Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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A consensus control strategy for dynamic power system look-ahead scheduling Yaping Li a,b,n, Taiyou Yong b, Jinde Cao c,d, Ping Ju a, Jianguo Yao b, Shengchun Yang b a
College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China China Electric Power Research Institute (Nanjing), Nanjing 210003, China c Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China d Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia b
art ic l e i nf o
a b s t r a c t
Article history: Received 21 October 2014 Received in revised form 10 March 2015 Accepted 6 May 2015 Communicated by Y. Liu
Flexible loads are important resources to help maintain the power balance of smart grid. However, the control center is not able to exactly sense and control them because of their large quantity and wide distribution. In order to get the flexible loads to participate in the dynamic power system look-ahead scheduling, this paper proposes a three-layer ‘centralized coordination, distributed control’ structure in which the load agents are introduced to perform the coordination based on the consensus control. Then, the optimal control strategy of the control center and the consensus control strategy of the load agents are designed. With the communication among different flexible loads, the distributed cooperative control is implemented. At last, the efficiency of the proposed mode and strategies is proven through the simulation carried out under the standard IEEE 9-bus system, and the effect of topology and communication is also analyzed. & 2015 Elsevier B.V. All rights reserved.
Keywords: Smart grid Look-ahead scheduling Distributed cooperative control Consensus protocol Multi-agent
1. Introduction One of the core issues in smart grid operation is power balance between supply and demand. The traditional control mode is ‘generation following load’. Basically, the generation resources are dispatched to satisfy the load demand by unit commitment (UC) and economic dispatching (ED) in the look-ahead scheduling and automatic generation control (AGC) in the real-time control, the loads are considered to be passive and fixed. With the rapid development of smart grid technologies, the penetration of fast demand response resources, electric vehicles (EVs), energy storages and other flexible loads is increasing rapidly in the power grid, and the regulating ability at the demand side can be significantly improved. Hence, the loads can become important resources to help maintain the power balance and be conducive to handle the small probability but high-risk incidents. Especially in the real-time control, with the participation of the flexible loads, the regulating needs on the AGC units can be effectively reduced. This can help to improve grid security and control performance [1]. But these loads are massive and distributed in different locations, they cannot be accurately detected and precisely controlled by the control center, which makes the existing centralized and accurate control mode no longer applicable.
n
Corresponding author. E-mail address:
[email protected] (Y. Li).
Generally, for a system with a large number of flexible loads, there are three kinds of control strategies: centralized control, decentralized control and distributed control. Nowadays, the centralized control is widely adopted in smart grid, mainly in the small scale grids or the grids with sufficient communication capacity [2]. When considering the massive and distributed flexible loads, the centralized control will be too expensive to implement subject to the limitation of communication and computing ability. Compared with the centralized control, the decentralized control has some advantages in terms of low complexity and easy implementation. It has been used in the controller design of grid elements [3], power control in the microgrid [4], etc. For example, the grid friendly household appliances, a typical class of flexible loads, can automatically monitor the system frequency and then reduce their consumption in a decentralized way. The current researches focus on tuning of action threshold, time delay, response amplitude and so on. Some commercial products have already been developed in some countries. Pacific Northwest National Laboratory (PNNL), in a project supported by the U.S. Department of Energy, is developing the Grid Friendly Controller fitted to domestic and industrial consumers to provide load-shedding at times of excessive power-system stress by monitoring the frequency signals [5]. ResponsiveLoad Ltd, a U.K. firm, developed a frequency-dependent load controller using various frequency limits to affect the probability of switching. In this way, the controller can move into different modes of operation, depending on the grid frequency at the time [6]. Those methods above are all examples of flexible loads helping the smart grid regulation. But from the view of the whole regional power grid,
http://dx.doi.org/10.1016/j.neucom.2015.05.015 0925-2312/& 2015 Elsevier B.V. All rights reserved.
