This paper proposes an efficient energy management system (EMS) for industrial microgrids (MGs). Many industries deploy large pumps for their processes. Oftentimes, such pumps are operated during hours of peak electricity prices. A lot of industries use a mix of captive generation and imported utility electricity to meet their energy requirements. The MG considered in this paper includes diesel generators, battery energy storage systems, renewable energy sources, flexible loads, and interruptible loads. Pump loads found in shipyard dry docks are modelled as exemplar flexible industrial loads. The proposed EMS has a two-stage architecture. An optimal MG scheduling problem including pump scheduling and curtailment of interruptible loads (ILs) is formulated and solved in the first stage. An optimal power flow problem is solved in the second stage to verify the feasibility of the MG schedule with the network constraints. An iterative procedure is used to coordinate the two EMS stages. Multiple case studies are used to demonstrate the utility of the proposed EMS. The case studies highlight the efficacy of load management strategies such as pump scheduling and curtailment of ILs in reducing the total electricity cost of the MG.
Industrial power networks may comprise distributed generators, battery energy storage systems (BESSs), and different types of loads. As such, industrial power networks can be treated as grid-connected MGs. An EMS facilitates efficient MG operation by minimizing the overall electricity cost. The EMS determines an optimal schedule and dispatch for each distributed generator, BESS, flexible load, and interruptible load (IL) in the MG while respecting various technical and operational constraints. The EMS is also capable of incorporating load management strategies in its optimal scheduling problem formulation. Furthermore, the EMS needs to consider power flow equations and system security constraints while optimally dispatching the MG components. This is considered in an optimal power flow (OPF) problem incorporated in the EMS architecture. Thus, formulating an efficient energy management (EM) problem is a complex task due to the need to integrate both unit commitment (UC) and OPF problems. This normally results in the EM problem being formulated by ignoring network losses and system security constraints. The EM problem then simplifies to a UC problem which is usually formulated as a mixed integer linear programming (MILP) or mixed integer quadratic programming (MIQP) problem. However, the feasibility of results obtained using such formulations is questionable owing to potential violations of the network constraints and the absence of power losses in the formulation.
In Singapore, the wholesale electricity prices are updated every 30 minutes. Large industrial customers have the option of sourcing their electricity requirements directly from the wholesale electricity market through SP Services Limited. In this scenario, industries need to contend with the risk of increased costs due to volatile electricity prices. The contestable consumers’ electricity bills usually comprise two segments: (i) energy charge and (ii) capacity charge. The energy charge is calculated by taking the product of electricity charge and energy consumed. The capacity charge is computed on a monthly basis. The capacity charge is calculated by taking the product of contracted capacity and contracted capacity price. A huge uncontracted capacity charge is incurred if the maximum power demand exceeds the contracted capacity at any point of time. Large pumps constitute a major portion of the electrical load demand in many industrial facilities. Due to the large pumping requirements in many industries, pump capacities are typically in the region of several MWs. In other words, pump usage has a significant bearing on the maximum load demand in many industrial facilities. Pump usage is also constrained by operational requirements in many industries whereby a certain quantity of water or other liquid needs to be pumped within a defined time frame. Optimal planning and scheduling of pump usage along with timely curtailment of ILs can help in lowering the maximum demand of the industrial facility, thereby leading to a reduction in the electricity cost.
With the advent of deregulated power systems, load management strategies have recently attracted wide research interest. A recent survey of existing demand response models and approaches can be found in [
Development of EMSs for MGs has been an active research area in recent years. In this context, model predictive control (MPC) based schemes have been widely adopted in recent years for power system scheduling applications. A few typical examples of such schemes can be found in [
In this paper, comprehensive, component wise models of exemplar MGs are first developed. The MGs modelled in this paper comprise diesel generators (DGs), BESSs, RESs, flexible pump loads, and ILs. The MLD framework is used to model the DGs, BESSs, and ILs. Subsequently, an EMS is proposed for optimally scheduling the MG. The proposed EMS has a two-stage architecture along the lines of [
The remainder of this paper is organized as follows: Section
This section develops first principle models of the DGs, BESSs, RESs, flexible pump loads, and ILs considered in this paper.
