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Heuristic approach for transactive energy management in active distribution systems

2020; Institution of Engineering and Technology; Volume: 3; Issue: 3 Linguagem: Inglês

10.1049/iet-stg.2019.0221

2515-2947

Batchu Rajasekhar, Naran M. Pindoriya,

Microgrid Control and Optimization

IET Smart GridVolume 3, Issue 3 p. 406-418 Research ArticleOpen Access Heuristic approach for transactive energy management in active distribution systems Batchu Rajasekhar, Corresponding Author Batchu Rajasekhar batchu.rajasekhar@iitgn.ac.in orcid.org/0000-0002-7963-9629 Indian Institute of Technology Gandhinagar, Gujarat, IndiaSearch for more papers by this authorNaran M. Pindoriya, Naran M. Pindoriya orcid.org/0000-0002-0551-2828 Indian Institute of Technology Gandhinagar, Gujarat, IndiaSearch for more papers by this author Batchu Rajasekhar, Corresponding Author Batchu Rajasekhar batchu.rajasekhar@iitgn.ac.in orcid.org/0000-0002-7963-9629 Indian Institute of Technology Gandhinagar, Gujarat, IndiaSearch for more papers by this authorNaran M. Pindoriya, Naran M. Pindoriya orcid.org/0000-0002-0551-2828 Indian Institute of Technology Gandhinagar, Gujarat, IndiaSearch for more papers by this author First published: 20 May 2020 https://doi.org/10.1049/iet-stg.2019.0221Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The advent of distributed energy resources (DERs), which include small conventional and renewable generation units, energy storage, and flexible loads in distribution network needs distributed coordination for effective management. In this paper, a stochastic transactive management framework is proposed to minimize overall cost and avoid network constraints violation at the distribution network level. This framework includes day-ahead scheduling of electric vehicles and air conditioning loads under demand response aggregators (DRAs), and DERs under distributed generation owners (DGOs) into day-ahead wholesale market in a network managed by a distribution network operator (DNO). An agent called distribution independent system operator (DISO) is responsible for coordination among DRAs, DGOs, and DNO. A heuristic step-size update approach is proposed to calculate the Lagrange multiplier iteratively and improve the convergence speed. This framework is modeled as a quadratic constraint programming (QCP) problem and solved using the GAMS solver. Simulation results on a modified 33-bus system with considerable penetration of loads and DERs, shows that the suggested framework can efficiently reduce the iterations to converge and returns an optimal schedule. And demonstrate the effect of network congestion, demand, and generation uncertainties on the resulting objective values of the agents and magnitude of the Lagrange multiplier values. 1 Nomenclature Indices index AND set of buses in the network index and set of child nodes for bus b index and set of ancestor node for bus b index and set of distributed generators (DGs) set of DGs connected bus b i index of the iterations index and set of air conditioning (AC) appliances at each bus index and set of storage devices (SDs) set of SDs connected bus b index of time slot and time period index of scenarios and scenario set index and set of demand response aggregators (DRA) index and set of distributed generation owners (DGO) DNO index of distribution network operator Parameters generation cost of DG unit g charging and discharging cost of storage device s forecasted renewable power (PV/wind) generation , line resistance and reactance between buses k and b base power of the system predicted electricity price in day-ahead and real-time markets load curtailment penalty price for DRAs at time t value of renewable generation curtailment , coefficients denoting heat transfer and thermal efficiency of AC appliances at bus b occurrence probability of scenario of stochastic variable Functions bidding function of DRA objective function of DGO objective function of DNO Variables generation dispatch of DGO in day-ahead market generation dispatch of DGO in real-time market demand procurement of DRA in day-ahead market demand procurement of DRA in real-time market allowable active power by DNO at bus b and time t allowable reactive power by DNO at bus b and time t total demand of fixed loads (FLs) at time t, bus b amount of curtailable load (CL) at time t, bus b demand of individual AC at time t, bus b demand of individual EV at time t, bus b active power flow in the branch kb power generation by conventional DG unit at bus b renewable power (PV or wind) dispatch discharging schedule of energy storage s charging schedule of energy storage s voltage of bus b at time t dual variable/Lagrange multiplier of global constraint step size for updating Other variables net active/reactive power injection at bus