Please cite this article as: Y. Li, et al., A consensus control strategy for dynamic power system look-ahead scheduling, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.015i
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the decentralized control scheme is difficult to determine the overall amount of load response, which is prone to lead to over or less control, thus not helpful to the frequency stability of the grid. It is known that a distributed control scheme can combine the positive features of both centralized and decentralized controls while limiting their disadvantages [7,8], which has been widely used in smart grid [9–11]. A distributed cooperative control is used to design the secondary voltage control of a micro-grid system in [12] by considering DGs as agents in a networked multi-agent system. A conceptual framework for ‘Market-based Control’ which can gain an optimal utilization of distributed resources is presented in [13], and a distributed control strategy is represented for system control. In [14], a center-free control strategy is proposed for multiple photovoltaic generators (PVs) to provide power regulating service. These researches demonstrate that, a controller under a distributed control scheme sends instructions to a part of agents and each agent shares its own information with some of their neighbors. This scheme can not only improve the control accuracy, but also reduce the negative impact on consumer's consumption. The related research work mentioned above has done some beneficial exploration on load-side resource control from the aspect of distribution and micro-grid. However, there are not many research results on how to utilize abundant flexible loads to participate in active power control from the aspect of transmission layer. The control center cannot effectively control every single load because it is not able to exactly capture the electricity consumption data. Motivated by this, this paper proposes a novel control scheme to solve the load control problem that balances load and generation. The main contribution of this paper will be presented in the following aspects. Firstly, we propose an original look-ahead scheduling mode in which the load agents are introduced to perform the coordination based on the Multi-Agent System (MAS) and the consensus control theory. The main feature of this scheme is a three-layer ‘centralized coordination, distributed control’ mode. As far as we know, the control mode we addressed is different from all the schemes mentioned in the relevant literature. Secondly, an optimal control strategy of the control center is designed. With this strategy, the control center allocates the unbalanced power to generators and load agents. Therefore, flexible loads can constitute a virtual power plant (VPP) and participate in the power balance, which extends the ‘generation following load' control mode. Thirdly, taking into account that it is an impossible task for a centralized scheme to get massive flexible loads to change their electricity consumption, a distributed strategy is designed within a load agent. With the distributed control, each load only needs to communicate with its neighbors and regulate its power coordinately. Thus the high cost and complex control strategy for controlling all loads can be avoided. Finally, a consensus protocol is introduced to make the consumption of all flexible loads equal and make their total output achieve to a given value quickly. The rest of this paper is organized as follows. Some preliminary notions are introduced in Section 2. In Section 3, the three layer control mode is described. In Section 4, the optimal control strategy for the control center and the distributed control strategy for the load agents are illustrated. The numerical simulations based on the benchmark 9-bus system are provided in Section 5 and conclusions are drawn in Section 6.
2. Preliminaries In this section, some preliminary notions in graph theory, matrix theory and consensus control that will be used for the following analysis are provided. Let G ¼ ðv; ε; AÞ be a weighted undirected graph of order N, where v ¼ fv1 ; v2 ; …; vN g is the set of nodes, ε Dv v is the set of edges, and A ¼ ½aij NN is a weighted adjacency matrix. An
undirected edge eij of G is denoted by ðvi ; vj Þ D ε, meaning that nodes vi and vj can exchange information with each other. In this paper, only positively weighted undirected graphs are considered which indicates that the communications among agents are all bidirectional, thus, aij ¼ aji 4 0 if and only if there is an edge ðvi ; vj Þ between nodes vi and vj, otherwise, aij ¼ aji ¼ 0. Then the set of neighbors of node vi is denoted by Ni ¼ fj A vj ðvj ; vi Þ D εg. A path between nodes vi and vj in G is a sequence of edges ðvi ; vi1 Þ, ðvi ; vi2 Þ, …, ðvil ; vj Þ. A graph is said to be connected, if there exists a path between any pair of distinct nodes vi and vj in G. Given C ¼ ½cij A Rnr , it is said that C Z 0 (C is nonnegative) if all its elements are nonnegative, and it is said that C 4 0 (C is positive) if