DGs are controllable in nature. The fuel cost of DG
Technical parameters of the DGs in the MGs.
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1 | 80 | 30 | 1 | 0.1 | 3 | 50 | 3 |
2 | 200 | 60 | 2 | 0.1 | 3 | 30 | 3 |
3 | 1000 | 50 | 3 | 0.1 | 3 | 5 | 3 |
In this work, a realistic BESS model is considered including intertemporal constraints on the state of charge (SOC). A battery degradation cost function accounts for the impact of charging and discharging events on the cost of purchasing the BESS. The overall BESS model is presented below [
Renewable energy sources such as solar photovoltaic (PV) and wind power plants are included as components of the MGs which are modelled in this paper. The operating costs of these RESs are assumed to be 0 [
The power output from the wind power plant is proportional to the cube of the wind velocity and is calculated using the following equation:
Among other PV performance models, the five-parameter array performance model has been extensively used by researchers [
These are loads in the MG which are considered to be less important. ILs provide the EMS with a lot of flexibility while scheduling the MG components. The ILs may be shed if sufficient monetary compensation is paid. The total cost associated with the curtailment of all the ILs in a MG is calculated as follows [
Pump loads found in shipyard dry docks have been used as exemplar industrial loads in this paper. The power consumed by pump
Pumps are required to pump a certain amount of water or other liquid within the specified optimization period. This constraint is expressed as follows:
Large pumps cannot be started up or shutdown too frequently during the optimization period due to their large inertias. This constraint is expressed as follows:
The MLD formalism is a class of hybrid dynamical systems which has been used by several researchers for formulating power system scheduling problems. A few examples of such problems can be found in [
The proposed EMS comprises two sequential stages for minimizing the total MG operating cost. The motivation behind adopting this two-stage approach is to decrease the complexity of the overall optimization problem, thereby ensuring that it is solved within a reasonable time. The two stages of the proposed EMS are described below.
The UC problem for the MG is solved in Stage 1 wherein all the DGs, BESSs, pumps, and ILs are optimally scheduled to satisfy the active power demand. The overall optimization problem solved at this stage is described below.
The overall optimization problem is solved in an MPC framework with a prediction horizon of 24. In Stage 1, the overall optimization problem turns out to be an MIQP problem. The optimization problem is described in MATLAB using YALMIP [
Optimal power flow (OPF) is a key optimization problem in power system operations. It is used to determine optimal setpoints for the system variables while satisfying power demand and respecting generator and network constraints. The main objective of the OPF problem is usually to minimize the power generation cost of the system. Importantly, the OPF problem also accounts for power losses in the system. Thus, the OPF problem can also be formulated to minimize power losses in the system. As the system load demand varies with time, it is essential to solve the OPF problem within a reasonable time. However, OPF is a nonconvex, nonlinear optimization problem which is NP-hard to solve [
Let
The constraints for the OPF problem mainly adhere to Kirchhoff’s laws and are formulated to ensure that the active and reactive powers are balanced at each bus while satisfying generation capability margins and voltage bounds. The constraints for the OPF problem are enumerated below.
It is assumed that the pump loads and ILs consume reactive power equivalent to 50% of their active power consumption and that the converters of the BESSs and RESs at the PCC are capable of maintaining a power factor greater than 0.7. The sets of DGs, BESSs, RESs, ILs, and pumps connected to bus
The EMS solves Stage 1 and Stage 2 alternately. In Stage 1, binary statuses and dispatch values for all the DGs, BESSs, pumps, and ILs in the MG are determined. In addition to this, a schedule for exchanging power with the utility grid is also determined. The power exchange schedule and dispatch values of the DGs, BESS, pumps, and ILs are shared with the OPF problem in Stage 2. The OPF problem is formulated by permitting a small degree of freedom around the scheduled power exchange values and dispatch values of the DGs and BESSs generated in Stage 1. In Stage 2, the network power losses are determined and power flow convergence is checked. The power losses are shared with Stage 1 which solves the UC problem including the power losses. The dispatch and power exchange values are shared with Stage 2. This iterative process continues till convergence. This process is illustrated in the flowchart shown in Figure
Flowchart for EMS layer computations.
