Artigo Revisado por pares

Coordinated dispatch of networked energy storage systems for loading management in active distribution networks

2016; Institution of Engineering and Technology; Volume: 10; Issue: 9 Linguagem: Inglês

10.1049/iet-rpg.2016.0269

ISSN

1752-1424

Autores

Dongxiao Wang, Ke Meng, Fengji Luo, Colin Coates, Xiaodan Gao, Zhao Yang Dong,

Tópico(s)

Microgrid Control and Optimization

Resumo

IET Renewable Power GenerationVolume 10, Issue 9 p. 1374-1381 Research ArticleFree Access Coordinated dispatch of networked energy storage systems for loading management in active distribution networks Dongxiao Wang, Dongxiao Wang Centre for Intelligent Electricity Networks, The University of Newcastle, Callaghan, 2308 NSW, AustraliaSearch for more papers by this authorKe Meng, Corresponding Author Ke Meng ke.meng@sydney.edu.au School of Electrical and Information Engineering, The University of Sydney, Sydney, 2006 NSW, AustraliaSearch for more papers by this authorFengji Luo, Fengji Luo School of Electrical and Information Engineering, The University of Sydney, Sydney, 2006 NSW, AustraliaSearch for more papers by this authorColin Coates, Colin Coates School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan, 2308 NSW, AustraliaSearch for more papers by this authorXiaodan Gao, Xiaodan Gao Centre for Intelligent Electricity Networks, The University of Newcastle, Callaghan, 2308 NSW, AustraliaSearch for more papers by this authorZhao Yang Dong, Zhao Yang Dong School of Electrical and Information Engineering, The University of Sydney, Sydney, 2006 NSW, AustraliaSearch for more papers by this author Dongxiao Wang, Dongxiao Wang Centre for Intelligent Electricity Networks, The University of Newcastle, Callaghan, 2308 NSW, AustraliaSearch for more papers by this authorKe Meng, Corresponding Author Ke Meng ke.meng@sydney.edu.au School of Electrical and Information Engineering, The University of Sydney, Sydney, 2006 NSW, AustraliaSearch for more papers by this authorFengji Luo, Fengji Luo School of Electrical and Information Engineering, The University of Sydney, Sydney, 2006 NSW, AustraliaSearch for more papers by this authorColin Coates, Colin Coates School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan, 2308 NSW, AustraliaSearch for more papers by this authorXiaodan Gao, Xiaodan Gao Centre for Intelligent Electricity Networks, The University of Newcastle, Callaghan, 2308 NSW, AustraliaSearch for more papers by this authorZhao Yang Dong, Zhao Yang Dong School of Electrical and Information Engineering, The University of Sydney, Sydney, 2006 NSW, AustraliaSearch for more papers by this author First published: 17 August 2016 https://doi.org/10.1049/iet-rpg.2016.0269Citations: 18AboutSectionsPDF 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 System overloading is becoming a critical issue in distribution system due to outdated infrastructure and growing electricity demand. Although renewable-based distributed generation is a promising solution to relieve this issue, its intermittency and uncertainty impose significant challenges on system operations. This study attempts to coordinate networked energy storage systems (NESSs) to manage network loading in distribution networks. The NESS can act as a buffer to absorb surplus energy during high generation periods and serve the demand during peak load periods. A consensus-based dispatch strategy is proposed to coordinate NESSs. Through limited communication among neighbouring NESSs, required active power curtailment is shared. The mathematical formulation of a state-of-charge weighting factor is introduced to improve the efficiency of NESSs. A sensitivity study is also conducted to demonstrate the performance of the proposed strategy. 1 Introduction 1.1 Background and motivation Electricity demand is growing rapidly around the world. It is expected that over 90% of this demand growth will come from developing countries in the coming decades. An annual electricity demand is estimated to increase up to 53.6 TWh by 2050 compared with 22 TWh in 2011 [1]. The global electricity demand is estimated to increase by 3.1% annually from 2010 to 2050. Conventional approaches such as building more fossil-fuel power plants to serve these loads are costly and environmentally unfriendly. With the proposal of the ‘smart grid’ [2], renewable energy sources such as photovoltaics and wind turbines are considered to be a promising solution to relieve system overloading and improve energy efficiency [3, 4]. However, the intermittent and stochastic nature of renewable energy imposes several significant issues on system operations, such as supply–demand balance, system reserve requirement, frequency/voltage stability, and operational planning in electricity markets [5, 6]. Furthermore, progress in material science and power electronics devices have boosted the effective employment of energy storage systems (ESSs), which can provide strong support for high renewable power penetration. ESSs are able to act as buffers to absorb surplus power during the peak generation periods and serve the demand during peak load periods [7]. Among the various ESS solutions, battery energy storage systems (BESSs) are often considered as the most cost-effective option for renewable integration and are thus utilised in this paper. 