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A novel approach to the regulation of a self-sufficient energy system using a system-state matrix
Electrical Power and Energy Systems 53 (2013) 893–899
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A novel approach to the regulation of a self-sufficient energy system using a system-state matrix Boštjan Drobnicˇ a,⇑, Andrej Pirc b, Mitja Mori a, Mihael Sekavcˇnik a a b
Faculty of Mechanical Engineering, University of Ljubljana, Aškercˇeva 6, 1000 Ljubljana, Slovenia Savaprojekt d.d., CKZˇ 59, 8270 Krško, Slovenia
a r t i c l e
i n f o
Article history: Received 6 August 2012 Received in revised form 5 June 2013 Accepted 6 June 2013
Keywords: Operating regulation System-state matrix Energy-system model MATLAB Simulink
a b s t r a c t In this paper we consider the optimal operating regulation of a self-sufficient energy network. To begin with we discuss the regulation of an optimised energy-supply system. Our task was initially focused on a theoretical description of the system-state matrix approach with a corresponding list of operating rules and actions. Secondly, a dynamic mathematical model consisting of the consumer, the energy-production facilities (a photovoltaic power plant and an internal combustion engine), the energy-saving capacities (a battery) and the regulation was set up. Thirdly, during the simulations with various regulation settings an optimised system of operating rules was set up to achieve a stable and rational supply of energy. Finally, the results, appropriate diagrams and guidelines for future work are presented. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction A stable, secure and sustainable supply of energy is vital for modern, energy-dependent societies. Traditional power grids are based on several large-scale power suppliers (i.e., utility power plants), a large number of power consumers and several minor suppliers of power, which currently includes power generation from renewable energy sources (RESs) [1]. The stability of the system, i.e., a constant frequency and voltage, is provided by the largescale suppliers [2]. Variations in the load for individual consumers as well as variations in the power production by small-scale suppliers are relatively small compared to the total capacity of the system. Therefore, the regulation of large-scale suppliers can effectively respond to the disturbances, even if the response time of the whole plant is relatively long. Since the future development of energy systems will tend towards the more extensive use of RESs [3], the structure of future power grids will change significantly [2]. The variations in power supply from RESs, which typically depend on local weather conditions and therefore can only be partially under control, will not be negligible and will have a significant effect on the stability of the entire system. Due to the unpredictability of the supply of power from RESs, an indispensable part of the system will have to include various technologies for energy storage. The regulation of such a system (called a smart grid) will require a different approach and strategies to keep the system stable and to provide a reliable energy supply. ⇑ Corresponding author. Tel.: +386 1 4771 715; fax: +386 1 2518 567. E-mail address: [email protected] (B. Drobnicˇ). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.06.010
The stability of energy systems with distributed energy generation is a more complex and challenging task due to the variety of energy sources, preferably renewable types [3–7], the need for energy storage and the size of the system. A complex energy network, such as a system for energy supply, storage, distribution and consumption, requires careful planning [3] using advanced numerical tools. Several codes have been developed for simulations and optimisations of energy systems. Considering a review of the capabilities of these codes [8] and requirements for our planned work, certain limitations of the existing tools were found [9]. Therefore, the decision to develop a custom-made model was taken. This model should be able to simulate the operation of different combinations of energy systems with an emphasis on the energy flow analysis and the accurate regulation of particular elements of the system. The models were set up in MathWork’s Simulink environment, which proved to be a useful tool for such research [10,11]. The usual approach in this process is to set different rules of operation based on multiple conditions regarding the state of the system’s elements, the available energy, the required energy, etc. However, with complex systems this approach can lead to an intricate list of conditions and rules, making it hard to have an overview of the system’s response under various conditions. It is also possible that blank areas of the entire system-operation region or overlapping of neighbouring areas can occur. This means that there are certain situations without predefined rules for operation or that the system’s state corresponds to more than one condition and several different rules can be valid in a particular situation.
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Nomenclature a A c C E H LCOE m n p P S w x
g
annuity factor, – area, m2 specific cost, €/kW cost, € energy, kW calorific value, kW h/kg levelized cost of electricity, € mass, kg investment period, year interest rate, – power, kW sum of products (by WSM), – walued factor, – value of criteria, – efficiency, –
The objectives of this paper are as follows: A novel approach to system regulation using a system-state matrix. A setting up of an energy-system model using MathWork’s Simulink. An optimisation of the energy-system model. An operating simulation of the energy system. 2. System-state matrix approach A more systematic and transparent way to define the rules for a system’s operation is by means of a system-state matrix, schematically shown in Fig. 1. In general, the regulation of a complex system depends on several representative parameters that sufficiently and uniquely describe the state of the system. 2.1. Definition of the matrix and the rules Each parameter has a value Pi that fits in one of the Ri ranges of various sizes, where the number and sizes of ranges can vary by parameter. If N is the number of observed parameters, an Ndimensional matrix is formed with a size of R1 R2 RN. Each cell of the matrix represents one unique situation in which the system’s operation could be classified regarding the combination of the observed parameters. It is also possible, however, that some cells in the matrix represent situations that are physically impossible for the observed system, but these can be neglected as they do not disrupt the control process and have no influence on the system’s operation. On the other hand, it is very important that all possible situations are considered in the system-state matrix and at the same time the matrix eliminates the possibility of the system’s state fitting in more than one situation. When the system-state matrix is constructed its cells need to be filled with the appropriate rules for responses of the system that will ensure optimal operation under a given set of conditions and will also retain the stability of the system. In general, each cell, i.e., each situation, can have a different rule. However, usually certain rules are applicable in multiple situations, so the number of rules can be significantly smaller than the number of matrix cells. It is important to fill all the cells that represent physically possible states of the system with the appropriate rules, so that the system controller has an operating instruction for every situation that might occur during the system’s operation.