all its elements cij are positive. A nonnegative matrix C is called to be stochastic if it satisfies C1 ¼ 1. In addition, A stochastic matrix C is called indecomposable and aperiodic (SIA) (or ergodic) if there exists a column vector v such that limk⟶1 Ak ¼ 1vT , where 1 ¼ ½1; 1; …; 1T with compatible dimensions. One of the basic tasks in a multi-agent system is the consensus of each agent's state [15,16]. Suppose that the multi-agent system under consideration consists of n autonomous agents with discrete-time dynamics, labeled 1 through n. Each agent is regarded as a node in the communication undirected graph G, and each edge ðvi ; vj Þ D εðGðkTÞÞ corresponds to an available information channel from ith agent to jth agent at time kT, and the set of the neighbors of the ith agent at time kT is denoted by Ni(kT), where k A Z þ ; T 4 0 is the sample time and G(kT) denotes the communication topology at time kT. In this paper, we replace kT by k to simplify the notation. Thus, in a system of n agents, each characterized by a state variable xi ðkÞ A Rn subject to a control input ui ðkÞ A Rn , given as follows: x_ i ðkÞ ¼ Axi ðkÞ þDf ðk; xi ðkÞÞ þ Bui ðkÞ;
i ¼ 1; 2; …; n;
ð1Þ
where Axi(k) and f ðk; xi ðkÞÞ denote the linear and nonlinear section of a system separately; A; D A Rnn are the coefficient matrix. We say the protocol ui to solve a consensus problem, if and only if the states of agents satisfy lim ðxi ðkÞ xj ðkÞÞ ¼ 0
k⟶1
8 i; j ¼ 1; 2; …; n
ð2Þ
To solve this consensus problem, the following protocol using the local information of ith agent and the distributed relative state information of its neighbors Ni(k) is introduced. ui ðkÞ ¼
n X
aij ðkÞðxi ðkÞ xj ðkÞÞ;
i ¼ 1; 2; …; n
ð3Þ
j¼1
Protocol (3) means the state of each agent asymptotically reaches to the state of its neighbors. When we design the protocol of the ith agent, only the state deviation between itself and its neighbors is used.
3. Control mode Some loads in the grid have energy storage properties that shortterm increase or decrease in their power consumption has little impact on the consumer's comfort. For example, the temperature is only reduced by 0.5 1C after an electric water heater turned off for 15 min [17], so there is no difference for the user experience. This kind of loads include Heating, Ventilating and Air Conditioning (HVAC), Lighting and so on. They can fast change their power consumption. The response speed of this type of loads can reach minutes or even seconds level according to the test results of the automatic demand response demonstration project in California [18]. To get the fast response loads to participate in the active power balance, a look-ahead scheduling mode is proposed in Fig. 1. It has three layers. The upper layer implements the optimal scheduling
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Fig. 1. The look-ahead scheduling mode in dynamic power system.
and the middle and lower layer implements coordination and local responsiveness respectively. The control center in the optimal scheduling layer calculates the system imbalance of power based on the short-term prediction of renewable generation and load demand at every 5 min. If the imbalance exceeds the regulating capacity of AGC units, the control center will send the control instructions to the units with slow ramp rate and load agents after the unified optimization. Suppose that the high level controller in the load agent can only control a part of load directly because of the limitation of communication, but the load can communicate with each other if they are connected. First, the agent converts the regulating target to a consensus variable and send it to the directly controlled loads, then through the consensus protocol, each load regulates its power coordinately to accomplish the task undertaken by the agent. It should be noted that, due to wide distribution of the system loads, multi-level coordination layer should be set up if necessary, thus will form a hierarchical control structure. Remark 1. When fast response loads are involved in power balance, a frequency-dependent load controller is usually used to monitor the system frequency signal and shed the corresponding load according to its inner strategy, such as in [5,6] and other relevant references. The interaction between the grid frequency stability and the aggregated electricity consumptions is not taken into account. But in this paper, we propose a novel ‘centralized coordination, distributed control’ mode. This scheme is able to get the fast response loads to participate in the look-ahead scheduling when the grid security is guaranteed. In this scheme, the control center allocates the imbalanced power to generators and load agents in centralized coordination. Then, each load agent will complete its power regulating task with the effort of its internal loads. Thus, the calculation and communication scale of the control center can be greatly reduced. In addition, this paper also designed the optimal control strategy in the control center and the consensus control strategy for load agents.