1.2 Related works Utilising distributed generation methods [8-10] and ESS solutions [10-13] to cope with network overloading has been widely studied in the literature. Many recent works have studied the coordination strategies for these distributed resources by utilising the distributed control technique due to its outstanding characteristics, which include reliability, flexibility, and low cost. The distributed control technique can be as efficient as centralised control but with reduced complexity, and as fast and robust as localised control but with global optimality. Various control schemes have been proposed to coordinate ESSs to stabilise smart grids by using the distributed control strategy. In [14], the authors put forward a novel BESS based energy acquisition model for use by distribution companies for regulating price or locational marginal price mechanisms. In [15], the authors presented a comprehensive ESS application design for mitigating wind power variation and increasing wind energy integration and grid voltage stability. In [16], a dual BESS scheme was proposed, where the generated wind power was charged into one BESS and the second BESS was to discharge power into the grid at the same time. A new decentralised strategy was proposed which ensured stored energy balance for a low voltage DC microgrid with distributed BESSs to achieve good storage energy balance and low voltage deviation in [17]. In [12], a state-of-charge (SOC) based adaptive droop control method was presented to share load power among ESSs. In [18], the authors considered the charge/discharge efficiency impacts on the ESS charging/discharging rate, and proposed a cooperative control scheme of ESSs in a microgrid. In [13], the authors coordinated energy storage units to manage voltage and loading in distribution networks. Despite the wide range of studies on the application of ESSs in power grids, the correlation between the SOC and discharge ability of ESSs has been largely ignored. The ESS's discharge ability is strongly related to the SOC level. For instance, ESSs with higher SOC are able to provide more energy to participate in the network loading management. To control and operate ESSs in a more effective way, the discharge ability difference based on different SOC level should be taken into consideration. 1.3 Contributions of this paper To address the aforementioned problems and motivated by the works in [13, 18], this paper proposes a consensus-based control strategy to coordinate networked energy storage systems (NESSs) to share required active power curtailment through limited communications with neighbouring NESSs. A novel equilibrium point can be achieved among participating NESSs after the introduction of a SOC weighting factor. If NESSs have larger SOC, they are capable of providing more energy to alleviate network overloading. By introducing a SOC weighting factor, NESSs with higher SOC are assigned a smaller weighting factor while NESSs with lower SOC are assigned a larger one. In this control scenario, more energy output is represented by more active power support over a required time period. Therefore, when one NESS is far away from the critical SOC, a smaller weighting factor means this NESS can produce more active power to share the required consensus ratio with other NESSs. Leader selection and sensitivity study are also conducted in this paper. The main contributions of this paper are listed below: (i) By taking into account the correlation between SOC and NESSs discharge ability and introducing weighting factors, an innovative ratio defined by required active power output compared with maximum active power is proposed as the consensus state; (ii) Instead of setting a virtual leader, one of the NESSs is defined as the leader and others as followers, which requires a simpler communication network and releases heavy load for the computational resources in the control centre; (iii) Leader selection among participating NESSs and sensitivity factor coefficient influence on convergence speeds are studied. The rest of the paper is organised as follows. In Section 2, the graph theory concepts and consensus algorithm preliminaries are briefly introduced for completeness; in Section 3, the proposed consensus-based coordinated dispatch strategy for network loading management is presented; Section 4 presents the simulation results on a modified IEEE 15-bus system; finally, Section 5 concludes this paper. 