A Novel Distributed Secondary and Tertiary Control for I-V Droop Controlled Paralleled DC-DC Converters Haojie Wang1*, Minxiao Han1, Josep M. Guerrero2, Juan C. Vasquez2, Bitew G. Teshager1 1
School of Electric and Electronic Engineering, North China Electric Power University, No.2 Beinong Road, Huilongguan Town, Changping District, Beijing, China 2 Department of Energy Technology, Aalborg University, 9220 Aalborg East, Denmark *
[email protected] Abstract: A hierarchical distributed control method for I-V droop controlled paralleled DC-DC converters in DC microgrid (MG) is proposed. The control structure includes primary, secondary, and tertiary levels. The secondary control level is used to remove the DC voltage deviation and improve the current sharing accuracy. An improved dynamic consensus algorithm is used in the secondary control to calculate the average values of bus voltage and voltage restoration in distributed. In the tertiary control level, as the main contribution in this paper, the system conversion efficiency is enhanced by using the average restoration value obtained in the secondary control level, instead of using the total load current which needs more communication traffic. When the converters are connected to batteries, the method for state of charge (SoC) management is proposed so that the SoC balance can be guaranteed. The effectiveness of the proposed method is verified by detailed experimental tests based on four 0.7 kW DC-DC converters. Keywords: Hierarchical distributed control, paralleled DC-DC converters, I-V droop control, dynamic consensus algorithm, efficiency optimization, SoC balance
1. Induction DC MGs have been recognized as more attractive for numerous uses due to higher efficiency, more natural interface to many types of renewable energy source (RES) and energy storage system (ESS), better compliance with consumer electronics, etc [1]-[4]. Paralleled operation of DC-DC converters have been widely used in various applications in DC MGs, such as connecting multi batteries to the common bus or connecting multiple busses with different voltages [5]-[6]. Hierarchical control, including primary, secondary and tertiary control levels [7]-[8] is commonly applied to MGs to achieve multiple control objectives. Since droop control method is a decentralized strategy which does not require communication links and offers higher reliability and flexibility, it is often used in the primary control level to make the system stable and guarantee load sharing between each converter. The existing secondary and tertiary controls of DC MGs can be summarized into two categories: centralized control and distributed control. A centralized control means the secondary and tertiary adjustment is completed in the MGs central controller. However, the single-point-of-failure should be noticed for centralized control diagram [5]. Distributed control is implemented in the local controllers, and the information used in the local control scheme is exchanged via communication network, so this method has emerged as an attractive alternative as it offers improved reliability, simpler communication network and easier scalability. This method can avoid the impact of single-point-of-failure in the centralized control [9]. Since transmission lines have differences in parameters and the measurements of different units have errors, poor load sharing and circulating current between converters can be caused [10]. In addition, when droop
control is applied, voltage deviation inevitably appears. Thus, the secondary control is used to solve the aforementioned problems and help improving the power quality of a MG. A distributed control based on low bandwidth communication is proposed to ensure proportional load sharing in lowvoltage DC MGs by using the average current of all converters in [11]. In [12], the secondary control is implemented locally, and the voltage restoration and current sharing accuracy enhancement can be achieved simultaneously, but every converter needs to obtain all the other converters’ output voltages and currents to calculate the average values. A dynamic consensus protocol is employed in [13], where a noise-resilient DC voltage observer using the neighbouring units’ information is developed to correct the local voltage set points. In [14], a generalized modelling method for the consensus algorithmbased distributed primary and secondary control is proposed and the influences of key control parameters, the