Distributed Economic Dispatch of Virtual Power Plant under a Non-Ideal Communication Network

Chi Cao 1, Jun Xie 1,*, Dong Yue 1,2, Chongxin Huang 2, Jixiang Wang 3, Shuyang Xu 3 and Xingying Chen 3 1 College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023, China; sscaoch@163.com (C.C.); medongy@vip.163.com (D.Y.) 2 Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 210023, China; huangchongxin@gmail.com 3 College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China; wjxwangjixiang@163.com (J.W.); 15850603207@163.com (S.X.); chenxyhhu@hhu.edu.cn (X.C.) * Correspondence: eejxie@gmail.com; Tel.: +86-25-8586-6511


Introduction
Efforts have been made to handle the energy crisis and environmental issues by exploiting distributed energy resources (DERs) [1,2].It is acknowledged that DERs possess the characteristics of cleanliness, renewability, and diversification.DERs mainly contain micro-gas generators (MGGs), wind generators (WGs), photovoltaic systems (PVs), and batteries (BEs) [2].Natural conditions (e.g., wind speeds, light intensity, etc.) will inevitably give rise to the intermittent and randomness of the DERs' power outputs.In addition, some non-ideal communication network factors may also interfere with DERs' scheduling [3].Communication time delays slow down the speeds of scheduling information and channel noises fluctuate DERs' power outputs, which disobey the power system's requirements for rapidity and stability.DERs' over-limit, plug-and-play, and channel faults are the common time varying topology events that disrupt the normal operation of economic dispatch, and even damage the system.If these large-scale and small-capacity DERs have access to the power system, they will pose challenges to the economic dispatch, power quality (e.g., frequency harmonics, voltage flicker, etc.), and the electricity market.Therefore, to realize the DERs' organized regulation is an urgent research task.The rest of this paper is organized as follows.Section 2 introduces the economic dispatch model of VPP.The method of DPDSM for solving the VPP economic dispatch model is presented in Section 3. Section 4 gives the numerical examples.Summaries are drawn in Section 5.

Economic Dispatch Model
The VPED model uses the scheduling objectives including minimizing total generation cost of DERs, maximizing profits of a VPP, and maximizing energy-saving and emission-reduction of a VPP.Depending on the power outputs of various DERs, an optimal allocation model of the energy storage system whose objective function includes economy, grid supply, and voltage is constructed in [19].A VPP's bidding strategy on the basis of electricity price is developed in [20], which breaks through the routine that the day-ahead transacted electricity quantity is equal to the forecasting load demand.Then it establishes a new electricity transaction model under a unified electricity market considering both the day-ahead and real-time stochastic load demand.Different from [20], a VPP's three-stage stochastic bi-level bidding strategy depending on DERs' the power outputs, loads demands and the competitor's history price is developed in [21].
In this paper, a VPED model with a variety of constraints is established.At the point of common coupling (PCC), the power running through PCC (recorded as P s ), which is the power exchanged between the VPP and the electricity market (or the main grid).The power collected by VPP can be sold to power users and VPP's profit is determined by the power outputs of all DERs, the P s , the purchase price from the main grid, and the sale price to the power users.

Objective Function
PVs and WGs cannot continuously generate power like MGGs, so it is significant to obtain its available power outputs according to the actual operation [22].Since this paper is aimed to study VPP's distributed dispatch, DERs' power outputs models will be shown in Appendix A. To stimulate PVs' and WGs' scheduling potential, they may operate in the schedulable model rather than the maximum power point model [22].A certain number of MGGs and BEs are used to stabilize the power output fluctuations of PVs and WGs.BEs can work in the charging or discharging modes.
The operation cost function of each DER can be modeled as: where n is the number of DERs and the actual power output of DER i is uniformity recorded as P Gi .The operation costs of DER i at P Gi is denoted by C i (P Gi ).The cost parameters are signified as a i , b i , and c i .
According to VPP's operation mode, we can get the optimization target of VPED as follows: max where P Dj is the power demand by consumer j and the consumers' number is m.θ, β are the purchase price and the sale price, respectively.If P s is negative, the power will flow from VPP into the main grid.P s is calculated by:

Constraints
Power output constraints of DERs: Capacity constraints of all types of DERs can be formulated as inequality constraints: where P min Gi is the minimum power output of unit i and P max Gi is the maximum one.Here, PVs' and WGs' maximum power outputs are their power outputs at the maximum power point.
Transmission constraints of power lines: These constraints satisfy a set of global inequality constraints: where P l means the power transmission limit of line l, L represents the power lines' number and O is the number of nodes.The power transmission coefficient of node o and its geographically adjacent line l is expressed as η ol .The symbol of i, j → o describes that unit i or consumer j may convey power and energy through the node o.Formula ( 5) is also equivalent to:

Mathematical Reformulation
The VPED is chiefly influenced by the power output of each DER and the P s .Some proper reformation can be done to make the optimization problem into a general economic dispatch problem.The P s can be eliminated by Formulas ( 2) and ( 3) and the objective function can be formulated as follows: max In this paper, β, θ, and the total loads are constant and are not dependent on the decision variables.Based on the principle of dual problem [16,18], the objective function can be reformulated as: If power output is written as x i , the sub-objective function will be denoted as f i , so the VPED model is equivalent to: where h s represents the global inequality constraints as shown in ( 6) and (7).X is the set of all x, indicates the local constraint of each DER in Equation ( 4) and q is the number of constraints.The Lagrange multiplier λ can be introduced to structure the Lagrange function: Now, the optimization problem can be written as:

Distributed Primal-Dual Sub-Gradient Method (DPDSM)
According to the principle of Lagrange multiplier method [16], the optimal solution L(x * , λ * ) in Equation ( 12) is also the optimal solution x * in the original optimization problem (Equation ( 2)).In order to obtain the optimal solution quickly, the method of DPDSM is adopted in this paper.

Under Ideal Communication Network Conditions
During the DPDSM iteration, the primary variables (with the symbol "ˆ") and secondary (with the symbol "-") variables are derived from the original variables x i , λ i : x where k ≥ 0 is the iteration number; ∆ is the derivation times and N is the number of iteration conducted by the original variables.That is, setting the value of ∆ can adjust the engagement of consensus algorithm in the distributed optimization.W n×n is the n order communication matrix and its element W ij is calculated by the following formula: where n is the number of DERs which are connected with DER i by communication links.Γ(i) is the set of DERs which are connected with DER i by communication links. where ) is the partial derivatives of λ i [k] at the same point.The sub-gradient value of f i and h s at x i [k] are S fi (x i [k]) and S hs (x i [k]), respectively: where According to the principle of Lagrange multiplier method [16], the optimal solution L(x * , λ * ) in Equation ( 12) is also the optimal solution x * in the original optimization problem (Equation ( 2)).In order to obtain the optimal solution quickly, the method of DPDSM is adopted in this paper.

Under Ideal Communication Network Conditions
During the DPDSM iteration, the primary variables (with the symbol "^") and secondary (with the symbol "-") variables are derived from the original variables xi, λi: where k ≥ 0 is the iteration number; Δ is the derivation times and N is the number of iteration conducted by the original variables.That is, setting the value of Δ can adjust the engagement of consensus algorithm in the distributed optimization.Wn×n is the n order communication matrix and its element Wij is calculated by the following formula: where n is the number of DERs which are connected with DER i by communication links.Γ (i) is the set of DERs which are connected with DER i by communication links. where where ˄ is the set of λi; the iteration step is α.PX and P ˄ are symbols of the projection operator whose definition and principle has been given in [17].