2 Preliminary 2.1 Basics of graph theory The network topology of a system can be represented by a weighted graph G = (V, E, A), where V = {v1, v2, …, vn} represents a set of nodes, denotes a set of edges and A = (aij) is a weighted adjacency matrix with non-negative elements. eij = (vi, vj) means an edge routed from node vi and ended at node vj, representing information flow from i to j. The non-negative adjacency elements are associated with the edges of the graph, i.e. eij ∈ E ⇔ aij > 0. A directed path from node vj to node vi is a sequence of edges with distinct nodes [19]. Mathematically, the Laplacian matrix L = (lij)N×N is a representation of a graph, which can be defined as: (1) The network performance is strongly connected with the eigenvalue of the Laplacian matrix, especially the second smallest eigenvalue λ2, which is called the algebraic connectivity of a graph [20]. Based on the research in [21], consensus algorithm performance/speed is measured by algebraic connectivity of the network topology. λ2 is relatively large for dense graphs and relatively small for sparse graphs under a noted observation regarding the Fiedler eigenvalue of an undirected graph [22]. Dense interactions means an agreement problem in a network is solved faster compared with a connected but sparse network, thus large λ2 determines faster convergence speed than small λ2. According to Olfati-Saber [23], the algebraic connectivity of small work networks can be greatly improved through proper design of the communication network topology. 2.2 Consensus algorithm Consensus problems have a long history and have attracted significant attentions in recent years, particularly in the area of automatic control and distributed computation. In many modern power applications including multi-agent systems, certain quantities of interest need to be agreed on among participating groups of agents. Specified in [24], a ‘consensus algorithm’ is an interaction rule that details the information exchange between an agent and all of its neighbouring agents on the network. Some fundamental research on consensus algorithms [25, 26] have been completed by this paper's authors, furthermore, we aim to demonstrate its application to distribution networks through this research. Next, we give some fundamental mathematical knowledge about consensus algorithm. Let xi ∈ R represent the state value of node i. The node state value might denote physical quantities such as network loading value and frequency. It can be said the nodes in a network have reached a consensus if and only if xi = xj for all i, j when time variable tends to infinity. For fixed or switching topology and zero communication time-delay, the following linear consensus protocol is used in [24]: (2) where, is the state update of node at time t after communication; xi, xj is the local consensus state of nodes , j at time t; aij is the (i, j) entry of the adjacency matrix A; Ni defines the set of neighbours node i can communicate with. It is worth noting the set of neighbours Ni is variable in networks with switching topology. This linear consensus protocol can also be written as (3) The discrete-time consensus algorithm is introduced to update the consensus state of a node with time delay: (4) where xi[k + 1] is the state update of xi[k] at iteration k + 1; xj[k] is the local consensus state discovered by node j at iteration k; dij is the (i, j) entry of row-stochastic matrix D, which is called the communication coefficient between nodes i and j. Different determination methods of dij provide different converging speeds. The definition of dij will be introduced in Section 3. 3 Consensus-based coordinated dispatch scheme for network loading management In this section, a consensus-based coordinated dispatch scheme is proposed, aiming to coordinate NESSs to manage the loading in distribution networks by sharing the required active power curtailment during peak demand hours. Since load shedding should be implemented among participating NESSs fairly, a consensus decision making method is needed among all participating members. In this control scheme, a virtual leader among participating NESSs is assigned to initiate the control scheme. It monitors the power exchange between the substation and main grid, which is further used as an input signal of the controller for network loading management. The other NESSs are assigned as followers. The control actions for each follower NESS can be determined through the information state from its neighbours or virtual leader. Let S(t) denote real-time apparent power and Smax −critical represent network