Real-time electric load management for DC zonal all-electric ship power systems

Electric Power Systems Research 154 (2018) 503–514

Contents lists available at ScienceDirect

Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

Real-time electric load management for DC zonal all-electric ship power systems Xianyong Feng a,∗ , Karen L. Butler-Purry b , Takis Zourntos c a b c

Center for Electromechanics, The University of Texas at Austin, 10100 Burnet Road, Austin, TX 78758, United States Department of Electrical & Computer Engineering, Texas A&M University, College Station, TX 77843-3128, United States Cestar College of Business, Health and Technology, North York, ON M2J 1S5, Canada

a r t i c l e

i n f o

Article history: Received 18 May 2017 Received in revised form 15 August 2017 Accepted 7 September 2017 Keywords: All-electric ship power system Cooperative control Dynamic balancing Multi-agent system Pulse load Real-time load management

a b s t r a c t All-electric ship power systems have limited generation and include a large portion of nonlinear loads and dynamic loads relative to the total power capacity. In DC zonal ship power systems, power converter constraints and motor load voltage constraints need to be satisfied in operational real time. Sudden load changes may cause significant frequency oscillations on the AC side of the system. The load dynamics and priorities also need to be considered. Thus, individual loads in the DC zonal system need to be optimally regulated in operational real time to improve the power quality and system level stability. In this paper, a heterogeneous multi-agent system (MAS) framework was developed for a DC zonal system of an allelectric ship power system to achieve dynamic generation and load balancing while satisfying operational constraints as well as considering load priorities. The developed method integrates system dynamics and various operational constraints into MAS and controls individual loads using decentralized cooperative controller. Simulation results on a two-zone notional all-electric ship power system simulated in PSCAD software show the viability and performance of the proposed technique. © 2017 Elsevier B.V. All rights reserved.

1. Introduction All-electric ship power systems have limited generation and low inertia compared with large power systems. These systems usually include large portions of dynamic loads and nonlinear loads relative to the total generation capacity [1,2], which may reduce the stability margin. Pulse loads in all-electric ship power systems draw a large amount of power in a short period of time [3], which may cause significant frequency or voltage oscillations. In the DC zonal system, various converter constraints and motor load voltage constraints need to be satisfied in operational real time [4]. The high priority loads need to be served before low priority loads. The impact of load dynamics on system level stability also needs to be considered. Thus, an effective real-time load management technique for DC zonal all-electric ship power systems should be developed to optimally regulate the power set-point or switch status of individual load while satisfying operational constraints and considering load priorities. Load management in large power systems aims to balance load and generation while achieving certain objectives, such as max-

∗ Corresponding author. E-mail address: [email protected] (X. Feng). http://dx.doi.org/10.1016/j.epsr.2017.09.014 0378-7796/© 2017 Elsevier B.V. All rights reserved.

imizing the profit margin and reducing the peak load [5–7]. The decision time step of load management for large power systems is in the order of minutes to hours. Dynamic programming [8] and intelligent computational techniques [9] are centralized methods used to solve load management problems. However, all-electric ship power systems include faster dynamics and limited rotating inertia, which requires a much smaller decision time step for load management to improve the system stability [10,11]. Otherwise, the system may go unstable before any control actions. The realtime load management for ships is defined as a secondary control problem, which requires a millisecond level decision interval. Centralized methods usually have difficulties in making load control decisions in such a short time interval for ships with multiple loads and complicated network circuits. Since MASs aim to cooperatively achieve group objectives that are difficult to reach by centralized methods [12], this work develops a decentralized MAS framework to solve the real-time load management problem for all-electric ship power systems. The MAS cooperative controller is inspired by biological phenomena [13], such as bird flocking, fish schooling, and bacteria foraging, which has been widely used in vehicle formations [14] and multi-robotic systems [15]. MAS techniques have been used to solve challenging problems in power engineering [16] such as power management [17], energy management [18–21], sec-

504

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

Fig. 1. One-line diagram of a notional all-electric ship power system model.

Table 1 Component definitions. Component name

Component description

MTG

3 ph, 13.8 kV AC, 36 MW, 1.49 s inertia constant, gas turbine generator 3 ph, 13.8 kV AC, 4 MW, 1.06 s inertia constant, gas turbine generator 3 ph, – connected, 13.8/4.16 kV AC 36.5 MW (rated power), 4.16 kV AC 13.8 kV AC; 10 MW/s ramp rate 1000 to 375, 650, and 800 V DC rectifiers 800 V DC to 3-ph, 450 V AC inverter 3-ph, 4.16 kV AC to 1000 V DC converter

ATG Transformer Propulsion load Pulse load PCM1 PCM2 PCM4

ondary voltage control [22,23], wide area control [24], restoration [25], protection [26], etc. Since power systems include various electrical components modeled by different dynamical systems, homogeneous MASs have difficulties in solving the real-time load management problem with heterogeneous component models. A previous study [27] has discussed advantages and challenges of applications of heterogeneous MASs in ship power systems. In this paper, a heterogeneous MAS cooperative control method for DC zonal ship power systems is presented which optimally determines switch status or power set-point of loads while satisfying operational constraints and considering load priorities. The outline of this paper is as follows. In Section 2, a notional allelectric ship power system model is presented. In Section 3, a novel heterogeneous MAS framework is presented to achieve real-time load management for the DC zonal all-electric ship power system. A case study is presented in Section 4 to illustrate the viability and effectiveness of the novel method. A summary for this work is given in Section 5. Finally, conclusions are stated in Section 6. 2. Notional all-electric ship power system model The one-line diagram of a notional all-electric ship power system is shown in Fig. 1. The component definitions are shown