Subscripts 0 initial value A annual fixed cost charge charging discharge discharging ef power-production efficiency F, fuel fuel i number of parameter, criteria j number of parameter, criteria I initial cost ICE internal combustion engine max maximum min minimum OP,M operating and maintenance cost PROD produced PV photovoltaic power plant re-use re-use
2.2. Regulation procedure The system-state matrix and the corresponding list of rules are the information that will enable the system controller to respond appropriately to every situation. The controller must monitor the values of the observed parameters, find in which of the predefined ranges each of the parameters fits and locate the appropriate cell in the system-state matrix according to the parameters’ values. The contents of the cell describe the actions that will, in a given situation, provide the optimal response and operation of the system, Fig. 2. Any selected operating rule is a list of actions (settings) that are sent to the local controllers of the system elements. The actions for all of the rules and all of the regulated elements can be put in the form of an action matrix where the parameter S(i, j) represents the signal for the jth element when the ith operating rule is applicable, Fig. 3. Furthermore, the selected rule can be represented by a vector where all the elements are 0, except for the ith element, which is 1. The product of the action matrix and the rule vector is a reg-
Fig. 1. Selecting representative parameters and creating a system-state matrix.
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Fig. 2. System regulation by means of the system-state matrix.
the viability of an individual power plant can be seen throughout the levelized cost of electricity. This cost of electricity that is generated by different sources is a calculation of the cost of generating the electricity at the point of connection to the load or electricity grid. It includes the initial capital, as well as the costs of operation, maintenance and fuel. The initial capital CI of a particular power plant is a product of the specific initial costs ci and the peak power of the system P.
C I ¼ ci P
Fig. 3. Product of the action matrix and the rule vector gives the vector of appropriate settings for all the system’s elements.
The annuity factor a depends on the investment period n and the interest rate p.
a¼ ulation vector with settings for all the system’s elements that correspond to the selected rule and the given system state at the same time. 2.3. System stability When defining the rules for the system’s operation in various cells of the system-state matrix it is not sufficient to ensure stable and optimal system operation within the observed cell. Transitions from one cell to another, and thus changing the rules of operation, should also be considered, and their influence on the system’s stability should be evaluated. If the system controller is fast enough then the system state can only move from the current cell to one of the neighbouring cells of the system-state matrix. In this case the changes in the operating rules are probably not so radical as to cause instability of the system. On the other hand, if the controller is too slow the system can jump to a cell that is not next to the current cell. In this case the new rules could force significant changes in the system’s operation, leading the system into an unstable operation. Therefore, it is recommended to set a numerical model of the system and test the preset regulation procedure under various normal as well as extreme operating conditions in order to examine the system’s response.
ð1Þ
pð1 þ pÞn ð1 þ pÞn 1
ð2Þ
The annual fixed costs CA are thus equal
CA ¼ CIa
ð3Þ
The total costs are the sum of the annual fixed costs CA, the operating and maintenance costs COP,M and the fuel costs CF. Finally, the levelized cost of electricity LCOE is equal to the total costs divided by the produced energy EPROD.
LCOE ¼
C A þ C OP;M þ C F EPROD
ð4Þ
3. Regulation and optimisation of a simple power-supply system with energy storage In order to present the applicability of the system-state matrix approach for regulation the energy-supply system, a simple system, schematically shown in Fig. 4, was modelled. 3.1. Energy-system elements 3.1.1. Power consumer A power consumer with a dynamically varying load [12] in the presented example is an industrial plant with a typical daily operation and minimal power consumption during the night-time and weekends. The weekly load of the observed plant is shown in Fig. 5.
2.4. Levelized cost of electricity Additionally, the stable system’s operation should not be the only observed parameter. Economics has a great influence on the energy system’s planning too. The information that predicts
3.1.2. Photovoltaic power plant A photovoltaic power-plant (PV) model [13] is used to describe the renewable energy system. It is limited by the surface position, the time and the weather conditions. The produced electrical
B. Drobnicˇ et al. / Electrical Power and Energy Systems 53 (2013) 893–899
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_ fuel Hfuel gef PICE ¼ m
ð6Þ
3.1.4. Battery Batteries are used for the storage of excess energy and the supply of peak-load energy. In the situations when the PV and ICE are unable to cover the power demand, the consumer is supplied with additional energy from the batteries. On the other hand, when the power demand is small, production systems can store the excess energy in the batteries. The re-used power Pre-use is the decreased charging power P0 due to the charging and discharging efficiency gcharge/gdischarge.
Pre-use ¼ gcharge gdischarge P0
ð7Þ
3.2. Basic operating constraints The basic purpose of the system regulator is to ensure that the system’s operation complies with the independent requirements from the system’s environment. To achieve this, various commands need to be sent to individual elements of the system. However, the regulator must also take into consideration the limitations that each of the elements might have. Thus, both the requirements and the limitations have to be considered when making the operating rules and the appropriate actions. The following are applicable for the observed system:
Fig. 4. Observed energy supply/storage/consumption system.
Fig. 5. Diagram of energy consumption.
power PPV depends on the efficiency gPV, the incident radiation flux Esol and the area of the photovoltaic panels A.
PPV ¼ gPV Esol A
ð5Þ
The average daily production of electricity from the photovoltaic power plant is shown in Fig. 6. 3.1.3. Internal combustion engine An internal combustion engine (ICE) with a power generator is a conventional energy source in the observed system to provide a stable energy supply. Its capacity is considerably smaller than the peak loads of the consumer. Also, the lowest output capacity is limited due to the decreased efficiency of the engine. The pro_ fuel , its duced electrical power depends on the supplied fuel rate m calorific value Hfuel and the power-production efficiency gef.
The total energy output of the PV, the ICE and the battery has to cover the power demands of the industrial plant. As is shown in Fig. 5, the power consumption does show daily and weekly patterns, but also includes considerable random variations, which means continuous monitoring of the power demand is necessary. Since actual continuous monitoring is not possible, at least the sampling time of the discrete values should be short enough to capture the dynamics of the load changes. In the presented case the available data are sampled at one-hour intervals and a simple linear interpolation is used between the measured points. Due to weather conditions, the energy production from a PV plant can only be partly predicted. PV-produced energy is firstly used to cover the consumer’s energy demand. Secondly, if there is an excess of produced energy, it is used for battery charging. Finally, the production of PV energy is adjusted to the current consumer’s demand when the battery is fully charged. ICE operation is regulated with respect to two parameters: first, is the energy difference between the consumer’s energy demand and the PV-produced energy; second, is the level of the battery charge. A particular ICE has a limited maximum power output and to avoid low-efficiency operation a lower power limit is also set. If the required power is below the limit the engine is shut down. It is also advisable to avoid frequent start ups and shut downs of the engine, so the operating rules should consider the current state of the engine’s operation. The capacity of the battery is also limited once an actual battery is chosen for the system. In addition, both overcharging and, even more importantly, excessive discharging of the battery should be avoided. So appropriate actions should be taken when certain charge levels are reached. In the observed case the energy difference between the consumer’s energy demand and the PV-produced energy can be divided into the following intervals, considering the ICE’s limitations:
Fig. 6. Electricity production from PV power plant, one day scale.
