1

**Abstract****–A simplified notional Next Generation Integrated **
**Shipboard Power System (NG IPS) model is introduced. Based **
**on the simplified system model, dynamic load management **
**method is presented considering equality and inequality **
**constraints of the system. The problem is formulated as a **
**dynamic optimization problem to maximize the energized loads **
**in the system without violating any constraint of the system. A **
**simplified NG IPS model is simulated in PSCAD, and three **
**scenarios are presented to illustrate the dynamic load **
**management method. The simulation results indicate that the **
**dynamic performance of the shipboard power system model with **
**load management is much better than its performance without **
**load management. **

**Index Terms****–Constant Load, Dynamic Load Management, **
**Propulsion Load, PSCAD, Pulse Load, Shipboard Power System **

I. INTRODUCTION

N navy shipboard power systems, battle damage or sudden increase in load demand, such as pulse load and other weapon loads, can easily overload the generators. Moreover, shipboard power systems have less generation capacity and rotational inertia relative to system load [1] and include large portion of dynamic loads and nonlinear loads relative to power generation capacity [2]. Therefore, it is necessary to balance the load demand and generation power of the system in real time. Otherwise the system cannot operate normally, or it even causes some devastating impact on the ship’s survivability. Therefore, an effective dynamic load management technique needs to be developed to match the load demand and generation power of the shipboard power system in real-time without violating operating constraints of the system.

Load management was firstly introduced in 1970s and aimed to control and modify the patterns of demands of various consumers of a power utility, which reduced the operating cost and maintained the reliability of the electric power network. Load management can be categorized into direct load control (DLC), indirect load control, and local energy storage. DLC mainly focuses on shedding load directly to satisfy certain objectives; indirect load control allows customers control their loads independently according to the price signal sent by the utilities; local energy storage allows both utilities and customers store energy in off-peak periods and use the stored energy during times of great demand.

This work was supported by Office of Naval Research under Grant N00014-09-1-0579.

X. Feng, T. Zourntos, K. L. Butler-Purry, and S. Mashayekh are with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77840 USA (e-mail: fxy8410@neo.tamu.edu, takis@neo.tamu.edu, klbutler@ece.tamu.edu, s.mashayekh@gmail.com).

time load management mainly focuses on matching the generation power and the consumed loads in real-time while achieving certain objectives, such as reducing operating cost [3], maximizing the profit margin [4], reducing peak load [3],

*etc*. Since the control status and load profile of the power
system can be accessed by the control center almost
instantaneously, real-time load management techniques can be
developed to optimally coordinate the most suitable customers
for the direct load control [5].

Even though load management has been developed for more than 30 years, the techniques are mainly applied to solve the load control problem in terrestrial power systems. Since shipboard power systems have much faster transients, it is necessary to take the dynamic characteristics of the system into consideration. Fortunately, concepts of real-time direct load control can be extended to shipboard power systems through including the system dynamics. If there is not enough generated power to serve all the loads in the system, only higher priority loads are energized and some non-vital loads are shed to avoid the generator overloading. The dynamic load management can be formulated as an optimization problem considering different load priorities. The objective of dynamic load management is to maximize the energized loads in shipboard power systems in real-time without violating system operating constraints.

In this paper, a simplified notional shipboard power system model is introduced. The simplified NG IPS model includes generators, transformers, propulsion load, pulse load, and two zones. In each zone, different priority loads are considered. A new dynamic load management method is presented, which aims to maximize the energized load subject to system constraints. Three case studies are presented to illustrate the dynamic performance of the dynamic load management. The simulation results using dynamic load management are compared to show the advantages of the load management approach.

This paper is organized as follows: section II discusses the simplified notional shipboard power system model. Section III presents the dynamic load management method. Three case studies are presented in section IV. The summary is given in section V. The conclusions and future work are given in section VI.

II. NOTIONAL SHIPBOARD POWER SYSTEM MODEL A simplified notional shipboard power system was modeled to illustrate the proposed dynamic load management method and study the dynamic performance of the system. The simplified notional shipboard power system includes one main turbine generator (MTG), one auxiliary turbine generator

### Dynamic Load Management for NG IPS Ships

Xianyong Feng, *Student Member, IEEE*, Takis Zourntos, *Senior Member, IEEE*, Karen L.
Butler-Purry, *Senior Member, IEEE*, and Salman Mashayekh, *Student Member, IEEE*

2

(ATG), two 13.8/4.16 kV transformers, one propulsion load, one pulse load, and two zones. The system also includes different kinds of power electronic components, such as DC-DC converters, inverters, and rectifiers. In the simplified system, the influence of cables is not significant, so the cable model is neglected.