in Table 1. The ship power system includes two main turbine generators (MTGs), two auxiliary turbine generators (ATGs), two propulsion loads, one pulse load, four transformers converting lineto-line voltage from 13.8 kV to 4.16 kV, and a DC zonal system including four identical DC zones. Each DC zone includes two DC distribution buses, a starboard side bus and a port side bus. The DC distribution buses are served by PCM4 (rectifier) which converts 4.16 kV 3-ph AC voltage to 1000 V DC voltage. Each PCM4 serves only one side of a zone at one time, the starboard side bus or the port side bus. The power capacity of each PCM4 is 2 MW. Each DC distribution bus is connected to a PCM1 which converts 1000 V DC into three voltage levels to serve DC loads at the various voltage levels. PCM2s (inverter) are served by a 800 V DC-DC converter and invert the 800 V DC to 3-ph 450 V AC to serve AC loads. The parameters and detailed descriptions of the system model can be found in Ref. [28]. In DC zones, the loads are designated as vital, semi-vital, and non-vital loads. The vital loads are required to maintain the ship’s military effectiveness [29,30]. Loss of vital loads is unacceptable to the survivability of the ship. The vital loads have a normal path and an alternate path, which improves the reliability of vital loads. Semi-vital loads are important to ship’s operation and survivability but can be shed to prevent total loss of ship’s power. Non-vital loads can be immediately shed without affecting the ship’s survivability [30]. Semi-vital and non-vital loads receive only a single power feed. 3. Heterogeneous MAS cooperative control for real-time load management in DC zonal system The real-time load management is responsible for optimally determining the switch status or power set-point of individual loads using communication and local measurements to achieve dynamic generation and load balancing, which is defined as a secondary control problem [28]. A general diagram of a MAS framework for a power system is shown in Fig. 2. The power system is partitioned into a group of electrical subsystems. Each agent

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

505

Fig. 2. Diagram of a multi-agent system framework for a power system.

Fig. 3. Diagram of a notional all-electric ship power system and its DC zonal multi-agent system.

measures the local information from each subsystem and communicates with its neighbors. A decentralized controller is employed by each agent to control individual loads in each subsystem. In this section, the novel heterogeneous MAS for real-time load management in the DC zonal all-electric ship power system is presented. Converter-layer and load-layer MASs are designed to achieve real-time load management using artificial potential functions and cooperative controllers. 3.1. DC zonal MAS overview A notional all-electric ship power system is partitioned based on individual electrical components, as shown in Fig. 3. The DC

zonal multi-agent system includes one converter-layer MAS which contains 24 converter agents, and each converter agent contains one load-layer MAS which contains N load agents. The communication hub is defined to simplify the communication network structure of the DC zonal MAS. Each communication hub communicates with the converter agents served by the same DC distribution bus, and exchanges information with each other. The converterlayer MAS, as shown in Fig. 4(a), includes communication hubs, convert agents, and communication links. The converter-layer MAS manages a group of converter agents and determines the available power for each load-layer MAS. Each converter agent can exchange information with other converter agents through the communication hubs. A load-layer MAS includes a converter agent and a group

506

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

Fig. 4. Topology of converter-layer and load-layer MASs.

Fig. 5. Diagrams of simplified agent models.

Table 2 Component time constant in DC zonal system.

3.2. Dynamic agent model

Component name

Time constant (s)

DC–DC converter AC motor in DC zones DC motor in DC zones PCM2 PCM4

0.1–0.5 0.5–1.0 0.5–1.0 0.1–0.5 0.5–1.0

of N load agents, as shown in Fig. 4(b). The loads served by the same converter are managed by a load-layer MAS, which determines the power set-point or switch status of each load. In each loadlayer MAS, the load agents communicate with each other and the converter agent via communication links. Each converter or load agent makes decisions using a cooperative controller based on local measurements and communications with other load, converter or communication hubs. The time constant of each individual component in DC zones is shown in Table 2 [28]. These time constants were verified in details in Ref. [28]. In this work, the decision interval of real-time load management for the DC zonal ship power system, t, was chosen as 10 ms, which was smaller than the time constant of components in DC zones [28]. The 10 ms decision interval is essential to maintain the system stability, especially when pulse loads are integrated [28].

In this section, dynamic agent models for converter agents, constant load agents and motor load agents are introduced. The simplified diagram of the converter agent model is shown in Fig. 5(a). In the simplified model, the PI controller and nonlinear parts of the DC–DC converter were neglected. The simplified converter agent model includes an ideal DC transformer, a capacitor, an inductor, and a lump load representing the loads served by the converter. The state space equation of converter agent i is expressed in Eq. (1).



i˙ in−i (t) = [Vin−i · di2 − vC−i (t) · di ]/Li

v˙ C−i (t) = 1/(Ci di ) · iin−i (t) − 1/Ci · iout−i (t)

(1)

where, iin−i and Vin−i are the input current and voltage of converter agent i; Ci , Li , and di are capacitance, inductance and duty ratio of converter agent i; and iout−i and vC−i are the output current and voltage of converter agent i. Vin−i is the input voltage of PCM1, which is equal to the output voltage of PCM4. PCM4 is a rectifier with 1000 V DC output voltage. Thus, the input voltage of each converter agent is around 1000 V. Since the double integrator agent model can simplify the cooperative controller design, the converter agent

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

model is transformed into a double integrator system. A coordinate transformation is defined as Eq. (2). xi (t) = iin−i (t) yi (t) =

i = 1, · · ·, 24

[Vin−i · di2

(2)

− vC−i (t) · di ]/Li

where, xi and yi are state variables of the double integrator system for converter agent i. The converter agent model is transformed into Eq. (3). x˙ i (t) = yi (t)

i = 1, · · ·, 24

(3)

y˙ i (t) = −xi (t)/(Li Ci ) + [di /(Li Ci )] · iout−i (t) A new control variable is defined as Eq. (4). uC−i (t) = −xi (t)/(Li Ci ) + [di /(Li Ci )] · iout−i (t)

(4)

where, uC−i is the control variable of the double integrator system for converter agent i. This control signal uC−i will be derived in the cooperative control design. The converter-layer MAS model consisting of 24 converter agents is converted into a double integrator system as shown in Eq. (5).



˙ x(t) = y(t)

(5)

˙ y(t) = uC (t)



i˙ L−j (t) = [vinL−j − vCL−j (t)]/LL−j

v˙ CL−j (t) = [Rj iL−j (t) − vCL−j (t)]/(CL−j Rj )

j = 1, · · ·, Ni1

(6)

where, Rj , CL-j and LL-j are the equivalent resistance, capacitance and inductance of constant load agent j; vinL-j is the load input voltage; vCL-j (t) and iL-j (t) are the capacitor voltage and inductor current of constant load j; and Ni1 is the number of constant loads served by converter i. To convert the load agent model into a double integrator system, the coordinate transformation is defined as Eq. (7). zj (t) = iL−j (t) qj (t) = (vinL−j (t) − vCL−j (t))/LL−j

(7)

where, zj and qj are state variables of the double integrator system for constant load agent j. The dynamic model is shown in Eq. (8).