Below P0: power production from the PV power plant is greater than the power consumption; the battery is charging and the ICE does not operate.
B. Drobnicˇ et al. / Electrical Power and Energy Systems 53 (2013) 893–899
From P0 to PICEmin: power demand is lower that the ICE lower limit; typically (but not in all situations) the engine should be shut down. From PICEmin to PICEmax: power demand is within the working range of the ICE; the engine should follow the current power demand; if necessary, it could also charge the battery. Above PICEmax: power demand exceeds ICE capacity; the engine should run on full load, and also battery backup is necessary to cover the power demand. On the other hand, the battery charge level can be divided into the following intervals: Below Cmin: the battery must be charged to avoid the possibility of complete discharge and damage to the battery. From Cmin to Cmax: the battery can be charged or discharged with regard to the current power demand and PV/ICE output. Above Cmax: the battery should not be charged any further in order to avoid overcharging. The third parameter that should be considered is the operating state of the engine: Engine is off: a start up should be avoided if the power demand is low and the battery charge is sufficient. Engine is on: a shut down should be avoided, even if the power demand is below the engine’s lower limit as long as the battery can still store the excess energy that is produced.
897
Fig. 7. System-state matrix for the observed system where power shortage is the difference between power demand and power production.
R1 R2 R3
Run engine with maximum power output Shut down engine Do not change engine’s operation
3.5. Determination of optimal configuration The objective solution for optimal system configuration can be determined by multi-criteria decision making method (MCDM) [15], where weighted sum method (WSM) is proposed. Particular criteria xi (i is number of criteria), of such as investor’s financial capabilities, levelized cost of electricity, local law on the minimum amount of use RES, are valued with factor wii (j is number of system configuration) according to their priority (the greater priority is valued with greater number). Optimal configuration is determined after finding the maximum sum of particular products S.
X S ¼ max xi wij
! ð8Þ
i
3.3. Design of the system’s components The sizing of particular components was chosen on the basis of an optimisation process. The primary goal of this process was to achieve a stable, secure and sustainable energy supply for a given energy consumption. The particular system’s components (Table 1) were set up for the specific power consumer, considering the following: a stable and secure energy supply throughout the whole operating period. the operation of particular elements of the system (i.e., the ICE’s cold starts, charging and discharging of the battery). the minimum sizes of particular elements with regards to the initial capital. the maximum utilisation of the renewable source of energy. the minimum operating costs and levelized cost of electricity.
3.4. System-state matrix Based on the previously mentioned parameters and the described intervals a 3 4 2 matrix can be formed. It can be simplified to a 3 4 matrix if the engine’s operating state is taken into consideration directly in terms of certain rules rather than making an additional dimension for the system-state matrix. The matrix with the appropriate rules is shown in Fig. 7, while the operating rules, where all the actions apply only to the engine, are:
4. Numerical model and results To test the observed system’s operation under the predefined parameters and rules, a numerical model of the system was set up using MathWork’s Simulink software [14], while Matlab was used to import the data and set up the operating parameters and rules. The numerical model of the system was given a typical oneweek time series of power consumption and the response of the system was observed. Although the entire time series was known in advance, the controller’s decisions were only based on past data. The main task of the controller was to supply a sufficient amount of power to cover the current load by starting and stopping the engine with respect to other variables. Nine different size variations of the energy system were possible, as shown in Table 1, but only three of them, see Table 2, were meaningful for a detailed analysis. The following results were taken into consideration in the analysis: Operating diagrams (one-week scale) for all the elements of the system. Levelized cost of electricity (€/kW h). Fuel use (kg/a). Factor of renewability (–). Number of cold starts of the internal combustion engine.
Table 1 List of a particular element’s size, its investment costs and the factors of renewability. Element of the system
Size/capacity/consumption
Specific initial capital
Factor of renewability
Consumer PV ICE Battery
170 kW h [30, 50, 80] kW [50, 35, 20] kW 300 kW h
/ 3200 €/kWp 800 €/kW 100 €/kW h
/ 1 0 /
B. Drobnicˇ et al. / Electrical Power and Energy Systems 53 (2013) 893–899
898 Table 2 Analysed size variations.
Table 3 Comparison of the results.
System code
PV (kW)
ICE (kW)
Battery (kW h)
System code
PV30-ICE50
PV50-ICE35
PV80-ICE20
PV30-ICE50 PV50-ICE35 PV80-ICE20
30 50 80
50 35 20
300 300 300
PV (kW) ICE (kW) Battery (kWh) Investment cost (€) Operating cost (€/a) LCOE (€/kW h) Fuel use (kg/a) Factor of renewability (–) ICE’s start-ups (–/a)
30 50 300 166,000 3000 0.3132 831.7 0.2436 260
50 35 300 218,000 2000 0.3079 678.6 0.3528 260
80 20 300 302,000 1000 0.3154 487.8 0.5512 104
4.1. Results Firstly, the energy system consists of a consumer with a peakpower consumption of 170 kW, an internal combustion engine with a 50-kW nominal output, a photovoltaic power-plant with an installed power of 30 kW and a battery with a power capacity of 300 kW h. The results of the described system are presented in Fig. 8 and Table 3. The analysed system operates stably and securely, and the operation of the battery is perfect due to a continuously repeated charging to maximum and discharging to the minimum level. All the electricity produced from the PV power plant is used to cover the consumer’s demands and to charge the battery. An advantage of the described system is the low initial investment. The disadvantages are the low factor of renewability and the many cold starts of the ICE, due to its nominal output being too large, both of which shorten the lifetime of the ICE. The second system consists of a consumer with a peak-power consumption of 170 kW, an internal combustion engine with a 35-kW nominal output, a photovoltaic power plant with an installed power of 50 kW and a battery with a power capacity of 300 kW h. The results of the described system are presented in Fig. 9 and Table 3. This system also operates stably and securely. The operation of the battery is perfect, too, due to the continuously repeated charging to maximum and discharging to the minimum level. The electricity produced from the PV power plant through the consumer’s high level of power use is used to cover the consumer’s demands and to charge the battery. But through the weekend, the electricity produced from the PV power plant is not fully used, due to the capacity of the battery being too small. An advantage of the described system is the low levelized cost of the energy. The disadvantages are the capacity of the battery being too small, and consequently an inability to make use of the electricity from the PV power plant, and the many cold starts of the ICE, due to its large nominal output, both of which shorten the lifetime of the ICE. The last analysed system consists of a consumer with a peak-power consumption of 170 kW, an internal combustion engine with a 20-kW nominal output, a photovoltaic power plant
Fig. 8. PV 30-kW and ICE 50-kW operating diagram, one-week scale.