b and time t power exchange in day-ahead market at substation bus 1 power exchange in real-time market at substation bus 1 Symbols expected value of 2 Introduction 2.1 Background The integration of stochastic renewable generation sources has an increased need for balancing generation and demand in energy markets. Aggregators having a group of proactive consumers are expected to provide balancing power to the grid by managing their flexibility. Meanwhile, undesirable line congestions and voltage violations may arise in the distribution network, when flexible resources respond to external control or price signals on a large scale [[1]]. Hence, the development of a useful framework to coordinate flexibility at the distribution system level subject to network limits is of utmost importance [[2]]. A typical active distribution system consists of few or all of the following agents namely, customers served by retailers and demand response aggregators (DRAs), distributed energy resources (DERs) managed by distributed generation owners (DGOs) and distribution network operator (DNO) and distribution level independent system operator (DISO) [[3]]. The following are the main issues in the optimal operation of the distribution system due to the inclusion of DERs controlled by multiple agents. The first is how to coordinate these agents with multiple objectives at multiple levels into power system operation and market operation. Second, is how to address fairness in risk management among agents when considering the volatility in price and uncertainties in demand and generation [[4]]. Third, how to address computational complexity and privacy in centralised frameworks and convergence rate in iterative decentralised frameworks. There have been some efforts in the literature for addressing these challenges in the collaborative operation of different agents in the active distribution network. They differ in following key aspects whether the agent is a price maker or a price taker, whether network constraints are taken into account or not, whether uncertainty is considered or not, whether the control is centralised [[5], [6]], distributed [[7]], peer-to-peer [[8]], and transactive energy (TE) approach [[9]]. We divided the related works into multiple themes. The first theme is concerned with coordination among the agents. Retailer's price maker bidding of customers flexible demand into the day-ahead (DA) electricity market is addressed as centralised [[10]] and decentralised mechanisms in [[11], [12]]. A single leader and multi-follower type bi-level model proposed in [[13]] to obtain trading strategies between proactive distribution company and DGOs and procure remaining demand requirement from the wholesale market and did not consider flexible demand bidding. Stratification of demand into service priorities based on traffic light concept applied to the flexibility services and customers [[2]]. TE management approaches based on distribution locational marginal prices (DLMPs) approaches or their underlying components are being explored recently as they enforce the interconnected constraints implicitly through price signal. Since LMPs (locational marginal prices) plays a vital role in the coordinated operation of power systems and electricity markets, and form a link between wholesale market/transmission grid and retail electricity market/distribution grid as discussed in [[14]] through hierarchical LMP concept. Similarly interaction of interconnected microgrids through zonal LMP is suggested in [[15]]. Li et al. [[16]] developed a Nash bargaining theory to model the TET framework which considers network loss allocation and develops a closed-form solution. Auction-based electricity market to balance DR and DERs in a microgrid in [[9]], however, this work overlooks the impact of trading on network congestion. Authors in [[3]] proposed a TE management system (TEMS) for managing constrained grids where DNO and retailers negotiate to meet network constraints through congestion price generated by the third party known as DISO. Here, Lagrange multiplier (LM) at each bus is equivalent of congestion price in DLMP, and DISO iteratively updates the price signal to coordinate among agents reasonably. However, the proposed approach does not consider distributed renewable generation and its uncertainties. It is to be noted here that, the distribution tariff increases without TE owing to the expenses in upgrading the network, which will eventually be passed on to end customers with an enhanced bill. For both DNO and end consumers, this scenario is neither beneficial nor efficient. Whereas in TEMS, the tariff is dynamic, and the congestion level can be prevented or reduced to minimise the overall cost further. The works in [[17]] presents a multi-agent TEMS based on oligopoly competition model to control