communication topology and the communication speed are studied. Tertiary control is the last control level that considers the economical concerns in the optimal operation of the MGs [15]. Due to the relationship between the conversion efficiency and the output current of one DC-DC converter, the gross efficiency of paralleled converters is relatively lower in light load conditions where more improvement is expected [16]-[17]. Thus, the optimization method is always in tertiary level for improving the overall system efficiency. When the paralleled converters are connected to batteries, the state of charge (SoC) of each unit should be balanced to prolong the lifetime of the energy storage units and avoid the overuse of a certain unit, so that the battery management should be considered in the tertiary control as well [18]-[22]. In [23], a distributed two-level tertiary control system to adjust the voltage set points of individual MGs and balance
1
the loading among all the sources throughout the cluster is studied, which builds upon the primary-secondary control method by the authors in [19]. In [24], the tertiary control is used for SoC management by regulating current reference as soon as the SoC reaches the limit value to prevent from over-charge or over-discharge. Authors in [25] propose a tertiary control level including an optimization method to achieve higher efficiency and lower energy losses. According to the method in [25], one converter undertakes the most of the load current in light load conditions which may cause fast wear and tear for this converter after long term operating, so an operation scheduling and priority shifting method is included in the tertiary control proposed in [26] to distribute the total workload. In [27], a SoC-based adaptive droop control method has been proposed, where the droop coefficient is inversely proportional to the nth order of SoC to realize the SoC balance. Compared with the conventional V-I droop control as shown in Fig. 1(a), the external droop control loop of I-V droop method is designed as a voltage loop with embedded virtual resistance (VR) as shown in Fig. 1(b), which avoids the use of a slow voltage loop and a separate extra virtual impedance loop that may limit the system bandwidth [28][29]. The comparison between two droop control methods has been analysed in detail in [29]. Based on the I-V droop control method, the load current can be shared in proportion to their reciprocals of VRs, and the output currents of converters increase with the bus voltage decreasing, which is like the V-I droop control method. Thus, the I-V droop control also can coordinate V-I droop control and any other controls of distributed energy resources (DERs) like V-I droop control [29]. However, the aforementioned secondary and tertiary control methods are based on the V-I droop controller. The hierarchical control method for the I-V droop controlled converters has not been studied so much in previous works. Additionally, the information of total load current is necessary to the tertiary control, but when the load is light, the load current can only be shared by the part of the converters and the other converters do not share the load current, so that the efficiency optimization in the tertiary control level usually needs to use communication algorithms to obtain the total load current, which needs more communication traffic. Thus in this paper, a novel hierarchical distributed control for I-V controlled paralleled DC-DC converters is proposed. First, the dynamic consensus algorithm proposed in [26] is improved by this paper so that the oscillation of average value can be avoided when the communication topology is changed under steady-state. By using the proposed consensus algorithm, the average values of bus voltage and voltage deviation can be achieved in the secondary control level to realize the accurate current sharing and voltage restoration. Second, the tertiary control is proposed to optimize the gross conversion efficiency of paralleled converters by using the average voltage restoration value obtained in the secondary control level, instead of using the total load current, so that the communication traffic can be reduced, which is the main contribution in this paper. For the paralleled converters connected to batteries, the algorithm for SoC management is considered in the tertiary control level as well. Finally, experiments are performed to verify the proposed control.
