under security constraints of the system. Moreover, it can be used in distributed models of market negotiations to evaluate the flexibility of prosumers. For example, if a prosumer is requested to provide a specific value of flexibility in proposed energy trading of the market, it can change the required parameter in its optimization procedure to deliver the requested power. The applications of the proposed indexes are out of the scope of the current study and would be modeled in detail in future works. In fact, the flexibility index is defined as the percentage of changes in prosumers’ bids in response to the signals received from the market. Equation (44) defines the index of flexibility for the power trading of prosumers. In this equation, $P_{i,t}^{trd,0}$ refers to the independent power-trading scheduling results of the prosumers in the first bid submission, and $P_{i,t}^{trd,cld}$ is the power-trading scheduling results in accordance with the signals received from the market or a new price estimation. ADMM is investigated in this paper to validate the effects of proposed flexibility indexes on market-clearing results, and $P_{i,t}^{trd,cld}$ is devoted to the scheduled values of energy trading after market negotiations. $P_i^{trd,base}$ is the base power-trading value to determine the per-unit values of bids. In this study, the connection transformer capacity is considered the maximum amount of power trading between the MEMGs and DS as the base power. Considering the positive values of $P_{i,t}^{trd}$ for the sales mode and the negative values for receiving power or buying, the flexibility index will show the flexibility of the MEMG against the trading of more and less power or energy. Equation (45) indicates the index of flexibility in energy trading, which is defined as the average of the flexibilities in power trading.

$${IP}_{i,t}^{Flx}=\frac{P_{i,t}^{trd,0}-P_{i,t}^{trd,cld}}{P_i^{trd,base}}$$

(44)

$${IE}_i^{Flx}=\frac{1}{T}\sum _{t=1}^T(\frac{P_{i,t}^{trd,0}-P_{i,t}^{trd,cld}}{P_{i,t}^{trd,base}})$$

(45)

3. Numerical Results

3.1. Case Study

In this study, a modified IEEE 33 bus power distribution system with four different MEMGs with integrated electrical, heat, and combined demand is adopted to demonstrate the proposed model. Figure 4 shows the case study structure for the proposed model.

Table 2. Component equipment of each Multi-Carrier Microgrid.

MEMG	Component
	CHP	MT	HP	Boiler	TES	EES
${\mathrm{M}\mathrm{E}\mathrm{M}\mathrm{G}}_1$	✔	✔	✔	✔	✔	✔
${\mathrm{M}\mathrm{E}\mathrm{M}\mathrm{G}}_2$	✘	✔	✔	✔	✔	✔
${\mathrm{M}\mathrm{E}\mathrm{M}\mathrm{G}}_3$	✔	✔	✔	✔	✔	✘
${\mathrm{M}\mathrm{E}\mathrm{M}\mathrm{G}}_4$	✔	✔	✘	✔	✔	✔

displays the equipment combination in each of the MEMGs. The maximum 5% is considered for a changeable load. The electrical, heat, and combined demand profiles of each MG are shown in Figure 5. Figure 6 also shows the active and reactive load profiles of the distribution network. The characteristics of the system’s components are presented in

Table 3. Characteristics of the systems’ components.

CHP	$P_{i,A}^{CHP}=250/P_{i,B}^{CHP}=217.6/P_{i,C}^{CHP}=81.98/P_{i,D}^{CHP}=100$		$H_{i,A}^{CHP}=0/H_{i,B}^{CHP}=180/H_{i,C}^{CHP}=104.8/H_{i,D}^{CHP}=0$		${\eta }_i^{CHP}=0.9$
MT	$P_i^{MT,max}=200$	${\eta }_i^{MT}=0.9$
EES	${SOC}_i^{EES,max}=300$	$P_i^{dCh,EES,max}=50$		${\eta }_i^{Ch,EES}=0.9/{\eta }_i^{dCh,EES}=0.8$
TES	${SOC}_i^{TES,max}=200$	$P_i^{dCh,TES,max}=100/P_i^{Ch,TES,max}=100$		${\eta }_i^{Ch,TES}=0.9/{\eta }_i^{dCh,TES}$= 0.8
Bo	$H_i^{Bo,max}$= 45	${\eta }_i^{Bo}=0.9$
HP	$H_i^{HP,max}=135$	$\alpha =2$
DG	$P_i^{DG,max}=900$	${\lambda }_{b8}^{DG}=6/{\lambda }_{b8}^{DG}=8$
TR	${\eta }_i^{trans}=0.9$

. By examining the results of the social welfare cost function in two centralized and distributed control models, the results for the proposed model can be validated. The simulation results are provided by General Algebraic Modeling System (GAMS) software, Version 25.1.2 under a home computer with Core i7 and 8 GB RAM.