Fig. 9. PV 50-kW and ICE 35-kW operating diagram, one-week scale.
with an installed power of 80 kW and a battery with a power capacity of 300 kW h. The results of the described system are presented in Fig. 10 and Table 3. The last analysed system again operates stably and securely. However, the charging and discharging of the battery is not so perfect, due to the charging to less than maximum and no discharging to the minimum level. The electricity produced from the PV power plant through the consumer’s high level of power use is employed to cover the consumer’s demands and to charge the battery. But through the weekend, the electricity produced from the PV power plant is only partly used, due to the small
Fig. 10. PV 80-kW and ICE 20-kW operating diagram, one-week scale.
B. Drobnicˇ et al. / Electrical Power and Energy Systems 53 (2013) 893–899
capacity of the battery. The advantages of the described system are the continuous operation of the ICE with a small number of cold starts and a large factor of renewability. The disadvantages are the capacity of the battery being too small, and consequently an inability to make full use of the electricity from the PV power plant, and the large initial capital. The advantage of this simulation model is the general applicability due to easy change of input data. The model can be used to simulate energy network at different areas and provides the optimum configuration of the system according to various criteria. These criteria can be investor’s financial capabilities, levelized cost of electricity, local law on the minimum amount of use RES and others. Results in Table 3 present only boundary cases for optimal system configuration; where others can be determined by WSM. The system PV30-ICE50 is the best solution with regards to the minimum initial capital. Secondly, the minimum levelized cost of electricity occurs with the system PV50-ICE35. Finally, if we consider the factor of renewability, the optimum system is PV80-ICE20. 5. Conclusion In this paper a theoretical description of the system-state matrix approach with a corresponding list of rules was made as method for finding the optimum configuration of a self-sufficient energy network and its regulation. Based on one week of a user’s energy consumption and the PV, ICE and battery characteristics, the regulation system was set up. The numerical modelling of the described system and the simulation were made using MathWork’s Simulink code. Based on our research work the following results were obtained: The sizing of particular components was made through the optimisation process, which took into consideration the following: – A stable and secure energy supply throughout the whole operating period (energy flow balance) – The operation of particular elements of the system (i.e., the ICE’s cold starts, charging and discharging of the battery). – The minimum sizes of particular elements with respect to their initial capital. – The maximum utilisation of the renewable source of energy. – The minimum operating costs. A regulation system with action rules was set up considering the inlet parameters with a matrix of the system state to achieve a stable and rational energy supply. The optimum solution of the simulations can be classified according to various criteria. System PV30-ICE50 requires the lowest initial investment; system PV50-ICE35 yields the lowest LCOE; and system is PV80-ICE20 has the highest factor of renewability.
899
The results show that the system controller had the situation under control in every case and it managed to provide a sufficient amount of energy to the consumer at any given moment and in any situation. The regulation of a particular energy system cannot be generalised because of its many different variables. Only the approach of advanced planning by taking into consideration all the influential parameters can be generalised. Future work guidelines point to the further modelling of different combinations of energy systems (such as a photovoltaic panel, wind turbine, CHP unit and fuel cell), setting up particular regulation systems and upgrading model with energy quality package (simulation of frequency and voltage). Acknowledgement Part of this work was carried out within the Centre of Excellence for Low-Carbon Technologies (CO NOT), Hajdrihova 19, 1000 Ljubljana, Slovenia. References [1] Tuma M, Sekavcˇnik M. Energetski sistemi, Fakulteta za strojništvo, Ljubljana; 2004 [in Slovenian]. [2] Asmus P. Microgrids, virtual power plants and our distributed energy future. Electr J 2010;23:72–82. [3] Cormio C, Dicorato M, Minoia A, Trovato M. A regional energy planning methodology including renewable energy sources and environmental constraints. Renew Sust Energy Rev 2003;7:99–130. [4] Franco A, Salza P. Strategies for optimal penetration of intermittent renewables in complex energy systems based on techno-operational objectives. Renew Energy 2011;36:743–53. [5] Hammons TJ. Integrating renewable energy sources into European grids. Electr Power Energy Syst 2008;30:462–75. [6] Kanase-Patil AB, Saini RP, Sharma MP. Integrated renewable energy systems for off grid rural electrification of remote area. Renew Energy 2010;35:1342–9. [7] Pavlas M, Stehlik P, Oralb J, Sikula J. Integrating renewable sources of energy into an existing combined heat and power system. Energy 2006;31:2499–511. [8] Connolly D, Lund H, Mathiesen BV, Leahy M. A review of computer tools for analysing the integration of renewable energy into various energy systems. Appl Energy 2010;87:1059–82. [9] Pirc A, Sekavcˇnik M, Drobnicˇ B, Mori M. Use of hydrogen technologies for saving electric energy in combination with renewable energy systems. In: 6th International workshop on deregulated electricity market issues in SouthEastern Europe; Demsee 2011. [10] Saheb-Koussa D, Haddadi M, Belhamel M, Hadji S, Nouredine S. Modeling and simulation of the fixed-speed WECS (wind energy conversion system): application to the Algerian Sahara area. Energy 2010;35:4116–25. [11] Ishaque K, Salam Z. Syafaruddin: a comprehensive MATLAB Simulink PV system simulator with partial shading capability based on two-diode model. Sol Energy 2011;85:2217–27. [12] Elektro Celje: Industrial plant’s weekly consumption of electrical energy. Measuring report; 2009 [in Slovenian]. [13] Wesselak V, Schabbach T. Regenerative Energietechnik. Heidelberg: Springer; 2009. [14] MathWorks: Simulink Help; 2011. [15] Pohekar SD, Ramachandran M. Application of multi-criteria decision making to sustainable energy planning – a review. Renew Sust Energy Rev 2004;8:365–81.