loading maximum critical value. If apparent power constraint S(t) > Smax −critical is violated, the NESSs control is initiated in discharging mode until the constraint is met. The main objective is to control the S(t) while keeping the same ratio between different NESSs after introducing the SOC weighting factor: (5) ɛ ∈ [ − 1, 1] is a ratio defined by NESS active power output PNESS compared with maximum available active power output , which is called information state in this article. Compared with consensus control schemes proposed in previous works, the required active power will be shared with respect to the SOC level which is a prominent parameter for NESS. wi is the weighting factor that should be introduced by considering different SOC levels of NESSs. If one NESS has smaller SOC, a larger weighting factor wi can be chosen to limit its active power contribution to network loading control. The weighting factor wi was first proposed in [27], however, it was set to 1 to simplify the question. In this study, we use an explicit mathematical formulation to represent wi. The weighting factor, wi, is time varying as the SOC of individual NESS will change over the control period. It is described as, (6) where, wi(t) is a dynamic single row matrix, composed of a set of elements cij(t). cij(t) is defined based on ith and jth NESS state of charge SOCi(t), SOCj(t) and intended discharge capacity IDCi(t), IDCj(t) as, (7) Depth of discharge (DOD) describes the degree to which a battery is emptied relative to its total capacity. It is an alternate method to SOC to indicate a battery's working condition. The battery life degrades dramatically if the DOD is increased to a high level, such as 90% in a discharge cycle. By restricting the possible DOD, the batteries life cycle can be significantly improved. As a consequence, we adopt 70% as the desirable DOD in this article to refrain from over discharging the NESSs. It is worth noting that when DOD equals 70%, the SOC at that moment is 30%, defined as SOCmin critical. Assuming in every control period NESSs discharge towards SOCmin critical, therefore, the individual discharge capacity can be represented as, (8) (9) According to (7)–(9), we can calculate the weighting matrix elements, (10) A dynamic discharge process model in [6] is introduced to show the changes in operating conditions, (11) where, neffi is the discharging efficiency coefficient; pi(t) is the discharging active power at time t; Ci represents battery capacity; ΔT is the discharging time interval. For simplicity, neffi is assumed to be constant at 0.95 over the whole control period. In an actual scenario, neffi is strongly connected with battery SOC level. Due to the limited page length, this discussion is not included in this paper's scope. Based on (10) and (11), time-varying cij(t) is calculated. For the followers, information state ɛ in a discrete-time consensus algorithm is discovered iteratively. The information state updating rule can be described as: (12) where g is iteration numbers in every control window; ɛi,g[t] is ith NESS information state at iteration g on control time t; dij is the (i, j) entry of row-stochastic matrix D, which is time-varying. It can be calculated using: (13) where, |lij| is the absolute value of communication network Laplacian matrix elements, which is defined in (1). The update rule for follower NESSs in the network is decided according to (12), and the leader NESS update rule will be defined as follows. To achieve the objective S(t) ≤ Smax −critical, define ΔS to indicate the mismatch between S(t) and Smax −critical. If S(t) is more than Smax −critical, the mismatch value is compensated in leader NESS information update for the difference: (14) Thus the update rule for the leader NESS is obtained as: (15) (16) where, ɛo,g[t] is the leader NESS information state at iteration g on time t; doj represents the communication coefficient between jth NESS and assigned leader NESS; μ is the sensitivity coefficient in the leader information update process which controls the leader NESS convergence speed. ΔS(t) is measured and collected at discrete time step. The function of μ is similar to proportional gain in proportional control. For a specific operating condition, μ can be determined by trial and error method [28]. Small μ causes slower convergence speed, while large μ could result in instability of the system. To obtain a satisfactory balance between convergence speed and stability, in this study μ is set as 0.3. Through keeping to the update rules stated in (12), (15) and (16), a common ratio ɛi,gmax will be reached asymptotically by the system converging process. The NESS active power output combined with weighting factor can be expressed as, (17) The proposed NESS consensus-based coordinated dispatch