4. Control strategies 4.1. Optimal control strategy of the control center Suppose that the compensation price and quantity of regulating power of the generator and the load agent is linear, which can
be denoted as LGi ðΔP Gi Þ ¼ ai ΔP Gi þ bi
ð4Þ
LAj ðΔP Aj Þ ¼ αj ΔP Aj þ βj
ð5Þ
where LGi denotes the compensation price of ith generator; ΔP Gi denotes regulating power of ith generator; LAj is the compensation price of jth load agent; ΔP Aj is the regulating power of jth load agent; ai, bi and αj, βj are the cost coefficients of ith generator and jth load agent, respectively. The variable production cost of ith generator and jth load agent in kth period can be expressed by C Gi ðΔP Gi ðkÞÞ ¼ ai ðΔP Gi ðkÞÞ2 þ bi ΔP Gi ðkÞ
ð6Þ
C Aj ðΔP Aj ðkÞÞ ¼ αj ðΔP Aj ðkÞÞ2 þ βj ΔP Aj ðkÞ
ð7Þ
In each 5-min look-ahead scheduling period, the control center allocates the power imbalance to the generators with slow ramp rate and the load agents with the objective of minimizing the dispatching cost. The objective function is minfC total ðkÞg ¼
m X i¼1
C Gi ðΔP Gi ðkÞÞ þ
n X
C Aj ðΔP Aj ðkÞÞ
ð8Þ
j¼1
where Ctotal is the total cost; m is the number of generators participate in the 5-min look-ahead scheduling; n is the number of load agents participate in the 5-min look-ahead scheduling. Constraints are listed as follows: (1) Power balance constraint: The system imbalance of power at Pm time k can be expressed as i ¼ 1 P Gi ðkÞ P D ðkÞ. After the generators and flexible loads are scheduled, new unbalanced P power of the whole system can be expressed as m i ¼ 1 P Gi ðkÞ Pm Pn P D ðkÞ þ ð i ¼ 1 ΔP Gi ðkÞ j ¼ 1 ΔP Aj ðkÞÞ. To reduce the pressure of AGC units in the real-time control, we must ensure the new unbalanced power to fall into the regulating capacity of AGC units: 2 0 13 m m n X X X dn P r 4 P Gi ðkÞ P D ðkÞ þ @ ΔP Gi ðkÞ ΔP Aj ðkÞA5 AGC
i¼1
rP up AGC
i¼1
j¼1
ð9Þ
where PGi is the power output of the ith generator; PD is the load forecasting value of the whole system; Pup AGC is the upper limit of AGC regulating capacity; Pdn AGC is the lower limit of AGC
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regulating capacity; The positive direction is set as follows: ΔP Gi is positive if the power output increases and ΔP Gi is negative if the output value decreases; ΔP Aj is positive if the power of jth load agent increases and vice versa for negative. (2) Unit regulating power constraint: The regulating power of the generator is limited by the regulation margin and the ramp rate. up max ΔP max Gi ðkÞ ¼ minðΔtRGi ; P Gi P Gi ðkÞÞ
ð10Þ
dn min ΔP min Gi ðkÞ ¼ maxðΔtRGi ; P Gi ðkÞ þ P Gi Þ
ð11Þ
max ΔP min Gi ðkÞ r ΔP Gi ðkÞ r ΔP Gi ðkÞ
ð12Þ
and ΔP min where ΔP max Gi Gi are the upper and lower limit of the regulation capacity of ith generator; Pmax and Pmin are the Gi Gi upper and lower limit of the power output of ith generator; PGi dn is the actual power output of ith generator; Rup Gi and RGi are the regulating rate of ith generator; Δt represents 5 min respectively. (3) Load agent regulating power constraint: max ΔP min Aj ðkÞ r ΔP Aj ðkÞ r ΔP Aj ðkÞ
variable is designed to make the loads within the agent to provide the same percentage of regulating duty. Here defines the regulating ratio as
ηi ðkÞ ¼
i ¼ 1; 2; …; n
ð15Þ
where the subscript i denotes the ith load; di and dimax are the active power and the maximum available power under the current environment condition, respectively. To make the consensus of all loads within a group, it follows from (3) that the control for the ith load is ui ðkÞ ¼
n X
ωij ðηi ðkÞ ηj ðkÞÞ
ð16Þ
j¼1
where ωij is the weight between ith load and jth load, assuming the ith load is as important as all its neighbors, so, ωij is defined as aij
ωij ¼ Pn
j¼0
ð13Þ
and ΔP min where ΔP max Aj Aj are the upper and lower limit of the regulation capacity of jth load agent.