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A novel approach to the regulation of a self-sufficient energy system using a system-state matrix Boštjan Drobnicˇ a,⇑, Andrej Pirc b, Mitja Mori a, Mihael Sekavcˇnik a a b
Faculty of Mechanical Engineering, University of Ljubljana, Aškercˇeva 6, 1000 Ljubljana, Slovenia Savaprojekt d.d., CKZˇ 59, 8270 Krško, Slovenia
a r t i c l e
i n f o
Article history: Received 6 August 2012 Received in revised form 5 June 2013 Accepted 6 June 2013
Keywords: Operating regulation System-state matrix Energy-system model MATLAB Simulink
a b s t r a c t In this paper we consider the optimal operating regulation of a self-sufficient energy network. To begin with we discuss the regulation of an optimised energy-supply system. Our task was initially focused on a theoretical description of the system-state matrix approach with a corresponding list of operating rules and actions. Secondly, a dynamic mathematical model consisting of the consumer, the energy-production facilities (a photovoltaic power plant and an internal combustion engine), the energy-saving capacities (a battery) and the regulation was set up. Thirdly, during the simulations with various regulation settings an optimised system of operating rules was set up to achieve a stable and rational supply of energy. Finally, the results, appropriate diagrams and guidelines for future work are presented. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction A stable, secure and sustainable supply of energy is vital for modern, energy-dependent societies. Traditional power grids are based on several large-scale power suppliers (i.e., utility power plants), a large number of power consumers and several minor suppliers of power, which currently includes power generation from renewable energy sources (RESs) [1]. The stability of the system, i.e., a constant frequency and voltage, is provided by the largescale suppliers [2]. Variations in the load for individual consumers as well as variations in the power production by small-scale suppliers are relatively small compared to the total capacity of the system. Therefore, the regulation of large-scale suppliers can effectively respond to the disturbances, even if the response time of the whole plant is relatively long. Since the future development of energy systems will tend towards the more extensive use of RESs [3], the structure of future power grids will change significantly [2]. The variations in power supply from RESs, which typically depend on local weather conditions and therefore can only be partially under control, will not be negligible and will have a significant effect on the stability of the entire system. Due to the unpredictability of the supply of power from RESs, an indispensable part of the system will have to include various technologies for energy storage. The regulation of such a system (called a smart grid) will require a different approach and strategies to keep the system stable and to provide a reliable energy supply. ⇑ Corresponding author. Tel.: +386 1 4771 715; fax: +386 1 2518 567. E-mail address: [email protected] (B. Drobnicˇ). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.06.010
The stability of energy systems with distributed energy generation is a more complex and challenging task due to the variety of energy sources, preferably renewable types [3–7], the need for energy storage and the size of the system. A complex energy network, such as a system for energy supply, storage, distribution and consumption, requires careful planning [3] using advanced numerical tools. Several codes have been developed for simulations and optimisations of energy systems. Considering a review of the capabilities of these codes [8] and requirements for our planned work, certain limitations of the existing tools were found [9]. Therefore, the decision to develop a custom-made model was taken. This model should be able to simulate the operation of different combinations of energy systems with an emphasis on the energy flow analysis and the accurate regulation of particular elements of the system. The models were set up in MathWork’s Simulink environment, which proved to be a useful tool for such research [10,11]. The usual approach in this process is to set different rules of operation based on multiple conditions regarding the state of the system’s elements, the available energy, the required energy, etc. However, with complex systems this approach can lead to an intricate list of conditions and rules, making it hard to have an overview of the system’s response under various conditions. It is also possible that blank areas of the entire system-operation region or overlapping of neighbouring areas can occur. This means that there are certain situations without predefined rules for operation or that the system’s state corresponds to more than one condition and several different rules can be valid in a particular situation.
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Nomenclature a A c C E H LCOE m n p P S w x
g
annuity factor, – area, m2 specific cost, €/kW cost, € energy, kW calorific value, kW h/kg levelized cost of electricity, € mass, kg investment period, year interest rate, – power, kW sum of products (by WSM), – walued factor, – value of criteria, – efficiency, –
The objectives of this paper are as follows: A novel approach to system regulation using a system-state matrix. A setting up of an energy-system model using MathWork’s Simulink. An optimisation of the energy-system model. An operating simulation of the energy system. 2. System-state matrix approach A more systematic and transparent way to define the rules for a system’s operation is by means of a system-state matrix, schematically shown in Fig. 1. In general, the regulation of a complex system depends on several representative parameters that sufficiently and uniquely describe the state of the system. 2.1. Definition of the matrix and the rules Each parameter has a value Pi that fits in one of the Ri ranges of various sizes, where the number and sizes of ranges can vary by parameter. If N is the number of observed parameters, an Ndimensional matrix is formed with a size of R1 R2 RN. Each cell of the matrix represents one unique situation in which the system’s operation could be classified regarding the combination of the observed parameters. It is also possible, however, that some cells in the matrix represent situations that are physically impossible for the observed system, but these can be neglected as they do not disrupt the control process and have no influence on the system’s operation. On the other hand, it is very important that all possible situations are considered in the system-state matrix and at the same time the matrix eliminates the possibility of the system’s state fitting in more than one situation. When the system-state matrix is constructed its cells need to be filled with the appropriate rules for responses of the system that will ensure optimal operation under a given set of conditions and will also retain the stability of the system. In general, each cell, i.e., each situation, can have a different rule. However, usually certain rules are applicable in multiple situations, so the number of rules can be significantly smaller than the number of matrix cells. It is important to fill all the cells that represent physically possible states of the system with the appropriate rules, so that the system controller has an operating instruction for every situation that might occur during the system’s operation.