The simplified notional shipboard power system diagram is shown in Fig. 1. The components’ definition is shown in Table I. The two transformers convert line-to-line voltage from 13.8 kV to 4.16 kV. Each zone has two DC distribution buses, a starboard side bus and a port side bus. The DC distribution buses on the same side are served by the same PCM4, which converts 4.16 kV 3-ph AC voltage to 1000 V DC voltage. PCM4 cannot serve starboard side bus and port side bus at the same time. The PCM4-1 is serving the DC distribution buses on port side. The PCM4-2 is serving the DC distribution buses on starboard side. And the capacity of each PCM4 is 2 MW. Each DC distribution bus is connected to a PCM1, which converts the 1000 V DC voltage into three voltage levels, 375 V DC, 650 V DC, and 800 V DC. PCM2 is connected to 800 V DC and inverts the 800 V DC to 3-ph 460V AC to serve AC loads.

In each zone, different kinds of loads are served by the DC
distribution buses. These loads may have different voltage
levels, different power levels, *etc*. In this simplified notional
shipboard power system, all the DC loads in zones are
constant resistance loads, and all the AC loads are constant
power loads. In order to illustrate the dynamic load
management method, load priorities need to be decided.
Assume that *LDC*_{12} and *LDC*22are vital loads; *LDC*11, *LDC*21,

13

*AC*

*L* , and *LAC*_{23} are semi-vital loads; *LDC*14 and *LDC*24 are

non-vital loads. The load priority information is shown in Table II. The weight-factor of each load is chosen based on load priority definition in load management method.

III. DYNAMIC LOAD MANAGEMENT METHOD

The objective of dynamic load management is to serve as many loads as possible considering priorities subject to the constraints of system. If the available generation power is decreased, the system may not serve the same amount of loads

TABLEI COMPONENT DEFINITIONS

No. Component Name Component Description 1 MTG 3 ph, 13.8 kV, 36 MW generator 2 ATG 3 ph, 13.8 kV, 4 MW generator 3 Transformer 1 3 ph, Δ-Δ connected, 13.8/4.16 kV 4 Transformer 2 3 ph, Δ-Δ connected, 13.8/4.16 kV 5 Pulse Load 12 MW, 0.3 s pulse width, 4.16 kV, AC 6 Propulsion Load 36.5 MW (rating), 4.16 kV, AC 7 Load ܮభభ 0.4 MW, 0.375 kV DC 8 Load ܮభమ 0.95 MW, 0.65 kV DC 9 Load ܮభయ 0.5 MW, 0.46 kV AC 10 Load ܮభర 0.2 MW, 0.375kV DC 11 Load ܮమభ 0.4 MW, 0.375 kV DC 12 Load ܮమమ 0.95 MW, 0.65 kV DC 13 Load ܮమయ 0.5 MW, 0.46 kV AC 14 Load ܮమర 0.2 MW, 0.375kV DC TABLEII LOAD PRIORITY

Load Weight Factor Load Type Load ܮభభ 1.5 Semi-vital Load ܮభమ 1.7 Vital Load ܮభయ 1.4 Semi-vital Load ܮభర 1.0 Non-vital Load ܮమభ 1.5 Semi-vital Load ܮమమ 1.7 Vital Load ܮమయ 1.4 Semi-vital Load ܮమర 1.0 Non-vital as before. In this case, load management needs to shed some non-vital loads in the system to make the system operate normally without violating operating constraints of the system. However, that load shedding is the last resort in dynamic load management. In order to formulate dynamic load management, dynamic characteristics of the system should be taken into consideration.

The dynamic load management problem can be formulated as an optimization problem. In normal state, the objective of load management is to maximize capacity of the energized loads. Through controlling the status of load switches, the loads will be matched with the power generation in real-time and the power system should operate within the system operating constraints at the same time.