demand and supply to minimise customers cost, and regulate voltage in the presence of high levels of renewable generation and EVs penetration. The second theme is concerned with computational complexity and scalability. A neurodynamic algorithm is proposed in [[18]] instead of optimisation to derive the bidding curve in real-time (RT) based on historical data, but the algorithm yields less accurate solutions if there is a considerable variation in magnitude of parameters. Nature inspired meta heuristics are used in [[19], [20]] to reduce communication overhead which reduces computational efforts. Multi-agent transactive control is an emerging technique for its ability to increase system scalability, autonomy, and resiliency. They reduce the levelled cost of energy for each node. We discussed related works based on the type of trading and proactive customers considered, i.e. whether peer-to-peer/intra microgrid [[21], [22]] peer-to microgrid, microgird–microgrid [[9], [15]] and microgrid-to-utility grid [[19]]. A multi-level TE approach for multi-micro gird is proposed in [[23]] where sharing priority is based on a heuristic approach. In this Liu et al. [[15]] proposed a novel sub-gradient based TEMS approach for coordinated operation of networked microgrids in a distribution network. The third theme is concerned with the uncertainties of renewable generation and DR flexibility forecasts, which puts system balance at risk and needs more reserve requirements, particularly when DISO has no access to historical data. Authors in [[4], [24]] proposed risk constrained decentralised algorithms for renewable energy integration and demand response integration, respectively. A new point estimate base stochastic method is proposed in [[25]] to estimate LMP. Liu et al. [[26]] implemented modified Harr's two-point estimation method to study the effect of correlation between renewable distributed generation and load uncertainties on probabilistic optimal power flow approach and it can estimate the mean and variance of the scheduling solutions compared to Monte Carlo simulation. The authors in [[27]] proposed a stochastic receding horizon control to handle the uncertainties in real time optimal operation of network. A chance constrained optimal power flow model is proposed in [[28]] which can handle the stochastic characteristics of electric vehicle (EV) load on voltage regulation. A stochastic decision making model for price setting by retailer under intermittent DER and DR is proposed in [[29]] but network constraints are not considered here. 2.2 Motivation To best of our knowledge, a detailed TE optimisation mechanism for the overall social cost minimisation and integration of stochastic demand and DERs into the market under network congestion has not been studied extensively in the literature. When compared with other distributed algorithms, the TE mechanism does not require partial derivatives and can lower computational time by selecting suitable step-size heuristically in updating LMs. Further, multiple roles of DISO needs to be redefined on how to handle network congestion, competition, and risk aversion between DGOs, DRAs, and customers in a fair manner. In this paper, we aim to address the impact of high penetration of stochastic renewable generation and demand on obtained LMs/congestion price for enforcing network constraints. And suggest a heuristic approach to update the LMs to improve the convergence speed. 2.3 Contributions Building forth on the previously developed network constrained TE (NCTE) framework in [[3], [30]], this work develops a stochastic operational framework to enable the participation of DRAs and DGOs located in distribution network managed by DNO, in the DA and RT markets. The model aims to maximise social welfare through energy exchange in DA and RT markets, optimal generation of conventional distributed generators (DGs), bidding renewable DGs, optimal scheduling of flexible loads, using load and generation curtailment options coordination by NCTE framework. In this model, DISO is responsible for updating congestion price and coordinate decisions among agents in an iterative approach. Scenario-based stochastic programming is used for addressing the demand, renewable generation and price information uncertainties into consideration. Additionally, this paper, suggests an approach to select the step-size heuristically for LM calculation to reduce the number of iterations to converge when compared to fixed and incremental step size update techniques. In summary, the main contributions of this paper are as follows: We follow up on a recently proposed network constrained TE management framework [[3]], and extend this to a scenario with: (i) high penetration of DERs such as solar photovoltaic and wind generation, energy storage devices (SDs), distributed generation