Subscripts 0 initial value A annual fixed cost charge charging discharge discharging ef power-production efficiency F, fuel fuel i number of parameter, criteria j number of parameter, criteria I initial cost ICE internal combustion engine max maximum min minimum OP,M operating and maintenance cost PROD produced PV photovoltaic power plant re-use re-use
2.2. Regulation procedure The system-state matrix and the corresponding list of rules are the information that will enable the system controller to respond appropriately to every situation. The controller must monitor the values of the observed parameters, find in which of the predefined ranges each of the parameters fits and locate the appropriate cell in the system-state matrix according to the parameters’ values. The contents of the cell describe the actions that will, in a given situation, provide the optimal response and operation of the system, Fig. 2. Any selected operating rule is a list of actions (settings) that are sent to the local controllers of the system elements. The actions for all of the rules and all of the regulated elements can be put in the form of an action matrix where the parameter S(i, j) represents the signal for the jth element when the ith operating rule is applicable, Fig. 3. Furthermore, the selected rule can be represented by a vector where all the elements are 0, except for the ith element, which is 1. The product of the action matrix and the rule vector is a reg-
Fig. 1. Selecting representative parameters and creating a system-state matrix.
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Fig. 2. System regulation by means of the system-state matrix.
the viability of an individual power plant can be seen throughout the levelized cost of electricity. This cost of electricity that is generated by different sources is a calculation of the cost of generating the electricity at the point of connection to the load or electricity grid. It includes the initial capital, as well as the costs of operation, maintenance and fuel. The initial capital CI of a particular power plant is a product of the specific initial costs ci and the peak power of the system P.
C I ¼ ci P
Fig. 3. Product of the action matrix and the rule vector gives the vector of appropriate settings for all the system’s elements.
The annuity factor a depends on the investment period n and the interest rate p.
a¼ ulation vector with settings for all the system’s elements that correspond to the selected rule and the given system state at the same time. 2.3. System stability When defining the rules for the system’s operation in various cells of the system-state matrix it is not sufficient to ensure stable and optimal system operation within the observed cell. Transitions from one cell to another, and thus changing the rules of operation, should also be considered, and their influence on the system’s stability should be evaluated. If the system controller is fast enough then the system state can only move from the current cell to one of the neighbouring cells of the system-state matrix. In this case the changes in the operating rules are probably not so radical as to cause instability of the system. On the other hand, if the controller is too slow the system can jump to a cell that is not next to the current cell. In this case the new rules could force significant changes in the system’s operation, leading the system into an unstable operation. Therefore, it is recommended to set a numerical model of the system and test the preset regulation procedure under various normal as well as extreme operating conditions in order to examine the system’s response.
ð1Þ
pð1 þ pÞn ð1 þ pÞn 1
ð2Þ
The annual fixed costs CA are thus equal
CA ¼ CIa
ð3Þ
The total costs are the sum of the annual fixed costs CA, the operating and maintenance costs COP,M and the fuel costs CF. Finally, the levelized cost of electricity LCOE is equal to the total costs divided by the produced energy EPROD.
LCOE ¼
C A þ C OP;M þ C F EPROD
ð4Þ
3. Regulation and optimisation of a simple power-supply system with energy storage In order to present the applicability of the system-state matrix approach for regulation the energy-supply system, a simple system, schematically shown in Fig. 4, was modelled. 3.1. Energy-system elements 3.1.1. Power consumer A power consumer with a dynamically varying load [12] in the presented example is an industrial plant with a typical daily operation and minimal power consumption during the night-time and weekends. The weekly load of the observed plant is shown in Fig. 5.
2.4. Levelized cost of electricity Additionally, the stable system’s operation should not be the only observed parameter. Economics has a great influence on the energy system’s planning too. The information that predicts
3.1.2. Photovoltaic power plant A photovoltaic power-plant (PV) model [13] is used to describe the renewable energy system. It is limited by the surface position, the time and the weather conditions. The produced electrical
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_ fuel Hfuel gef PICE ¼ m
ð6Þ
3.1.4. Battery Batteries are used for the storage of excess energy and the supply of peak-load energy. In the situations when the PV and ICE are unable to cover the power demand, the consumer is supplied with additional energy from the batteries. On the other hand, when the power demand is small, production systems can store the excess energy in the batteries. The re-used power Pre-use is the decreased charging power P0 due to the charging and discharging efficiency gcharge/gdischarge.
Pre-use ¼ gcharge gdischarge P0
ð7Þ
3.2. Basic operating constraints The basic purpose of the system regulator is to ensure that the system’s operation complies with the independent requirements from the system’s environment. To achieve this, various commands need to be sent to individual elements of the system. However, the regulator must also take into consideration the limitations that each of the elements might have. Thus, both the requirements and the limitations have to be considered when making the operating rules and the appropriate actions. The following are applicable for the observed system:
Fig. 4. Observed energy supply/storage/consumption system.
Fig. 5. Diagram of energy consumption.
power PPV depends on the efficiency gPV, the incident radiation flux Esol and the area of the photovoltaic panels A.
PPV ¼ gPV Esol A
ð5Þ
The average daily production of electricity from the photovoltaic power plant is shown in Fig. 6. 3.1.3. Internal combustion engine An internal combustion engine (ICE) with a power generator is a conventional energy source in the observed system to provide a stable energy supply. Its capacity is considerably smaller than the peak loads of the consumer. Also, the lowest output capacity is limited due to the decreased efficiency of the engine. The pro_ fuel , its duced electrical power depends on the supplied fuel rate m calorific value Hfuel and the power-production efficiency gef.
The total energy output of the PV, the ICE and the battery has to cover the power demands of the industrial plant. As is shown in Fig. 5, the power consumption does show daily and weekly patterns, but also includes considerable random variations, which means continuous monitoring of the power demand is necessary. Since actual continuous monitoring is not possible, at least the sampling time of the discrete values should be short enough to capture the dynamics of the load changes. In the presented case the available data are sampled at one-hour intervals and a simple linear interpolation is used between the measured points. Due to weather conditions, the energy production from a PV plant can only be partly predicted. PV-produced energy is firstly used to cover the consumer’s energy demand. Secondly, if there is an excess of produced energy, it is used for battery charging. Finally, the production of PV energy is adjusted to the current consumer’s demand when the battery is fully charged. ICE operation is regulated with respect to two parameters: first, is the energy difference between the consumer’s energy demand and the PV-produced energy; second, is the level of the battery charge. A particular ICE has a limited maximum power output and to avoid low-efficiency operation a lower power limit is also set. If the required power is below the limit the engine is shut down. It is also advisable to avoid frequent start ups and shut downs of the engine, so the operating rules should consider the current state of the engine’s operation. The capacity of the battery is also limited once an actual battery is chosen for the system. In addition, both overcharging and, even more importantly, excessive discharging of the battery should be avoided. So appropriate actions should be taken when certain charge levels are reached. In the observed case the energy difference between the consumer’s energy demand and the PV-produced energy can be divided into the following intervals, considering the ICE’s limitations:
Fig. 6. Electricity production from PV power plant, one day scale.