11
*DC*
*L* *LDC*12 *LAC*13 *LDC*_{21} *LDC*22 *LAC*23
14
*DC*
*L* *LDC*_{24}

3

*A. Objective Function *

The objective function of dynamic load management can be expressed as follows:

### ∑

∈*L*⋅ ⋅

*k*

*k*

*k*

*k*

*W*

*t*

*y*

*t*

*P*() () max (1) where

*L*is the load set in the power system,

*yk*(

*t*) is the

switching function, which has a value of 0 or 1 (*y _{k}*(

*t*)=1: load

*P*is connected to the power system at time

_{k}*t*,

*y*(

_{k}*t*)=0: load

*P*is not connected to the system at time

_{k}*t*),

*W*is the weight-factor of load

_{k}*k*, and

*P*(

_{k}*t*) is the consumed power by load

*k*, and can be determined using (8).

In order to serve as many higher priority loads as possible,
loads are categorized as vital, semi-vital and non-vital loads.
In shipboard power systems, vital loads include combat
systems, mobility systems, fire systems, navigation system,
communication system, *etc*. Non-vital loads are those that can
be shed during an electrical casualty [6]. A technique was
developed in earlier work for determining weight factor of
shipboard power system loads [6], [7] as shown in (2)-(4).

For vital load: 1

max
max
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ _{+}
=
*k*
*Semi*
*Non*
*k* _{P}*P*
*P*
*W*
(2)
For semi-vital load: 1

max
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
*k*
*Non*
*k* _{P}*P*
*W*
(3)
For non-vital load: *Wk* =1_{ (4)}
where *W _{k}* is weight-factor of load

*k*,

*PSemi*max is equal to the maximum value of the largest semi-vital load, and

*PNon*max is equal to the maximum value of the largest non-vital load in the system. The contribution (

*T*) of each vital load

_{i}*i*in the objective function is given by [6]:

*i*
*Semi*
*Non*
*i*
*Semi*
*Non*
*i*
*i*
*i*
*i* _{P}*P* *P* *P*
*P*
*P*
*P*
*W*
*P*
*T* = + +
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ _{+}
⋅
=
⋅

= max max _{1} max max _{ (5) }

The contribution (*Tj* ) of each semi-vital load *j* in the
objective function is given by:

*j*
*Non*
*j*
*Non*
*j*
*j*
*j*
*j* _{P}*P* *P*
*P*
*P*
*W*
*P*
*T* = +
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
=
⋅
= max _{1} max
(6)
The contribution (*T _{k}*) of each non-vital load

*k*in the objective function is given by:

*k*
*k*
*k*
*k*
*k* *P* *W* *P* *P*
*T* = ⋅ = ⋅1= _{ (7) }

The total contribution of the vital load *k* in the objective
function is elevated by *PNon*max+*PSemi*max. As *PNon*max and *PSemi*max are
the values of the largest semi-vital and non-vital load
respectively, it can be seen that the contribution of each vital
load will be greater than the contribution of each semi-vital or
non-vital load. Therefore, all vital loads will be served before
the semi-vital and non-vital loads. For the same reason, all
semi-vital loads will be served before the non-vital loads.

*B. Load Model *

In this formulation, only constant resistance loads and constant power loads are considered. The constant resistance load model is expressed as follows:

### (

### )

*k*

*k*

*k*

*R*

*t*

*V*

*t*

*P*2 ) ( ) ( = (8) where

*R*is the resistance of the load

_{k}*k*,

*V*(

_{k}*t*) is the load voltage at time

*t*, and

*Pk*(

*t*) is the power consumed by the

load. In the work reported in this paper, all DC loads are constant resistance loads, and all AC loads are constant power loads.

*C. Equality Constraints *

The solution of dynamic load management should satisfy the system dynamic equations, which are represented by Differential-Algebraic Equations (DAEs) [1], [8] shown as follows:

### (

### )

### (

**x**

**u**

**y**### )

**g**

**y**

**u**

**x**

**f***), ( ), ( 0 ), ( ), (*

**x***t*

*t*

*t*

*t*= = & (9) where

*(*

**x***t*) is the state vector of the system,

*(*

**u***t*) is the vector of control input to the system,

**y****is the vector of load switch**states,

*(⋅) is the vector of system dynamic equations,*

**f***(⋅) is the vector of system algebraic constraints.*

**g***D. Inequality Constraints *

In addition to the equality constraint, the system should also satisfy operating inequality constraints. In the formulation, available power source capacity constraints, voltage limit constraints, flow constraints, and load constraints are considered as follows:

1)* Constraint on Available Power Source Capacity*: The
sum of all bus loads and total losses of the power system
should not be larger than the capacity of available power
sources. The constraint can be expressed as follows:

]
,
0
[
)
(
)
(
)
(
)
(*t* *y* *t* *P* *t* *P* *t* *t* *T*
*P*
*S*
*j* *G*
*losses*
*L*
*k* *k* *k* *j*
∈
≤
+
⋅

### ∑

### ∑

∈ ∈_{ }(10) where

*Plosses*(

*t*) is the total losses of the power system at

time *t*, *PG _{j}*(

*t*) is the available power of generator

*j*, and

*S*is

the set of generators in the system.