Δdi ðkÞ ; dimax di ðkÞ
ð17Þ
aij
where aij is the entry of the adjacency matrix defined in (14). Because aij ðkÞ ¼ aji ðkÞ, so (16) can be simplified as ui ðkÞ ¼ ηi ðkÞ þ
n X
ωij ηj ðkÞ
ð18Þ
j¼1
4.2. Consensus control strategy of load agent To fulfil the power regulating needs allocated by the control center, each load agent adopts a distributed control strategy. That is to say that the individual load under the load agent needs to communicate with its neighbors. Let adjacency matrix A represents the real time communication topology and information flows among the loads, given as follows: 2 3 a10 ðkÞ a11 ðkÞ a12 ðkÞ ⋯ a1n ðkÞ 6 7 6 a20 ðkÞ a21 ðkÞ a22 ðkÞ ⋯ a2n ðkÞ 7 7 A¼6 ð14Þ 6⋮ 7 ⋮ ⋮ ⋯ ⋮ 4 5 an0 ðkÞ an1 ðkÞ an2 ðkÞ ⋯ ann ðkÞ where ai0 denotes the load directly connected to the high level controller of the agent, and aij ðj4 0Þ denotes the connection between two loads. So, if ith load can exchange information with the jth load, then aij ¼ 1, which means jth load is a neighbor of ith load at time k. Otherwise aij ¼ 0. Thus, the set of neighbors of ith load is established, denoted by Ni(k). Also, it can be noted aii ¼ 1 is satisfied for all i, which means that each load can acquire its own output information at any time. Moreover, aij ðkÞ ¼ aji ðkÞ is satisfied because of the bidirectional communication among loads. In the adjacency matrix A, when all elements of the first column are ones, which means all loads are connected to the high level controller, the control degenerates to the centralized mode. Similarly, when none of the loads exchange information with each other and the high level controller, the control is indeed decentralized. Thus, the centralized and decentralized control modes are two special cases of the proposed control schemes. Under the distributed control strategy, A is a highly sparse symmetric matrix with each of the main diagonal elements equal to 1. All loads expect that the impact on their consumption behavior is minimized, while the agent tends to allocate more regulating needs to the loads with large potential and less regulating needs to the loads with small potential. Hence, the objective is the fair utilization profile which makes the fair ancillary duty. The same regulating ratio for each load is an easy and practical way to achieve the fairness and balance the power mismatch of the system. That is to say that the consensus
Eqs. (17) and (18) are protocols for ith load. With the iteration of the control law, the state of each load can reach agreement.
Fig. 2. Diagram of the IEEE 9-bus system.
Table 1 Parameters of generators and load agents. Gen.
ai
bi
P Gi ð0Þ
Agent
αj
βj
P Aj ð0Þ
G10 G11 G12
0.002 0.002 0.004
9.82 10.10 15.21
80 120 100
LA13 LA14
0.002 0.003
10.05 10.08
90 100
Table 2 Power distribution among generators and load agents. Gen.