managed by DGOs, and flexible load of residential customers managed by DRAs; (ii) customers appliance and discomfort model into consideration; and (iii) operational decision making in both DA and RT markets with uncertainties in renewable generation, load demand and market price. Formation of a stochastic optimal decision-making framework for DISO considering distribution network power flow constraints, and power and price uncertainties to study the impact on economic and system operating issues due to TE-based framework in an approximated but holistic manner. A heuristic step size calculation is suggested to update LM iteratively to achieve relatively faster convergence with reasonable accuracy. Finally, validate the proposed approach with a stochastic environment on a modified 33-bus system. Then demonstrate the impact of heuristic step-size on the convergence, and impact of uncertainties on optimal solutions, discussion on cost and benefits for each agent, i.e. DRA, DGO and DNO. The rest of the paper is organised as follows. Section 2 introduces the framework of the DISO, and the detailed mathematical models for DRA, DGO, and DNO. Section 3 presents the LM-based reformulation of the problem and sub-gradient based solution strategy with heuristic step-size update. Section 4 provides case studies to illustrate the performance of the proposed method. Section 5 concludes the paper. 3 Problem formulation This work considers the problem of congestion price update by the coordinator to improve convergence in a TEMS-based control of demand and supply of agents in a distribution system. Fig. 1 represents a network-constrained TE management method to schedule flexible demand and DERs. In this system, we assume that in addition to supplying electricity to loads, DRAs manage the curtailable, air-conditioning, and EV loads on behalf of certain group customers to minimise the overall cost. Hence, each DRA represents the interests of a group of customers and aims at minimising their operating costs by optimally participating in the DA spot market and RT balancing markets. Fig. 1Open in figure viewerPowerPoint Representative radial distribution network with Intelligent loads (ILs), distributed generator (DGs), renewable energy sources (RES), storage devices (SDs), and capacitor bank (CB) Similarly DGOs try to bid their stochastic generation, SDs power into the electricity market to maximise the profit. These operations should comply with DNO's network security constraints. The DISO is therefore introduced as an independent system operator who coordinates the DRAs, DGOs, and the DNO's operational interests by the transactive-energy approach. If there is a network constraint violation by the actions of the DRAs and DGOs, congestion prices ware generated by the DISO proportional to the amount of power deviation and shared to DNO, DRAs, and DGOs to minimise the congestion in an iterative manner. The final load schedules will be sent to customers by DRAs. It is to be noted here that, for simplicity, we consider DRA knows the customer preferences and can directly control their appliances usage. We omit the discussion on how to divide the payoff or profit among the customers in coalition, i.e. among members under the DRA which is usually done using popular solutions like shapely value in case of cooperative game theory. Alternatively, there can be another level of TE trading/scheduling between DRA and its non-cooperative customers [[31]]. Similarly for DGO agent, we assume DERs under it form a coalition to bid into the market to maximise their profit. 3.1 DRA's optimisation model Each DRA has to decide the amount of energy to be procured to meet its customers demand and minimise the cost. Residential customers is assumed to have following intelligent loads (ILs) such as EV and air conditioning (AC) loads, and conventional loads with portion of it as curtailable. The DRA's objective is to minimise the cost of discomfort, energy consumption cost by strategic procurement of energy from DA and RT markets, and load curtailment options. In this study we use the model presented in [[3]] to characterise the AC and EV loads as follows: (1) s.t. (2a) (2b) (2c) (2d) (2e) (2f) (2g) is the variable set. The relation between indoor temperature and power demand is modelled by (2a). Assume that the customer desires a most comfortable temperature and there is a range of temperature that the customer can bear as denoted by (2b) and AC power demand limits are denoted by (2c). For EV load, the cumulative power should be equal to the requested energy at the end of the charging period (2d). Here, represents the state of charge of individual EV. The constraints (2e) and (2f) represent limits on charging power and curtailable load (CL), respectively. The aggregated power for DRA to be procured from DA and the RT