2)* Voltage Limit Constraints*: The voltage magnitudes
should vary within certain limits, otherwise, most of the
electric devices connected to the bus will not operate
satisfactorily. A general expression for voltage constraints is
shown as

### {

1,2, ,### }

[0, ] ) ( max min

_{V}

_{t}

_{V}

_{m}

_{M}

_{t}

_{T}*V*≤

_{m}*≤*

_{m}*∀ ∈ L ∈*

_{m}_{ }(11)

where *M* is the total number of system buses, *V _{m}*(

*t*) is the voltage magnitude at bus

*m*,

*Vm*min and

*Vm*max are the minimum and maximum tolerable voltage magnitudes at bus

*m*, respectively.

3) *Flow Constraints*: The power flow in a branch should
not exceed the capacity of the branch if the line is closed [9].
The power flow constraints on each branch are shown as
follows:

]
,
0
[
)
(*t* *C*max *l* *B* *t* *T*
*Plxy* ≤ *lxy* *xy*∈ ∈ _{ }(12)
where *lxy* is the transmission line (cable) connecting bus *x*

and *y*, *C _{l}*max

*is the power flow capacity of branch*

_{xy}*lxy*,

*B*is the

set of *directed branches*(including all branches) of the system,

)
(*t*
*P*

*xy*

*l* is power flow on branch *lxy*.

4) *Load Constraints*: The total loads on bus *k* should not
exceed the power capacity of the bus. The load constraints are
formulated as follows:
]
,
0
[
)
(_{t}* _{C}*max

_{t}

_{T}*P*≤

_{k}*∈*

_{L}_{k}_{ }(13) where

*C*max

_{L}*is the power capacity of load bus*

_{k}*k*, and

*P*(

_{k}*t*) is the power consumed by load bus

*k*.

IV. ILLUSTRATION OF DYNAMIC LOAD MANAGEMENT In this section, the dynamic load management is illustrated based on the simplified notional shipboard power system PSCAD model. The objective is to maximize the energized loads in shipboard power systems without violating available power source capacity constraint and PCM4 capacity constraint. The PCM4 capacity constraint means that the total loads connected to starboard (or port) side in zones should not exceed 2 MW. In case 1, the available power source capacity constraint is studied to show that the dynamic load management can keep the total load demand less than power generation capacity. In case 2, PCM4 capacity constraint is illustrated to show that dynamic load management can make the PCM4 capacity constraint satisfied. In case 3, pulse load is considered in the system to show that dynamic load management can consider the pulse loads.

Assume that the priority of propulsion loads is higher than that of loads in zones, which means that propulsion should be served before the loads in zones. Moreover, we assume the pulse loads have higher priority than propulsion loads, since most pulse loads are weapon loads, which have higher priority. In order to illustrate the load management method, the available power source capacity constraint and PCM4 capacity constraint are considered. Therefore, the problem can be reformulated as shown in (14).

### ∑

### ∑

### ∑

### ∑

### ∑

∈ ∈ ∈ ∈ ∈ ≤ + ⋅ ≤ ≤ ⋅ ⋅*S*

*l*

*G*

*losses*

*L*

*k*

*k*

*k*

*Port*

*j*

*j*

*Starboard*

*i*

*i*

*L*

*k*

*k*

*k*

*k*

*t*

*P*

*t*

*P*

*t*

*y*

*t*

*P*

*t*

*P*

*t*

*P*

*t*

*s*

*W*

*t*

*y*

*t*

*P*

*l*() ) ( ) ( ) ( MW 2 ) ( MW 2 ) ( . . ) ( ) ( max (14)

where, *L* is the load set in shipboard power system, *Starboard*

is the set of loads served by starboard side DC distribution
buses, *Port* is the set of loads served by port side DC
distribution buses, and* S* is the set of available generators in
the system.

*A. Case *1

In this case, the available power source capacity constraint

is illustrated based on dynamic load management. The system dynamic performance without load management is studied firstly, and the available power source capacity constraint may be violated. Then the system with dynamic load management is studied to show that the available power capacity constraint is always satisfied.