The control variable of the dynamic system is defined as uˆ L−j (t) = 1/Rj . The control variable determines the load demand of the constant load agent. A new control variable is defined in Eq. (9) to convert the constant load agent model into a double integrator system. uL−j (t) = −zj (t)/(LL−j CL−j ) + [vinL−j (t) − LL−j · qj (t)] · uˆ L−j (t)/(LL−j CL−j )

z˙ j (t) = qj (t) q˙ j (t) = −zj (t)/(LL−j CL−j ) + [vinL−j (t) − LL−j · qj (t)] · (1/Rj )/(LL−j CL−j )

(8)

(9)

where, uL-j is the control variable of the double integrator system for constant load agent j. This new control variable is used to control the double integrator system. The control signal will be derived in the cooperative control design. The control signal of the actual constant load agent, uˆ L−j , is derived through reverse transformation. In DC zones, motor loads include DC motors and AC motors. Motor loads are modeled using a second order linear system. The input and output of the motor model are the switch status and the actual power demand of the motor. The dynamic model of motor load agent k is shown in Eq. (10). Pd−k (s) =

Pmotor−k uˆ L−k (s) k = (Ni1 + 1), · · ·, Ni T2−k s2 + T1−k s + 1

(10)

where, T1-k and T2-k are coefficients of motor agent k; Ni is the number of all the loads served by converter i; uˆ L−k is the switch status of motor k; Pmotor-k and Pd-k are the steady state load demand and the actual load demand of motor k. The state space equation of this agent is shown in Eq. (11).



where, x(t) = [x1 (t), x2 (t), · · ·, x24 (t)]T , y(t) = [y1 (t), y2 (t), · · ·, y24 (t)]T , and uC (t) = [uC−1 (t), uC-2 (t), · · ·, uC-24 (t)]T , which is the control vector of the converter-layer MAS. The double integrator system simplifies the cooperative controller design. DC zones include variable-type loads and fixed-type loads [29]. For the variable-type loads, the loads can be served from 0 to their maximum ratings. The variable-type loads represent a lump load in a panel consisting of groups of loads, which can be on and off independently. For the fixed-type loads, the loads can be either connected or disconnected. In the DC zones, all the constant loads are variable-type loads; all the motor loads are fixed-type loads. The system consists of 24 load-layer MAS and each load-layer MAS is modelled as a double integrator system to simply the cooperative controller design. To describe the load-layer MAS, it is assumed that the i-th load-layer MAS consists of Ni1 constant load agents and Ni - Ni1 motor load agents. The diagram of a constant load agent model is shown in Fig. 5(b). The state space equation of the load agent model is expressed in Eq. (6).

507

z˙ k (t) = qk (t) q˙ k (t) = (−zk (t) − T1−k qk (t) + Pmotor−k · uˆ L−k (t))/T2−k

(11)

where, zk (t) is the actual active power demand of motor k; qk (t) is a state variable of the motor agent model. A new control variable is defined as uL-k (t) = (-zk (t) - T1-k qk (t) +Pmotor−k · uˆ L−k (t))/T2−k to convert the model into a double integrator system. This control signal for the double integrator system, uL-k , will be derived in the cooperative control design. Consequently, the control signal for the actual motor agent model, uˆ L−k , can be derived through reverse transformation. The i-th load-layer MAS model consisting of Ni load agents is expressed as Eq. (12).



˙ z(t) = q(t)

(12)

˙ = uL (t) q(t) where, T

z(t) = [z1 (t), z2 (t), · · ·, zNi (t)]T ,

q(t) = [q1 (t), q2 , (t), · · ·,

qNi (t)] and uL (t) = [uL−1 (t), uL−2 (t), · · ·, uL−Ni (t)]T , which is the control vector of the load-layer MAS. 3.3. Objective of DC zonal MAS The group goal of the DC zonal MAS is to dynamically regulate individual loads in operational real time while satisfying available power capacity constraint, motor load voltage constraints, and PCM4 capacity constraints as well as considering load priorities. The objective is achieved using the developed converter-layer and load-layer MASs. In the DC zonal MAS system, it is assumed that PCM4-1 and PCM4-2 serve the port side PCM1s and PCM4-3 and PCM4-4 serve the starboard side PCM1s. The objective of the converter-layer MAS is expressed as Eq. (13).

24

max

24

s.t.

3 i=1

i=1

i=1

(13.a)

Vin−i xi (t)

Vin−i xi (t) ≤ PTotal (t)

Vin−i xi (t) +

9 i=7

(13.b) Capacity

Vin−i xi (t) ≤ PPCM4−1

(13.c)

508

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

6 i=4

Vin−i xi (t) +

15 i=13

18 i=16

12

Vin−i xi (t) + Vin−i xi (t) +

i=10

Capacity

Vin−i xi (t) ≤ PPCM4−2

21 i=19

24 i=22

(13.d)

Capacity

Vin−i xi (t) ≤ PPCM4−3 Vin−i xi (t) ≤

Capacity PPCM4−4

x˙ i (t) = yi (t)

(13.e) EC = EAC + (13.f) (13.g)

y˙ i (t) = uC−i (t)

i = 1, · · ·, 24

(13.h)

where, t is the time variable; t is the MAS decision time step, which is chosen as 10 ms in this work; uC-i (t) is the control variable of converter agent i, which is periodically updated every t; Vin-i and xi (t) are the input voltage and current of converter agent i; PTotal is the total available power to the DC zonal system; and Capacity Capacity PPCM4−1 to PPCM4−4 are the power capacity of PCM4-1 to PCM4-4, respectively. The objective function (13.a) is to maximize the energized loads in the DC zonal system while satisfying the available power capacity constraint (13.b) and PCM4 capacity constraints (13.c)–(13.f). Eqs. (13.g) and (13.h) are the dynamic converter agent model, which are derived based on the simplified diagram of the converter model as shown in Fig. 5(a). Since uC-i (t) is the control signal of the double integrator system, the signal was transformed into the original control signal iout-i (t) to determine the available current for the i-th load-layer MAS, which is expressed as Eq. (14). iout−i (t) = [Li Ci · uC−i (t) + xi (t)]/di

The artificial potential function for the converter-layer MAS is shown in Eq. (16), which is designed based on the objective and constraints of the converter-layer MAS as shown in Eq. (13).