Mode
P Gi ð0Þ
ΔP Gi
Agent
Mode
P Aj ð0Þ
ΔP Aj
G10 G11 G12
AGC Look-ahead Look-ahead
80 120 100
25 6.25 12.5
LA13 LA14
Look-ahead Look-ahead
90 100
18.75 7.5
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4.3. Control algorithm According to the control strategies of control center and the load agent mentioned above, the control algorithm of look-ahead scheduling with flexible loads is designed as follows: (1) At time k, the following information in the next 5-min is known to the control center by short-term prediction: the output power of each generator PGi(k), the load demand of the whole system PD(k), then the control center calculate the P whole unbalanced power in the system m i ¼ 1 P Gi ðkÞ P D ðkÞ.
5
(2) The control center allocates the system imbalance of power based on (8) and sends the results to generators and load agents. (3) The load agent converts the load reduction ΔP Aj ðkÞ to a regulating ratio:
η0 ðkÞ ¼
ΔP Aj ðkÞ P Ajmax P Aj ðkÞ
ð19Þ
and transmits η0 ðkÞ to the directly controlled load. (4) Each load receives the ηj ðkÞ from all neighbors j A N i ðkÞ, and calculates ui(k) as (18).
Fig. 3. Dynamics with respect to the change of power supply: (a) the regulating ratio of the loads, L38–L47; (b) power command of the load agents, LA13, LA14; (c) the frequency of the system.
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(5) Each load computes the load reduction Δdi ðkÞ, where Δdi ðkÞ is defined in (15). So far, the control process is completed. At time k þ 1, repeat (1)
Remark 2. With the distributed control, each load only needs to communicate with its neighbors, which can greatly reduce the calculation and communication scale of the control center. In addition, the load agent only needs to control a few load directly connected to it, which avoids the high cost and complex control strategy for controlling all loads. 5. Simulation results In this section, simulations on the IEEE 9-bus system are performed to validate of the proposed strategy. Suppose that the load under B5 and B7 are flexible loads, they can participate in system power balancing. Thus, two agents LA13 and LA14 are set under B5 and B7 respectively, each agent is consisted of two load groups and each group has ten loads. L15 under B9 is a fixed load, whose power cannot be regulated. G11 and G12 participate in the 5-min look-ahead scheduling because they need more time to change the power output. G10 is an AGC unit, with fast regulating rate, participates in the realtime control, with the regulating range of [ 25 MW, 25 MW]. Fig. 2 shows the topology of the system and the grid elements. The initial state and parameters of generators and load agents are shown in Table 1. The expected disturbance is that power supply decreases 70 MW at 0 s because of a sudden loss of generation. In the look-ahead scheduling, G11, G12 and LA13, LA14 is scheduled to offset the 45 MW power imbalance, and the remaining 25 MW will be eliminated by AGC unit G10. The power distribution is shown in Table 2.
a same value after the consensus control. This means the load can change its electricity consumption by itself after communicating with its neighbors, thus it is controlled indirectly from the view of the control center.
5.2. Dynamic response to topology change In order to test the effect of topology change on the convergence of the proposed strategy, two different topologies are designed as shown in Fig. 4. Case1: radial topology between loads. Case2: random topology between loads. Generally, the convergence rate depends on the end node, when the end node convergences to the consensus track, the whole group will achieve stable. So, we take the end node as an example to compare the convergence under different topologies, the result is shown in Fig. 5. It can be seen from Fig. 5, the strategy is robust under different topologies, the closer links among loads and the shorter from the high level controller, the larger convergence rate.
Remark 5. Note that the convergence rate of the distributed consensus protocol (18) is determined by the communication topology among flexible loads. The convergence rate for discrete-time MAS is defined as
ρ ¼ sup lim sup xð0Þ a 0
t-1
ΔðxðtÞÞ Δðxð0ÞÞ
ð20Þ
For a given communication topology, it is easy to derive ρ ¼ j λ2 j , where λ2 is the eigenvalue of matrix A with modulus closet to 1. Obviously, the larger ρ, the larger convergence rate. High Level Controller
Remark 3. In the traditional look-ahead scheduling, the power imbalance in the system is entirely allocated to the generators. When the flexible loads participate in power balancing, they can change their consumptions to meet the power imbalance partially. As in this simulation, G11 and G12 only undertake 18.75 MW unbalanced power while LA13 and LA14 undertake 26.25 MW. This reduces the generators’ cost and can be a better choice for the control center.