Under Non-Ideal Communication Network Conditions
As mentioned in the introduction, the non-ideal communication network conditions consist of communication time delays, channel noises, DERs' power output over-limit, DERs' plug-and-play, and channel faults.The primary and secondary variables introduced in the proposed method are all auxiliary variables.All of the non-ideal communication network conditions will exist and be addressed in the primary variables, and the time varying topology events are mainly addressed in the secondary variables: is the set of λ i ; the iteration step is α.P X and P According to the principle of Lagrange multiplier method [16], th Equation ( 12) is also the optimal solution x * in the original optimizatio order to obtain the optimal solution quickly, the method of DPDSM is a

Under Ideal Communication Network Conditions
During the DPDSM iteration, the primary variables (with the sym the symbol "-") variables are derived from the original variables xi, λi: where k ≥ 0 is the iteration number; Δ is the derivation times and N conducted by the original variables.That is, setting the value of Δ ca consensus algorithm in the distributed optimization.Wn×n is the n orde its element Wij is calculated by the following formula: where n is the number of DERs which are connected with DER i by c the set of DERs which are connected with DER i by communication link at the same point.The sub-gradient value of fi and (xi[k]), respectively: where ˄ is the set of λi; the iteration step is α.PX and P ˄ are symbo whose definition and principle has been given in [17].

Under Non-Ideal Communication Network Conditions
As mentioned in the introduction, the non-ideal communication n communication time delays, channel noises, DERs' power output over and channel faults.The primary and secondary variables introduced in auxiliary variables.All of the non-ideal communication network c addressed in the primary variables, and the time varying topology eve the secondary variables: are symbols of the projection operator whose definition and principle has been given in [17].

Under Non-Ideal Communication Network Conditions
As mentioned in the introduction, the non-ideal communication network conditions consist of communication time delays, channel noises, DERs' power output over-limit, DERs' plug-and-play, and channel faults.The primary and secondary variables introduced in the proposed method are all auxiliary variables.All of the non-ideal communication network conditions will exist and be addressed in the primary variables, and the time varying topology events are mainly addressed in the secondary variables: Energies 2017, 10, 235 6 of 18 where k ≥ 0 is the iteration number; τ ij (k) and η ij [k] are the time delays and channel noises from agent j to i at iteration k, respectively.c[k] is the gain function [3] and its details are described in the Appendix A.
The adjacency matrix based on the communication topology has the element of a ij .If there exists a communication link between i and j, the value of a ij will be 1; otherwise, the value of a ij will be 0. l ij represents the Laplacian matrix element in the network topology and it is relevant to the adjacency matrix element a ij .
W n×n can be designed as a dynamic matrix under the non-ideal network conditions and the W ij is calculated by a new formula: where n is the number of DERs which are connected with DER i by communication links.Γ(i) is the set of DERs which are connected with DER i by communication links.

Numerical Examples
In this paper, to verify the validity of the proposed VPED strategy, two VPP systems are built by modifying the IEEE-34 bus test system and the IEEE-123 bus test system, respectively.In this work, the power error tolerance ε in Figure 1 is 0.05 kW and the iteration step α is set to 0.002 s.For the convenience of simulation, the gain function c[k] is 0.5[1 + ln(k + 1)]/(k + 1) which can meet the conditions in the Appendix A. The algebraic sum of power flowing through PCC is Ps and the total loads are recorded as PD.The purchase price θ is 0.076$/kWh and the sale price β is 0.072$/kWh.The parameters and the capacity limits of DERs are listed in Table 1 and Table 2, respectively.According to [3,9], the changes of Laplacian matrix and communication matrix can reflect the situation of the time varying topology.The flowchart of DPDSM, considering the non-ideal network Energies 2017, 10, 235 7 of 18 conditions, is shown in Figure 1.The left part of Figure 1 displays the basic progress of the proposed algorithm; the right part provides details about how non-ideal network conditions influence the distributed dispatch.When time varying topology occurs, the value of a ij will be updated according to the actual communication topology.Then, the Laplacian matrix and communication matrix will be updated along with a ij .If there are time delays and channel noises in the communication lines, the dispatch will also be affected.