For
The power supplies from the grid and the BESSs are bidirectional. Therefore, based on the power flow direction, the shifted domain is defined as follows.
For
Importantly, the OPF problems solved in Stage 2 are decoupled from each other. Hence, parallel solving techniques can be used to further increase the computational performance if necessary. The OPF problem in Stage 2 computes the power loss during each hour. This calculation is shown below in (
Two exemplar MGs are modelled in this paper. First, the optimal scheduling of a modified IEEE 30-bus system is performed under the following operational scenarios to demonstrate the efficacy of the proposed EMS and pump scheduling formulations: Without optimal pump scheduling and ILs, water is pumped in the shortest possible time using only the 3 main pumps. Optimal pump scheduling is performed using the 3 main pumps alone. Optimal pump scheduling is performed using only the 3 main pumps and the 4 auxiliary pumps. Optimal pump scheduling is performed using only the 3 main pumps and the 3 ILs. Optimal pump scheduling is performed using the 3 main pumps, the 4 auxiliary pumps, and the 3 ILs.
Subsequently, to further validate the versatility and efficacy of the proposed EMS for different networks, the optimal scheduling of a modified IEEE 57-bus system is performed under Scenario 5.
A modified IEEE 30-bus system is adopted as an exemplar MG for this case study. The base value is considered as 8000 kVA and the line resistance and reactance values are increased to 3 and 1.5 times the p.u. values provided in the standard MATPOWER case file for the IEEE 30-bus system, respectively [
For all the simulation scenarios, it was assumed that the main pumps were switched off prior to the start of the optimization period. For Scenarios 3 and 5, it was assumed that the auxiliary pumps were switched off prior to the start of the optimization period. Furthermore, it was assumed that
All the scenarios were simulated under the assumption that accurate point forecasts for load demand (excluding pump loads), electricity prices, and RES generation were available. The electricity price forecasts in this paper were adapted from [
Forecasts of (a) load demand, (b) RES generation, and (c) electricity price.
The final dispatch values of the DGs in Scenarios 1–5 are shown in Figures
Scenario 1: (a) dispatch values of DG 1, DG 2, and DG 3, (b) BESS charge and discharge profiles, and (c)
Scenario 2: (a) dispatch values of DG 1, DG 2, and DG 3, (b) BESS charge and discharge profiles, and (c)
Scenario 3: (a) dispatch values of DG 1, DG 2, and DG 3, (b) BESS charge and discharge profiles, and (c)
Scenario 4: (a) dispatch values of DG 1, DG 2, and DG 3, (b) BESS charge and discharge profiles, and (c)
Scenario 5: (a) dispatch values of DG 1, DG 2, and DG 3, (b) BESS charge and discharge profiles, and (c)
Curtailment of ILs in Scenario 4.
Curtailment of ILs in Scenario 5.
In Scenario 1, it is assumed that the 3 main pumps are switched on during the first 3 hours of the day in order to pump the water in the shortest possible time. This action has major cost implications since the overall system load demand is high during the first 3 hours of the day. This is evidenced by the results shown in Table
Cost breakdown and computational times for Scenarios 1–5.
Scenario # | Uncontracted capacity cost ($) | Interruptible load cost ($) | Total cost ($) | Percentage reduction in total cost | Computational time (s) |
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1 | 11,991.50 | - | 34,710.10 | - | 38.11 |
2 | 0 | - | 29,997.80 | 13.58% | 60.59 |
3 | 0 | - | 29,945.11 | 13.73% | 136.04 |
4 | 0 | 864.21 | 22,995.63 | 33.75% | 60.81 |
5 | 0 | 861.90 | 22,911.79 | 33.99% | 108.53 |
Schedule of main pumps for Scenarios 1–5.