scheme can be expressed as the flowchart in Fig. 1a. The NESSs control structure can be depicted as Fig. 1b. Fig. 1Open in figure viewerPowerPoint Flowchart of NESSs consensus control algorithm and NESSs control structure (a) Flowchart of NESSs consensus control algorithm, (b) NESSs control structure 4 Case studies The proposed NESS dispatch method is tested with a modified IEEE 15-bus radial distribution system. All the simulation programs are executed on a 4 core, 64-bit DELL Desktop with Intel Core i5-3570S CPU and RAM 8 Giga-byte. 4.1 Experimental setup The operational states are characterised as follows. One modified IEEE 11 kV, 15-bus radial distribution system is adopted. Fig. 2a denotes the single-line diagram of this distribution network which consists of 14 loads and three BESSs. Each battery storage system is connected through power lines and communication units. Three NESSs are assumed to be located at bus 9, bus 13 and bus 14, respectively. One is selected as the leader and the other two are selected as followers. NESSs relevant parameters are shown in Table 1. Network loading maximum critical value is intentionally set as 23 MW. Overall simulation period is set as 60 min to test control effect, during which loading data is more than the maximum critical value. In this study, one-minute interval is adopted and simulation results demonstrate it is much more than enough for the proposed control scheme to achieve equilibrium. By trial and error method [26], we find small iteration times might cause NESSs information state cannot converge to the same value, while overly large iteration times could delay the control time in vain. In our proposed one-minute control, we set 60 iterations to guarantee information state convergence and network loading control effect. The calculation time for 60 iterations converging process is 0.324 s, which is fast enough for one-minute time window optimisation. Fig. 2Open in figure viewerPowerPoint Modified IEEE 15-bus radial distribution system, NESSs communication topology and 24-hour network loading value (a) Modified IEEE 15-bus radial distribution system, (b) NESSs communication topology, (c) 24-hour network loading value Table 1. NESSs parameters Unit Project capital cost, $ Battery unit price, $/MWh Battery capacity, MWh Battery efficiency, % /MW Initial SOC, % NESS1 200,000 250,000 0.8 95 0.5 80 NESS2 200,000 250,000 0.8 95 0.4 70 NESS3 200,000 250,000 0.8 95 0.6 90 4.2 Case study The NESS communication topology in Case 1 is depicted in Fig. 2b, where NESS1 is defined as the leader; NESS2 and NESS3 are considered as followers. NESS2 has direct communication with NESS1 and NESS3, while there is no direct shared information between NESS1 and NESS3. The distribution network loading figure throughout a day is shown in Fig. 2c. As Fig. 2c shows, the loading exceeds maximum critical value during 15:30-19:00. As discussed in Section 3, the proposed model is used to evaluate its performance on managing overloading in radial distribution network, thus we only consider the NESSs discharge process. A 60-minute period from 16:00–17:00 is chosen to verify the effectiveness of the proposed control scheme. As Table 1 shows, the initial SOC for NESSs are 0.8, 0.7 and 0.9, respectively, at 16:00. During the control process, the SOC decreases gradually. It is assumed the NESSs can continuously provide the maximum active power during the one hour simulation time period. Under this assumption, it can be said the required active power curtailment will be shared with respect to the NESSs corresponding SOC value [27]. Fig. 3a shows the NESSs dynamic information state change processes at 10th minute and 50th minute, respectively. The results show that both would finally converge to a value. Since NESS1 acts as the leader, its information update changes faster than followers NESS 2 and NESS 3. After 40 iterations, three NESSs converge to almost the same information state, whose difference is <0.001. In this circumstance, the consensus goal can be considered to be reached. Fig. 3Open in figure viewerPowerPoint NESSs information state change process and active power output (a) NESSs information state change process at 10th minute (up) and 50th minute (down), (b) NESSs active power output at 10th minute (up) and 50th minute (down) Fig. 3b shows the NESS active power outputs at 10th minute and 50th minute, respectively. At the 10th minute, after 40 iterations, NESSs discharge 0.2315, 0.1852, and 0.2778 MW, respectively, which are calculated as , where ɛi,gmax equals 0.463 after 40 iterations. Similarly, at the 50th minute, after 40 iterations, NESS1 discharges 0.2840 MW, NESS2 discharges 0.2272 MW and NESS 3 discharges 0.3408 MW, respectively. Fig. 4a compares the network loading control effects with and without