3.2. Simulation Result

3.2.1. Power Flexibility Index Analysis

Figure 7 shows the power flexibility indexes for each MG. According to the obtained results, under the proposed DRP model, ${IP}_{i,t}^{Flx}$ in the direction of selling more power have generally increased. By shifting the load from the peak to the off-peak duration, the flexibility in the direction of providing power would increase. On the other hand, on shifting the load to the off-peak hour, the flexibility of off-peak durations in the direction of receiving more power increased. ${IP}_{i,t}^{Flx}$ indirectly reflects the deficiency or adequacy of power for each hour. At hour 1 for MEMG1, the ${IP}_{\mathrm{1,1}}^{Flx}$ is reported as 19%, which is changed to −37% after DRP employment. For a peak hour, such as hour 16, the ${IP}_{\mathrm{1,16}}^{Flx}$ is changed from 51% to −8%, which shows a decrease in power requests in accordance with the change in demand to the thermal kind. However, the flexibility of selling power is still lesser for peak hours in comparison to off-peak hours. As an example, electrical and thermal demands were shifted from peak hours (13–14) to off-peak hours such as (5–6) and 23. This scheduling reduced the demand values in hours (13–14) and enabled MEMG1 to be more flexible in power delivery. On the other hand, with the shift of load to duration (5–6), the energy demand increased and caused MEMG1 to agree to receive more power, which creates more flexibility in receiving power. The proposed DRP model would also change the flexibility of MGs in buying energy. In MEMG2, the DRP is considered in the form of electric to thermal load change in the scheduling horizon. Thus, under the reduction of demand for power, MEMG2 showed less flexibility for receiving power in hours (1–11). However, during peak hours (15–16) and hour 23, when the price of power is low, the flexibility in receiving power increased. MEMG3 without any energy storage used the DRP as an opportunity for energy arbitrage. Results show that the flexibility of MEMG3 in buying power at off-peak hours and selling power at peak hours had already increased. MEMG4 does not include any HP unit, so the DRP model was executed in this unit to transfer the thermal and electric power from peak durations. So, with the shift of electrical and thermal demand from hour 11 to 6, the flexibility of MEMG4 in receiving power increased in the off-peak hours. An analysis of the results for the ${IP}_{i,t}^{Flx}$ indicates that these indexes can be used in the system for demand management, and create an opportunity for market operators to enhance the system efficiency under a wider bid range of prosumers.

3.2.2. Energy-Flexibility Index Analysis

The energy-flexibility index includes a quantitative statement for the changes in the energy-trading schedule of the MEMGs compared to the initial programmed values. Without the DRPs, MEMG1 received 516.64 kWh of energy less than the initial scheduled value. Employment of DRPs changes the state to receive 206,250 kWh of energy more than the scheduled value. Employing the DRP in the MEMG1 caused the MEMG to shift the heat and power loads from peak hours to off-peak hours. This new feature of MEMG made it economic to buy more power in energy-trading negotiations. This is because under a more flexible system, MEMG has more jurisdiction to use market opportunities. So, according to the employment of DRP as flexibility resources, the energy FI changed from −7.18% to 28.65%, which indicates achieving more energy in comparison to the scheduled value. The flexibility of MEMG2 in receiving energy increased from −4.73% to −5.10% with DRP. These negative FIs mean MEMG2 agreed to achieve 23 kWh energy less underemployment of DRP (340.85 kWh in comparison to 367.23 kWh). Similarly, the energy FI increased from −5.82% to −6.20% under DRPs for MEMG3. This 0.38% difference is equivalent to an agreement on achieving 27.82 kWh of energy less than the state of no DRP employment (418.69 kWh in comparison to 446.51 kWh).

Table 4. Energy-flexibility index.

	Value Changes	With DRP	Without DRP
MEMG1	35.83%	28.65%	−7.18%
MEMG2	−0.37%	−5.10%	−4.73%
MEMG3	−0.38%	−6.20%	−5.82%
MEMG4	−0.80%	−3.23%	−2.43%
Average Index Values	9.34%	10.79%	5.04%

presents the energy FIs for each MEMG with and without DRPs. The results indicate that employing the proposed DRP model would enhance the energy-flexibility index of MEMGs. Although the proposed DRP model was the same for all of MEMGs, the results show that according to the different energy equipment of MGs, the results of flexibility changes would be different. In this study, MEMG1 with the greatest diversity of resources, experienced the greatest flexibility improvement.

3.2.3. Proposed Shiftable and Changeable DRP Model

Figure 8 illustrates the results of the proposed DRP model in different MEMGs. With the obtained results, it can be concluded that the employment of different DRPs is integrated with MEMG resources and price parameters. All of the results indicate that the DRP model tried to shift and change the energy demand to a more economic type, and shifted the demand from peak hours and more expensive energy carriers to the cheaper kind. To analyze the effect of the proposed DRP model on the operating costs, the related results are presented in

Table 5. Cost analysis under DRP.

	Improvement	Without DRP	With DRP
DSO	0.09%	133,305	133,189
MEMG1	7.47%	24,087	22,414
MEMG2	6.55%	13,931	13,075
MEMG3	6.28%	35,934	33,810
MEMG4	10.98%	10,705	9646
Total Cost	2.75%	217,964	212,133

. As can be seen in the results, the use of DRP models improved the social welfare function by 2.75%, which shows the effectiveness of the proposed model in reducing system-operating costs. Under demand-response programming, the operating costs of MEMGs decreased between 6.28 and 10.98 percent. The proposed DRP also reduced the costs of operation for DSO by 0.09% under the reduction of the market-clearing prices. Due to the increase in flexibility on the MG side, DRPs demonstrated a prominent effect on the MG side. However, the effects of increasing flexibility in social welfare improvement and reducing DSO costs have also been reported.

3.2.4. Convergency and Flexibility

This section discusses the impact of flexibility on the convergence process of a market. To analyze the results, hours 6, 14, and 16 for the negotiations between MEMG4 and DS were studied. Figure 9 shows the negotiations for the selected hours of MEMG4. Hour 6 with a flexibility index of 32.16% has the highest index in the direction of receiving energy. By examining the convergence process of this MG at 6 o’clock, it can be seen that this MG reached an agreement with DSO after only 11 iterations to receive 230.063 kW power instead of the scheduled 133.593 kWh of energy. In contrast, hour 14 with a flexibility index of 16.67 for the sale of energy could reach an agreement with DSO after 499 iterations. This indicates the role of the player’s flexibility on the speed of convergence. At hour 16, MEMG4 had no flexibility and emphasized the sale of 152.52 kWh of energy to DSO. In this regard, DSO had to employ more flexibility to agree with this power purchase and provide the balance of a transaction to make an agreement. The results show that, if a player is not flexible at all, the opposite player in the transaction needs to employ more flexibility if it is essential to reach an agreement. On the other hand, more flexibility would increase the possibility of reaching a common solution and would improve the convergence speed of the problem. This is because there are more possibilities and strategies to reach an agreement. In this study, the players are considered rational without any intrigue in abusing the flexibility while employing the ADMM method for modeling the negotiations. Moreover, in the ADMM method, the number of iterations continues until all transactions reach convergence, and the results may change until the global optimal solution is determined. So, the number of iterations mentioned in this section to consider the required iteration of negotiation is related to the first stable solution without any changes.

3.2.5. Operation Scheduling and Market-Clearing Results

Figure 10 shows the electrical and thermal power balance constraints for each MEMG. Employing the DRP in the MEMG1 causes the CHP unit to allocate more capacity to generate thermal energy for the duration of (1–6) and change the combined load to the heat kind. MEMG2 is considered without any CHP unit. In this MG, the MT generates electrical energy at maximum capacity. Due to the lack of CHP units, energy converter equipment and storage devices play a fundamental role in supporting DRP. MEMG3 does not include EES, so it cannot use the energy arbitrage revenue. Despite the excess energy generation in this MG, MEMG3 had to purchase power in the peak hours (19–22) with high power prices. The use of changeable load models reduced the amount of power purchased in peak hours (13–16) by about 18 kW, and in the period (20–23) by about 24 kW. MEMG4 does not have any energy converter equipment or a heat pump unit, and thus the role of TES devices during peak heat demand hours is very significant. As can be deduced from the results, MEMG1 with the greatest diversity of resources and the highest flexibility index, and MEMG4 with the lowest index value due to the lack of an HP, made maximum use of shifting feature of the load. In this study, DSO operation scheduling is related to determining the amount of generation for each of the DGs and scheduling the purchase and sale of energy from TSO and MGs. With Figure 11, it can be deduced that in times of peak energy prices, DGs generated power with their maximum capacity, so that in addition to buying energy from MGs and internal generation, they can trade the excess energy purchased in the upstream market. Due to the higher marginal cost of DG2 compared to 1 (8 ¢/kWh and 6 ¢/kWh), DG1 generated more energy in comparison to DG2. Figure 12 shows the market-clearing prices for power trading. The energy requirement of the DSO is mostly provided through buying energy from the upstream market, and using the DG capacity for providing power is not an effective solution with respect to the market prices. This is because, in general, the market-clearing price is less than 6 ¢/kWh, which creates a more economical solution for DSO to trade energy with MGs. It is clear why DSO shows more flexibility in energy-trading negotiations in purchasing power from MGs.

4. Conclusions

In this paper, a new flexibility analysis for MEMGs is executed in accordance with bilateral energy transactions in a local energy market. In this regard, a new model of DRP is proposed to enhance the flexibility of MEMG operation and analyze the effects of participants’ flexibility improvement in the market-clearing process and social welfare enhancement. Moreover, two new metrics for flexibility indexes are proposed. The simulation results indicate that the proposed DRP model increased the flexibility index in buying and selling energy by 0.81% and 35.82%, respectively, which improved the social welfare value of the system by 2.75%. Moreover, the results of the iteration number for the convergency process indicate that, with more flexible market participants, the market-clearing process would be easier under more adaptable negotiators. This concept can be used as an option for market participants in market payments to obtain more financial benefits for the participants who submit bids with a flexibility index for energy transactions. This study showed that using the flexibility of prosumers in market clearing would enhance the social welfare of the entire system; this can be employed in new market structures. For future studies, it is recommended that the effects of the flexibility of prosumers on the security margins of the system also be studied.