(14)

min K5 · s.t.

Vkmin

l=1

2

zl (t) − iout−i (t)

−

≤ Vk (t) k = (Ni1 + 1), · · ·, Ni

Ni l=1

term

E . i=1 PCM4−i

EAC = −B1 ·

i=1

(15.c)

q˙ j (t) = uL−j (t) j = 1, · · ·, Ni1

(15.d)

z˙ k (t) = qk (t)

(15.e)

q˙ k (t) = uL−k (t) k = (Ni1 + 1), · · ·, Ni

(15.f)

where, zl is the input current of load l; Wl is the weight factor of load l; iout-i (t) is the available current of the i-th load-layer MAS, as shown in Eq. (14), which is given by the converter-layer MAS; K5 is a positive constant; and Vk (t) and Vkmin are actual and minimum allowed input voltages of load l. The objective function (15.a) of the i-th load-layer MAS is to maximize the loads served by converter i and to minimize the mismatch between the available current and the actual load current while satisfying motor voltage constraints (15.b) and considering load priorities. Eqs. (15.c)–(15.f) are dynamic load agent models, which are derived based on the constant load model (6) and the motor load model (10). 3.4. Artificial potential function The artificial potential function is designed to integrate the objective and constraints into the MAS, which consists of an attractor term and a repulsor term [31]. The attractor term increases with the increase of the mismatch of the system state and the desired state, which drives the system to the desired state. The repulsor term decreases when the system state leaves constraint regions. The function reaches its minimum value when the system state reaches the desired state.

B2 ·

(Vin−i xi (t)) − PTotal (t)



24 i=1

 (Vin−i xi (t))−PTotal (t)

(17)

where, B1 and B2 are positive constants. EAC ensures that the

24

converter-layer MAS maximizes the served loads, (V x (t)), i=1 in−i i in DC zones while satisfying the available power capacity constraint. EPCM4-1 to EPCM4-4 are shown in Eq. (18), which ensures PCM4 capacity constraints satisfied; where, K1 to K4 are positive Capacity Capacity constants; and PPCM4−1 to PPCM4−4 are the power capacity of PCM41 to PCM4-4, respectively.

 EPCM4−1 =

0

if

0

EPCM4−2 =

3 i=1

[Vin−i xi (t)] +

9

Capacity

i=7

[Vin−i xi (t)] ≤ PPCM4−1

3 2 9 Capacity K · [Vin−i xi (t)] + [Vin−i xi (t)] − PPCM4−1 else i=1 i=7  1   6 12 Capacity if

i=4

[Vin−i xi (t)] +

i=10

[Vin−i xi (t)] ≤ PPCM4−1

6 2 12 Capacity K · [Vin−i xi (t)] + [Vin−i xi (t)] − PPCM4−2 else i=4 i=10  2   15 21 Capacity 0

if

i=13

[Vin−i xi (t)] +

i=19

[Vin−i xi (t)] ≤ PPCM4−3

i=22

[Vin−i xi (t)] ≤ PPCM4−4

15 2 21 Capacity K · [Vin−i xi (t)] + [Vin−i xi (t)] − PPCM4−3 else i=13 i=19  3   18 24 Capacity 0

z˙ j (t) = qj (t)

(16)

The attractor term is shown in Eq. (17).

 24

+(B1 /B2 ) · e

(15.a) (15.b)

EPCM4−i

4

EPCM4−3 =

[zl (t) · Wl ]

i=1

This function includes the attractor term EAC and the repulsor

The objective of the i-th load-layer MAS is shown in Eq. (15).

Ni

4

if

EPCM4−4 = K4 ·

18

i=16

i=16

[Vin−i xi (t)] +

24

[Vin−i xi (t)] +

i=22

Capacity

[Vin−i xi (t)] − PPCM4−4

2

else

(18)

The attractor term of the artificial potential function for the i-th load-layer MAS, as shown in Eq. (19), is monotonically decreasing with the decreased mismatch of the system state and the desired state; where, K5 is a positive constant. The attractor term is designed based on the objective function of the i-th load-layer MAS as shown in Eq. (15). ELA = K5 ·

Ni l=1

2

zl (t) − uˆ C−i (t)

−

Ni l=1

[zl (t) · Wl ]

(19)

The repulsor term of the artificial potential function for the i-th load-layer MAS, as shown in Eq. (20), is used to drive the motor bus voltage greater than the minimum allowed value; where,  k is a positive constant. The repulsor term is designed based on constraints of the load-layer MAS as shown in Eq. (15). ELrepulsor = k ELrepulsor =

Ni 

Ek k=Ni1 +1 Lrepulsor 2

k · (Vk (t) − Vkmin ) if Vk (t) < Vkmin 0

(20)

otherwise

3.5. MAS cooperative control The cooperative controller for the converter-layer MAS is shown as Eq. (21); where, k1 is a positive constant; yref is the reference signal, which is 0; L1 is a graph Laplacian. This cooperative controller is derived based on the artificial potential function as shown in Eq. (16). The control signal should be transformed into the original

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

509

Fig. 6. Diagram of a simplified notional 2-zone all-electric ship power system model for case studies.

control signal to determine the available current for each load-layer MAS using Eq. (14).

uL-j (t) is the jth element of the cooperative control vector, uL , as shown in Eq. (23).

uC (t) = −∂EC /∂x(t) − L1 y(t) − k1 (y(t) − y ref )

uˆ L−j (t) =

(21)

The graph Laplacian is determined based on the topology of the converter-layer MAS. The topology of the converter-layer MAS is a complete graph since each converter agent can communicate with the others in the group. The graph Laplacian [32] is defined as L = D - A; where, A and D are adjacency and diagonal matrices of the graph. The adjacency matrix [32] is defined as A = [aij ] ∈ Rn×n ; where, aij = 1, if j ∈ Nbi ; aij = 0, otherwise. Nbi is the set of neighbor agents of agent i, and n is the total agent number. The degree matrix [32] of the graph is defined as Eq. (22).