In case 1, MTG generator was connected, and ATG
generator was out of service. Thus, the generation capacity
was 36 MW. The power demand of propulsion load was
increased from 30.5 MW to 32.5 MW at 8 s, and decreased
from 32.5 MW to 30.5 MW at 11 s. In zones, *LDC*_{24} was not

served, and *LDC*_{11}, *LDC*12, *LDC*21, *LDC*22, *LAC*13, *LAC*23, and
14

*DC*

*L* were served, where, *LDC*_{12} and *LDC*22 were served by

port side DC distribution buses, and the other loads were served by starboard side DC distribution buses. The load demand in the two zones was 3.9 MW. Therefore, the load demand of the system was changed from 34.4 MW to 36.4 MW at 8 s, and the demand was returned to 34.4 MW at 11 s. The total losses of the system were about 1.6 MW. The total load demand of the system includes the power consumed by loads and losses of the system. The forecasted load demand and generation capacity are shown in Fig. 2. The load status is shown in Table III.

From 8 s to 11 s, the forecasted load exceeded the generation capacity. If load management method was not applied, the available power source capacity constraint was violated between 8 s and 11 s, which is shown in Fig. 3(a). The frequency of MTG generator was decreased from 60 Hz to 58.7 Hz at 8 s due to the increased load, and the frequency returned to 60 Hz after the load demand decreased at 11 s, which is shown in Fig. 3(b).

0 5 10 15 34 35 36 37 38 39 40 Time (Sec) Po w er (MW ) Forecasted load Generation capacity

Fig. 2. Forecasted load and generation capacity for case 1. TABLEIII

LOAD STATUS WITHOUT LOAD MANAGEMENT

Time 0~8 s 8~11 s 11~15 s Load ܮభభ served served served

Load ܮభమ served served served

Load ܮభయ served served served

Load ܮభర served served served

Load ܮమభ served served served

Load ܮమమ served served served

Load ܮమయ served served served

Load ܮమర not served not served not served

Pulse Load not served not served not served Propulsion Load 30.5 MW 32.5 MW 30.5 MW

5 6 7 8 9 10 11 12 13 14 15 30 32 34 36 38 40 42 Time (Sec) Po w er (MW ) Generation capacity Forecasted load Total load demand

(a) Total load demand

6 7 8 9 10 11 12 13 14 15 57 58 59 60 61 62 Time (Sec) M T G ge ne ra to r f re que nc y ( H z) (b) MTG generator frequency

Fig. 3. Dynamic performance of simulated model without load management.
To improve the dynamic performance of the system model,
the dynamic load management method was applied to the
shipboard power system model to maximize the energized
load in real-time without violating operating constraints of the
system. The forecasted load exceeded the generation capacity
at 8s. In order to ensure that total consumed power was less
than generation capacity, load management method was
applied at 7.8 s to shed some lower priority loads in zones.
The loads were shed based on the load priority to make the
objective function optimal. In this case, all non-vital and
semi-vital loads *LDC*_{11}, *LDC*14, *LDC*21,*LAC*13, and *LAC*23 were shed

which total 2 MW. Only the two vital loads *LDC*_{12} and *LDC*22

were still served, which made the objective function optimal.
Therefore, the total load demand was decreased from 38 MW
to 36 MW. After 11 s, the power demand of the propulsion
load was decreased from 32.5 MW to 30.5 MW. At 11.2 s,
load management method was applied to restore loads *LDC*_{11},

14

*DC*

*L* , *LDC*_{21}, *LAC*13, and *LAC*23, which were shed at 7.8 s. The

load status of the system is shown in Table IV. Fig. 4(a) indicates that the generation power does not exceed the capacity of the generation except several spikes.

After shed 2 MW loads at 7.8 s, the frequency began to increase slowly, and then the propulsion load increased to 32.5 MW, so the frequency was maintained at 60 Hz, which is shown in Fig. 4(b). At 11 s, the total load demand was decreased to 34 MW, and the loads were restored after 0.2 s. In this period, the frequency changed in the range of 59.9 Hz to 60.0 Hz. The load management method began to work before the total load demand exceeded the generation capacity, which prevented the frequency of MTG dropping. After shedding 2 MW loads in the zones, the total load demand in

the system was decreased to about 36 MW, which satisfied the available power source constraint.