This paper is structured as follows. In Section II, the improved dynamic consensus algorithm, and the primary and secondary control levels are presented. In Section III, the tertiary control is proposed. In Section IV, the proposed hierarchical distributed control is verified by experiments. Section V concludes this paper. u
Urate
+
uref
+
-
-
Voltage PI iref controller
+
Current PI controller
-
d
PWM
DC/DC
i
r
a u
Urate
+
-
1/r
iref
+
-
Current PI d controller
PWM
DC/DC
i
b Fig. 1. Two droop control implementations (a) V-I droop control, (b) I-V droop control
2. Primary and secondary control levels 2.1. Dynamic Consensus Algorithm The discrete-time average consensus algorithm based on the multi-agent system can be described as [30] N
i (k 1) i (k ) aij [ j (k 1) i (k )]
(1)
i 1
where i=1, 2, …, N and N is the total number of agent nodes, ξi(k) is the state of agent i at time k, A=[aij]∈Rn×n is the weighted adjacency matrix with nonnegative adjacency elements aij which indicates the connection status between node i and node j: aij = 0 if the nodes i and j are not linked and aij =ε if the nodes i and j are linked where ε is the constant edge weight. Thus, the states of all agents converge to a consensus value: 1 N lim i (k ) i (0) (2) k N i 1 In addition, in order to ensure the accurate consensus in dynamically changing environment, the algorithm (1) is modified by introducing an additional variable δij(k) for each neighbor j of agent i, which stores the cumulative disagreement between two agents at time k. Thus, (1) can be rewritten as [31] N
i (k 1) i (k 1) aij ij (k 1)
(3)
ij (k 1) ij (k ) j (k 1) i (k )
(4)
i 1
where δij(0) is zero for all i and j, γi(k) is the input of agent i at time k. In steady-state, when the communication topology is forced to change, although the algorithm is able to tolerate the topology change and ensure the accurate averaging, the oscillation of average value in each node is inevitable [26]. In order to improve this problem, according to (3) and (4), (5) can be derived as
2
N
N
i 1
i 1
i (k 1) i (k 1) aij ij (k ) aij [ j (k ) i (k )] i (k 1) i (k ) i (k ) N
N
i 1
i 1
(5)
aij ij (k ) aij [ j (k ) i (k )] N
i (k 1) i (k ) i (k ) aij [ j (k ) i (k )] i 1
Thus, each agent i converge to: 1 N lim[i (k ) i (k )] 0 (6) k N i 1 In steady-state, ξi(k)=ξj(k) for any i and j, so compared with algorithm (3) and (4), algorithm (5) can keep the average value constant in each node and the oscillation of average value can be avoided when the communication topology is changed. The Laplacian matrix L=[lij]∈RN×N for the N-agent nodes is defined as i j aij N lij (7) i j aim m 1, m i The fastest converging linear iteration of multi-agent system can be ensured if and only if ε is given by [32] 2 (8) 1 N 1 where λi denotes the i-th largest eigenvalue of the Laplacian matrix. A simulation example is given to demonstrate the influence of communication topology changes on the both dynamic consensus algorithms. The sampling time of the consensus algorithms is set to 10ms. Based on the topology of ring shape as shown in Fig. 2, the optimal ε can be given as 0.23 according to (8). At 0.5 s, the inputs of all the agents are changed and Fig. 2 demonstrates that both algorithms can provide accurate average value for each agent under dynamic environment and their converging speeds are equal. At 1s, the communication link between agent 1 and agent 6 is broken so that the topology of communication topology is changed from ring to line shape. Fig. 2(a) shows that the oscillations of average values are caused by using the algorithm (3) and (4). Fig. 2(b) shows that the steady-state is not affected by topology changes and the average values are kept constant by using the algorithm (5). 104 104
1
103 103
6
102 102
1 5
2 3
4
104 104
6
3
101 101
100 100
100 100
99 99
99 99
98 98
98 98
97 97
1
6
3
5 3
4
4
50 0.5
100 1
Time/s
150 1.5
200 2
96 96
(9) (10)
where irefi, di and iLi are the current reference, duty ratio and average inductor current (namely output current) of the converter of agent i respectively, r is the VR of all the converters, Urate is the voltage reference of droop characteristic, KCI and KCP are the integral and proportional terms of current PI controller and xi(k) is the estimation value of average bus voltage of agent i which can be obtained by using (5): N
xi (k 1) xi (k ) aij [x j (k ) xi (k )] ui (k 1) ui (k ) (11) i 1
where ui(k) is the voltage sampled by agent i at time k. Thus, the decentralized current sharing proportional to the reciprocal of VRs can be achieved. Since the voltage deviation inevitably appears when droop control is applied, voltage restoration is considered in secondary control. The voltage restoration value of agent i can be computed as