⎛ D = diag ⎝

 j ∈ Nb1

a1j , · · ·,



⎞ anj ⎠

(22)

j ∈ Nbn

∂ELrepulsor ∂ELA + − L 2 q(t) − k2 (q(t) − qref ) ∂z(t) ∂V(t)

vinL−j (t) − LL−j · qj (t)

j = 1, · · ·, Ni1

(24)

The cooperative controller for each original motor agent model is shown in Eq. (25); where, uL-k (ti ) is the kth element of the cooperative control vector uL , as shown in Eq. (23). uˆ L−k (t) = (T1−k · qk (t) + T2−k · uL−k (t) +zk (t))/Pmotor−k

k = (Ni1 + 1), · · ·, Ni

(25)

The motor can either be connected or disconnected. If uˆ L−k (t) is greater than 90% of the load demand, motor k is connected; if uˆ L−k (t) is less than 10% of the load demand, the motor is disconnected; otherwise, the switch status is not changed. 4. Simulation results

The cooperative controller for the i-th load-layer MAS is shown as Eq. (23); where, k2 is a positive constant; qref is the reference signal, which is 0; and V(t) is the voltage vector of the i-th loadlayer MAS, which is shown as V(t) = [V1 (t), V2 (t), · · ·, VNi (t)]T . The controller is derived based on the artificial potential functions as shown in Eqs. (19) and (20). uL (t) = −

(LL−j CL−j ) · uL−j (t) + zj (t)

(23)

The topology of the load-layer MAS is a complete graph, which determines the graph Laplacian L2 . Since uL (t) is the control vector for the double integrator MAS model, the control signal should be transformed into the original control signal to control each individual load. For constant load agent j, the cooperative controller uˆ L−j is shown in Eq. (24); where

In the simulation study, a 2-zone notional all-electric ship power system, as shown in Fig. 6, was used to illustrate the dynamic behavior of the novel MAS framework. The all-electric ship power system model and the DC zonal MAS framework were both implemented in PSCAD. The parameters of the ship power system model can be found in Ref. [28]. The diagram of the simulation environment is shown in Fig. 7. The simulation step size of the ship power system, , was chosen as 12 ␮s. The MAS measured system states and controlled the switch status or power set-point of loads in real time. The decision and measurement time steps of MAS, t, were chosen as 10 ms. For the studies, it was assumed that the ATG generator was in service, and the MTG generator was out of service. Thus, the total generation capacity was 4 MW. It was also assumed that the propulsion load was out of service and a pulse load was served in the

510

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

Fig. 7. MAS and all-electric ship power system model simulation diagram.

Fig. 9. Pulse load demand.

Table 5 Switch status of some loads in DC zone 2. Fig. 8. Diagram of the pulse load charging circuit model [21]. Table 3 Parameters of converter agents. Parameters

L (mH)

C (␮F)

d

375 V DC converter 650 V DC converter 800 V DC converter

234 228 160

100 100 100

0.375 0.65 0.8

Table 4 Parameters of motor agents. Component name

Kd

T1

T2

DC motor 1 DC motor 2 DC motor 3 DC motor 4 DC motor 5 DC motor 6 AC motor 1 AC motor 2 AC motor 3 AC motor 4

1 1 1 1 1 1 1 1 1 1

0.2203 0.3289 0.3648 0.2203 0.3648 0.3123 0.1789 0.2763 0.3394 0.3

0.01 0.01 0.01 0.01 0.01 0.01 0.002 0.0116 0.0105 0.02

MVAC system at certain times of the simulation. Since the focus of this work was to study the impact of the pulse load charging circuit on the power quality of the ship power systems, we only modeled the charging circuit of the pulse load and neglected the discharging process of the pulse load. The pulse load was modeled using a pulse charging circuit [33], as shown in Fig. 8. A rectifier was used to convert AC voltage into DC voltage to supply power to the pulse load, which was modeled as a resistor. When the pulse charging circuit was in charge, it produced a pulse in the power system. A small value was chosen for the resistor in the charging circuit to emulate the charging process of the pulse load; in contrast, a very large value was chosen for the resistor to emulate the disconnection of the charging circuit from the power system. The inductor LP and capacitor CP in the charging circuit were chosen as 1 mH and 10 mF, respectively. The system also includes two identical DC zones. The two DC zones totally served 44 loads with various priorities and power ratings. The parameters of converter agent models and motor agent models are shown in Tables 3 and 4. The equivalent inductance and capacitance of each constant load agent were chosen as 0.005 H and 0.0002 F, respectively. The parameters of cooperative controllers are chosen as k1 = 10, k2 = 100, K1 = K2 = 7000, K5 = 105 , B1 = 300, B2 = 10, Wvital = 108 , Capacity Capacity Wsemi-vital = 107 , Wnon-vital = 1,  k = 100, PPCM4−1 = PPCM4−2 = 2MW;