High Level Controller
36 37 38
38
37
39
36
40
40
41 43
Remark 4. It is an impossible task for a centralized scheme to get massive flexible loads to change their electricity consumption. However, the regulating ratio of each load can quickly converge to
41
42
45
44
43
44 45
Fig. 4. Structure of communication.
0.76 0.74 0.72 0.7 regulating ratio
After the load agent received the power regulation instruction, first, it calculates the target regulating ratio based on expression (15) and chooses the result as consensus variable, then, it releases the consensus variable to the directly connected load. Meanwhile, the AGC unit continues to track the system frequency deviation, and regulate the remaining 25 MW power. The dynamics with respect to the change of power supply is shown in Fig. 3 In this figure, Fig. 3(a) shows that the consensus control makes the regulating ratio of each load converge to a desired position, at which the fair utilization of all loads is satisfied, even the high level controller does not send the command signal to each load. Fig. 3(b) shows that the total power of each load agent can track the command well, implying that the control strategy is valid. Fig. 3(c) shows that after the joint regulation of flexible loads and generators, the frequency can restore to 50 Hz. Consequently, the load agent can be considered to be a virtual power plant, which is friendly to the power system.
39
42
5.1. Dynamic response to power supply change
0.68 0.66 0.64 0.62 0.6 0.58 0
1
2
3
4
5
6
7
8
9
10
t/s
Fig. 5. Convergence rate under different topologies.
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Fig. 6. Dynamics with respect to the change of communication: (a) power command of the load agents, LA13; (b) regulating ratio, L45; (c) the frequency of the system.
5.3. Dynamic response to communication change Dynamics with respect to the change of communicate is divided into three cases. Case1: the initial communication topology. Case2: communication is interrupted between 40# load and 39# load, thus, the network is still connected. Case3: communication is interrupted
between 40# load and 39# load, 40# load and 38# load, thus, the network is not connected. It can be seen from Fig. 6(a), Case2 has little effect on the dynamic response of the load agents and the convergence because the network is still connected. But in Case3, the actual response of the load agent LA13 is 4.7 MW less than the control center expected, thus, LA13 does
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not fulfill its regulating needs. Fig. 6(b) shows that some loads cannot track the consensus protocol because communication is interrupted, so information cannot be passed by their neighbors. Fig. 6(c) shows that in Case3, AGC unit will increase its output power to eliminate the unbalanced power, so the system frequency can still return back to 50 Hz, but there will be some time delay compared with the other two cases. In a distributed control strategy, the agent cannot know the actual response of the inner load agents exactly, so uncertainty will exist on the whole regulation power of the agent. In this case, the control center should be aware of this uncertainty and the optimal control should become stochastic optimization, further study shall be taken in the future.
6. Conclusions Flexible loads are important regulating resources in smart grid. They can provide more economical choices to maintain the power balance of system, which is conducive to the power system operation. In order to get the flexible loads to participate in look-ahead scheduling, this paper proposed a distributed strategy based on consensus control. Also, the optimal control strategy of the control center and the consensus control strategy of the load agents are designed. The simulation results show that distributed strategy is a feasible way to control the massive flexible loads by designing an appropriate consensus protocol. Also be noted that, DR scheduling relies on incentive mechanism, market mechanisms and other relevant policies, and real-time price (RTP) is a more common and reasonable pilot signal. So, further research is needed in the electricity pricing mechanism, the distributed scheme based on RTP and the response uncertainty of flexible loads.
Acknowledgments This work was jointly supported by the National Natural Science Foundation of China (Grant no. 51407165) and the State Grid Corporation of China project: ‘Study on Key Technologies for Power and Frequency Control of System with ‘Source-Grid-Load’ Interactions’.