The voltage of Load *LDC*_{11} is shown in Fig. 5. This load

was shed at 7.8 s and restored at 11.2 s. Therefore, the voltage
of *LDC*_{11} was zero between 7.8 s and 11.2 s. The input voltage

of PCM2-1 in zone 1 is shown in Fig. 6. The voltage was also
zero between 7.8s and 11.2s. The voltage of Load *LDC*_{12} is

shown in Fig. 7. This load had highest priority in the system,
and was not shed. Thus, the voltage was always kept at 650 V.
The voltage of Load *LDC*_{14} is shown in Fig. 8. This load had

lowest priority in the system, and was shed at 7.8 s and
restored at 11.2 s. Thus, the voltage of *LDC*_{14} was 0 between

7.8 s and 11.2 s.

TABLEIV

LOAD STATUS WITH LOAD MANAGEMENT

Time 0~7.8 s 7.8~8 s 8~11 s 11~11.2 s 11.2~15 s Load ܮభభ served shed shed shed served

Load ܮభమ served served served served served

Load ܮభయ served shed shed shed served

Load ܮభర served shed shed shed served

Load ܮమభ served shed shed shed served

Load ܮమమ served served served served served

Load ܮమయ served shed shed shed served

Load ܮమర not served not served not served not served not served

Pulse Load not served not served not served not served not served Propulsion Load 30.5 MW 30.5 MW 32.5 MW 30.5 MW 30.5 MW 6 7 8 9 10 11 12 13 14 15 30 32 34 36 38 40 42 Time (Sec) Po w er ( M W ) Generation capacity Forecasted load Total load demand

(a) Total load demand

6 7 8 9 10 11 12 13 14 15 57 58 59 60 61 62 Time (Sec) MT G g en er at or freq uen cy (H z) (b) MTG generator frequency

0 5 10 15
0
50
100
150
200
250
300
350
400
t (s)
11
*DC*
*L*
Time (Sec)
Fig. 5. Voltage of Load ܮభభ.

0 5 10 15 -100 0 100 200 300 400 500 600 700 800 900 t (s)

Fig. 6. Input voltage of PCM2-1 in Zone 1.

0 5 10 15
0
100
200
300
400
500
600
700
t (s)
12
*DC*
*L*

Fig. 7. Voltage of Load ܮభమ.

0 5 10 15
-100
0
100
200
300
400
500
t (s)
14
*DC*
*L*

Fig. 8. Voltage of Load ܮభర.
*B. Case *2

In this case, the PCM4 capacity constraint is illustrated to show that the dynamic load management method can make the PCM4 capacity constraint satisfied. The propulsion load was set to 25 MW. The total capacity of the system was 40 MW by assuming that MTG generator and ATG generator were both available. Thus, the system can still serve another 15 MW loads without violating the available power source capacity

constraint. If the PCM4 capacity constraint was not considered, all the loads in zones can be served, since the total power demand by the loads in zones was 4.1 MW.

Firstly, all the loads in zones were connected to the system. The two vital loads were connected to port side DC distribution buses, and the other loads were connected to starboard side DC distribution buses. The load status of the system is shown in Table V. The input power to PCM4-1 and PCM4-2 is shown in Fig. 9 and Fig. 10, respectively. The input power to PCM4-1 did not exceed the capacity of PCM4. However, the input power to PCM4-2 exceeded the capacity of PCM4, which meant that the PCM4 capacity constraint was violated in this case.

In order to handle this problem, the load management
method was applied. *LDC*_{24} is non-vital load and has the

lowest priority. Thus, *LDC*_{24} was shed at 2 s to reduce the

input power to PCM4-2 and make the objective function optimal. The load status of the system is shown in Table VI.

TABLEV

LOAD STATUS WITHOUT LOAD MANAGEMENT

Time 0~2 s 2~5s

Load ܮభభ served served

Load ܮభమ served served

Load ܮభయ served served

Load ܮభర served served

Load ܮమభ served served

Load ܮమమ served served

Load ܮమయ served served

Load ܮమర served served

Pulse Load not served not served Propulsion Load 25 MW 25 MW 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 Time (Sec) Po w er (MW ) Capacity of PCM4 Input power to PCM4-1

Fig. 9. The input power to PCM4-1 without load management.

1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 Time (Sec) Po w er (MW ) Capacity of PCM4 Input power to PCM4-2

7 Fig. 11 shows that the PCM4 capacity constraint is satisfied

after shedding *LDC*_{24}. The transients from 2 s to 2.5 s were

caused by the switch changes of DC-DC converter in PCM1.