Below P0: power production from the PV power plant is greater than the power consumption; the battery is charging and the ICE does not operate.
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From P0 to PICEmin: power demand is lower that the ICE lower limit; typically (but not in all situations) the engine should be shut down. From PICEmin to PICEmax: power demand is within the working range of the ICE; the engine should follow the current power demand; if necessary, it could also charge the battery. Above PICEmax: power demand exceeds ICE capacity; the engine should run on full load, and also battery backup is necessary to cover the power demand. On the other hand, the battery charge level can be divided into the following intervals: Below Cmin: the battery must be charged to avoid the possibility of complete discharge and damage to the battery. From Cmin to Cmax: the battery can be charged or discharged with regard to the current power demand and PV/ICE output. Above Cmax: the battery should not be charged any further in order to avoid overcharging. The third parameter that should be considered is the operating state of the engine: Engine is off: a start up should be avoided if the power demand is low and the battery charge is sufficient. Engine is on: a shut down should be avoided, even if the power demand is below the engine’s lower limit as long as the battery can still store the excess energy that is produced.
897
Fig. 7. System-state matrix for the observed system where power shortage is the difference between power demand and power production.
R1 R2 R3
Run engine with maximum power output Shut down engine Do not change engine’s operation
3.5. Determination of optimal configuration The objective solution for optimal system configuration can be determined by multi-criteria decision making method (MCDM) [15], where weighted sum method (WSM) is proposed. Particular criteria xi (i is number of criteria), of such as investor’s financial capabilities, levelized cost of electricity, local law on the minimum amount of use RES, are valued with factor wii (j is number of system configuration) according to their priority (the greater priority is valued with greater number). Optimal configuration is determined after finding the maximum sum of particular products S.
X S ¼ max xi wij
! ð8Þ
i
3.3. Design of the system’s components The sizing of particular components was chosen on the basis of an optimisation process. The primary goal of this process was to achieve a stable, secure and sustainable energy supply for a given energy consumption. The particular system’s components (Table 1) were set up for the specific power consumer, considering the following: a stable and secure energy supply throughout the whole operating period. the operation of particular elements of the system (i.e., the ICE’s cold starts, charging and discharging of the battery). the minimum sizes of particular elements with regards to the initial capital. the maximum utilisation of the renewable source of energy. the minimum operating costs and levelized cost of electricity.
3.4. System-state matrix Based on the previously mentioned parameters and the described intervals a 3 4 2 matrix can be formed. It can be simplified to a 3 4 matrix if the engine’s operating state is taken into consideration directly in terms of certain rules rather than making an additional dimension for the system-state matrix. The matrix with the appropriate rules is shown in Fig. 7, while the operating rules, where all the actions apply only to the engine, are:
4. Numerical model and results To test the observed system’s operation under the predefined parameters and rules, a numerical model of the system was set up using MathWork’s Simulink software [14], while Matlab was used to import the data and set up the operating parameters and rules. The numerical model of the system was given a typical oneweek time series of power consumption and the response of the system was observed. Although the entire time series was known in advance, the controller’s decisions were only based on past data. The main task of the controller was to supply a sufficient amount of power to cover the current load by starting and stopping the engine with respect to other variables. Nine different size variations of the energy system were possible, as shown in Table 1, but only three of them, see Table 2, were meaningful for a detailed analysis. The following results were taken into consideration in the analysis: Operating diagrams (one-week scale) for all the elements of the system. Levelized cost of electricity (€/kW h). Fuel use (kg/a). Factor of renewability (–). Number of cold starts of the internal combustion engine.
Table 1 List of a particular element’s size, its investment costs and the factors of renewability. Element of the system
Size/capacity/consumption
Specific initial capital
Factor of renewability
Consumer PV ICE Battery
170 kW h [30, 50, 80] kW [50, 35, 20] kW 300 kW h
/ 3200 €/kWp 800 €/kW 100 €/kW h
/ 1 0 /
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898 Table 2 Analysed size variations.
Table 3 Comparison of the results.
System code
PV (kW)
ICE (kW)
Battery (kW h)
System code
PV30-ICE50
PV50-ICE35
PV80-ICE20
PV30-ICE50 PV50-ICE35 PV80-ICE20
30 50 80
50 35 20
300 300 300
PV (kW) ICE (kW) Battery (kWh) Investment cost (€) Operating cost (€/a) LCOE (€/kW h) Fuel use (kg/a) Factor of renewability (–) ICE’s start-ups (–/a)
30 50 300 166,000 3000 0.3132 831.7 0.2436 260
50 35 300 218,000 2000 0.3079 678.6 0.3528 260
80 20 300 302,000 1000 0.3154 487.8 0.5512 104
4.1. Results Firstly, the energy system consists of a consumer with a peakpower consumption of 170 kW, an internal combustion engine with a 50-kW nominal output, a photovoltaic power-plant with an installed power of 30 kW and a battery with a power capacity of 300 kW h. The results of the described system are presented in Fig. 8 and Table 3. The analysed system operates stably and securely, and the operation of the battery is perfect due to a continuously repeated charging to maximum and discharging to the minimum level. All the electricity produced from the PV power plant is used to cover the consumer’s demands and to charge the battery. An advantage of the described system is the low initial investment. The disadvantages are the low factor of renewability and the many cold starts of the ICE, due to its nominal output being too large, both of which shorten the lifetime of the ICE. The second system consists of a consumer with a peak-power consumption of 170 kW, an internal combustion engine with a 35-kW nominal output, a photovoltaic power plant with an installed power of 50 kW and a battery with a power capacity of 300 kW h. The results of the described system are presented in Fig. 9 and Table 3. This system also operates stably and securely. The operation of the battery is perfect, too, due to the continuously repeated charging to maximum and discharging to the minimum level. The electricity produced from the PV power plant through the consumer’s high level of power use is used to cover the consumer’s demands and to charge the battery. But through the weekend, the electricity produced from the PV power plant is not fully used, due to the capacity of the battery being too small. An advantage of the described system is the low levelized cost of the energy. The disadvantages are the capacity of the battery being too small, and consequently an inability to make use of the electricity from the PV power plant, and the many cold starts of the ICE, due to its large nominal output, both of which shorten the lifetime of the ICE. The last analysed system consists of a consumer with a peak-power consumption of 170 kW, an internal combustion engine with a 20-kW nominal output, a photovoltaic power plant
Fig. 8. PV 30-kW and ICE 50-kW operating diagram, one-week scale.