market is calculated according to (2g). The value of expected demand at each bus b and interval t is given below, which is obtained by summing the DA value and weighted sum of RT values (3) 3.2 DGO's optimisation model A DGO can have three types of resources namely conventional generation, renewable generation and SDs. The uncertainties in renewable generations and RT electricity prices are represented by scenario-based method. For profit maximisation, each DGO should commit a fixed power in DA and RT markets rationally while minimising the expected cost. The DGO objective (4) indicates minimisation of minus profit, which consists minus revenue of selling committed generation quantities with market prices and the cost of generation and storage usage, and cost of renewable generation curtailment (4) s.t. (5a) (5b) (5c) (5d) (5e) (5f) (5g) (5h) (5i) With the optimisation variables as . At each time interval t, constraints (5a), (5b), identify total active power available for DGO to bid. The energy balance constraints for each SD is enforced by (5c), and bounded by (5d) while capabilities of the charge/discharge active power are constrained by (5e) and (5f), respectively. DG's power is constrained by (5g). Renewable generation schedule and curtailment are represented by (5h) and (5i), respectively. It is to be noted that, in case if a DGO has only SDs and then the market price will be the purchasing price in case of charging power and selling price in case of discharging power in this formulation. The value of expected generation at each bus b and interval t is given as (6) To enforce the network power flow constraints on the values of power schedules by DRA and DGO assume their values are deterministic instead of stochastic for simplicity. The impact of their deviation due to uncertainties on network utilisation is of future research interest. Let is expected net power at each bus given as (7) where index m and n denote the number of DGOs and DRAs in the system, respectively. 3.3 DNO's optimisation model For DNO, the objective is to control the optimal power schedules at each bus from DRAs and DGOs, subject to network voltage constraints and power limits as well as to minimise power losses. The first term in (8) is squared difference between allowable power schedules by DNO and net value of actual power schedules by DRAs and DGOs, and the second term is approximated power loss. The linearised power flow equations described in [[32]] is used here for radial distribution network model. These power flow equations that must hold in a network are imposed as set of constraints (9a)–(9e). Here, bus 1 is the substation connected to the external transmission network, and remaining buses represent local load and DERs. Each bus has a unique ancestor denoted by and set of child nodes denoted by except for terminal buses. Similarly, the line connecting ancestor bus k to bus b is labelled as line kb having to have resistance and reactance (8) s.t. (9a) (9b) (9c) (9d) (9e) (10a) (10b) where is the optimisation variable set. The approximated power loss is calculated by (10a). Assuming reactive power consumption is minimal and power factor at each bus is fixed in (10b), it changes in proportion to the real power . 3.4 Centralised social cost minimisation problem From a social cost minimisation point of view, it is required to minimise the following objectives together: DRAs cost, DGOs minus of profit, and the DNO's capacity allocation mismatch plus losses, subject to all their constraints as well as (11c). The overall problem formulation is as follows: (11a) s.t. (11b) (11c) where and (11c) is a global constraint for the DNO and all agents, implying sum of optimal power of DRAs minus sum of optimal power of DGOs should be less than or equal (or exactly equal) to optimal allowable power by the DNO. This coupling constraint mitigates congestion and avoids the undesirable impact of the DRAs and DGOs actions on the distribution network. Let denote the set of LMs corresponding to coupling inequality constraint (11b). By keeping the rest of the constraints implicit, the Lagrangian function for the centralised problem is: (12) To solve Lagrangian in a centralised way, DISO requires not only the distribution network information but also the private information of the customers (i.e. utility functions and appliance schedules) and DERs. To protect customer privacy and make the DR scalable, we propose a dual decomposition algorithm-based TE management scheme to solve the problem. 