Numerical Examples
In this paper, to verify the validity of the proposed VPED strategy, two VPP systems are built by modifying the IEEE-34 bus test system and the IEEE-123 bus test system, respectively.In this work, the power error tolerance ε in Figure 1 is 0.05 kW and the iteration step α is set to 0.002 s.For the convenience of simulation, the gain function c[k] is 0.5[1 + ln(k + 1)]/(k + 1) which can meet the conditions in the Appendix A. The algebraic sum of power flowing through PCC is P s and the total loads are recorded as P D .The purchase price θ is 0.076$/kWh and the sale price β is 0.072$/kWh.The parameters and the capacity limits of DERs are listed in Tables 1 and 2, respectively.The simulation implemented on the modified IEEE-34 bus test system is mainly designed to study the impact of communication time delays and channel noises on the distributed dispatch and the influence of changing ∆ over the distributed dispatch algorithm.The modified IEEE-123 bus test system is aimed to investigate the adaptability of the distributed VPED algorithm under a large scale non-ideal communication network.It primarily discusses the time varying communication topology conditions arising from channel faults of communication links, DERs' over-limit, and DERs' plug-and-play.

The Modified IEEE-34 Bus Test System
As shown in Figure 2, there are twenty schedulable DERs in the modified IEEE-34 bus test system.For the sake of making better use of renewable energies, PVs, and WGs will operate at their maximum power output.BEs can work in both charging and discharging modes and the MGGs may reduce their outputs to cut the fuel expenditure.BEs and MGGs are also able to adjust their outputs to deal with some unexpected events, which is aimed to maintain the system power balance.In comparison, Table 3 offers the results optimized by using the centralized dispatch under the same operation condition and Table 4 shows VPP's average profits made by the two dispatch strategies.Three scheduling scenarios are provided as follows: (A) a distributed dispatch under the ideal communication network; (B) a distributed dispatch considering time delays and channel noises in communication network; and (C) a distributed dispatch with a different ∆.  (1) Scenario A: Distributed Dispatch under Ideal Communication Figure 3 indicates the optimal scheduling results of each DER and Figure 4 provides the variation of Ps during the distributed optimization process.From Figure 3 and Table 3, we can find that the distributed dispatch proposed in this paper achieves the same scheduling scheme as the centralized dispatch does, which shows the effectiveness of the distributed dispatch strategy.From the viewpoint of profits, it is not difficult to find in Table 4 that the distributed dispatch is the same with the centralized one.Figure 4 illustrates that the VPP can sell electric energy to the main grid when its overall power is higher than load demands, but if the overall power is lower than the total loads, VPP will absorb power from the main grid to maintain the supply-demand balance.(1) Scenario A: Distributed Dispatch under Ideal Communication Figure 3 indicates the optimal scheduling results of each DER and Figure 4 provides the variation of P s during the distributed optimization process.From Figure 3 and Table 3, we can find that the distributed dispatch proposed in this paper achieves the same scheduling scheme as the centralized dispatch does, which shows the effectiveness of the distributed dispatch strategy.From the viewpoint of profits, it is not difficult to find in Table 4 that the distributed dispatch is the same with the centralized one.Figure 4 illustrates that the VPP can sell electric energy to the main grid when its overall power is higher than load demands, but if the overall power is lower than the total loads, VPP will absorb power from the main grid to maintain the supply-demand balance.In practice, it is necessary to consider