the consensus algorithm. It can be seen that original loading figure from 16:00–17:00 is higher than the maximum critical value, thus system blackout might otherwise occur during this period without control. With consensus algorithm control, all the data is controlled to be no larger than the maximum critical value limit, guaranteeing power system security in the distribution network. Fig. 4Open in figure viewerPowerPoint Network loading controls compare and NESSs state of charge change in control period (a) NESSs loading controls compare, (b) NESSs state of charge in control period The three NESSs state of charge level over the simulation period is shown in Fig. 4b. Note that in (11), SOC decreases during the discharge process. Since the maximum active power output of NESS3 is larger than NESS1, and the maximum active power output of NESS1 is larger than that of NESS2, the SOC change rate is scaled proportionally, as can be observed in Fig. 4b. 4.3 Leader selection Leader selection is an important issue in the leader–follower consensus algorithm. In [29], the authors recommended a leader selection method based on heuristic approach by using the existing node centrality indices, such as degree centrality, closeness centrality, and eigenvector centrality. In [30], the authors selected each agent as the leader in turn and compared the spectral radius of certain matrix associated with them, then chose the one with the smallest as the leader. In this three-NESS distribution network, the selection of leader affects network convergence speed. Based on Fig. 2b, we can tell there is no difference between NESS1 and NESS3 as the leader. However, because NESS2 has direct communication with NESS1 and NESS3 at the same time, it is acting a different function compared with NESS1 and NESS3. To test the leader selection influence on convergence speed, we choose NESS2 as the leader, as shown in Fig. 5. μ is also set as 0.3 under this circumstance. Fig. 5Open in figure viewerPowerPoint Revised communication topology Similar to Fig. 3a, Fig. 6a indicates NESSs converge to the same information state at the 10th and 50th min, while it is 20 iterations in Fig. 6a and 40 iterations in Fig. 3a. Although the control effect is the same, the convergence speed improves in this instance compared with the former method, which greatly improves the control efficiency. From the revised communication topology, it can be seen that NESS1 and NESS3 play the same role in the consensus process, which is certified in Fig. 6a. The information update processes for NESS1 and NESS3 are same, which leads to the overlapped lines in this figure. The network loading control effect is the same as shown in Fig. 4a, where all the data points are inside the maximum critical limit. Fig. 6Open in figure viewerPowerPoint NESSs information state and active power output when NESS2 is selected as the leader (a) NESSs information state at 10th minute (up) and 50th minute (down), (b) NESSs active power output at 10th minute (up) and 50th minute (down) The relative NESSs active power outputs at the 10th and 50th min are given in Fig. 6b. Compared with Fig. 3b, NESSs have common active power output when their information states are stable, while Fig. 6b shows much faster convergence speed. 4.4 Sensitivity analysis In the leader–follower consensus algorithm, the sensitivity scalar in the leader information update process determines the leader change rate, which further influences overall system convergence speed. In [31], the authors investigated the modelling method for dc microgrids through dynamic consensus algorithm based hierarchical control. Meanwhile, underlying communication topology and sensitivity analysis were fully considered in this research. According to Xiao and Boyd [32], the sensitivity analysis in [31] is based on the fastest distributed linear averaging (FDLA) problem. It did not consider about additive noise in distribute average consensus, which is actually more widely used in power system analysis. The sensitivity study based on consensus algorithm with additive noise is considered in this research. In (15), μ acts as a positive sensitivity scalar in the leader information update process. Based on the communication topology in Fig. 2b, in this section we give the sensitivity study under different positive scalar μ to investigate its influence on system convergence speed. Fig. 7a shows NESSs’ information state and active power output dynamic responses when μ equals 0.5. The system is stable and finally converges after around 25 iterations, which is faster than the case where μ equals 0.3 in Fig. 3a. The network loading control effect is same as that shown in Fig. 4a. Fig. 7Open in figure viewerPowerPoint NESSs information update and active power output at differentμ (a) NESSs information update and active power output at 10th minute when μ = 0.5, (b) NESSs information update and active power output at 10th minute when μ = 0.1 When μ equals 0.1, Fig. 7b indicates the system has much slower convergence speed. When iterations reach 60, it gradually converges to the same information state value as Fig. 3a. From Fig. 8, one can see the network loading control effect is not satisfactory with all the result higher than the maximum critical value 23 MW. This is because an overly slow convergence speed influences NESSs active power output value in every-minute control period, which further weakens the network loading control effect. Fig. 8Open in figure viewerPowerPoint Network loading control compare whenμ = 0.1 From the results, it can be seen that in the leader–follower consensus algorithm, overly small values of μ would result in much slower convergence speed. By contrast, overly large values of μ could lead to system instability. When μ approaches 0.7, the system begins to be unstable, which is certified by our simulation test. Therefore, the sensitivity scalar on leader information update not only influences the convergence speed, but also impacts the system stability. Xiao et al. proposed distributed average consensus with additive noise problem in [33], which is called the least-mean-square consensus problem. They proved that the optimal μ should lie in the interval (1/λ1(L)) ≤ μ ≤ (2/λ1(L)), which corresponds to (1/3) ≤ μ ≤ (2/3) in this research's communication topology. This has been verified in our system. With μ = 0.5, the convergence performance is better than the situation when μ = 0.3 or μ = 0.1. Proper leader in the communication topology and sensitivity scalar μ need to be chosen in actual system analysis. Under realistic scenario, large amount of computation load can be assigned to distributed controllers and this control method is applicable in this situation. 5 Conclusion This paper studies the distribution network overloading problem. By employing distributed NESSs in the network, a novel consensus-based coordinated dispatch scheme is proposed to effectively solve the problem. Through distributed control strategy, required active power curtailment can be shared among participating NESSs based on their discharge ability. By introducing a novel SOC weighting factor in the NESSs consensus control, their utilisation efficiency is improved. Leader selection and sensitivity study are also conducted in this research. Simulation studies show the effectiveness of proposed method. Future work would be focused on a larger benchmark test system with multiple communication agents with consideration of communication link failure and delayed information exchange. The optimised communication topology analysis among multiple agents would also be done in future. 6 Acknowledgment This work was supported in part by the Faculty of Engineering and IT Early Career Researcher and Newly Appointed Staff Development Scheme 2016, in part by funding from the Faculty of Engineering and Information Technologies, The University of Sydney, under the Faculty Research Cluster Program, in part by the 2015 Science and Technology Project of China Southern Power Grid (WYKJ00000027), and in part by the Hong Kong Polytechnic University Postdoctoral Fellowship Scheme (1-YW1Q). 7 References 1 World Energy Council: ‘ Global electricity initiative 2014 report’ ( GEI Secretariat, 2014) 2Belhaiza, S., Baroudi, U.: ‘A game theoretic model for smart grids demand management’, IEEE Trans. Smart Grid, 2015, 6, (3), pp. 1386– 1393 3Meng, K., Yang, H.M., Dong, Z.Y., et al: ‘Flexible operational planning framework considering multiple wind energy forecasting service providers’, IEEE Trans. Sustain. Energy, 2016, 7, (2), pp. 708– 717 4Mokhtari, G., Nourbakhs, G., Ledwich, G., et al: ‘A supervisory load-leveling approach to improve the voltage profile in distribution network’, IEEE Trans. Sustain. Energy, 2015, 6, (1), pp. 245– 252 5Luo, F., Meng, K., Dong, Z., et al: ‘Coordinated operational planning for wind farm with battery energy storage system’, IEEE Trans. Sustain. Energy, 2015, 6, (1), pp. 253– 262 6Luo, F., Dong, Z., Meng, K., et al: ‘Short-term operational planning framework for virtual power plants with high renewable penetrations’, IET Renew. Power Gener., 2016, 10, (5), pp. 623– 633 7Teng, J.H., Luan, S.W., Lee, D.J., et al: ‘Optimal charging/discharging scheduling of battery storage systems for distribution systems interconnected with sizeable PV generation systems’, IEEE Trans. Power Syst., 2013, 28, (2), pp. 1425– 1433 8Mancarella, P., Chicco, G.: ‘Real-time demand response from energy shifting in distributed multi-generation’, IEEE Trans. Smart Grid, 2013, 4, (4), pp. 1928– 1938 9Rahbari-Asr, N., Ojha, U., Zhang, Z., et