Component name

Rating

Switch closed

Switch open

DC motor 1 DC motor 4 AC motor 3 Constant load 4 Constant load 10

36 kW 36 kW 192.6 kW 70 kW 85 kW

4–9 s 5–11 s 3–10 s 2–7 s 1–8 s

0–4 s; 9–12 s 0–5 s; 11–12 s 0–3 s; 10–12 s 0–2 s; 7–12 s 0–1 s; 8–12 s

where, Wvital , Wsemi-vital , and Wnon-vital are weight factors for vital, semi-vital, and non-vital loads. The cooperative controller coefficients k1 and k2 are used to control the dynamic response of the multi-agent system to minimize the value of the artificial potential function. The larger the coefficient, the faster the converge speed of the multi-agent system. However, the higher value of the coefficients may cause overshot of the controlled signals. Thus, there is a trade-off to determine appropriate control system coefficients. The coefficients are selected through sensitivity studies in the numerical simulation. The minimum allowed input voltage for each motor was chosen as 95% of the nominal voltage. Each fixed-type load was either connected or disconnected; each variable-type load was quantized based on 10 A current rating. In this section, a typical case study is used to illustrate the dynamic behavior of the DC zonal MAS. The dynamic performance of the developed MAS method is also compared with a conventional under-frequency load shedding method. The performance analysis is conducted to verify the performance and viability of the developed MAS method. 4.1. Case study In the case study, both pulse load demand and individual load demand in DC zones were varied to study the dynamic behavior of the proposed method. The pulse load had a 5 s pulse width and 0.8 MW magnitude. The ramp rate of the pulse load was 10 MW/s. The pulse load was served from 3 to 8 s, as shown in Fig. 9. In DC zone 2, the switch status of five loads was changed to vary the total load demand in the DC zonal system, as shown in Table 5. The DC zonal system available power and total load demand are shown in Fig. 10. At t = 3 s, the available power to the DC zonal system was decreased due to the connection of the pulse load; the total load demand of the DC zonal system was also decreased immediately to track the available power signal to satisfy the available power capacity constraint. At t = 8 s, the available power to the DC zonal system was increased due to the disconnection of the pulse load. The total load demand in the DC zonal system was increased slowly to track the available power signal, since the load demand of AC and DC motor loads was increased gradually when these loads were served. When the pulse load was not served, the avail-

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

Fig. 10. Total load demand and available power of the DC zonal system.

511

Fig. 13. Output voltages of port side PCM1 in DC zone 1.

Fig. 14. Power demand of some loads on port side of DC zone 1. Fig. 11. Input power of PCM4-1 and PCM4-2 in the DC zonal system.

Fig. 15. Dynamic behavior of the artificial potential function for the MAS. Fig. 12. Frequency behavior of the ATG generator.

able power was greater than the total load demand. All the loads served by PCM4-1 reached their maximum power ratings and the input power to PCM4-2 reached the power capacity of PCM4, as shown in Fig. 11, so the total load demand in the DC zonal system already reached the maximum allowed power. The total load demand changes happened at 2 and 7 s, as shown in Fig. 10, caused by load changes in DC zone 2. At t = 2 s, constant load 4 in DC zone 2 was connected to the system, which caused the total load demand oscillations. The frequency behavior of ATG generator is shown in Fig. 12. The frequency oscillations were caused by sudden load changes in the system. The maximum frequency deviation was 0.9 Hz, which was less than the steady state frequency tolerance (3% of the nominal value) as given in IEEE-STD-45 [34]. The agent control signal is not derived based on this frequency limit, but this frequency deviation tolerance is used as a reference to show the performance of the control system. The output voltages of DC–DC converters of port side PCM1 in DC zone 1 are shown in Fig. 13. Since output voltages

of DC–DC converters were controlled by local voltage regulators, the voltages were well maintained at nominal values. Small voltage variations existed when load changes happened. The motor input voltage constraints were satisfied in operational real time, since the voltage decrease was much less than 5% of the nominal value. The power demand of some individual loads on port side of DC zone 1 is shown in Fig. 14. At t = 2 s, some non-vital loads were interrupted or disconnected to compensate the load change in DC zone 2. At t = 3 s, the pulse load was connected to the system and the load demand of non-vital loads was immediately reduced to 0 to make available power capacity constraint satisfied. Constant load 9, a semi-vital load, was disturbed when the pulse load was energized. After the pulse load was disconnected from the system, all the loads were served at their maximum power. The dynamic behavior of the artificial potential function is shown in Fig. 15. The value of the artificial potential function was gradually reduced after system disturbances happened at 3 s, which indicated that the system state could gradually converge to a new desired state using the MAS cooperative controller.

512

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514 Table 7 Summary of the frequency behavior of ATG — Scenario I. Case no.

Max freq. deviation (Hz) pulse load connection

Max freq. deviation (Hz) pulse load disconnection

1 2 3 4

0.85 0.70 0.80 0.60

0.35 0.30 0.70 0.75

Table 8 Summary of pulse loads — Scenario II.

Fig. 16. Frequency behavior of the ATG generator with UFLS and without load management. Table 6 Summary of pulse loads — Scenario I. Case no.

Pulse magnitude (MW)

Pulse width (s)

Ramp rate (MW/s)

1 2 3 4

1.2 1.2 1.2 1.2

5 5 5 5

1 2 5 10

An under-frequency load shedding (UFLS) method was implemented to compare with the developed MAS method. When the system frequency drops to 59.4 Hz, 10% of loads (0.4 MW) are disconnected; when the frequency drops to 58.8 Hz, UFLS algorithm sheds another 10% of loads (0.4 MW). Since the pulse load was served from 3 to 8 s, the frequency started to decline from 3 s and the UFLS algorithm totally shed 20% of loads before the frequency was restored, as shown in Fig. 16. At 8 s, the pulse load was disconnected and a frequency overshoot happened due to the sudden load decrease. The maximum frequency deviation was 1.8 Hz. A restoration algorithm was needed to restore the disconnected loads gradually, which might take longer time to reenergize the disconnected loads. Thus, the developed MAS method had advantages over the UFLS method due to the improved dynamic performance and the reduced load interruption time. The dynamic behavior of the system frequency without load management was also simulated, as shown in Fig. 16. When the pulse load was connected, the frequency declined quickly, which would cause a blackout in a few seconds. 4.2. Performance analysis In the performance analysis, two scenarios were designed to evaluate the dynamic performance of the DC zonal MAS. In Scenario I, four cases were used to study the impact of the ramp rate of the pulse load on the dynamic performance of the DC zone multi-agent system. In each case, the pulse load had the same power magnitude, but had different ramp rates. In Scenario II, five cases were used to study the impact of the magnitude of the pulse load on the dynamic performance of the DC zonal multi-agent system. In each case, the pulse load had the same ramp rate, but had different power magnitudes. 4.2.1. DC zone multi-agent system — Scenario I It was assumed that the pulse load was served from 3 to 8 s with a 1.2 MW magnitude. The ramp rate of the pulse load was chosen as 1, 2, 5, and 10 MW/s. The definitions of pulse loads in DC zonal multi-agent system — Scenario I are summarized in Table 6. The dynamic performance of the ATG generator frequency for pulse loads with different ramp rates was evaluated. The results are summarized in Table 7. The results indicated that the magnitude of

Case no.

Pulse magnitude (MW)

Pulse width (s)

Ramp rate (MW/s)

1 2 3 4 5

0.4 0.6 0.8 1.0 1.2

5 5 5 5 5

10 10 10 10 10

Table 9 Summary of the frequency behavior of ATG — Scenario II. Case no.