communication time delays and channel noises.When implementing the optimization, the delays are randomly distributed between 0 and 3; meanwhile,  In practice, it is necessary to consider communication time delays and channel noises.When implementing the optimization, the delays are randomly distributed between 0 and 3; meanwhile, the noises are randomly distributed between 0 and 5 kW. Figure 5 shows the optimization curves of this scenario.Figure 6 provides the variation of P s and the power imbalance during the optimization.Since the transmission of the iteration information is postponed by time delays, curves for showing the variation of P s and the power imbalance will appear in cross-sections, such as M1 in Figure 5c.Channel noises will cause the oscillation of power outputs; for example, M4 from the 16th to the 25th iterations.The more serious the delays and noises are, the rougher the curves will be.By the aid of the main grid, VPP can shrink the whole fluctuation and keep the system power balance (see Figure 6).In the centralized scheduling, prediction of communication time delays and channel noises is needed and it will increase the scheduling burden.Based on the local communication mechanism, the proposed method can still reach the same result, but in a way of real-time scheduling, meaning that the proposed method is useful to improve the system noise immunity.The simulation shows the effectiveness of the distributed scheduling strategy in handling time delays and channel noises.as M1 in Figure 5c.Channel noises will cause the oscillation of power outputs; for example, M4 from the 16th to the 25th iterations.The more serious the delays and noises are, the rougher the curves will be.By the aid of the main grid, VPP can shrink the whole fluctuation and keep the system power balance (see Figure 6).In the centralized scheduling, prediction of communication time delays and channel noises is needed and it will increase the scheduling burden.Based on the local communication mechanism, the proposed method can still reach the same result, but in a way of real-time scheduling, meaning that the proposed method is useful to improve the system noise immunity.The simulation shows the effectiveness of the distributed scheduling strategy in handling time delays and channel noises.as M1 in Figure 5c.Channel noises will cause the oscillation of power outputs; for example, M4 from the 16th to the 25th iterations.The more serious the delays and noises are, the rougher the curves will be.By the aid of the main grid, VPP can shrink the whole fluctuation and keep the system power balance (see Figure 6).In the centralized scheduling, prediction of communication time delays and channel noises is needed and it will increase the scheduling burden.Based on the local communication mechanism, the proposed method can still reach the same result, but in a way of real-time scheduling, meaning that the proposed method is useful to improve the system noise immunity.The simulation shows the effectiveness of the distributed scheduling strategy in handling time delays and channel noises.(3) Scenario C: Distributed Dispatch with a Different ∆ Changing the value of ∆ means adjusting the consensus parameters in the distributed dispatch.∆ is set at 3 in scenario a while ∆ is set at 10 in this scenario.Contrasting Figures 7 and 8 with Figures 3  and 4, it is clear that the larger the value is, the faster the convergence speed, but the larger the oscillation that will be occurred in the optimization.
Energies 2017, 10, 235 12 of 19 (3) Scenario C: Distributed Dispatch with a Different Δ Changing the value of Δ means adjusting the consensus parameters in the distributed dispatch.Δ is set at 3 in scenario a while Δ is set at 10 in this scenario.Contrasting Figures 7 and 8 with Figures 3 and 4, it is clear that the larger the value is, the faster the convergence speed, but the larger the oscillation that will be occurred in the optimization.