Scenario | Main Pump 1 | Main Pump 2 | Main Pump 3 |
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Schedules of auxiliary pumps for Scenarios 3 and 5.
Scenario | Aux. Pump 1 | Aux. Pump 2 | Aux. Pump 3 | Aux. Pump 4 |
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From Table
Compared to Scenario 2, a reduction of 1 hour in main pump usage is observed in Scenario 3 due to the introduction of auxiliary pumps. Consequently, as observed in Table
As observed from Table
The trends in Figures
Figure
Evolution of (a) total operating cost and (b) total power loss over 24 hours.
A modified IEEE 57-bus system is adopted as an exemplar MG for this case study. The optimal scheduling of the modified 57-bus MG is performed under Scenario 5. The base value is considered as 7000 kVA and the line reactance values are decreased by 50% when compared with the p.u. values provided in the standard MATPOWER case file for the IEEE 57-bus system [
For this case study, it was assumed that all the main pumps and auxiliary pumps were switched off prior to the start of the optimization period. Furthermore, it was assumed that initial SOCs for the two BESSs in the MG were 0.6 and 0.5, respectively. Finally, it was assumed that all the DGs in the MG were switched off prior to the start of the optimization period.
This case study was performed under the assumption that accurate point forecasts for load demand (excluding pump loads), electricity prices, and RES generation were available. The load demand forecast for this case study is shown in Figure
Forecasts of load demand and wind power plant generation for Case Study 2.
The final dispatch values of the DGs in this case study are shown in Figure
Optimal scheduling of modified IEEE 57-bus system: (a) dispatch values of DG 1, DG 2, and DG 3, (b) charge and discharge profiles of BESSs, and (c)
The results of this case study largely agree with those of Case Study 1. The pumps are generally operated during the valley periods in the load profile which coincide with the late night hours. A clear indication of this is the operation of 1 main pump and 3 auxiliary pumps during hour 15. From Figure
Curtailment of ILs in modified IEEE 57-bus system.
Finally, Figure
Evolution of (a) total operating cost and (b) total power loss over 24 hours.
This section discusses the limitations of this paper and how the assumptions made could potentially impact the optimal MG scheduling results. Furthermore, some possible future research directions are also presented. Case Study 1 clearly established the potential of load management strategies in reducing the MG operating cost. In Scenario 1, it was assumed that the main pumps would be switched on during the first 3 hours of the day to pump out the water in the fastest possible time. Even if this assumption was not true, load management strategies such as pump scheduling and curtailment of ILs still provide the maximum reduction in operation cost without compromising on any operational requirements.
The MG models in this paper were developed using the MLD approach which essentially results in a state-space representation of the system as shown in (
In this paper, the optimal MG scheduling is performed on the basis of fixed forecasts for RES generation, electricity price, and load demand. In case of any uncertainties in the RES generation and electricity price forecasts, the resulting MG schedules which are generated by the EMS may be suboptimal. One way to deal with the uncertainties is to introduce spinning reserve constraints in the scheduling problem which would enable the MG to manage the loss of the largest RES. The objective of this paper was to present the EMS architecture and problem formulation. The authors have not focused on handling uncertainties in this work. In this context, one possible direction for future work is to develop a scenario-based robust optimization approach for handling forecast uncertainties in the optimal scheduling of MGs while also respecting the network constraints using the EMS architecture explained in this paper.
The concept of eco-industrial parks (EIPs) has been recently gaining research attention. A significant attribute of EIPs is the sharing of energy between different business entities. Typically, industrial parks consume and produce both heat and electricity. In future, the framework proposed in this paper could be integrated with an industrial park level waste heat recovery network with combined cycle gas turbines bridging the electrical and thermal energy streams. Future studies could also focus on designing efficient load management strategies for such multienergy networks.