*C. Case *3

In case 3, a 12 MW pulse load was incorporated into the system model. In the simplified notional shipboard power system, the pulse load was modeled as an AC constant power load, whose voltage level was 4.16 kV. The pulse width of the load was 0.3 s and this load should be served at 10 s. In order to simplify the problem, only propulsion load and pulse load were considered, which meant that all the loads in zones were disconnected. In this case, MTG generator was available and ATG generator was out of service. Thus, the generation capacity of the system was 36 MW. The power demand of propulsion load was 30 MW and the pulse load was served from 10 s to 10.3 s. The total load demand exceeded the available power source capacity from 10 s to 10.3 s shown in Fig. 12 (a), so the frequency dropped from 60 Hz to 59.2 Hz, and the frequency returned to 60 Hz gradually after the pulse load was disconnected, which was shown in Fig. 12(b).

Dynamic load management was applied to improve the dynamic performance of the system and make the available power source capacity constraint satisfied. In order to ensure system constraints were satisfied, propulsion load should be adjusted from 30 MW to 18 MW, when the pulse load was served. Therefore, the propulsion load was decreased from 30 MW to 18 MW at 9.9 s, before pulse load served, and increased to 30 MW at 10.4 s, after the pulse load disconnected. Fig. 13(a) shows that total load demand is always less than generation capacity. The MTG generator frequency changes between 59.7 Hz and 60.2 Hz, which is shown in Fig. 13(b).

TABLEVI

LOAD STATUS WITH LOAD MANAGEMENT

Time 0~2 s 2~5s

Load ܮభభ served served

Load ܮభమ served served

Load ܮభయ served served

Load ܮభర served served

Load ܮమభ served served

Load ܮమమ served served

Load ܮమయ served served

Load ܮమర served shed

Pulse Load not served not served Propulsion Load 25 MW 25 MW 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 Time (Sec) Po w er (MW ) Capacity of PCM4 Input power to PCM4-2

Fig. 11. The input power to PCM4-2 with load management.

The MTG generator frequency with and without load management is compared in Fig. 14. The frequency drop of the system without load management was much larger than the frequency drop with load management, which indicated that load management was an alternative way to incorporate the pulse load into shipboard power system.

6 7 8 9 10 11 12 13 14 15 20 25 30 35 40 45 50 Time (Sec) Po w er (M W ) Forecasted load Total load demand Generation capacity

(a) Total load demand

6 7 8 9 10 11 12 13 14 15 59 59.2 59.4 59.6 59.8 60 60.2 Time (Sec) M T G ge ne ra to r f re que nc y ( H z) (b) MTG generator frequency

Fig. 12. Dynamic performance of the system without load management.

6 7 8 9 10 11 12 13 14 15 15 20 25 30 35 40 45 Time (Sec) Po w er ( M W ) Forecasted load Total load demand Generation capacity

(a) Total load demand

6 7 8 9 10 11 12 13 14 15 59 59.5 60 60.5 Time (Sec) MT G g en era to r fre qu en cy ( H z) (b) MTG generator frequency

9 10 11 12 13 14 15 59 59.5 60 60.5 Time (Sec) MT G g en erat or fre qu en cy (H z)

MTG frequency without load management MTG frequency with load management

Fig. 14. MTG generator frequency comparison with and without load management.

V. SUMMARY

In section IV, the dynamic load management method was illustrated considering available power source capacity constraint and PCM4 capacity constraint. Moreover, the pulse load was also incorporated into the system through using dynamic load management method. In case 1, the available power capacity constraint was illustrated through making the total load demand exceed the generation capacity. If the dynamic load management was not applied in the system, the MTG generator frequency would decreased from 60 Hz. After incorporating the dynamic load management method, several lower priority loads were shed to make the available power source capacity constraint satisfied. The simulation results indicated that the system dynamic performance with load management was much better than its performance without load management. In case 2, PCM4 capacity constraint was studied. When the PCM4 served more than 2 MW loads, the PCM4 capacity constraint would be violated. The dynamic load management method was applied to shed some non-vital load to make the constraint satisfied. In case 3, a pulse load was incorporated into the system. When the pulse load was served, the available power source capacity constraint was violated. In order to solve the problem, dynamic load management method was used to shed some propulsion load to eliminate the constraint violation. Simulation results indicated that the MTG generation frequency drop of the system with load management was much less than that without load management.