4 TE modelling and implementation In practice, DISO does not have direct control over all agents nor access to their private information. Alternatively, to solve the optimisation problem (12), a dual decomposition method is applied that can decompose this problem into sub-problems. Each DRA's minimisation problem can be written as (13) s.t. the same aggregator constraints presented in Section 2.1. Each DGO's minimisation problem can be written as (14) s.t. the same DGO constraints presented in Section 2.2. The DNO's minimisation problem is now (15) s.t. the same DNO constraints given in Section 2.3. This approach not only reduces the problem complexity but also provides decision-making right to each agent in the network. The problems include the DGO's, DRA's and DNO's optimisation problems, coordinated by the DISO by updating the LMs/dual variables . The idea is to determine the vectors such that obtained equilibrium corresponds optimal solution of the centralised social welfare optimisation problem (11a). To solve the dual optimisation problem of (12), we apply the sub-gradient method [[33]] based distributed TE algorithm concept, which requires multiple iterations of information exchange among agents to determine equilibrium as described in Algorithm 1. This strategy is applicable because the problem is convex and constraints are also linear. The KKT and slaters conditions are satisfied and a feasible solution exists and is unique [[4], [34]]. Algorithm 1.Distributed TE approach to reach EquilibriumInitialisation:• To DGOs and DRAs predicted market prices. To DISO initialise error tolerance, set iteration index.Repeat1. DGOs: Each DGO produces their profiles by solving (13), i.e. minus profit minimisation, s.t. availability of DG's and SD's constraints.2. DRAs: Each DRA produces their profiles by solving (14), i.e. cost plus discomfort minimisation, s.t. appliance constraints.3. DISO: Calculates net power based on received profiles from DGOs, DRAs and sends net profiles at each bus to DNO.4. DNO: Produces allowable profile at each bus by solving (15), i.e. minimisation of losses and maximisation of utility, s.t. network constraints.5. DISO: if No mismatch between allowable power profiles by DNO and sum of scheduled profiles by agentsthen Ends, as no congestion and net demand at substation bus is purchased from DA Energy Market.else Coordinate the DRAs, DGOs and DNO by calculating the LMs/congestion prices via (16) or (17) and communicate to agents.6. Update step size via (18).7. Iteration number update .Until . In each iteration, all agents receive the updated LMs at corresponding buses and send their optimal power schedules in return to the DISO. 4.1 DISO update The DISO updates the LMs using the power difference according to following equations, if , then (16) else (17) where i is the index for the iterations. is a step size, which has to be positive to guarantee convergence. The superscript i for any variable represents its value in iteration i. Note that the difference in (16) and (17) is that the constraint (11b) is enforced as strict equality constraint if the bus has both demand and generation and as inequality if the bus has only demand. Because as concluded in [[3]], enforcing (11b) as inequality constraint at demand bus is beneficial for overall social cost minimisation. Moreover, enforcing as equality at a bus with both generation and demand or only generation improves overall social cost minimisation based on our studies. so, can be positive or negative for and is non-negative for . 4.2 Step size update Instead of using a scalar step-size while performing the LMs update in each iteration using either (16) or (17), we suggest a heuristic step-size update to improve the convergence speed. A value which depends on the amount of deviation of power schedule from the allowable power by DNO. We compared the convergence with other step-size update techniques mentioned below and observed the improvement in convergence speed. 4.2.1 Fixed step size (FS) update In this approach, a simple step-size , is chosen to update the LMs by DISO. 4.2.2 Incremental step size (IS) update This approach it is proportional to iteration number, i.e. , where and are positive constants. 4.2.3 Heuristic step size (HS) update In this, the initial value is chosen as a different value for each bus and time interval based on historical data learning. Then step size is also updated by a value proportional to power deviation at each iteration (18) where and are positive constants whose value is generally chosen as 1000 times smaller than the maximum value of the power difference. In practice, the information exchanges can be facilitated by a system shown in Fig. 1, which shows the implementation of the proposed transactive control for network-constrained management. In such a framework, the DISO manages congestion prices (i.e. the LMs) and sends updated values to the DNO and aggregator agents to achieve convergence. 5 Simulations results and discussions 5.1 Case study setup The suggested approach is implemented over a modified IEEE 33-bus radial distribution network shown in Fig. 2. The modified network has following loc