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Yaping Li received the B.S. degree from Sichuan University, Chengdu, China, the M.S. degree from Nanjing Automation Research Institute, Nanjing, China, in 2003 and 2006 respectively. Currently she is pursuing her Ph. D. degree in Hohai University, Nanjing, China, all in Power System and its Automation. She has been a senior engineer with China Electric Power Research Institute. Her research interests include demand response, power system simulation and control.
Taiyou Yong received the B.S. and M.S. degrees from Tsinghua University, Beijing, China in 1991 and 1995, respectively, and the Ph.D. degree from University of Wisconsin-Madison, USA in 2001. He had worked and consulted with ABB, California ISO and EPRI for more than 15 years. Currently he is with China Electric Power Research Institute. His research interests include electricity market operations, power system operations and renewable integration.
Jinde Cao received the B.S. degree from Anhui Normal University, Wuhu, China, the M.S. degree from Yunan University, Kunming, China, and the Ph.D. degree from Sichuan University, Chengdu, China, all in mathematics/applied mathematics, in 1986, 1989, and 1998, respectively. From March 1989 to May 2000, he was with the Yunnan University. In May 2000, he joined the Department of Mathematics, Southeast University, Nanjing, China. From July 2001 to June 2002, he was a postdoctoral Research Fellow at the Department of Automation and Computer-Aided Engineering, Chinese University of Hong Kong, Hong Kong. In the period from 2006 to 2008, he was a Visiting Research Fellow and a Visiting Professor at the School of Information Systems, Computing and Mathematics, Brunel University, UK. Currently, he is a distinguished professor and a doctoral advisor at the Southeast University and also distinguished adjunct professor at the King Abdulaziz University, prior to which he was a Professor at Yunnan University from 1996 to 2000. He is the author or coauthor of more than 300 journal papers and five edited books. His research interests include nonlinear systems, neural networks, complex systems and complex networks, stability theory, and applied mathematics. Dr. Cao was an Associate Editor of the IEEE Transactions on Neural Networks, Journal of the Franklin Institute and Neurocmoputing. He is an Associate Editor of the IEEE Transactions on Cybernetics, Differential Equations and Dynamical Systems, Mathematics and Computers in Simulation, and Neural Networks. Dr. Cao is a Reviewer of Mathematical Reviews and Zentralblatt-Math. He is a ISI Highly-Cited Researcher in Mathematics and Engineering listed by Thomson Reuters.
Please cite this article as: Y. Li, et al., A consensus control strategy for dynamic power system look-ahead scheduling, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.015i
Y. Li et al. / Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Ping Ju received the B.S. and M.S. degrees in electrical engineering from Southeast University, Nanjing, China in 1982 and 1985, respectively, and the Ph.D. degree in electrical engineering from Zhejiang University, Hangzhou, China. He is now a professor of Electrical Engineering in the College of Energy and Electrical Engineering at Hohai University, Nanjing, China. Dr. Ju was an Alexander-von-Humboldt Fellow at University of Dortmund, Dortmund, Germany. His research interests include power system modeling and control.
9 Shengchun Yang received the B.S. degree from Huazhong University of Science and Technology, Wuhan, China in 1995, and M.S. degree from Nanjing Automation Research Institute, Nanjing, China in 1998. Currently, he is pursuing his Ph.D. degree in the School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China. He had worked with Nanjing Automation Research Institute for more than 15 years, specialized in power system operations and renewable integration. His research interests include demand response and power system operations with high penetration of flexible load and renewable generation.
Jianguo Yao received the B.S. and M.S. degrees from Zhejiang University, Hangzhou, China in 1985 and 1988 respectively. He has been engaged in technology development and research management of Power System and its Automation for a long time, and currently the deputy chief engineer of China Electric Power Research Institute. Mr. Yao is a well-known expert in dispatching automation and smart grid with State Grid Corporation of China. His research interests include power system analysis, power grid dispatching technical support system, smart grid, and ‘Source-Grid-Load’ interactive operation and control.
Please cite this article as: Y. Li, et al., A consensus control strategy for dynamic power system look-ahead scheduling, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.015i