Max freq. deviation (Hz) — pulse load connection

Max freq. deviation (Hz) — pulse load disconnection

1 2 3 4 5

0.91 0.81 0.71 0.64 0.60

0.25 0.36 0.49 0.85 0.75

the ATG generator frequency deviation in each case was much less than the maximum allowed frequency deviation in steady state (3% of the nominal value). Thus, the dynamic behaviors of the ATG generator frequency in cases 1–4 satisfied the frequency requirements in IEEE-STD-45. When the pulse load was connected, the maximum frequency deviation was almost the same in each case; when the pulse load was disconnected, the maximum frequency deviations in cases 1 and 2 were smaller than the values in cases 3 and 4. 4.2.2. DC zone multi-agent system — Scenario II It was assumed that the pulse load was served from 3 to 8 s and the ramp rate of the pulse load was 10 MW/s in each case. The pulse magnitude was chosen as 0.4, 0.6, 0.8, 1.0, and 1.2 MW. The definitions of pulse loads in Scenario II are summarized in Table 8. The results are summarized in Table 9. The results indicated that the magnitude of the ATG frequency deviation in each case was much less than the maximum allowed frequency deviation. Thus, the dynamic behavior of the ATG generator frequency in cases 1–5 satisfied the frequency requirements in IEEE-STD-45. When the pulse load was connected, the maximum frequency deviation was almost the same in each case; when the pulse load was disconnected, the maximum frequency deviation was increased with the increase of the magnitude of the pulse load. If there is no real-time load management implemented in the simulation, the maximum frequency deviation will increase as the increase of pulse load rate of change or the pulse power magnitude. With the real-time load management, this trend doesn’t exist since the loads in DC zones could be interrupted as required. If a supply and demand mismatch is detected, the multi-agent system controller would quickly response to balance the supply and demand in operational real time. 5. Summary The developed real-time load management method is the first use of the heterogeneous MAS cooperative control method in the

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

power system area. The MAS cooperative control approach has been widely used in control community to solve problems including vehicle formation and multi-robotic coordination. In these applications, there is no physical coupling between agents such as robots or vehicles. The agents are only coupled through communication links. However, the power system is a tightly coupled cyber-physical energy system. The physical components are tightly coupled with each other. For example, generators and loads are coupled by cables or other electrical components. Due to the physical couplings in the power system, the conventional cooperative control developed for multi-robotic and multi-vehicle applications could not be directly used for the power system control. In this work, the power system is partitioned into different electrical subsystems based on the network topology and the cooperative controller is designed to achieve the group objectives while considering the impact of physical couplings. To achieve real-time load management using the MAS cooperative controller, a 2-zonal notional all-electric ship power system was partitioned based on individual electrical components such as converters and loads. Detail load and system dynamics as well as various operational constraints were integrated into the MAS. Comparing with the previously developed homogeneous MAS for real-time load management [11], the proposed heterogeneous MAS had more flexibility to include various kinds of agents with different dynamic models and various operational constraints. The developed application is equivalent to the power system dynamic balancing, which is classified as a secondary control in the isolated power system operation [28,35,36]. For the studies, the dynamic behavior of the developed MAS method was improved since more load and system dynamics were considered in the MAS design. Comparing the performance of our new real-time load management method with a conventional under frequency load shedding method, the developed MAS method achieved better dynamic performance and reduced the load interruption time. 6. Conclusion In this paper, a novel heterogeneous MAS-based real-time load management method was developed for all-electric ship power systems to balance the generation and load in real time while satisfying operational constraints and considering load priorities. The MAS framework integrates various electrical elements with different dynamic models using artificial potential functions, which coordinates various electrical elements in the power system to achieve group goals and improves the dynamic behavior of the system. Simulation results indicated that the generation and load were dynamically balanced in operational real time while satisfying PCM4 capacity constraints and motor voltage constraints. Moreover, higher priority loads were served before lower priority loads. Further, the multi-agent system-based cooperative controller successfully solved the hybrid problems with continuous and binary control variables. The simulation results indicated that the developed MAS method achieved better performance than a conventional under frequency load shedding method. The MAS method can also be used in other isolated power systems, such as microgrids and industrial facilities, to improve the system stability. Acknowledgement This work was performed at Texas A&M University and supported in part by the Office of Naval Research under Grant N00014-09-1-0579. References [1] S. Sudhoff, Currents of change, IEEE Power Energy Mag. 9 (July/August (4)) (2011) 30–37.