The Modified IEEE-123 Bus Test System
The modified IEEE-123 bus test system is shown in Figure 9.In this example, forty DERs are dispersed in four areas in this test system.The operation parameters are the same with the previous test system.Three simulation scenarios are implemented as follows: (D) a distributed dispatch (3) Scenario C: Distributed Dispatch with a Different Δ Changing the value of Δ means adjusting the consensus parameters in the distributed dispatch.Δ is set at 3 in scenario a while Δ is set at 10 in this scenario.Contrasting Figures 7 and 8 with Figures 3 and 4, it is clear that the larger the value is, the faster the convergence speed, but the larger the oscillation that will be occurred in the optimization.

The Modified IEEE-123 Bus Test System
The modified IEEE-123 bus test system is shown in Figure 9.In this example, forty DERs are dispersed in four areas in this test system.The operation parameters are the same with the previous test system.Three simulation scenarios are implemented as follows: (D) a distributed dispatch

The Modified IEEE-123 Bus Test System
The modified IEEE-123 bus test system is shown in Figure 9.In this example, forty DERs are dispersed in four areas in this test system.The operation parameters are the same with the previous test system.Three simulation scenarios are implemented as follows: (D) a distributed dispatch under the condition of the DERs' over-limit; (E) a distributed dispatch under the condition of channel faults; and (F) a distributed dispatch under the condition of DERs' play-and-plug.under the condition of the DERs' over-limit; (E) a distributed dispatch under the condition of channel faults; and (F) a distributed dispatch under the condition of DERs' play-and-plug.(1) Scenario D: Distributed Dispatch under the Condition of DERs' Over-Limit In order to ensure the safe operation of the VPP, it is essential to consider the capacity limits of DERs.Suppose a few MGGs' and BEs' power outputs have reached the limits during the optimization.Figure 10 shows that the over-limit DERs will run at the power limit and no longer iterate in the optimization, but continue to deliver data to their neighbors.Based on this local communication mechanism, the over-limit DERs may only affect the adjacent DERs rather than the whole.Figure 11 indicates that, with regard to DERs' over-limit events, the distributed method can still maintain the system power balance constraint.In order to ensure the safe operation of the VPP, it is essential to consider the capacity limits of DERs.Suppose a few MGGs' and BEs' power outputs have reached the limits during the optimization.Figure 10 shows that the over-limit DERs will run at the power limit and no longer iterate in the optimization, but continue to deliver data to their neighbors.Based on this local communication mechanism, the over-limit DERs may only affect the adjacent DERs rather than the whole.Figure 11 indicates that, with regard to DERs' over-limit events, the distributed method can still maintain the system power balance constraint.(2) Scenario E: Distributed Dispatch under the Condition of Channel Faults Channel faults will lead to the change of the communication topology.After the wrong channels are removed, the system recovers its power balance by reconstructing a new communication topology.The damaged channels are shown in Figure 9 and the dispatch progress is displayed in Figures 12 and 13.The channel faults can disturb DERs' normal operation.Then, the system will build a new stable state by distributed VPED optimization.(2) Scenario E: Distributed Dispatch under the Condition of Channel Faults Channel faults will lead to the change of the communication topology.After the wrong channels are removed, the system recovers its power balance by reconstructing a new communication topology.The damaged channels are shown in Figure 9 and the dispatch progress is displayed in Figures 12  and 13.The channel faults can disturb DERs' normal operation.Then, the system will build a new stable state by distributed VPED optimization.Compared with non-ideal communication conditions, DERs' plug-and-play is most likely to occur under an actual large-scale VPP system.There are two DERs that temporarily plug-and-play during the distributed scheduling in this scenario.From Figure 14, we can see that a PV plug off at about the 45th iteration for some reasons, but plug on at about the 50th iteration.However, by adjusting the power of MGGs, Bes, and Ps, the VPP system immediately realizes a new supply-demand power balance (see Figure 15).When this event happens again on a WG, the VPP system still restores its stability within a short time.Faced with the DER plug-and-play conditions, the system employing the proposed method in this paper shows a strong robustness.(3) Scenario F: Distributed Dispatch with DERs' Plug and Play Compared with non-ideal communication conditions, DERs' plug-and-play is most likely to occur under an actual large-scale VPP system.There are two DERs that temporarily plug-and-play during the distributed scheduling in this scenario.From Figure 14, we can see that a PV plug off at about the 45th iteration for some reasons, but plug on at about the 50th iteration.However, by adjusting the power of MGGs, Bes, and P s , the VPP system immediately realizes a new supply-demand power balance (see Figure 15).When this event happens again on a WG, the VPP system still restores its stability within a short time.Faced with the DER plug-and-play conditions, the system employing the proposed method in this paper shows a strong robustness.

Summary
The VPP is often adopted to manage large-scale DERs but there are non-ideal conditions of the communication network during its economy dispatch.With the consideration of various constraints, communication time delays, channel noises, and time varying topology, this paper establishes a VPP dispatch model and proposes a DPDSM to solve it.Compared with the centralized method under the same simulation scenarios, it can be found that the VPP can integrate DERs effectively and economically.Simulation results show that the larger communication time delays and channel noises are, the more unstable the system is.The frequent-and-diverse time varying topology events can also disturb its steady operation.The DPDSM can converge fast in the scheduling process and respond quickly to these non-ideal communication conditions.Simulations analysis illustrates the validity and superiority of the proposed method.Some issues, such as the