al: ‘Incremental welfare consensus algorithm for cooperative distributed generation/demand response in smart grid’, IEEE Trans. Smart Grid, 2014, 5, (6), pp. 2836– 2845 10Toledo, O.M., Filho, D.O., Diniz, A.S.A.C.: ‘Distributed photo-voltaic generation and energy storage systems: A review’, Renew. Sustain. Energy Rev., 2010, 14, (1), pp. 506– 511 11Toledo, O.M., Filho, D.O., Diniz, A.S.A.C., et al: ‘Methodology for evaluation of grid-tie connection of distributed energy resources-case study with photovoltaic and energy storage’, IEEE Trans. Power Syst., 2013, 28, (2), pp. 1132– 1139 12Lu, X., Sun, K., Guerrero, J.M., et al: ‘State-of-charge balance using adaptive droop control for distributed energy storage systems in DC microgrid applications’, IEEE Trans. Ind. Electron., 2014, 61, (6), pp. 2804– 2815 13Mokhtari, G., Nourbakhsh, G., Zare, F., et al: ‘Smart coordination of energy storage units(ESUs) for voltage and loading management in distribution networks’, IEEE Trans. Power Syst., 2013, 28, (4), pp. 4812– 4820 14Zheng, Y., Dong, Z.Y., Luo, F., et al: ‘Optimal allocation of energy storage system for risk mitigation of DISCOs with high renewable penetrations’, IEEE Trans. Power Syst., 2013, 29, (1), pp. 212– 220 15Le, H.T., Santoso, S., Nguyen, T.Q.: ‘Augmenting wind power penetration and gird voltage stability limits using ESS: application design, sizing, and a case study’, IEEE Trans. Power Syst., 2011, 27, (1), pp. 161– 171 16Moghadam, M.R.V., Ma, R.T.B., Zhang, R.: ‘Distributed frequency control in smart grids via randomized demand response’, IEEE Trans. Smart Grid, 2014, 5, (6), pp. 2798– 2809 17Diaz, N.L., Dragicevic, T., Vasquez, J.C.: ‘Intelligent distributed generation and storage units for dc microgrids—a new concept on cooperative control without communications beyond droop control’, IEEE Trans. Smart Grid, 2014, 5, (5), pp. 2476– 2485 18Meng, K., Dong, Z.Y., Xu, Z., et al: ‘Cooperation-driven distributed model predictive control for energy storage systems’, IEEE Trans. Smart Grid, 2015, 6, (6), pp. 2583– 2585 19He, W., Chen, G., Han, Q.L., et al: ‘Network-based leader following consensus of nonlinear multi-agent system via distributed impulsive control’, Inf. Sci. (in press), 2015, https://doi.org/10.1016/j.ins.2015.06.005 20Fiedler, M.: ‘Algebraic connectivity of graphs’, Czechoslovak Math. J., 1973, 23, (98), pp. 298– 305 21Olfati-Saber, R., Fax, J., Murray, R.: ‘Consensus problems in networks of agents with switching topology and time-delays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 1520– 1533 22Godsil, C., Royle, G.: ‘ Algebraic graph theory (graduate texts in mathematics)’ ( Springer-Verlag, New York, 2000, 1st edn.) 23Olfati-Saber, R.: ‘ Ultrafast consensus in small-world networks’. Proc. American Control Conf., Portland, USA, 2005, vol. 4, pp. 2371– 2378 24Olfati-Saber, R., Fax, J., Murray, R.: ‘Consensus and cooperation in networked multi-agent systems’, Proc. IEEE, 2007, 95, (1), pp. 215– 233 25Li, H., Chen, G., Liao, X., et al: ‘Leader-following consensus of discrete-time multiagent systems with encoding-decoding’, IEEE Trans. Circuits Syst. II Express Briefs, 2015, 63, (4), pp. 401– 405 26Li, H., Chen, G., Huang, T., et al: ‘Event-triggered distributed average consensus over directed digital networks with limited communication bandwidth’, IEEE Trans. Cybern., 2016, (in press) 27Mokhtari, G., Ghosh, A., Nourbakhsh, G., et al: ‘Smart robust resources control in LV network to deal with voltage rise issue’, IEEE Trans. Sustain. Energy, 2013, 4, (4), pp. 1043– 1050 28Xu, Y., Zhang, W., Liu, W., et al: ‘Distributed subgradient-based coordination of multiple renewable generators in a microgrid’, IEEE Trans. Power Syst., 2014, 29, (1), pp. 23– 33 29Zhang, Z., Chow, M.Y.: ‘Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid’, IEEE Trans. Power Syst., 2012, 27, (4), pp. 1761– 1768 30Zhao, Y., Chen, B., Fan, Y., et al: ‘ Convergence speed analysis and optimization for distributed control of virtual power plant’. 10th IET Int. Conf. on Advances in Power System Control, Operation and Management (APSCOM2015), Hong Kong, November 2015 31Meng, L., Dragicevic, T., Roldan-Perez, J., et al: ‘Modeling and sensitivity study of consensus algorithm-based distributed hierarchical control for DC microgrids’, IEEE Trans. Smart Grid, 2016, 7, (3), pp. 1504– 1515 32Xiao, L., Boyd, S. : ‘Faster linear iterations for distributed averaging systems’, Syst. Control Lett., 2004, 53, pp. 65– 78 33Xiao, L., Boyd, S., Kim, S.J.: ‘ Distributed average consensus with least-mean-square deviation’. Proc. of the 17th Int. Symp. on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, July 2006, pp. 2768– 2776 Citing Literature Volume10, Issue9October 2016Pages 1374-1381 FiguresReferencesRelatedInformation

Referência(s)
Altmetric
PlumX