513

[2] N. Doerry, Naval power systems: integrated power systems for the continuity of the electrical power supply, IEEE Electr. Mag. 3 (June (2)) (2015) 12–21. [3] J.M. Crider, S.D. Sudhoff, Reducing impact of pulsed power loads on microgrid power systems, IEEE Trans. Smart Grid 1 (December (3)) (2010) 270–277. [4] N. Doerry, J. Amy, DC voltage interface standards for naval applications, in: Proc. IEEE Electric Ship Technologies Symposium, Alexandria, VA, June, 2015, pp. 318–325. [5] A. Safdarian, M. Fotuhi-Firuzabad, M. Lehtonen, Optimal residential load management in smart grids: a decentralized framework, IEEE Trans. Smart Grid 7 (July (4)) (2016) 1836–1845. [6] S.A. Saleh, P. Pijnenburg, E. Castillo-Guerra, Load aggregation from generation-follows-load to load-follows-generation: residential loads, IEEE Trans. Ind. Appl. 53 (March/April (2)) (2017) 833–842. [7] S.A. Arefifar, M. Ordonez, Y.A.I. Mohamed, Energy management in multi-microgrid systems – development and assessment, IEEE Trans. Power Syst. 32 (March (2)) (2017) 910–922. [8] Y.-Y. Hsu, C.-C. Su, Dispatch of direct load control using dynamic programming, IEEE Trans. Power Syst. 6 (August (3)) (1991) 1056–1061. [9] L. Yao, W.C. Chang, R.L. Yen, An iterative deepening genetic algorithm for scheduling of direct load control, IEEE Trans. Power Syst. 20 (August (3)) (2005) 1414–1421. [10] X. Feng, T. Zourntos, K.L. Butler-Purry, S. Mashayekh, Dynamic load management for NG IPS ships, in: Proc. 2010 IEEE/PES General Meeting, Minneapolis, MN, July, 2010, pp. 4760–4767. [11] X. Feng, K.L. Butler-Purry, T. Zourntos, Multi-agent system-based real-time load management for all-electric ship power systems in DC zone level, IEEE Trans. Power Syst. 27 (November (4)) (2012) 1719–1728. [12] V. Gazi, B. Fidan, Coordination and control of multi-agent dynamic systems: models and approaches Swarm Robotics, vol. 4433, Springer-Verlag, Berlin, Germany, 2007, pp. 71–102. [13] W.K. Potts, The chorus-line hypothesis of manoeuvre coordination in avian flocks, Nature 309 (May) (1984) 344–345. [14] J.A. Fax, R.M. Murray, Information flow and cooperative control of vehicle formations, IEEE Trans. Automat. Contr. 49 (September (9)) (2004) 1465–1476. [15] R. Fierro, P. Song, A.K. Das, V. Kumar, Cooperative control of robot formations, in: Cooperative Control and Optimization, Kluwer, The Netherlands, 2002, pp. 73–93. [16] S.D.J. McArthur, E.M. Davidson, V.M. Catterson, A.L. Dimeas, N.D. Hatziargyriou, F. Ponci, T. Funabashi, Multi-agent systems for power engineering applications—part I: concepts, approaches, and technical challenges, IEEE Trans. Power Syst. 22 (November (4)) (2007) 1743–1752. [17] W.-S. Im, C. Wang, L. Tan, W. Liu, L. Liu, Cooperative controls for pulsed power load accommodation in a shipboard power system, IEEE Trans. Power Syst. 31 (November (6)) (2016) 5181–5189. [18] W. Zhang, Y. Xu, W. Liu, C. Zang, H. Yu, Distributed online optimal energy management for smart grids, IEEE Trans. Ind. Inform. 11 (June (3)) (2015) 717–727. [19] Z. Zhang, M.-Y. Chow, Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid, IEEE Trans. Power Syst. 27 (November (4)) (2012) 1761–1768. [20] N. Rahbari-Asr, Y. Zhang, M.-Y. Chow, Consensus-based distributed scheduling for cooperative operation of distributed energy resources and storage devices in smart grids, IET Gener. Trans. Distrib. 10 (April (5)) (2016) 1268–1277. [21] S. Kar, G. Hug, J. Mohammadi, J.M.F. Moura, Distributed state estimation and energy management in smart grids: a consensus + innovations approach, IEEE J. Selected Topics Signal Process. 8 (October (6)) (2014) 1022–1038. [22] A. Mehrizi-Sani, R. Iravani, Potential-function based control of a microgrid in islanded and grid-connected modes, IEEE Trans. Power Syst. 25 (November (4)) (2010) 1883–1891. [23] X. Chen, Y. Hou, S.Y.R. Hui, Distributed control of multiple electric springs for voltage control in microgrid, IEEE Trans. Smart Grid 8 (May (3)) (2017) 1350–1359. [24] H. Ni, G.T. Heydt, L. Mili, Power system stability agents using robust wide area control, IEEE Trans. Power Syst. 17 (November (4)) (2002) 1123–1131. [25] T. Nagata, H. Sasaki, A multi-agent approach to power system restoration, IEEE Trans. Power Syst. 17 (May (2)) (2002) 457–462. [26] S. Su, K.K. Li, W.L. Chan, X. Zeng, X. Duan, Agent-based self-healing protection system, IEEE Trans. Power Deliv. 21 (April (2)) (2006) 610–618. [27] X. Feng, K.L. Butler-Purry, T. Zourntos, Analysis of various partitioning strategies for multi-agent system-based real-time load management for NG IPS ships, in: Proc. IEEE Electric Ship Technologies Symposium, Alexandria, VA, April, 2011, pp. 173–180. [28] X. Feng, A bio-inspired multi-agent system framework for real-time load management in all-electric ship power systems, Ph.D. dissertation, Dept. Elect. Eng., Texas A&M Univ., College Station, TX, 2012. [29] K.L. Butler-Purry, N.D.R. Sarma, I.V. Hicks, Service restoration in naval shipboard power systems, IEE Proc. Gener. Transm. Distrib. 151 (January (1)) (2004) 95–102. [30] NAVSEA Design Practice and Criteria Manual for Electrical Systems for Surface Ships, Naval Sea Systems Command, Engineering Directorate, Electrical Engineering Group, 1992, ch. 300. [31] N.E. Leonard, E. Fiorelli, Virtual leaders, artificial potentials and coordinated control of groups, in: Proc. IEEE Conference on Decision and Control, Orlando, Florida, Dec, 2001, pp. 2968–2973.

514

X. Feng et al. / Electric Power Systems Research 154 (2018) 503–514

[32] R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and Cooperation in Networked Multi-Agent Systems, Proc. IEEE 95 (January (1)) (2007) 215–233. [33] M. Steurer, M. Andrus, J. Langston, L. Qi, S. Suryanarayanan, S. Woodruff, P.F. Ribeiro, Investigating the impact of pulsed power charging demands on shipboard power quality, in: Proc. IEEE Electric Ship Technologies Symposium, Arlington, VA, May, 2007, pp. 315–321. [34] IEEE Recommended Practice for Electrical Installations on Shipboard, IEEE Std 45TM -2002, The Institute of Electrical and Electronics Engineers, Inc., New York, NY, 2002.

[35] X. Feng, Dynamic balancing for low inertia power systems, in: Proc. 2013 IEEE/PES General Meeting, Vancouver, Canada, July, 2013, pp. 1889–1893. [36] R.E. Hebner, F.M. Uriarte, A. Kwasinski, A.L. Gattozzi, H. Estes, A. Anwar, P. Cairoli, R.A. Dougal, X. Feng, H.-M. Chou, L. Thomas, M. Pipattanasomporn, S. Rahman, F. Katiraei, M. Steurer, M.O. Faruque, M.A. Rios, G.A. Ramos, M.J. Mousavi, T.J. Mccoy, Technical cross-fertilization between terrestrial microgrids and ship power systems, J. Mod. Power Syst. Clean Energy 4 (April (2)) (2016) 161–179.