Summary
The VPP is often adopted to manage large-scale DERs but there are non-ideal conditions of the communication network during its economy dispatch.With the consideration of various constraints, communication time delays, channel noises, and time varying topology, this paper establishes a VPP dispatch model and proposes a DPDSM to solve it.Compared with the centralized method under the same simulation scenarios, it can be found that the VPP can integrate DERs effectively and economically.Simulation results show that the larger communication time delays and channel noises are, the more unstable the system is.The frequent-and-diverse time varying topology events can also disturb its steady operation.The DPDSM can converge fast in the scheduling process and respond quickly to these non-ideal communication conditions.Simulations analysis illustrates the validity and superiority of the proposed method.Some issues, such as the sensitivity of the results to parameters, VPP's multi-period dispatch, etc., still need further exploration.

Figure 2 .
Figure 2. The modified IEEE-34 bus test system in Scenario A.

Figure 2 .
Figure 2. The modified IEEE-34 bus test system in Scenario A.

Figure 3 .
Figure 3. Dispatch results in Scenario A. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 4 .
Figure 4.The simulation of power balance in Scenario A. (a) Power at PCC; and (b) The variation of power imbalance.(2) Scenario B: Distributed Dispatch Considering Communication Time Delays and Channel

Figure 3 .Figure 3 .
Figure 3. Dispatch results in Scenario A. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 4 .
Figure 4.The simulation of power balance in Scenario A. (a) Power at PCC; and (b) The variation of power imbalance.(2) Scenario B: Distributed Dispatch Considering Communication Time Delays and Channel Noises

Figure 4 .
Figure 4.The simulation of power balance in Scenario A. (a) Power at PCC; and (b) The variation of power imbalance.

18 ( 2 )
Scenario B: Distributed Dispatch Considering Communication Time Delays and Channel Noises

Figure 5 .
Figure 5. Dispatch results in Scenario B. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 6 .
Figure 6.The simulation of power balance in Scenario B. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 5 .
Figure 5. Dispatch results in Scenario B. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 5 .
Figure 5. Dispatch results in Scenario B. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 6 .
Figure 6.The simulation of power balance in Scenario B. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 6 .
Figure 6.The simulation of power balance in Scenario B. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 7 .
Figure 7. Dispatch results in Scenario C. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 8 .
Figure 8.The simulation of power balance in Scenario C. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 7 .
Figure 7. Dispatch results in Scenario C. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 7 .
Figure 7. Dispatch results in Scenario C. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 8 .
Figure 8.The simulation of power balance in Scenario C. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 8 .
Figure 8.The simulation of power balance in Scenario C. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 9 .
Figure 9.The modified IEEE-123 bus test system in Scenario D.

Figure 10 .Figure 10 .
Figure 10.Dispatch results in Scenario D. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 10 .
Figure 10.Dispatch results in Scenario D. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 11 .
Figure 11.The simulation of power balance in Scenario D. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 11 .
Figure 11.The simulation of power balance in Scenario D. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 12 .
Figure 12.Dispatch results in Scenario E. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 12 .Figure 12 .
Figure 12.Dispatch results in Scenario E. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 13 .
Figure 13.The simulation of power balance in Scenario E. (a) Power at PCC; and (b) The variation of power (3) Scenario F: Distributed Dispatch with DERs' Plug and Play

Figure 13 .
Figure 13.The simulation of power balance in Scenario E. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 14 .
Figure 14.Dispatch results in Scenario F. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 14 .
Figure 14.Dispatch results in Scenario F. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 14 .
Figure 14.Dispatch results in Scenario F. (a) Power output of PV; (b) Power output of WG; (c) Power output of MGG; and (d) Power output of BE.

Figure 15 .
Figure 15.The simulation of power balance in Scenario F. (a) Power at PCC; and (b) The variation of power imbalance.

Figure 15 .
Figure 15.The simulation of power balance in Scenario F. (a) Power at PCC; and (b) The variation of power imbalance.

Table 2 .
Capacity limits of DERs.

Table 4 .
VPP's average profits made by the two dispatch strategies.

Table 3 .
Optimal dispatch results under the centralized dispatch.

Table 4 .
VPP's average profits made by the two dispatch strategies.