VI. CONCLUSIONS AND FUTURE WORK

A simplified notional shipboard power system model was introduced to illustrate the performance of a new dynamic load management method where balances power generation and load demand of the system in real-time. The method and model were simulated in PSCAD. The simulation results were compared considering available power source capacity constraint and PCM4 capacity constraint. Further, a pulse load was incorporated into the system. Through using dynamic load management, pulse load was incorporated into the system successfully without violating any constraint of the system. The simulation results indicated that the dynamic load management could maximize the energized loads without violating any system constraints in real-time. The system dynamic performance was much better than its performance

without load management.

Further research work for the dynamic load management includes developing a multi-agent system based on the dynamic load management method to achieve the load balancing in real-time without violating system operating constraints.

VII. REFERENCES

[1] C. J. Dafis, "An observability formulation for nonlinear power systems modeled as differential algebraic systems," Ph.D. dissertation, Dept. Electrical Eng., Drexel Univ., Philadelphia, 2005.

[2] S. Khushalani and N. N. Schulz, "Restoration optimization with
distributed generation considering islanding," in *Proc. 2005IEEE Power *
*Engineering Society General Meeting*, pp. 2445-2449.

[3] A. I. Cohen and C. C. Wang, "An optimization method for load
management scheduling," *IEEE Trans. Power Systems*,vol. 3, pp.
612-618, May 1988.

[4] K. H. Ng and G. B. Sheble, "Direct load control-A profit-based load
management using linear programming," *IEEE Trans. Power Systems*,
vol. 13, pp. 688-694, May 1998.

[5] H. R. Lu and L. Yao, "On-line load optimization for two way load
management system," in *Proc. 2006IEEE International Conference on *
*Systems, Man and Cybernetics*, pp. 3250-3255.

[6] K. L. Butler-Purry, N. D. R. Sarma and I. V. Hicks, "Service restoration
in naval shipboard power systems," *IEE Proc. Gener. Transm. Distrib., *

vol. 151, pp. 95-102, Jan. 2004.

[7] K. L. Butler-Purry and N. D. R. Sarma, "Self-healing reconfiguration for
restoration of naval shipboard power systems," *IEEE Trans. Power *
*Systems*,vol. 19, pp. 754-762, May 2004.

[8] C. O. Nwankpa and R. M. Hassan, "A stochastic based voltage collapse
indicator," *IEEE Trans. Power Systems*, vol. 8, pp. 1187-1194, Aug.
1993.

[9] T. Nagata and H. Sasaki, "A multi-agent approach to power system
restoration," *IEEE Trans. Power Systems*, vol. 17, pp. 457-462, May
2002.

VIII. BIOGRAPHIES

**Xianyong Feng **(S’08)received his B.S. degree in Electrical Engineering

in 2005 from Harbin Institute of Technology in China. He received his M.S. degree in Automation in 2008 from the University of Science and Technology of China. He joined the Ph.D. program in Electrical Engineering at Texas A&M University in 2008. His research interests are in multi-agent system based dynamic load management for shipboard power system.

**Takis Zourntos**(SM’09) received the B.S., M.S., and Ph.D. degrees in

Electrical and Computer Engineering from the University of Toronto, Toronto, ON, Canada, in 1993, 1995, and 2003, respectively. He is currently an Assistant Professor in Electrical and Computer Engineering at Texas A&M University. His research is centered on the application of nonlinear systems and control theory to a wide range of problems, including behavior generation for autonomous agents, integrated analog circuits, and signal processing.

**Karen L. Butler-Purry** (SM’01) received her B.S. (summa cum laude) in

Electrical Engineering in 1985 from Southern University in Baton Rouge, Louisiana. She was awarded her M.S. degree in 1987 from the University of Texas at Austin and her Ph.D. in Electrical Engineering in 1994 from Howard University in Washington, D.C. She joined Texas A&M University in 1994, where she currently serves as Associate Head and Professor in the Department of Electrical and Computer Engineering. Her research interests are in the areas of distribution automation and intelligent systems for power quality, equipment deterioration, and fault diagnosis.

**Salman Mashayekh** (S’09) received his B.S. and M.S. in Electrical

Power Systems from University of Tehran, Iran, in 2006 and 2008, respectively. He joined Power System Automation Lab in Texas A&M University as a PhD student in 2008. His research interests are in power system management for next generation of Integrated Shipboard Power Systems. His job focuses on contingency analysis, dynamic stability and security studies, and other power management system requirements.