uδi (k ) ( KVP
KVI ) (U rate xi (k )) s
(12)
where uδi(k) is the compensating term of agent i for voltage restoration, KVI and KVP are the integral and proportional terms of voltage restoration controller. However, the voltage estimation values (namely xi(k)) of all the agents are not identical in any time, so the voltage restoration values of all the agents can be unequal. Thus, the dynamic consensus algorithm (5) is used so that the average compensating terms can be achieved by all agents: N
yi (k 1) yi (k ) aij [ y j (k ) yi (k )] i 1
(13)
uδi (k 1) uδi (k ) where yi(k) is the average compensating term for agent i. Considering (11) and (13), (9) can be rewritten as (14)
Let X(k)=[x1(k), x2(k), …, xN(k)]T, Y(k)=[y1(k), y2(k), …, yN(k)]T, U(k)=[u1(k), u2(k), …, uN(k)]T, Uδ(k)=[uδ1(k), uδ2(k), …, uδN (k)]T, then the matrix form can be obtained as
97 97 0 0
1 irefi [U rate xi (k )] r K di ( KCP CI ) (irefi iLi ) s
1 irefi [U rate yi (k ) xi (k )] r
6
2
5
2
102 102
4
101 101
96 96
1
103 103
5
2
controller, is in charge of voltage and current regulation. The I-V droop controller is achieved by linearly increasing the current reference when the bus voltage decreases as shown in Fig. 1. Considering that the load current cannot be accurately shared when transmission lines have differences in parameters or the measurements of different converters have errors, the secondary control based on multi-agent system is installed and the follows can be obtained as
00
50 0.5
100 1
150 1.5
200 2
Time/s
a b Fig. 2. Information consensus under input and topology change 2.2. Primary and Distributed Secondary Control
0 X (k ) X ( k + 1) I N L Y ( k + 1) = 0 I N L Y ( k ) U ( k ) - U ( k + 1) + U δ ( k ) - U δ ( k + 1)
(15)
where IN is N-dimensional identity.
Primary control, including an I-V droop controller or virtual admittance and a current proportional integral (PI) 3
io io ( i ) ( i 1)， io i iop-i ( io ) ( io )， i i i o op-i i 1 i
3. Distributed tertiary control level Although modern power electronic system provides high-efficiency conversion, losses are inevitable and minimization of losses is required. In addition, balancing the SoC of each cell is necessary when the paralleled converters are connected to batteries. Therefore, the multi-agent system based tertiary control method is proposed to achieve the optimization of conversion efficiency and SoC management.
0.96
(17)
Highest efficiency point
0.94 0.92
Efficiency
3.1. Efficiency Optimization
0.9
For N paralleled DC-DC converters, the losses are mainly related with conversion losses which are caused by switching, driver and filter parasitic elements in each converter. Even if constant input and output voltages are assumed, efficiency of each converter changes with its output current, as shown in Fig. 3. The highest efficiency point of the curve exists, which is usually reached between 30% and 60% load. Let ihep represent the current value of the highest efficiency point and η(z) represent the efficiency function where z is the output current of any converter. The efficiency curve is monotone increasing as the output current is less than ihep while monotone decreasing as the output current is greater than ihep. Since the efficiency is relatively much lower in light load conditions, there exists a room for optimization. According to the properties of this efficiency curve, if i is a positive integer, there exists iop-i>ihep, such that
i iop-i i 1
)，
i iop-i i 1
[0, ihep ]
(16)
Let io represent the total load current of the system. Considering (16), and the monotone increasing and decreasing zone of the efficiency curve, the following inequalities can be obtained as
Outpur current (A)
Priority Priority n (n-1)
0.86
Monotone increasing 0.84
5
imax 20
(i 1) iop-(i -1) io i iop-i
(18)
where iop-0=0. However, it is a problem to measure io. In order to solve this problem without increasing more communication traffic, the efficiency optimization method by using the information of the consensus voltage restoration values is proposed. First the initial priority order of all the converters should be designed. The integers’ range is from 1 to N with smaller values representing higher priorities to share the load current, and we define the converter of agent i as the converter of priority i. According to (17) and (18), the following optimization principles can be obtained:
iop-1 iop-2 iop-(n-1) (n-1)iop-(n-1)/n iop-1/2
Priority Priority n (n-1)
Priority Priority 2 1 iop-1 iop-2 iop-(n-1)
…
(n-1)iop-(n-1)/n iop-1/2 Note: Now 0