Fig. 9. PV 50-kW and ICE 35-kW operating diagram, one-week scale.
with an installed power of 80 kW and a battery with a power capacity of 300 kW h. The results of the described system are presented in Fig. 10 and Table 3. The last analysed system again operates stably and securely. However, the charging and discharging of the battery is not so perfect, due to the charging to less than maximum and no discharging to the minimum level. The electricity produced from the PV power plant through the consumer’s high level of power use is employed to cover the consumer’s demands and to charge the battery. But through the weekend, the electricity produced from the PV power plant is only partly used, due to the small
Fig. 10. PV 80-kW and ICE 20-kW operating diagram, one-week scale.
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capacity of the battery. The advantages of the described system are the continuous operation of the ICE with a small number of cold starts and a large factor of renewability. The disadvantages are the capacity of the battery being too small, and consequently an inability to make full use of the electricity from the PV power plant, and the large initial capital. The advantage of this simulation model is the general applicability due to easy change of input data. The model can be used to simulate energy network at different areas and provides the optimum configuration of the system according to various criteria. These criteria can be investor’s financial capabilities, levelized cost of electricity, local law on the minimum amount of use RES and others. Results in Table 3 present only boundary cases for optimal system configuration; where others can be determined by WSM. The system PV30-ICE50 is the best solution with regards to the minimum initial capital. Secondly, the minimum levelized cost of electricity occurs with the system PV50-ICE35. Finally, if we consider the factor of renewability, the optimum system is PV80-ICE20. 5. Conclusion In this paper a theoretical description of the system-state matrix approach with a corresponding list of rules was made as method for finding the optimum configuration of a self-sufficient energy network and its regulation. Based on one week of a user’s energy consumption and the PV, ICE and battery characteristics, the regulation system was set up. The numerical modelling of the described system and the simulation were made using MathWork’s Simulink code. Based on our research work the following results were obtained: The sizing of particular components was made through the optimisation process, which took into consideration the following: – A stable and secure energy supply throughout the whole operating period (energy flow balance) – The operation of particular elements of the system (i.e., the ICE’s cold starts, charging and discharging of the battery). – The minimum sizes of particular elements with respect to their initial capital. – The maximum utilisation of the renewable source of energy. – The minimum operating costs. A regulation system with action rules was set up considering the inlet parameters with a matrix of the system state to achieve a stable and rational energy supply. The optimum solution of the simulations can be classified according to various criteria. System PV30-ICE50 requires the lowest initial investment; system PV50-ICE35 yields the lowest LCOE; and system is PV80-ICE20 has the highest factor of renewability.
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The results show that the system controller had the situation under control in every case and it managed to provide a sufficient amount of energy to the consumer at any given moment and in any situation. The regulation of a particular energy system cannot be generalised because of its many different variables. Only the approach of advanced planning by taking into consideration all the influential parameters can be generalised. Future work guidelines point to the further modelling of different combinations of energy systems (such as a photovoltaic panel, wind turbine, CHP unit and fuel cell), setting up particular regulation systems and upgrading model with energy quality package (simulation of frequency and voltage). Acknowledgement Part of this work was carried out within the Centre of Excellence for Low-Carbon Technologies (CO NOT), Hajdrihova 19, 1000 Ljubljana, Slovenia. References [1] Tuma M, Sekavcˇnik M. Energetski sistemi, Fakulteta za strojništvo, Ljubljana; 2004 [in Slovenian]. [2] Asmus P. Microgrids, virtual power plants and our distributed energy future. Electr J 2010;23:72–82. [3] Cormio C, Dicorato M, Minoia A, Trovato M. A regional energy planning methodology including renewable energy sources and environmental constraints. Renew Sust Energy Rev 2003;7:99–130. [4] Franco A, Salza P. Strategies for optimal penetration of intermittent renewables in complex energy systems based on techno-operational objectives. Renew Energy 2011;36:743–53. [5] Hammons TJ. Integrating renewable energy sources into European grids. Electr Power Energy Syst 2008;30:462–75. [6] Kanase-Patil AB, Saini RP, Sharma MP. Integrated renewable energy systems for off grid rural electrification of remote area. Renew Energy 2010;35:1342–9. [7] Pavlas M, Stehlik P, Oralb J, Sikula J. Integrating renewable sources of energy into an existing combined heat and power system. Energy 2006;31:2499–511. [8] Connolly D, Lund H, Mathiesen BV, Leahy M. A review of computer tools for analysing the integration of renewable energy into various energy systems. Appl Energy 2010;87:1059–82. [9] Pirc A, Sekavcˇnik M, Drobnicˇ B, Mori M. Use of hydrogen technologies for saving electric energy in combination with renewable energy systems. In: 6th International workshop on deregulated electricity market issues in SouthEastern Europe; Demsee 2011. [10] Saheb-Koussa D, Haddadi M, Belhamel M, Hadji S, Nouredine S. Modeling and simulation of the fixed-speed WECS (wind energy conversion system): application to the Algerian Sahara area. Energy 2010;35:4116–25. [11] Ishaque K, Salam Z. Syafaruddin: a comprehensive MATLAB Simulink PV system simulator with partial shading capability based on two-diode model. Sol Energy 2011;85:2217–27. [12] Elektro Celje: Industrial plant’s weekly consumption of electrical energy. Measuring report; 2009 [in Slovenian]. [13] Wesselak V, Schabbach T. Regenerative Energietechnik. Heidelberg: Springer; 2009. [14] MathWorks: Simulink Help; 2011. [15] Pohekar SD, Ramachandran M. Application of multi-criteria decision making to sustainable energy planning – a review. Renew Sust Energy Rev 2004;8:365–81.