This paper developed a first principle model of industrial MGs including DGs, BESSs, pump loads, and ILs. Subsequently, a 2-stage EMS was proposed for optimally scheduling the MGs. The EMS adopted an iterative procedure to integrate the UC and OPF problems, thereby satisfying network constraints. Load management strategies including pump scheduling and curtailment of ILs were adopted by the EMS to reduce the total electricity cost. The efficacy of the EMS including load management strategies was demonstrated on a 30-bus exemplar MG system under five operational scenarios. From the scheduling results obtained for the 5 scenarios, it was observed that the nonadoption of efficient load management strategies led to significant uncontracted capacity charges. The results also demonstrated the potential of optimal pump scheduling in realizing significant cost savings through the reduction or elimination of uncontracted capacity charges. The impact of auxiliary pumps and curtailment of ILs on the total cost of the system was also analyzed. It was found that while auxiliary pumps had a marginal impact on the total cost, curtailment of ILs realized significant cost savings. Finally, the scalability and efficacy of the EMS were demonstrated on an exemplar 57-bus MG. The 57-bus case study demonstrated the scalability of the EMS architecture while also validating the results obtained in the 30-bus case study.
Index for time (hours)
Index for diesel generators (DGs)
Index for battery energy storage systems (BESSs)
Index for interruptible loads (ILs)
Index for pumps
Index for renewable energy sources (RESs)
Index for lines
Index for buses.
Set of all hours in a day; that is,
Set of DGs in the MG
Set of BESSs in the MG
Set of ILs in the MG
Set of pumps in the MG
Set of RESs in the MG
Set of buses in the MG
Set of lines in the MG.
Lower bound of the corresponding parameter
Upper bound of the corresponding parameter
DG start-up cost coefficient ($)
Fuel cost curve coefficients in $/
BESS charging/discharging efficiency percentages
Power required by the BESS to charge 100% in one hour (kW)
BESS purchase cost ($)
BESS capacity (kWh)
Number of cycles for BESS to reach end of life (
Average number of hours BESS charges/discharges in a day
Power coefficient which is a function of the tip speed ratio
Air density
Area swept by the rotor blades
Light current and diode saturation current, respectively
Series and shunt resistances, respectively
Pump capacity in MW
Pump flow rate in
Optimization interval
Volume of liquid to be pumped in 24 h in
Contracted capacity in MW
Uncontracted capacity cost coefficient in $/MW/month
Series conductance and susceptance, respectively
Line charging susceptance.
Binary variable indicating DG start-up status
Binary variable indicating DG commitment status
Real power output of DG (kW)
BESS state of charge (SOC) (scale of 0-1)
BESS charging/discharging power (kW)
Wind velocity
Operating voltage and current of PV module, respectively
Compensation paid in $/MWh to IL
Binary variable indicating IL status
Amount of IL curtailed (kW)
Binary variable indicating pump status
Binary variable indicating pump start-up status
Real power produced by RES in kW
Price at which electricity is purchased from the utility grid in $/kWh
Real power purchased from the utility grid in kW
Price at which electricity is sold to the utility grid in $/kWh
Real power sold to the utility grid in kW
Uncontracted capacity in MW
Magnitude of the voltage phasor
Phase angle of the voltage phasor
Complex power injection in MVA
Generated active power in kW
Generated reactive power in kvar
Active power demand in kW
Reactive power demand in kvar
Active power flow through line
Reactive power flow through line
Total power loss in kW
Dispatch value of generator
Commitment status of generator
Value of power flow from the BESS received by Stage 2 from Stage 1 in kW.
The authors declare that they have no conflicts of interest.
The authors would like to acknowledge funding support from NTU Start-Up Grant. The work of L. P. M. I. Sampath was supported by the International Center of Energy Research (ICER), established by Nanyang Technological University (NTU), Singapore, and Technische Universität München (TUM), Germany.